摘要:

R . NEIHOF A N D K. SOLLNER 101 SIMULTANEOUS DIFFUSION OF ELECTROLYTES AND MEMBRANES NON-ELECTROLYTES THROUGH ION-EXCHANGE BY G. MANECKE AND H. HELLER, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin Received 30th January, 1956 The simultaneous diffusion of electrolytes and non-electrolytes in cation-exchange membranes has been investigated. The change in the ratio of concentrations of non- electrolytes and electrolytes (enrichment) after passing through a membrane is determined. The diffusion mechanisms of non-electrolytes and of electrolytes are explained with the help of Fick’s first diffusion law. In this connection the distribution coefficients of the non-electrolytes as well as the swelling behaviour of membranes have been investigated. The diffusion of the non-electrolyte depends primarily on the swelling capacity of the mem- brane whereas the diffusion of the electrolyte depends also on the simultaneous presence of non-electrolytes.The enrichment of the non-electrolyte depends on the diffusion coefficients of the sub- stances as well as on their concentration gradients in the membrane. The concentration gradients of the electrolytes calculated with the help of the Donnan equation have different values for 1 : 1, 2 : 1 and 1 : 2 electrolytes.102 SIMULTANEOUS DIFFUSION Ion-exchange membranes may contain up to 70 % water, and consequently they are quite permeable. When such a membrane is brought into contact with a solution of electrolyte a certain amount of this electrolyte diffuses into the mem- brane. The equilibrium concentration is governed by the Donnan equilibrium equation.According to this equation in the cation-exchange membrane a portion of the cations is neutralized by the fixed ions, which are the seats of the oppositely charged ions, and usually a smaller portion of the cations is neutralized by the same kind of anions present in the external solution. The amount of electrolyte in the membrane which consists of mobile anions and the corresponding amount of mobile cations is defined here as the excess electrolyte of the membrane. If the concentration of the fixed ions is large compared to the concentration of the electrolyte of the external solution, the con- centration of the excess electrolyte in the membrane can be very small (e.g. only 1/10 or even less of the amount present in the external solution).Non-electrolytes also diffuse from an aqueous solution into the ion-exchange membrane. In equilibrium conditions the concentration of non-electrolyte in the membrane can be approximately equal to that in the external solution. The exact value of the ratio of the concentrations of a non-electrolyte in the internal and external solutions has to be determined for each individual case, and this ratio can be greater or smaller than 1 . Now, if an ion-exchange membrane separates two cells, one of which contains a solution of an electrolyte and a non-electrolyte (solution l), the concentration of the electrolyte being small compared to the concentration of the fixed ions in the mem- brane, and the other cell contains pure water (solution 2) then the amount of the non-electrolyte diffusing to cell 2 would initially be greater than that of the electro- lyte even if the diffusion coefficients and concentrations of the components are approximately equal.In this way one can increase the concentration of the non-electrolytic component in the cell 2. In favourable cases, by continuously renewing the pure solvent in cell 2 one could eventually separate the electrolyte almost completely from the non-electrolyte. Ion-exchange membranes as agents for the separation of electrolytes and non- electrolytes have already been discussed by Sollner.1 Concrete examples of its application are, however, not known. A method of separation of electrolytes and non-electrolytes based on the different adsorption capacity of ion-exchange resins is the ion-exclusion method of Wheaton and Bauman.2 In this method one uses a normal exchange column filled with resin particles.It must be noted that here the concept of non-electrolyte has only a relative significance. It denotes that one substance shows a much smaller dissociation constant than the other, e.g. acetic acid can be considered as a non-electrolyte in a mixture with HCl solution. In the sequel the simultaneous diffusion of non-electrolytes and electrolytes through cation-exchange membranes is investigated and the possibility of separation of them with the help of ion-exchange membranes is considered. EXPERIMENTAL An apparatus, which is similar to that used by Northrup and Anson 3 for the deter- mination of diffusion coefficients of dissolved substances, is empioyed.The diffusion cell consists of a cylindrical body made of Plexiglas and separable into two parts. The membrane, which is placed between the two parts, separates the inner space of the cylinder into two almost equal volumes 01 and 212 (primary side and secondary side). v1 contains the solution to be investigated (solution 1) and 212 contains originally the pure solvent (water) and later on the solution 2. The primary side is furnished with a U-tube mano- meter and the secondary side with a simple capillary tube. In this way the volume 01 is sealed and thus the osmosis is practically stopped and hence the streaming of the solution from v2 to 01.G . MANECKE AND H. HELLER 103 The apparatus is arranged such that the membrane is vertical. The membrane facing solution 2 is supported by a cross-stand.Both the solutions are stirred magnetically (ca. 1000 rev/min). For the adjustment of the initial concentration gradient in the mem- brane each experiment begins with a preliminary starting period. After 60 min both the solutions are thrown away and replaced by the original ones, and the actual experiment begins. RESULTS AND DISCUSSION Fig. la depicts the experiment at the initial stage and fig. l b at a later stage. The concentration gradient for the excess electrolyte in the charged membrane is not strictly linear (cf. Teorell4 and Schlogl5). This refinement is not considered here. After each experiment the concentrations in the cells as well as their volumes v1 and v2 are measured.The latter do not remain exactly constant as the membrane is slightly displaced from its original position. The ratio of 711 (or 712) to the mem- brane volume vM is approximately 20/ 1. N a C l N I A-N I NaCl Acetone NaCl N K l N a C l FIG. 1. The maximum duration of the experiment is such that c2 remains smaller than c0/3. Here c2 denotes the concentration of the diffusing substance in the solution 2 and co the initial concentration in solution 1. Strong acid cation-exchange membranes prepared from phenolsulphonic acid and formaldehyde solution (Manecke 6) are used. The general properties of such membranes have already been described.’* 8 Their fixed ion concentrations are 1-4-1-5 equiv.11. The enrichment of the non-electrolyte (En) is defined as (conc.of non-electrolyte/conc. of electrolyte) in soln. 2 (initial conc. of non-electrolyte/initial conc. of electrolyte) in soln. 1 En = En = 1 means that the ratio of the relative concentration of the components do not change as a result of the diffusion. Table 1 gives the values of En after 2 h for all the systems investigated. Expt. 1 and 2 show the influence of stirring on the diffusion process at the same concentrations CO. Helfferich 9 has shown that the effect of stirring on the diffusion through ion-exchange membranes is absent at about 850 revlmin. All the experi- ments except no. 1 have therefore been carried out at lOOOrev/min. Further, according to Helfferich,lo the kinetics of the solution films on the membrane need not be considered. The enrichment is greatest in presence of a 1 : 2-valent electrolyte. It is least in presence of 2 : 1-valent electrolytes (cf.expt. 14, 13 and 5 or 15,9 and 12). The enrichment of one and the same non-electrolyte is greater if the initial con- centration of the electrolyte is smaller (cf. expt. 2 and 3, 4 and 5, 7-9 or 10-12).104 SIMULTANEOUS DIFkUSION The enrichment of the non-electrolyte is small in the presence of a 2 : 1-valent electrolyte even when the Concentration of the electrolyte in solution 1 is very low (cf. expt. 10). The diffusion coefficient is inversely proportional to the particle size, i.e., larger particles diffuse comparatively slowly. Consequently the enrichment is a function of the size of the non-electrolyte molecule and of the size of the anions of the electrolyte for a particular cation.This can be seen from the experiments carried out with acetone and formaldehyde and from expt. 16-1 8 in which the effect of the anion is observed. TABLE 1 no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 counter - ion Na+ Na+ Na + Mg2+ Mg2+ Ca2 + Na+ Na+ Na+ Mg2+ Mg2+ Mg2+ H+ H+ Na+ H+ H+ H+ non-electrolyte acetone acetone acetone acetone acetone acetone formaldehyde formaldehyde formaldehyde formaldehyde formaldehyde formaldehyde acetone acetone formaldehyde CH3COOH CH-jCOOH formaldehyde initial solutions mole: 1 electrolyte equiv.11. 0-5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.1 0.5 NaCl NaCl NaCl MgC12 CaC12 NaCl NaCl NaCl MgC12 MgC12 MgCl2 HC1 Na2S04 HCl p-naphthalene sulphonic acid MgCl2 CC13COOH 0.02 0.02 0.1 0.02 0.1 0.1 0.0 1 0.02 0.1 0.0 1 0.02 0.1 0.126 0.123 0.17 0.1 0.1 0.1 enrichment after 2 h 3.5 without stirring 6.0 1.8 1.3 1.0 1.0 50-100 after 6 h 7-8 2.2 2.2 1.5 1-2 2.6 9.25 7.0 2.6 3.5 12.75 The enrichment of the non-electrolyte is a function of time since the concentra- tion gradient of the non-electrolyte in the membrane becomes smaller much more rapidly than that of the electrolyte.Fig. 2 gives some examples. Furthermore, the enrichment of the non-electrolyte taking place in solution 2 increases the ratio of concentration of electrolyte/concentration of non-electrolyte in solution 1. Provided the above experimental conditions are fulfilled the diffusion is quasi- stationary. Hence Fick's first law can be used for the diffusion processes of non-electrolytes and electrolytes through membranes.Detailed theoretical considerations are to be found in the publications of Barnes,ll Gordon,l2 Dean 13 and Barrer.14 In Fick's equation Dq dc 9- - - _ - dt ~2 dx' D denotes the differential diffusion coefficient. It is to be noted that ourexperiments involve the integral diffusion coefficient (cf. Gordon 12). q is the effective surface area of the membrane and dc/dx the concentration gradient in the membrane. All the above experiments are carried out so that a concentration gradient exists only in the membrane, whose effective thickness is d. C1 denotes the con- centration in the membrane at the phase boundary with solution 1. co denotes the initial concentration of solution 1 and c1 its concentration at time t.C2 and c2 are the concentrations at the phase boundary with solution 2. At both these phaseG . MANECKE AND H. HELLER 105 boundaries equilibrium exists between the external solution and the internal solution of the membrane. Consequently I4 2 1 2 - u E r - U .- : 10- w 8 - 6 - 4 - 2 - which equation is valid both for the electrolyte and for the non-electrolyte. The diffusion equation for the non-electrolyte is also given by - In (3) the concentration gradient in the membrane is expressed in terms of the con- centrations of the external solutions and of the factor a. a denotes the distribution coefficient for the non-electrolyte, when the external and internal solutions are in equilibrium. 1 O 2 4 b 8 T i m c , hours FIG. 2.-Enrichment of non-electrolytes as a function of time.Curve 1 : expt. 18; curve 2: expt. 14; curve 3 : expt. 8 ; curve 4 : expt. 2. E ate r no I so I u t i on conce n t ra t i on [m ole/ I FIG. 3. It is defined by the ratio conc. of the non-electrolyte in the internal soln. (C) conc. of the non-electrolyte in the external soln. ( c ) a = Since the ion-exchange resin matrix of the membranes may also adsorb some of the non-electrolyte, another distribution coefficient ct’ is introduced. It is defined as a’ = Ctot/c, where Ctot is the total number of moles of the non-electrolyte in the swollen membrane per litre of internal solution. The dependence of a’ on the concentration of the external solution has been investigated for acetone. In fig. 3, curve 1, Ctot =f(c); curve 2, ct’ = f ( c ) ; and curve 3, (Ctot - c) = f(c) for a Na-membrane.106 SIMULTANEOUS DIFFUSION In the concentration range c = 0.5 M-1.5 M, curve 3 has only a small inclination with the abscissa, In the same region a’ becomes independent of c.Hence one can assume that the concentration of the internal solution is equal to that of the external solution and a definite maximum amount of the acetone can be adsorbed. One is therefore inclined here to take aaC as independent of the con- centration so that a,, = 1. Similar curves were obtained with Mg- and Ca-membranes although the intake of acetone was greater. For all other experiments on other non-electrolytes a 1 2 4 6 8 T i m e , h o u r s b , , , , , I 2 4 b B T i m e , h o u r i FIG. 4a 9 soln. 1 : 0.5 M acetone/Na-membrane, + soln.1 : 0.5 M acetone + 0.1 N NaCl/Na-membrane, 0 soln. 1 : 0.5 M acetone/Mg-membrane, soln. 1 : 0.5 M acetone + 0-1 N MgClZ/Mg-membrane. FIG. 4b 8 soln. 1 : 0.5 M formaldehyde + 0.02 N NaCl/Na-membrane, (> soln. 1 : 0.5 M formaldehyde + 0-1 N NaCl/Na-membrane, soln. 1 : 0.5 M formaldehyde + 0-02 N MgClz/Mg-membrane, 0 soln. 1 : 0-5 M formaldehyde + 0.1 N MgClz/Mg-membrane. investigated, a’ has been found approximately equal to 1. The integration of the diffusion equation (3) becomes possible if Di is assumed to be independent of the concentration. Integrating we have : The observed results can be graphically represented as a function of time. The plots are straight lines passing through the origin, and justify the application of Fick’s first law as well as the assumption made for a. Fig.4a shows some of the results obtained for acetone and fig. 4b for formaldehyde.G . MANECKE A N D H . HELLER 107 The slope of the straight lines is given by where /I is the angle of inclination. The diffusion coefficient Di, however, cannot be determined since q and d in eqn. ( 5 ) are unknown. 9 is the effective surface area of the membrane and is pro,- portional to its cross-section A. d is the effective thickness of the membrane, i.e. the mean length of the pores. It can be assumed to be proportional to the measured thickness 1 of the membrane. One can therefore write qld = kA/1, (6) when the proportionality factor k is a constant for the membrane. Hence from ( 5 ) it follows that, The product of Di and k is defined as the permeability P of the membrane.Thus (tan /3) 2.303 1vp2 P = Dik = A a (v1 + v2) When a is known or is put equal to 1, P can be determined from eqn. (8). P describes the permeability of a membrane with respect to a definite substance. It is a physical quantity similar to the diffusion coefficient and the dimensions of P and Di are the same. From the values of P one can get an estimate of Dj even when their absolute values are not known. The values of P can be compared only for one and the same membrane. It is seen from table 2 that the permeabilities and hence the diffusion coefficients of acetone are different for different membranes. They decrease in the sequence, Na-, Mg-, Ca-membrane, in agreement with their swelling capacities as shown later. TABLE 2.-PERMEABILITY OF ACETONE THROUGH MEMBRANES WITH DIFFERENT COUNTER IONS WITH AND WITHOUT ELECTROLYTES initial solution P x 106 (cmzlsec) membrane counter ion acetone mole/l electr.equiv./l no. I Na+ 0.5 - 2-74 I Na+ 0.5 0.1 NaCl 2-58 I Mg2+ 0.5 - 2.37 I Mg2+ 0-5 0.1 MgC12 2.37 111 Ca2+ 0.5 - 2-19 I11 Ca2+ 0-5 0 . 1 CaCl2 2.23 Further, table 2 shows that the addition of NaCl to the initial solution decreases the diffusion of acetone whereas equal amounts of MgC12 and CaC12 are without effect. The swelling of the membrane in the Na-form is the greatest and decreases notice- ably in the sequence, Na-, Mg-, Ca-form.8 The dependence of the swelling capacity on the concentration of the external solution is shown in table 3. (Two different membranes have been used.They are marked I and 11. One should compare the relevant values either for I or for 11.) The membrane shrinks very little in the Mg-form if the concentration of MgC12 in the external solution is increased. The measured values vary within experimental error. The swelling capacity of the Na-membrane shows a distinct dependence on the electrolytic concentration in the external equilibrium solution. Ca- membranes behave similarly to Mg-membranes. Hence the swelling of the mem- brane influences the diffusion of the non-electrolyte through the membrane. In addition, an effect of a possible interaction between acetone and Mg2f or Ca2+ in the membrane is not excluded as shown later.108 SIMULTANEOUS DIFFUSION The observed dependence of the diffusion of a non-electrolyte on the nature of the counter-ions of the membrane and of the concentration of the electrolyte in solution 1 for acetone are also confirmed with formaldehyde (see table 4).TABLE 3 .-SWELLING CAPACITY OF THE MEMBRANES IN RELATION TO THE CONCENTRATION OF ELECTROLYTES IN THE EXTERNAL SOLUTION membrane condensation [MgClz] or water content of the nature of the [NaCl] in the membrane in % by cation in the external weight of water in membrane solution respect to the N o n i c equiv.11. resin matrix, I Mg2+ 0.02 60.0 I Mg2+ 0.1 59.0 I Mg2+ 0.5 58.5 I Na+ 0.1 62.7 I1 Na+ 0.02 61.5 I1 Na + 0.1 58.8 I1 Na+ 0.5 57.2 TABLE 4.-PERMEABILITY OF FORMALDEHYDE THROUGH MEMBRANES WITH DIFFERENT COUNTER-IONS AND WITH ADDITION OF DIFFERENT AMOUNTS OF ELECTROLYTES membrane no. counter ion V Na+ V Na' V Na+ V Na+ V Mg2+ V Mg2+ initial solution CH20 mole.!l. electr.equiv./l P x 106 (crn2isec.) 0.5 NaCl 0.01 3.35 0.5 NaCl 0.02 3.12 0.5 NaCl 0.1 2-42 0.5 Na2S04 0.17 2.73 0.5 MgC12 0.02 2.26 0.5 MgC12 0.1 2.24 The smaller permeability of non-electrolytes through Mg- and Ca-membranes caused principally by the smaller swelling capacity of these membranes may also decrease the enrichment of the non-electrolyte in presence of 2 : 1 -electrolytes. To explain the mechanism of the enrichment of the non-electrolytes the diffusion of the electrolytes through the cation-exchange membranes should also be analysed. Here, we first considered the concentration gradients of the excess electrolyte in the membranes. The concentrations of the excess electrolyte C1 and C2 at the phase boundary in the membrane are equal to the respective concentrations of the anion in the membrane.Hence using Donnan's equation they can be expressed as func- tions of the concentrations of the external solutions cl and c2. The Donnan equation for a salt dissociating into y2 cations and rn anions is given by :15 (9) Hence one can derive the following diffusion equations if c1 is expressed as a function of co and c2. (All concentrations are expressed as equiv./l.) (F &)"+"[cat] $ [an] $ = (f =t)"tn[cat] [an] F. for 2 : 1-electrolytes ; for 1 : 1-electrolytes ; and for 1 : 2-electrolytes.G. MANECKE A N D H. HELLER 109 The above equations have been derived under the following conditions : (i) As long as the electrolytic concentration of the external solutions is suffi- ciently small cat]^ > [an]M and the electroneutrality in the membrane is given by cat]^ % [R-1.(ii) The concentrations C1 and C2 are almost equal as long as the concentrations of the external solutions are small. Hence the activity coefficient (F -A-) in the membrane can be given a mean value. In these equations the secondrfactor denotes the concentration gradient of the excess electrolyte in the membrane. Putting (F -k) = (f i)~, (f i-)sz, one can roughly estimate the values of the concentration gradients in the cation- exchange membranes when co < .[R-]. It is then found that the gradient for the 2 : 1-electrolyte > 1 : 1-electrolyte > 1 : 2-electrolyte. Therefore the enrichment of the non-electrolytes must be different in the 3 cases mentioned above if the activity coefficients and Di do not differ greatly from one substance to the other.(b) 0 2 4 6 T i m e , hours 0 2 4 6 8 FIG. 5.-DIFFUSED AMOUNTS OF ELECTROLYTE AND NON-ELECTROLYTE il (5u) Expt. I (0) NaCl (5b) Expt. 1 (0) MgC12 Expt. 2 (0) NaC1, ( 8 ) acetone . Expt. 2 (0) MgC12, (9) acetone (5c) Expt. 1 (0) CaCl2 Expt. 2 (0) CaC12, (9) acetone. It has been shown in table 1 that the enrichment of a non-electrolyte becomes greater if the initial concentration of the electrolyte co is made smaller. This can also be explained by the fact that the concentration gradient of the electrolyte has also become smaller. The exact values of the concentration gradients are difficult to determine since the values of the mean activity coefficients can differ largely from case to case.Moreover the values of (F 5) cannot be determined exactly in the region of very small concentrations of the external solution. On the other hand, to integrate the equations one must use a mean value (f +)s instead of (f -l-)sl and (f+)s,. The value of ( j - 5 ) ~ can be only roughly guessed. Further, Dj must be independent of the concentration. The diffusion coefficient Di also determines the rate of diffusion of the electro- lyte through the membrane. The dependence of the rate of diffusion on the swelling110 SIMULTANEOUS DIFFUSION capacity of an ion-exchange resin is known.16 In this work it was considered of value to determine how the addition of the non-electrolytes affects the diffusion of electrolytes.For this purpose, the diffused amounts of electrolytes NaCl, MgCl2 and CaC12 were determined as a function of time with and without the addition of acetone. The initial concentrations co amounted to 0.5 mole/l. for acetone and 0.1 equiv.Pl. for the salts. The curves of fig. 5 show a decrease in the rate of diffusion of MgCl2 and CaC12 in the presence of acetone. The values of NaCl remain unaffected. In order to explain these phenomena the swelling behaviour of Na-, Mg- and Ca-membranes at different acetone concentrations of the external solution (0-1-1-5 mole/l.) has been first investigated. The swelling capacity of the membrane remained constant. Hence one might assume an interaction between acetone and Mg2+ and Ca2f (complex formation). In this connection it might be mentioned that Herz and Knaebel17 observed an effect of MgCl2 and CaCl2 on the capillary activity of acetone.They ascribed this to the tendency of acetone to combine with Mg2+ and Ca2+ ions. It is found here that the amount of acetone adsorbed by Mg- and Ca-membranes is approxi- mately double that adsorbed by Na-membrane. This also seems to indicate possible complex formation. Summarizing one can state that with the exception of the 2 : 1-electrolyte the enrichment of the non-electrolyte gives satisfactory results as long as the concentration of the electrolyte in the external solution is very small, compared to that of the fixed ions in the membrane. Naturally, a complete separation of one of the components could not be expected under our experimental conditions. But one could almost attain this if the solution on the secondary side of the membrane is continuously renewed by pure solvent. For the initial concentrations of the 2 : 1-electrolyte used here a satisfactory enrichment of the non-electrolyte could not be obtained in practice using cation exchange membranes. An anion exchange membrane might, however, give satisfactory results here. The authors’ thanks are due to Professor K. Vetter for discussions. 1 Sollner, Ann. N.Y. Acad. Sci., 1953, 57, 177. 2 Wheaton and Bauman, Ind. Eng. Chem., 1953, 45, 228 ; Ann. N. Y. Acad. Sci., 3 Weissberger, Technique of Organic Clzemistry (Interscience Publishers, Inc., New 4 Teorell, 2. Elektrochem., 195 I, 55, 460 ; Progress in Bioplrysics, 1953, 3, 305. 5 Schlogl, 2. physik. Chem., 1954, 1, 305. 6 Manecke, 2. physik. Chem., 1952,201, 193. 7 Manecke, 2. Elektrochem., 1951, 55, 672 ; 2. physik. Chem., 1952, 201, 1. 8 Manecke and Otto-Laupenmuhlen, 2. physik. Chem., 1954, 2, 336. 9 Helfferich, Diplomarbeit (Gottingen, 1952). 10 Helfferich, Z. physik. Chem., 1955, 4, 386. 11 Barnes, Physics, 1934, 5, 4. 12 Gordon, Ann. N. Y. Acad. Sci., 1945-46, 46, 285. 13 Dean, Chem. Rev., 1947,41, 503. 14 Barrer, Diffusion in and through Solids (Cambridge University Press, 1951). 15 McInnes, The Principles of Electrochemistry (Reinhold Publishing Corporation, 16 Boyd and Soldano, J. Amer. Chem. SOC., 1953, 75, 6091. 17 Herz and Knaebel, 2. physik. Cliem. A, 1928, 131, 389. 1953, 57, 159. York, 2nd ed., 1949), vol. 1, part 1, p. 604. New York 1939), p. 133.

ISSN:0366-9033    

DOI:10.1039/DF9562100101

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

THE SORPTION AND DIFFUSJON OF ETHANOL IN A CATION EXCHANGE RESIN MEMBRANE BY J. S. MACKIE * AND P. MEARES Chemistry Dept., University of Aberdeen, Scotland Received 7th December, 1955 The sorption of ethanol by the cation-exchanger Zeo-Karb 315 in the hydrogen and sodium forms has been studied at 25" C. The sorption isotherms are almost linear and the alcohol is salted into the resin phase. The temperature coefficient of sorption is very small. The results conform with the theory of lyotropic salting-in. The data suggest that about one-third of the alcohol in the resin is adsorbed on to the polymer chains. The remainder is in solution in the water swelling the resin and is free to diffuse. The diffusion of ethanol in Zeo-Karb 315 has been studied at 15", 25" and 35". The purpose of this investigation was to compare the behaviour of a non- electrolyte solute in a water-swollen cation-exchange resin membrane with that of electrolytes.l.293 It was found that, although the complications due to the interaction of charges were removed, other factors became operative which pre- vented a direct comparison.The present experiments, though less exhaustive than those with the electrolytes, were sufficient to elucidate the main influences controlling the sorption and diffusion. EXPERIMENTAL MATERIALS.-The cation-exchange resin was a Zeo-Karb 3 15 disc. Its properties have already been described.1 The ethanol solutions were prepared by weighing, using " de-ionized " water. ANALYSIS.-T~~ analysis of the very dilute solutions of ethanol was based on the method of Scandrett.4 This involved oxidizing the alcohol with potassium dichromate in sulphuric acid and estimating the excess dichromate.2 K2Cr207 + 3 C2H50H + 8 H2SO4 = 3 CH3COOH + 2 K2S04 + 2 Cr2(SO4)3 + 11 H20. The dichromate, 0.05 and 0.10 N, was made up in concentrated sulphuric acid. It was estimated by diluting and adding excess 5 % potassium iodide solution followed by titration of the liberated iodine with sodium thiosulphate. 10 ml of the alcohol solution were added to the standard dichromate at 0" C and further concentrated sulphuric acid added, if required, to keep the acid concentration above 50 %. The mixture was left to stand overnight at room temperature and the excess dichromate estimated by titration. Hastening the reaction by refluxing gave high results.Test experiments with 0.01 and 0-50 M solutions of ethanol gave consistently accurate results. SoRPnoN.-The method of equilibrating the resin with the external solution was similar to that used with electrolytes.1 As before, the experimental data gave the ratio c/d, where c is the concentration in moles/cm3 and d the density of the solution in the resin. Data are available 5 for the densities of aqueous ethanol solutions as a function of con- centration. Calculating c from the experimental c/d involves the assumption that the densities of solutions in the resin are equal to the densities of free solutions of the same concentration. This is a good approximation for resins of low cross-linking such as Zeo-Karb 3 15. DwFusIoN.-The diffusion experiments were carried out using the apparatus described previously.3 While maintaining a constant effluent flow rate, samples were collected at intervals and analyzed.A steady state of diffusion was established when the samples collected at different times contained equal concentrations of ethanol. * present address : Applied Chemistry Division, National Research Council, Ottawa, Canada. 1 1 4112 SORPTION AND DIFFUSION RESULTS SORPTION The sorption of ethanol from aqueous solutions at 0-1, 0.5 and 1.0 M by the Zeo-Karb disc in the hydrogen and sodium forms at 25" C has been studied. Measurements were also made with a 1.0 M solution at 35". Results for 25" appear in fig. 1 as a plot of external solution concentration against - concentration in the membrane expressed as moles of alcohol sorbed per cm3 of solution swell- ing the disc.Each point is the mean of several determinations. The value at 35" was not significantly different from that at 25". 1.0 - 0.8 - - 0 E DIFFUSION The rates of permeation of ethanol from 0-1, 0 5 and 1.0 M solutions through the membrane in the hydrogen form into water were measured at 15", 25" and 35". The results, expressed as moles of alcohol permeating in 1 sec through 1 cm2 of available membrane surface,Z 3 appear in table 1. Each result is the mean of a number of values determined at different effluent - ' 0 . 2 0 . 4 0;6 0.8 C moie/i. FIG. 1.-The sorption of ethanol by Zeo-Karb 315 at 25". 0 hydrogen form, 0 sodium form. flow rates. TABLE OBSERVED PERMEATION OF ETHANOL THROUGH ZEO-KARB 315 flux Jobs mole cm-2 sec-1 x 10-8 Concentration cz mmolecm-3 15" 25' 3 5 O 0.1 18 0.34 0-45 0-58 0-587 1 -52 1.96 2-53 1-175 2.76 3-58 4-26 DISCUSSION SORPTION In both cationic states ethanol is salted into the resin phase.This observation corresponds well with the theory of lyotropic salting-in suggested by Bockris, Bowler-Reed and Kitchener.6 A quantitative application of the theory is not possible as the necessary parameters are not available for the resin network. The effect of an electrolyte on the activity of neutral molecules in solution is a combination of the coulombic effect due to the ion charges and the dispersion effect due to interaction between the ions and the neutral molecules. For an organic resin network this dispersion interaction will be large and produce a considerable tendency towards salting-in.The coulombic effect acts in opposition to this. For a low-capacity resin, such as was used here, the salting-in effect outweighs the coulombic effect. For a resin of high capacity and a solute of high molecular polarization the coulombic interaction may become the larger term and produce a net salting-out. Thus Gregor, Collins and Pope 7 found that ethanol was saltedJ . S. MACKIE A N D P . MEARES 113 out of a sulphonated polystyrene cation-exchange resin in the potassium form in which the ionic strength was about 20 times that of Zeo-Karb 315. Several less polar neutral molecules studied by these workers were salted into the resin. Reichenberg 8 has studied the sorption of various alcohols by sulphonated cross-linked polystyrene resins of high capacity, in both the hydrogen and the sodium form.In all cases the sorption was greater with the hydrogen form of the resin. Reichenberg attributes this difference to solvation of the hydrogen ions by the alcohol molecules. Such an effect seems to be largely absent in the case of ethanol and the phenol-sulphonic acid resin Zeo-Karb 315. The sorption data are represented in fig. 2 by the more sensitive plots of c/C against 2, where 2 is the external solution concentration. It can be seen that at high concentrations the salting-in effect is greater for the hydrogen form resin which may indicate slight solvation of the hydrogen ions by ethanol. There seems no doubt, however, that the main influence in determining the extent of salting-in with Zeo-Karb 315 is interaction between the ethanol and the resin network.0 . 2 0.4 0.6 0 . 8 - C rnole/I. FIG. 2.--c/F against C for ethanol in Zeo-Karb 315 at 25". 0 hydrogen form, 0 sodium form. If c and y are the concentration in moles/cm3 and related activity coefficient of ethanol in the resin phase, expressed in terms of the volume of imbibed solutions and F and 7 the corresponding quantities in the external solution, then the equilibrium condition is cy R T ' Here 17 is the network tension of the resin and V the partial molar volume of the ethanol in the resin phase; R and T have their usual significance. Both L! and Y may be regarded as independent of concentration for the dilute solutions used here. Hence if - In a is written for IIVlRT, (I) becomes cy = a+.(2) A relation between In y and c is required in the interpretation of the diffusion data and has been obtained as follows. The experimental isotherm for the H-form is almost linear and hence may be expressed approximately by C = bc, (3) where b is the slope. The activity coefficients in the resin and in the external solution are then related by y = aby. (4) Shaw and Butler9 have measured the partial vapour pressures of aqueous ethanol solutions ; rational activity coefficients f I , using pure alcohol as the standard state, may be calculated from these. The partial molar free energy of ethanol is then where N is the mole fraction and G& the standard molar free energy of alcohol. = G% + RT Inf'N, ( 5 )114 SORPTION AND DIFFUSION If the standard state of alcohol is infinite dilution in water G = (Gk)w + RTlnfN = (Gz)w + RTln ~ y , ( G ) w = ( G ) W + RTln (dO/~o). (6) where (G&)w and (G:)w, the standard free energies on the mole fraction and molar concentration scales respectively, are related by (7) Here do is the density and MO the molecular weight of water.For ethanol at 25" it has been found that 10 - (G&)w - G$ = 740 cal/mole. (8) Combining (5) to (8) enables as linear with c. Thus, where g is a constant, Hence with (3) and (4) to be obtained from f I . For dilute solutions In 7, which differs only slightly from zero, may be treated h?=ggc. (9) (10) In y = bgc + In (ab). For Zeo-Karb 315,17 is 7.8 atm.1 V will be close to the partial molar volume of ethanol in dilute aqueous solution, i.e.54-7 ml. Hence a = 0.98. From the experimental isotherm for the hydrogen form resin (fig. l), The data of Shaw and Butler give 9 Thus for ethanol in the hydrogen form of Zeo-Karb 31 5 from (lo), b = 0.85. g = 15.8 cm3/mole. In y = 13.4 c - 0.183. (1 1) DIFFUSION The general membrane diffusion equation 2 may be simplified in the present If J is the flux in the x direction in moles case by omitting the electrical terms. C w 2 sec-1 at a point distant x through the membrane, then D is the differential diffusion coefficient of the solute in the membrane and (T the rate of osmotic flow of solution in the x direction ((T is numerically negative if J is positive). For a membrane thickness 6 the steady state permeation rate is given by The activity coefficient 7 may be eliminated using (lo).'CO J r dx=- [r Ddc- jci Dbgcdcf cr cdx, . o 1: (13) where ci is the concentration of solute in the membrane at x = 0 and co at x = 6. Provided ci and co are not widely different (e.g. a dilute solution diffusing into pure solvent) D may be treated as varying linearly with c, i.e., D = Do + kc, (14) where DO and k are constants. Thus from (13), J [ d X = - 5'' (Do f kc)(l + bgc)dc + cr 1 cdx. CiJ . S . MACKIE A N D P . MEARES 115 The relation between c and x , required for integration of the osmotic term, is obtained from solution of the steady-state equation dJ/dx = 0. (16) Exact solution of this equation is possible only if the variations of activity coefficient and diffusion coefficient with concentration are neglected. As the osmotic term is only a small correction to the total flux this approximation introduces no appreciable error.Hence (1 6) becomes d2c dc Do - - O - = 0, dx2 dx for which the appropriate solution is Integration of (1 5) then gives c0 - ciexp (&/DO)] 1 - exp (a6/&) J6 =* .5(Dobg + k)(ci2 - co2) + 4kbg(ci3 - co3) + 06 [- (18) In the experiments described here c" was always zero, thus ci exp (08/Do) 1 - exp (06/Do) J6 = *(Dobg + k)ci2 + 4kbgci3 - 08 - The diffusion coefficient of ethanol in the Zeo-Karb disc has been estimated by dividing the diffusion coefficient in water by the square of the " increased path length factor ", as described previously.2? 3 The most precise determinations of the diffusion coefficient of ethanol in water at 25" are by Hammond and Stokes.11 Values of Do at 15" and 35" have been derived from these using the activation energy for diffusion, 3.88 kcal/mole, given by Smith and Storrow.12 The temperature dependence of the concentration factor k has been neglected. These values and the derived ones for diffusion in the membrane are collected in table 2.TABLE 2.-DIFFUSION COEFFICIENTS OF ETHANOL IN WATER AND RESIN temp. in water in resin Do cm2 sec-1 x 10-5 "C DO cm2 sec-1 x 10-5 15 25 35 0-986 0.482 1.240 0.612 1.542 0.775 k cm5 sec-1 mole-1 - 1.42 x 10-3 - 0.70 x 10-3 The rate of osmotic flow at each temperature and concentration has been estimated from experimental determinations with hydrochloric acid solutions as described elsewhere.3 The theoretical flux has been calculated for each experi- mental concentration and temperature using the above values with bg from (1 1 .) These results and also the ratios Jobs/Jcalc appear in table 3.TABLE 3.-cALCULATED PERMEATION OF ETHANOL THROUGH ZEO-KARB 3 15 Rux Jcalc mole cm 2 sec - 1 x 10-8 Jobs IJcalc concentration 1 5 O 25" 350 1 5 O 2 5 O 350 ci mmole cm-3 ___- 0.118 0-55 0.70 0.88 0-62 0.64 0.66 0.587 2.44 3.12 3-79 0.62 0.63 0.67 1.175 4.14 5.34 6.19 0.67 0.67 0.69116 SORPTION AND DIFFUSION It is clear that the observed flux is substantially less than that calculated. This could arise from the use of a diffusion coefficient for ethanol in the membrane which was too large. The method for estimating this was found to be reliable for the mobilities of inorganic ions in the membrane 3, 13 and is likely to fail only if the diffusing particles are large enough to experience sieve effects in passing through the polymer matrix.Calculation of the overall activation energy Ep for the permeation process from gives 4.3 and 3.8 kcal/mole at 0.5 and 1.0 M respectively. These are only slightly different from the value quoted above for diffusion in free aqueous solution. A sieve effect considerably increases the activation energy for diffusion so there is no evidence for it in the present case though it does occur in more highly cross- linked resins.14 The low observed flux is more probably due to part of the alcohol in the resin being immobilized by the strong dispersion forces in a solvating layer on the polymer chains. Only the remainder, free in the internal aqueous phase, is able to take part in the transport process.This supports the suggestion of Gregor7 that neutral molecules are adsorbed by the resin matrix. The detailed behaviour of Jobs/Jcalc is also consistent with this explanation. At constant temperature the ratio increases with increasing concentration indicating the normal decreasing slope of the adsorption isotherm. At constant concentration Jobs/Jcalc increases with temperature just as the amount adsorbed usually decreases as the temperature is raised. If the alcohol in the resin phase can be considered as divided between an adsorbed layer on the polymer chains and a portion free in the internal aqueous phase, then the thermodynamic equilibrium in the sorption experiments should be regarded as between the external solution and the internal aqueous phase.With Jobs/Jcalc (E 0.65) giving approximately the fraction of alcohol in the resin which is in this phase, the activity coefficient of this alcohol appears to be about 1.3. This is a reasonable value when taking into account only the salting-out effect of the counter ions. A similar state of distribution in the resin would be expected for other neutral solutes ; for less polar substances the extent of adsorption and immobilization would be greater than with ethanol. This behaviour is in contrast with that of ionic solutes. Although a considerable fraction of the ions must be concentrated into a small volume around the fixed charges,ls the evidence is that almost all the small ions in the resin phase are free to diffuse through the internal sol~tion.~ 1 Mackie and Meares, Proc. Roy. SOC. A, 1955, 232,485. 2 Mackie and Meares, Proc. Roy. Sac. A , 1955, 232, 498. 3 Mackie and Meares, Proc. Roy. SOC. A, 1955, 232, 510. 4 Scandrett, Analyst, 1952, 77, 132. 5 Inter. Crit. Tables (McGraw-Hill, New York, 1933), 6, 242. 6 Bockris, Bowler-Reed and Kitchener, Trans. Faraday Soc., 1951, 47, 184. 7 Gregor, Collins and Pope, J . Colloid Sci., 1951, 6, 304. 8 Reichenberg, private communication. 9 Shaw and Butler, Proc. Roy. SOC. A, 1930, 129, 519. 10 Butler, Thomson and McLennan, J. Chem. SOC., 1933, 674. 11 Hammond and Stokes, Trans. Faraday SOC., 1953, 49, 890. 12 Smith and Storrow, J. Appl. Chern., 1952, 2, 225. 13 Meares, J. Polymer Sci., 1956, 20, 507. 14 Boyd and Soldano, J . Amer. Chem. SOC., 1953, 75, 6091. 15 Alfrey, Berg and Morawetz, J . Polymer Sci., 1951, 7 , 543.

ISSN:0366-9033    

DOI:10.1039/DF9562100111

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

GENERAL DISCUSSION 117 GEhTERAL DISCUSSION Dr. T. L. Hill (Bethesda U.S.A.) said Both the Donnan and McMillan-Mayer methods can be applied to the more general situation in which one or more species are present on both sides of a membrane but have different electrochemical potentials on the two sides. Such a difference in electrochemical potential for any particular species might arise either (i) because the molecules or ions cannot pass through the membrane (e.g. protein molecules) or (ii) because the membrane does work to maintain the electrochemical potential difference (e.g. active trans-port of sodium ions). This extension of the present paper is discussed in more detail elsewhere.1 Prof. G. Scatchard (M.Z. T. Cambridge Mass.) said I am very much interested in Dr.Hill’s finding that the term in the second virial coefficient which the Donnan treatment attributes to unequal diffusible ion distribution is attributed by the MacMillan-Mayer method to repulsion between non-diffusible ions. This shows how dangerous it would have been to believe that the measurements prove either explanation to be correct. In this case a common basis of the two explanations is easy to find in that they both require that each solution be electrically neutral. Dr. B. A. Pethica (Cambridge University) said It is of interest to allow for the specific interaction of ions in the Donnan treatment of the equilibrium across a membrane impermeable to one charged species. The occurrence of ion pairing between the diffusible species introduces no special additional factors but if the non-diffusible species specifically binds gegenions the assumption that its charge is invariant with respect to the concentration of diffusible electrolyte is no longer valid.The Donnan correction for the “ excess osmotic pressure ” of the diffusible ions is still obtained however from the membrane potential directly as in the usual formula for small potentials. The question of specific interaction is of particular interest in systems involving for example the equilibrium of a detergent ion with a protein where the strong binding (even in dilute solutions) is measured by an equilibrium dialysis method. Prof. Teorell mentioned that it is possible to treat the ionic distribution at the boundary of a charged membrane by methods other than the Donnan.The use of the Donnan equilibrium in the fixed charge theory seems natural for thick membranes in which a volume charge density is a variable of choice. For a very thin charged membrane (e.g. Prof. Danielli’s bimolecular lipid membrane) it would seem preferable to treat the fixed charge in terms of a two-dimensional charge density. The Gouy and Stern theories are applicable in this case. As Davies and Rideal have shown 2 the simple Donnan treatment for a surface charge is closely related to a Gouy treatment. Similarly, it may be shown that the Stern method for surface charge is similar to a Donnan treatment in which specific interaction is allowed for It is hoped to give a fuller account of these points in due course. Ing. J. Straub (Utrecht) said I would like to add a personal tribute to the honours accorded to Prof.Donnan. I recall that Prof. Donnan realized that the Donnan equilibrium is always an imperfect equilibrium. Unless one of the liquids is put under a static pressure there remains in equili-brium a difference in total osmotic concentration that must cause a steady per-meation of water. A perfect equilibrium would be established only if on both sides of the membrane non-permeating ions of the same concentration but of different sign were present. This possibility has now been realized by my col-laborator P. Hirsch Ayalon. It is mentioned in a paper given by Dr. Hirsch in the International Congress on Polyelectrolytes at Rehoboth 1srael.j Prof. G. Scatchard (M.Z.T. Cambridge Mass.) said I believe that the differ-ences between Kirkwood’s treatment and Schlogl’s are probably even smaller 1 Hill J .Amer. Chem. SOC. (in press). 3 cp. also P. Hirsch Ayalon Rec. trav. chim. 1956 (in press). 2 J . Colloid Sci. 1948 3 3 13 118 GENERAL DISCUSSION than Dr. Schlogl indicates but that any discrepancy must be due to an error in Schlogl’s treatment rather than in Kirkwood’s. The fact that Kirkwood’s treatment leads to non-linear equations when the diffusion coefficients are not invariant is due to the nature of the systems and not to his treatment. The “ discontinuous ” method gives average values of these coefficients which must depend upon the detailed conditions. Moreover even in the simple cases in which each is the corresponding Gab at some point in the membrane there is no reason to suppose that this relation holds for any two of them at the same point.Prof. R. Schlogl (Guttingen) said In reply to Prof. Scatchard I would like to remark that I do not believe that there is any serious discrepancy between Kirkwood’s treatment and Schlsgl’s treatment. May I quote from my paper: “ In practice Kirkwood’s treatment will always be a very good approximation, and any small deviations will almost certainly be insignificant compared with experimental errors ”. More important than the difference between both approaches is the inter-pretation of Kirkwood’s coefficients wap. My objection to these coefficients (the calculation of which has been performed correctly by Kirkwood) is just what Prof. Scatchard mentions they are not invariant to the nature of the system (but rather depend on the applied “forces” APE) so that the flux equations become non-linear.Kirkwood in his paper states that the wag’s depend on the concentrations of the solutions as well as on the membrane properties. However, it seems to have escaped his attention that the wafi’s depend also on the forces, for example the applied pressure difference or the electric field; in any case he does not mention this in his paper. But I fear that this dependence deprives these coefficients of their practical value. (I mentioned in my paper that the dependence has no significance as long as the system is close to equilibrium. In this case however the integration across the membrane carried out by Kirkwood is unnecessary.) Dr.G. Manecke (Berlin) said As I understand the results of Dr. Schlogl, he found that the convection contribution to the total conductivity constituted between 7 and 45 %. Now by measuring the conductivity of cation exchangers of the same chemical composition and with a water content of 60-70 % we determined the composite mobility of potassium and chloride ions and found that the mobility of the cation is greater than that of the chloride ion. Does he consider it correct that one can calculate the share due to convection in the ion transport from the difference determined by measuring the conductivity and transference in the mobilities of K and C1 within the membrane ? In addition, it must be assumed that the true mobilities of K and C1 in the membrane are practically equal as is found in free solution.In such a case I would obtain from my experiments a contribution of approximately 25 % for the convection con-ductivity at an outer concentration of 0.1 M. Dr. R. Schlogl (G2ttingen) said Since the water content in the membranes studied by Manecke was relatively high it seems to me that the assumption of equal characteristic mobilities for K and C1 is sufficiently justified as an ap-proximation. In my opinion with this assumption Manecke’s method of calcula-tion of the convection part of the conductivity is correct. Schodel found for the concentration Manecke mentioned a convection contribution of about 30-40 % according to the degree of cross-linking. That would agree quite well with Manecke’s estimated value especially since his membranes possessed a somewhat smaller water content.Prof. G. Scatchard (M.I.T. Cambridge Mass.) said It is most unfortunate that neither Prof. Nagasawa nor Prof. Kagawa is here to discuss this paper. Everything which T can check in it seems to me wrong. Their eqn. (4) contains five unexplained parameters. Even if they are explained in previous papers they are apparently all determined from the membrane potential measurements. Th GENERAL DISCUSSION 119 fact that none of the five explicitly contains the water activity cannot be taken as proof that the water activity does not affect the potential. In fig. 8 the authors appear to permit no parameters in Teorell’s equation to be determined from the potential measurements and the values they choose seem to me most improbable.We know that the capacity of Nepton CR-51 is about 1.2 rather than 0.1 and that U can vary only between - 1 and + I with the probable value about + 0.25. Yet they use 2 and 3. Concerning the fact that their results are never close to the theoretical limit one can only say that other observers have approached it much more closely. Once the curve starts to rise with increasing activity it should continue rising with slope about equal to that at the inflection as drawn. Dr. M. Nagasawa and Dr. I. Kagawa (Japan) (communicated) Prof. Scatchard stated that our eqn. (4) contains five unexplained parameters. The five which he referred to may be kl k2 k3 a and p. Originally we had three parameters kl, k2 and k3 as was introduced in the previous paper where these three were finally reduced to cc and /3.Here is our explanation of their relationship : Curve ( 3 ) in fig. 2 does not correspond to the experimental results. k2(2+ + I-) + k3I+ ’ = kl(& + I-) Therefore we thought our task in the paper under discussion was to determine the values a and fi by experiments. As to the water activity we do not think it is essential to the membrane potential of ion-exchange membrane considering the good agreement between our experi-mental values and the values calculated without water activity. As pointed out by Prof. Scatchard the capacity of Nepton CR-51 is about 1.2 mequiv./cm3 resin or 1.7 mequiv./cm3 of water in the resin. To use this analytical concentration of counterion in the resin for A in our opinion would be,entirely in-correct because A concerns the activity of the counterion in the membrane.There-fore the appropriate value of A is to be determined from the experimental results. If A = 0.1 is used the considerable although not satisfactory agreement be-tween experimental and calculated values seems to be found in experiments in which the concentration of the solution on one side of the membrane is maintained constant as seen in our fig. 7. On the other hand in the experiments in which the ratio of concentrations on both sides is maintained constant we found it impossible to obtain the suitable values of A and U which would enable us to keep the agreement between observed and calculated values over the entire range of concentration. To bring out this feature we included fig.8 in which the cal-culated values were compared with the experimental values by the convenient use of A = 0.1 and 1+/1- = 2 or 3 . These results lead to our conclusion that the membrane potential of the ion-exchange membrane is characterized by the ab-normal behaviour of the ion activity in the resin phase which could never permit A = const. It is true that the symbol U was mistakenly used instead of l+//- in fig. 7 and 8, where it is well known that Curve (3) in fig. 2 is not the experimental results; the values of (RT/Fln (~*l/a*2) are calculated under the condition of Q/CZ = 2 to show the limiting values in an ideal case. Dr. P. Meares (Aberdeen University) said The abnormally low activity co-efficient of univalent counterions in a cation-exchange resin membrane in the absence of sorbed electrolyte is shown by Nagasawa and Kagawa to give rise to deviations from the Meyer and Teorell equation for membrane potentials .when this is derived on the basis of simple-assumptions regarding the activity coefficients.means (/+/I- - l)/(/+/I- + 1) 120 GENERAL DISCUSSION This unusual activity coefficient behaviour has been noticed by various authors and is usually attributed to binding of counterions into an electrical double layer around the polymer chains of the matrix. Thus in their appendix Nagasawa and Kagawa find as a necessary condition for normal activity coefficient behaviour that there must be a uniform electrical potential within the membrane. This would eliminate the tendency to double-layer formation.It has been noted 1 that for divalent counterions the activity coefficients of the ions in the membrane differ relatively little from those in free solution. Pre-sumably the double-layer effect is less important here as its thickness is inversely proportional to the valency of the counterions. It would be interesting to know whether any measurements have been made to test the adequacy of the Meyer and Teorell equation for calculating the membrane potentials obtained with solu-tions of such higher valence type electrolytes. Prof. Karl Sollner (Bethesda Maryland U S A .) said The potentiometric data of Dr. Bergsma and Dr. Staverman are similar to results obtained in our laboratory with anion-selective as well as with cation-selective permselective collodion matrix membranes.2sjs 4 With these membranes however lines with the theoretical slope of 59-1 mV fit the experimental points with only minor devi-ations at high concentrations.With reference to the very interesting electric ion transfer experiments of Dr. Bergsma and Dr. Staverman I should like to draw attention to the similarity in the reasoning in their paper and the paper by Dr. Neihof and myself.5 We have studied the ratios of the simultaneous exchange across permselective collodion matrix membranes of two or more species of ions A B C coexisting at various combinations of concentrations in one solution against another species of per-meable ions in the other solution. The ratios of the fluxes from solution 1 to solution 2 of the ions A B and C obtained in these experiments agree generally within 15 to 20 % in many instances considerably closer with those calculated from the bi-ionic potentials.In continuation of this work we have recently started in Bethesda experiments like those described by Dr. Bergsma and Dr. Staverman including some in which the competing ions under consideration are present in solution at concentration ratios other than 1 1. The preliminary results obtained thus far indicate satis-factory numerical agreement between the calculated and experimental transference ratios. In our first experiments along these lines we calculated for instance from the B.I.P. for K+ and Li+ when present at the same concentration a transfer ratio of 7.50 1 and found experimentally 7.85 1 ; with a concentration ratio of 1 5 the computed value is 1 1-50 the experimental value was 1 1.53; with a 5 1 ratio these ratios were 37.5 1 against 33.7 1.I have only a limited experience with commercial type ion-exchanger mem-branes but I am inclined to concur with the suggestion of Dr. Bergsma and Dr. Staverman that a good part of the numerical disagreement which they find between calculated and experimental values might be due to the transportation of water across these membranes which is much more copious than that across our much denser collodion matrix membranes. This conclusion is also supported by the potentiometric measurements of Wyllie and Kanaan with very dense cation exchanger membranes.6 1 Mackie and Meares Proc. Roy. SOC. A 1955 232,498. 2 Dray Ph. D.Thesis University of Minnesota Minneapolis Minn. 1954. 3 Sollner Dray Grim and Neihof Ion Transport across Membranes edited by H. T. Clarke and D. Nachmansohn p. 144 Academic Press Inc. New York 1954; EZectrochemistry in BioZogy and Medicine edited by T. Shedlovsky p. 65 John Wiley and Sons Inc. New York Chapman and Hall Ltd. London 1955. 4 Dray and Sollner Biochim. et Biophys. Acta in press. 5 Neihof and Sollner this Discussion. 6 Wyllie and Kanaan J. Physic. Chem. 1954 58 73 GENERAL DISCUSSION 121 Dr. F. L. Tye (The Permutit Co. Ltd. London) said Dr. Bergsma and Dr. Staverman have listed cation transport number ratios obtained directly for com-parison with ratios deduced from bi-ionic potentials. It should I think be made clear that the ratio they have determined directly is (1) where t; and t; are the transport numbers of cations X and Y through the central cation-selective membrane and t i and t,’ are the transport numbers of the same cations through an adjacent anion-selective membrane.The ratio really required for comparison with bi-ionic potentials is ( t - tcx)/(t - a , tilt;. (2) If the adjacent anion membrane is perfectly selective then t and t; are zero and the measured ratio (1) reduces to the desired ratio (2). However in two of the four combinations considered by the authors one of the cations is hydrogen and it is extremely difficult to prepare anion-selective membranes which are im-permeable to hydrogen ions-even at 0.05 N concentrations. Thus if Y is hydro-gen t$ could be appreciable and the measured ratio (1) would not be identical with the desired ratio (2).This doubt can be removed or its importance assessed if the authors were to list the quantity which should be obtainable from their measurements. If the quantity (3) is unity, then ratios (1) and (2) must be identical. If however quantity (3) is less than unity then the difference between (3) and unity gives the maximum possible value of t + ty+. Dr. A. Despid and Dr. G. J. Hills (Imperial College London) said With regard to the paper by Bergsma and Staverman we should like to draw attention to the two possible values of an ionic mobility in any one membrane system and to comment on their relevance to transport numbers and calculated flux ratios. The transport number of an ion in a membrane is defined as t i - t i + t; - t t (3) where c represents concentration and u ionic mobility in an applied electrical potential gradient.u = h/F where h is the measured ionic conductance. This transport number is distinct from a similar quantity I UiCi t’ = -W C ’ where u’ represents ionic mobility derived from a self-diffusion coefficient. In a membrane u and uf are different the relation between them being given by u = uf i- Au, where Au is the electro-osmotic mobility in the same direction as u. Similarly, there are two different flux ratios of two competing ions UiCi/Ujcj and u~ci/u~ci. Perhaps Dr. Bergsma and Dr. Staverman or any of the other authors concerned with membrane potential would comment on which of these ratios they consider to be relevant to bionic potentials and membrane potentials in general.When the flux ratio or mobility ratio of two counterions species in a membrane are discussed in relation to B.I.P. it is generally assumed that this ratio is constant, i.e. independent of the total or of the individual ionic concentrations and equal to the limiting mobility ratio in water. If the relevant mobility ratio is that in the absence of an external field this is in fact so. We have found that ionic mobilities derived from self-diffusio 122 GENERAL DISCUSSION coefficients obey a modified form of the Debye-Huckel-Onsager equation over the whole concentration range i.e., zc’ = (N/F)(l - K*dY)(A - VR), where A” is the limitingionic conductance in water a* is the Onsager coefficient for the time of relaxation effect I the ionic strength and ( A - VR) is a term taking into account the viscous resistance of the membrane phase.In any one membrane containing two mobile ionic species the mobility ratio will be given by and since K* dj and ( A - VR) are the same for both ions, Dr. F. Helfferich (Giittingen) said I believe that the deviations between experiment and theory found by Bergsma and Staverman can be explained quali-tatively if the following points are considered. (i) Because of the low flow rate the bi-ionic systems are likely to be partially film-controlled. If this is the case the Donnan potentials are lower than the theoretical values and the transference number ratio calculated from the BIP is too unfavourable for the ion preferred by the membrane.In all systems except for NaCl + KCl the deviations found by the authors show this tendency; as may be expected it is most pronounced in the system involving H+ and the weakly basic Amberlite IRC-50 membrane. The more dilute the solution of the ion not preferred by the membrane the more serious should be the deviation. (ii) The activity coefficient ratio ys/yI in the bi-ionic systems (eqn. (5)) is not identical with that in the transference systems (eqn. (6)). The latter involves the coefficients in equilibrium with the mixed solution used whereas in the former ys is in equilibrium with a pure solution of S and yr in equilibrium with a pure solution of I. If the ion exchange equilibrium constant depends on mole fraction, differences between the two ratios are to be expected.Furthermore in this case the full equation for the BIP contains correction terms for the variation of the yr through the membrane. (iii) The theory of the BIP assumes that co-ions (i.e. ions of the same sign as the fixed charges) are virtually excluded from the membrane phase. This is a good approximation for membranes with high concentration of fixed charges in contact with dilute solutions but it is not likely to hold for the low capacity membranes A-58 and A-71 (0.27 and 0-42 mequiv./g dry weight respectively) in the concentration range studied. This might explain the abnormally small slopes in the BIP curves found with these membranes. The higher the con-centrations used and the larger the absolute value of the diffusion potential within the membrane the more serious should be the deviation.A quantitative com-parison is of course not possible because the necessary data are lacking. It will be interesting to see the results of the investigation announced by the authors on the significance of water transfer. Dr. J. E. Salmon (Battersea Polytechnic London) said I note that in many papers both “ homogeneous ” and heterogeneous membranes are employed. It appears to be assumed that the theoretical treatment to be applied for the two cases should be identical but to what extent this is justified seems doubtful to me. With the so-called homogeneous membranes it is probably correct to assume that a Donnan effect will occur only at the two membrane-liquid sur-faces. With heterogeneous membranes however the structure consists essenti-ally of a series of resin beads located in a series of interconnected cavities in the hydrophobic matrix of the “filler”.Whilst the resin beads are effectively close packed they will be surrounded by and separated by a film of electrolyte throug GENERAL DISCUSSION 123 which electrical conduction from bead to bead must occur. Hence with the heterogeneous membranes a series of Donnan equilibria must be set up between each bead and its surrounding film of electrolyte and these must be affected by changes in (i) concentrations of the solutes in the electrolyte across the membrane (i.e. the concentration profile) (ii) in properties of the solvent (i.e. in degree of association and in dielectric constant) within the membrane (iii) polarization of solvent and solute molecules near the functional groups of the resin.Dr. R. J. P. Williams (Oxford University) said Many of the authors describing the study of bi-ionic potentials do not refer to the way in which their membranes are prepared. It is not clear that membranes will come into equilibrium with solutions rapidly for example see papers by Scatchard and Helfferich and by Hutchings and Williams. In experiments with bi-ionic cells and with the " ab-normal " cells of Scatchard and Helfferich we have shown that a steady potential may not be obtained for hours or even days. Such slow equilibria will be most important for ions which are strongly retained at the surface of the membrane. Systems of importance are bi-ionic cells in which one of the ions is a simple uni-valent ion such as sodium which equilibrates rapidly between the membrane and the solution and the other is a divalent ion such as barium.Perhaps the silver cation equilibrates slowly with the membrane and some of the observations of Bergsma and Staverman may be due to non-steady state conditions ? We feel that it would be advantageous if authors gave details of the preparation of the membranes and of the changes of properties with time. Dr. G. J. Hills (Imperid College) said With respect to the paper of Mackie and Meares I would like to emphasize that transport processes through a mem-brane are dependent upon at least three variables the swelling or pore size of the membrane the composition of solution in the membrane and the temperature. None of these can normally be varied independently and in studying for example, rates of permeation as a function of temperature the simultaneous variation of the other parameters must be taken into account.I would therefore like to ask these authors if their energies of activation are not in fact more complex quantities than they state ? Prof. Karl Sollner (Bethesda Maryland U.S.A.) said When I proposed the term bi-ionic potential (B.I.P.) several years ago this term was intended to denote the dynamic membrane potential which arises across membranes of extreme ionic selectivity separating the solutions of two electrolytes at the same concentration having different permeable ions which exchange across the membrane and the same nonpermeable ion.1 As the etymology of the word bi-ionic indicates this term is meant to refer to situations in which two and only two species of ions are of essential significance.This situation does not prevail if diffusion layers play a significant role.2 In this case one is really dealing with three-ionic systems with three effective transition zones in series as shown so ably by Dr. Helfferich. Under these conditions one of the basic assumptions concerning the nature of B.I.P. systems as originally defined is not fulfilled namely identity of the con-centrations in the two bulk solutions with the concentrations of the two liquid layers in contact with the membrane.2 Since it is of some importance to have the clear and well-defined original mean-ing associated with the term bi-ionic potential particularly in the discussion of polyionic potentials across membranes of extreme ionic selectivity and the exchange kinetics of such systems I should like to suggest that this term be used only in its original meaning.The B.I.P. so defined is for a given membrane and a given pair of critical (permeable) ions a characteristic constant which over a fairly wide range is independent of the concentration of the solutions used and of the nature of the nonpermeable ions. 1 Sollner J. Physic. Chem. 1949 53 121 1 1226. 2 Dray Ph.D. Thesis (University of Minnesota Minneapolis 1954). Dray and Sollner Biochim. Biophys. Acta 1955 18 341 1 24 GENERAL DISCUSSION Dr. A. M. Peers (Low Temperature Research Station Cambridge) (communi-cated) In order to calculate a bi-ionic potential by the method of Dr.Helfferich, one must first calculate 6 the diffusion-layer thickness from membrane potential measurements. An independent and more direct estimate of 6 may be obtained by observing the limiting current-density at the membrane. The simple theory which has been applied for example in polarographic studies is also applicable to a membrane + solution system for which one can accept the simplifying assumptions (i) and (ii) in Q 3 of Dr. Helfferich’s paper (i.e. negligible transport of water and neben-ions). For a cation-permeable membrane and a solution of a single uni-univalent salt at concentration c the total current-density i may be written i = t+i + id, where t+ is the cation transport number in the bulk solution and id is the “ diffusion current ” through the stationary layer.For the limiting-current case id = FDc/6, where D is the diffusion coefficient of the salt and the first equation yields i = ilim = FDc/t-8 where t- = (1 - t+). The following figure shows a current-voltage curve obtained with a Permutit, C-10 cation-exchange membrane bathed on both sides with (flowing) 0.01 N NaCl solutions. The-potential measurements were made with a high-impedance 0 I 2 3 4 5 A V = ( V i - l R i = o ) volts FIG. 1 valve voltmeter connected to a pair of AgCl “ probe ” electrodes situated on opposite sides of the membrane. The experimental arrangement was such that the concentration of the bulk solution was virtually independent of time and current density. (The current in excess of ilim was found to be carried partly by hydrogen ions but mostly by chloride.) A further remark concerning the transport number measurements of Bergsma and Staverman when using direct current to measure the combined transport numbers of two or more ions of the same sign the effect of the diffusion layer is to diminish preferentially the “ interfacial concentration ” of the ion whose transport number changes by the greater amount on passing from solution t GENERAL DISCUSSION 125 membrane.To obtain the ratio which would be observed in a membrane in equilibrium with the bulk solution the transport-number ratio may be plotted against current-density and the curve extrapolated to zero current. These con-siderations are consistent with the better agreement between “ experimental ’’ and “ calculated ” ratios obtained by Neihof and Sollner (whose measured flux-ratios are equivalent to those given by the zero-current intercept) and with the manner in which the “experimental” ratios of Bergsma and Staverman differ from those calculated from potential measurements.The above arguments are illustrated by the figures in the final column of the following table. flux ratio 100 (expt.-calc.) work of N. & S . expt. calc. calc. K+ - Naf 2.6 2.5 + 4 % H+ - Na+ 24.0 22.0 + 9 % transport no. ratio expt. calc. work of B. & S . K+ - Na+ 1.6 1.7 - 6 % H+ - Na+ 4-4 7.1 - 38 % Dr. F. Bergsma and Dr. A. J. Staverman (DelJt) (communicated) In reply to Dr. Helfferich we think it will be worth while to calculate the B.I.P. for the general case of combination of membrane diffusion and film diffusion combining the cal-culations of Helfferich with the technique of Wyllie and using the general formula for the B.I.P.(different concentrations on both sides of the membrane). We agree with his first remark. It is possible that closer agreement may be obtained if more attention was paid to changes in activity in the membrane. If leakage of the Cellophane membrane was the reason for the small slopes in the B.I.P. curves we should have found that the slope depended on the con-centration. This was not the case ; up to about 0.1 N we found a nearly constant slope. As the Cellophane-type membranes have a greater permeability I believe that film diffusion is responsible for the deviation In reply to Dr. Tye we used the arrangement sketched in our fig.1 to avoid the difficulties with reversible electrodes. It is possible especially if one of the cations is hydrogen that there is some leakage of these ions through the anion solution membranes. This should give too low a transport number for the hydrogen ion. We think it will be useful to investigate this effect. We can apply in cells 2 and 5 a suspension of an anion-exchange resin in distilled water by analogy with the experiments by Kressman and Tye. In reply to Dr. Peers in our transport number measurements we used a very low current-density (about 0.5 mA/sq. cm) and circulating solutions. Therefore we expect that the concentration ratio of the two cations in the diffusion layer did not differ very much from that in the bulk solution.Nevertheless it will be worth while to perform a series of transport measurements with varying current density extrapolating to zero current. In reply to Dr. Salmon for a heterogeneous membrane with a hydrophobe, non-conducting matrix exchange between the two solutions is possible only through ion-exchange beads in contact with each other (path 2 of the left-hand diagram of fig. 2 of the paper by Spiegler et d). In a bead of an ion-exchanger the pore-diameter is about lOA. If the distance between the two contact areas is of the same order of magnitude the membrane behaves as a homogeneous one. Dr. F. Hemerich (Giittingen) (communicated) It will prove very useful to have an independent method as that of Dr. Peers to measure the film thickness.Certainly the neglect of water transfer through the membrane is more serious with high current densities than in bi-ionic systems but since the film concept is an idealization anyhow the error introduced thereby will not affect the value of his method 126 GENERAL DISCUSSION Dr. P. Meares (Aberdeen University) (communicated) The studies of Manecke and Heller and of Mackie and Meares on the sorption of non-electrolytes by the sodium form of a phenol sulphonic acid + formaldehyde resin both indicate a partition of the non-electrolyte between an adsorbed layer on the resin matrix and free solution in the internal liquid. The authors appear to have reached slightly different conclusions regarding the equilibrium between the internal and external solutions. Closer examination of the data has resolved this matter satisfactorily.l o g c FIG. 1 .-Plot of Freundlich equation. la ethanol a r= 1.0 ; 16 ethanol a = 0.8 ; 2a acetone a = 1.0; 2b acetone a = 0.7. Using the nomenclature of Manecke and Heller the quantity a = C/c is equivalent to the salting-out coefficient between the internal solution which con-tains the counter-ions of the resin and the external solution containing no salt. a should therefore be almost independent of c over a reasonable concentration range but will vary with the non-electrolyte and with the concentration of counter-ions. The equilibrium between the internal solution and the adsorbed layer may be expected to follow a Freundlich type isotherm where x is the amount adsorbed and k and n are constants.The amount adsorbed by the matrix associated with 1 ml of imbibed solution is (Ctot - C) which can be written (Ctot - ac). If the degree of swelling is independent of c a condition which is justified experimentally for the concentration range studied the isotherm may be written Thus log (Ctot - ac) plotted against log c should be linear. The graph show-these plots for ethanol on Zeo-Karb 315 for a = 1.0 and a = 0.8 and for acetone on the resin of Manecke and Heller for a = 1-0 and a = 0.7. In each case the linear relation is not found for a = 1.0 but is obeyed for cc less than 1.0. The uncertainties attending the use of the Freundlich isotherm prevent this method being used for a more precise determination of a. None of the conclusions of Manecke and Heller is in any way affected by the foregoing considerations.x = kC1/", (Ctot - XC) = k'c'l"' GENERAL DISCUSSION 127 Dr. G. Manecke (Berlin) (communicated) We agree with Meares that a for acetone might have values less than 1.0. We had made that simplifying assumption as the value of cc has no bearing on our results. As it is not possible to determine the exact value for a it might be more convenient to transfer a to the left-hand side of our eqn. (8) so that it reads : P = Diak = (tan B) 2.303 1211212. 4 V l + 7J2) ’ with P defined in this way it is unnecessary to know the values of a in order to evaluate P. Our numerical values of P and our ultimate conclusions are not affected by this alteration. P has here the conventional definition for permeability of membranes it is the amount of substance transported in 1 sec through 1 cm* of surface of membrane 1 cm thick when the difference between the concentration of the solutions on the two sides of the membrane is 1 unit Dr.N. Krishnaswamy (India) (communicated) Studying two different mem-branes with three bound cations it has been shown that in the presence of acetone the sodium form of the membrane permits diffusion of the electrolyte to the same extent as in a solution without acetone. But the calcium and magnesium forms of the membrane are found to permit lower diffusion of the electrolyte in presence of acetone. From Manecke and Heller’s results in tables 1 and 2 it is shown that the swelling property of the sodium form of the membrane is governed by the external solution concentration while for the magnesium and calcium membranes change in the external concentration has little effect on their swelling property.Dr. Manecke and Dr. Heller have stated that the swelling behaviour of Na Mg and Ca membranes was determined at different acetone concentration of the external solution and the swelling capacity of the membrane remained constant. Does this mean that the swelling characteristics of the three forms of membranes depended on the external acetone concentration as with external electrolyte solution ? From fig. 5 in that paper it is shown that there is lower diffusion of electrolyte through the magnesium and calcium forms of the membrane and from the ob-served presence of more absorbed acetone in these membranes it is postulated that complex formation between magnesium and calcium ions with acetone may be responsible for the above findings.If complex formation is possible in the external solution phase also then the rate of diffusion of the electrolyte would be decreased through the membrane by the larger size of the complex ion. Hence besides the possible interaction between acetone and Mg2+ or Ca2f in the mem-brane as stated by these authors the interaction in the external solution also may be responsible for the lower diffusion. Dr. G. Manecke (Berlin) said In answer to Dr. N. Krishnaswamy the Na- Mg- and Ca membranes have a definite swelling capacity when they are in equilibrium with solutions of electrolytes. The addition of acetone did not alter that swelling capacity as we have stated within the experimental errors.The interaction in the external solution between acetone and Mg2+ and Ca2t-ions may also certainly be responsible for the lowering of the diffusion of those ions. As we have mentioned in our paper Herz and Knaebel observed an effect of MgCl2 and CaC12 on the capillary activity of acetone solutions. Prof. Karl SoIlner (Berlzesda Maryland U.S.A.) said The barrier function and separation action of ion exchange membranes can of course be studied and utilized in many situations other than the separation of electrolytes and non-electrolytes as described so clearly by Dr. Manecke and Dr. Heller. Just to mention a few situations involving permselective membranes,l electro-lytes and non-electrolytes may be separated by the simultaneous use of both cation-permeable and anion-permeable membranes of extreme ionic selectivity in exchange dialysis against the solution of an acid and a base respectively or in 1 Sollner J.Electrochem. Soc. 1950 97 139c; Ann. N. Y. Acad. Sci. 1953 57 177 128 GENERAL DISCUSSION an electrically short-circuited two-membrane three-compartment system or with greatly accelerated speed by electrodialysis in a three-cell outfit. The efficiency of this procedure particularly if carried out with dense non-swelling membranes, seems to be beyond doubt. Ions of the same charge may be separated selectively by the exchange of ions (or by electric transferences) across membranes of ion exchange character and high ionic selectivity,l the separation factors being calculable from the bi-ionic potentials across the same membrane arising with the ions under consideration, as is evident from the paper by Dr.Neihof and myself.2 Another interesting case the elaboration of a suggestion by Manegold,3 may be mentioned suppose we have a solution of an electrolyte A+B- and a non-electrolyte C a membrane of extreme ionic selectivity permeable to the A+ ions as well as to the non-electrolyte C and a second solution containing radioactively labelled A+*B-* at the same concentration as solution 1 . An exchange A+ + A+* will occur and C will diffuse from solution 1 to solution 2 while the membrane represents a definite barrier for any exchange of B- for B-*. If we were now to take a membrane composed of two superimposed layers one layer of extreme cationic selectivity permeable to A+ and A+* and to the C molecules and one layer of extreme anionic selectivity permeable to B- and B-* and to the non-electrolyte C.It is evident that the non-electrolyte can diffuse readily across such a layered membrane while it is an absolute barrier (like a wall of glass) to the penetration across its thickness of the ionic constituents of the two solutions. These and similar possibilities still await detailed experimental exploration. Prof. F. Runge and Dr. F. Wolf (Halle Saale Germany) said Dr. Manecke studied in his systems non-electrolytes such as acetone formaldehyde etc. In a similar manner we studied the behaviour of different phenols with the intention of separating the phenols from waste waters by means of ion-exchange resin mem-branes.On one side of the membrane was situated the phenolic aqueous solution, on the other a solvent such as methanol benzene or others. Qualitatively expressed the results were as follows. The different phenols diffuse and easily pass through the ion exchange membrane but after some hours the diffusion stops It is supposed that irreversible adsorption processes of the phenols in the resin phase together with possible shrinkage effects in the upper membrane surface layers on the side of the organic solvent are the reasons for this behaviour. The different steps of the diffusion processes were investigated. Dr. R. Schlogl (Gottingen) said In the paper by Mackie and Meares,4 (T was called “ the rate of osmotic or hydrostatic flow ”. As is implied in De Groot’s treatment of “ continuous systems ” (T must be the velocity of the centre of gravity of all components which make up the pore fluid.I agree entirely with the expres-sion “ rate of hydrostatic flow ” also with the expression “ rate of osmotic flow ” provided however that water is the dominant component of the pore fluid. I: I have understood correctly only dilute ethanol + water mixtures were used SO that this distinction will be of no consequence. However it seems to me incorrect to take values for (T measured for an arbitrary electrolyte and apply them to systems with other electrolytes or with non-electrolytes. As I have shown in my paper on anomalous osmosis,6 the factors responsible for the osmotic water transport are with electrolyte solutions not so much the osmotic difference between the two outer solutions as the pressure gradient and electrical field within the membrane.(+ can actually assume different signs with different electrolytes (negative and positive osmosis). Since for hydrochloric acid which was used in 1 Sollner J. Electrochem. SOC. 1950 97 139c ; Ann. N. Y. Acad. Sci. 1953 57 177. 2 Neihof and Sollner this Discussion, 3 Manegold Kapillar Systems vol. 1 (Strassenban Chemie and Technilc Verlags-4 Proc. Roy. SOC. A 1955,232,498. 5 Thermodynamics of Irreversible Processes (Amsterdam 1951) p. 119. 6 Z. physik. Chem. 1955 3 73. gesellschaft Heidelberg 1955) p. 637 GENERAL DISCUSSION 129 Meares' measurements the diffusion potentials arising are probably considerable, I believe that u will be appreciably larger in this system than in the ethanol + water system.A potential difference of 1 mV corresponds to approximately a pressure difference of 1 atm at room temperature. Dr. P. Meares (Aberdeen University) said In reply to Dr. Schlogl the quantity G is defined in the paper cited 1 as " the rate of osmotic or hydrostatic flow of the internal aqueous solution " ; the word solvent occurred in the defintion of (T in the pre-print of the present paper through an oversight. The rate of flow of solution was measured experimentally and was used in calculating the fluxes. I agree that the calculation of the small mass flow correction term ca has been greatly simplified and that there is a possibility of anomalous osmosis affecting results obtained with hydrochloric acid.Subsequent experiments 2 using only water and a hydrostatic pressure gradient gave the same flow rate per atmosphere, within 15 % as that calculated from the osmotic pressure of the hydrochloric acid solutions so that anomalous osmosis does not appear to have made an important contribution in the present case. I agree with Prof. Ubbelohde that it is difficult to distinguish between the interpretation suggested and the alternative possibility of a low diffusion coefficient for ethanol in the membrane. If this were to arise as suggested by Prof. Ubbelohde, from a reorientation of the hydrogen bonds in water and ethanol inside the mem-brane some effect on the energy of activation for diffusion and a heat of sorption would be expected but were not observed.Ideally one should measure the mobility of individual ethanol molecules in the internal solution to decide this question but no method has been devised for doing this. In reply to Dr. Hills the factors affecting the value of the overall activation energy for permeation Ep calculated for constant external concentrations are (i) the change in the surface concentrations within the membrane with temperature ; (iia) the change in membrane thickness due to increase of swelling with increase of temperature ; (iib) the change of diffusion path length due to increase of swelling ; (iii) the change of diffusion coefficient of ethanol in the internal solution with temperature. The sorption experiments show (i) to be negligible. Effects (iia) and (iib) tend to cancel one another ; allowance can be made for them using the membrane swelling data already published.3 This increases the value of E' by 0.033 kcal/mole.It may safely be concluded that the values of Ep represent within experimental error of & 0-2 kcal/mole the activation energies for diffusion of ethanol in the imbibed solution. Dr. E. Glueckauf (Harwell) said I wish to describe a new separation tech-nique based on the ion exclusion by semi-permeable membranes developed by G. P. Kitt and myself. Ionic transport in membranes is obviously dependent not only on the diffusivity but also on the concentration in which the ions are present in the membrane. If we have in the solution a univalent anion then the uptake of univalent cations is not dependent on concentration while that of poly-valent cations is.A simple mass law calculation shows that the distribution factor between uni- and divalent ions for a solution and an anion exchange resin, e.g. is given roughly by /?lilt ni;+ C capacity of resin m~2+ in;+ - m---N-=-ionic conc. in solution ' 1 Mackie and Meares Proc. Roy. SOC. A 1955 232,498. 2 Mackay unpublished work. 3 Mackie and Meares Proc. Roy. SOC. A 1955 232 510. 130 GENERAL DISCUSSION This is a considerable separation factor. Normally we cannot utilize this effect, because most of the ionic transport is done by the anions. But if we stop the anion transport by facing the anion exchange membrane with a cation exchange + -rll FIG. 1. membrane and apply a voltage then roughly half the current is carried by cations and then this separation effect comes into play.Fig. 1 shows schematically an arrangement. The electrolyte mixture to be separated is placed in the anode compartment the cathode side con-taining pure acid. Fig. 2 shows the transport across the membrane as function of time for an equimolar solution of K+ Ca2+ and Fe3+ nitrates of total concentration 0.12 N and the great preference for the transport of the univalent ion. When using ions of equal charge, the ion exclusion is dependent on the ratio of the activity coefficients and the effect is not as large as for differently charged cations. But it is still notice-able (fig. 3). The mechanism operating at moderately high current densities even in neutral solutions is far from simple.There are at least two distinct stages noticeable from the current-voltage curves. At very low voltages and current densities particularly in solutions above 0.3 N the ions of the electrolyte carry T i m e m l n u t e s FIG. 2. the current. At higher voltages across the membranes much current is trans-ported by H+ and OH- ions produced by dissociation of the water at the interface of the two membranes. A quantitative assessment of the process taking place has so far not been achieved. Mr. D. Reichenberg (C.R.L. Teddington) said I would like to refer to som GENERAL DISCUSSION 131 experimental work 1 on the sorption of organic compounds from aqueous solution by cation exchange resins. This sorption is molecular sorption not ion exchange, since the compounds studies were acetic propionic and n-butyric acids and ethyl, n-propyl and n-butyl alcohols.With the acids it was only possible to study their sorption by the resins (sulphonated polystyrenes of various degrees of cross-linking) in the H+ form; with the alcohols sorption by both the H+ and Na+ forms was studied. The degree of sorption has been found to be independent of the particle size of the resin showing that the phenomenon is one of true absorption and that T i m e . m i n u t e r FIG. 3. surface adsorption plays no appreciable part. The results may conveniently be expressed in terms of the molality of solute inside the resin phase divided by the molality in the outside solution. This quantity which we call the “ molality ratio ” is presumably equivalent to Dr.Manecke’s a’ and Dr. Meares’ C/c though both these authors speak of “ moles per litre of internal solution ” instead of the unambiguous “ moles per kilogram of sorbed water ” which we have used. The results .show that : (i) The molality ratio is not a constant for a given solute and a given resin in a given ionic form. In general it varies with the solute concentration. In most cases the molality ratio decreases with increasing solute concentration, in a few cases it is almost constant and with n-butyl alcohol in both the H+ and Naf forms of the resins it increases with increasing concentration. (ii) For a given solute at a given concentration and with the resin in a given ionic form (either Hf or Naf) the molality ratio has always been found to de-crease with increase of cross-linking over the range 5* to 15 % DVB.However, there are good grounds 1 for believing that at lower degrees of cross-linking some of the solutes at least must show an initial increase of molality ratio with increase of cross-linking. (iii) For a given resin in a given ionic form (either H+ or Na+) and a given concentration the molality ratio increases with the chain length of the solute molecule. Thus the molality ratio increases in the orders (a) acids; acetic < propionic < n-butyric; (b) alcohols ; ethyl < n-propyl < n-butyl. 1 Reichenberg and Wall submitted for publication J. Chem. Soc 132 GENERAL DISCUSSION (iv) For a given solute at a given concentration and a given degree of cross-linking the H+ form of a resin always absorbs much more of an alcohol than did the Na+ form.(About twice as much for the 5-4; % DVB and n-butyl alcohol.) Observation (iii) shows the contribution of London dispersion interactions between the hydrocarbon part of the organic solute and the benzene nuclei of the resin; (ii) shows a " salting-out " effect of the resin in both the H+ and Na+ forms; (iv) shows however that superimposed on this there is a " salting-in " effect of the polar groups when in the H+ form. This last effect is shown very strikingly by the increase in the miscibility of n-butyl alcohol and water brought about by HCl. Aqueous solutions of HC1 of molality 4.6 and higher are miscible in all proportions with n-butyl alcohol at 25" C. Both NaCl and LiCl cause a salting-out of n-butyl alcohol from water.However the miscibility of n-butyl alcohol with HCl solutions increases hardly at all until the HCl molality exceeds 1, when it increases very sharply. This may be of significance in connection with Dr. Meares' observation that there was no marked difference between the sorption of ethyl alcohol by the H+ and Na+ forms of his resin. His resin had a fixed charge concentration of about 0.5 molal whereas even our 5% % DVB resin had a fixed charge concentration of 3-6 molal in the H+ form. Making use of the effect of chain length on the degree of absorption I have separated 4.4 mg equiv. acetic acid and 2-7 mg equiv. n-butyric acid from a mixture of the two. The mixture was simply loaded on to the top of a column (85 cm X 0.79 cm2) of resin (53 % DVB sulphonated cross-linked polystyrene in Hf form-total capacity of column 100 mg equiv.) and eluted with water.The separation was nearly quantitative though I have not yet succeeded in getting a gap of pure water between the acetic acid band (which comes off the column first) and the n-butyric acid band. (The minimum total acid concentration between the two fronts was 0.01-0.02 N while the acetic acid peak was 0.8 N and the n-butyric acid peak 0-3 N). Prof. Karl Sollner (Bethesda Maryland U.S.A.) said I should like to make some remarks to the paper by Dr. Neihof and myself. First our theoretical predictions can be attained readily on a more general basis without reference to some of the specific assumptions made in our paper. The basic concept of transfer-ence numbers as pointed out some time ago is adequate for the handling of many problems related to bi-ionic potentials.19 2 Secondly our experiments may also be considered as the quantitative demon-stration of a selective separation process for ions of the same charge coexisting in solution somewhat similar to the separation of electrolytes and non-electrolytes described in the interesting paper by Dr.Manecke and Dr. Heller. The separation of various ions of the same charge can of course also be carried out by electro-dialysis.3 Thirdly the greatly different 4' ratios observed suggest the question of whether systems of the general type discussed in our paper show some interesting peculiarities in the kinetics of the exchange of ions while they drift towards equilibrium.4.5 1 Sollner J. Physic. Chem. 1949 53 121 1 1226. 2 Sollner Dray Grim and Neihof Ion Transport across Membranes ed. Clarke and Nachmansohn (Academic Press Inc. New York 1954) p. 144 ; Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York, Chapman and Hall Ltd. London 1955) p. 65 ; Dray Ph.D. Thesis (University of Minnesota Minneapolis Minn. 1954) ; Dray and Sollner Biochim. Biophys. Acta., in press. 3 Sollner J. Electrochem. SOC. 1950 97 139c; Ann. N.Y. Acad. Sci. 1953 57 177. 4 Sollner and Neihof Arch. Biochem. Biophys. in press. 5 Neihof and Sollner J. Physic. Chem. (Colloid Symposium Issue 1956) in press GENERAL DISCUSSION 133 Consider a system with an exclusively cation-permeable membrane I +@-+ I, solution 1 solution 2 BfX- 0.01N +@+ C+X- 0*15N, A+X- 0.01 N C+X- 0.01 N where A+ Bf and C+ represent the exchangeable (permeable) ions and X- the non-exchangeable anions.Suppose the species of ions A+ in solution 1 (which is of infinite volume) exchanges across the membrane at a rate which is exceedingly high compared with the rates of exchange of Bf against C+ or A+. Apartial membrane equilibrium with respect to A+ and Cf ions will be virtually reached before a significant quantity of Bf ions have penetrated across the membrane.1 While this state of partid equilibrium prevails (in which the Bf ions do not participate) the concentration of both A+ and Cf ions in solution 2 will be 0.075 N according to the Donnan equation. During a further prolonged period the B+ ions will exchange across the membrane until our system reaches the state of the true final membrane equilibrium in which according to Donnan’s equation A+ Bf and C+ will be present in solution 2 at the same concentration 0.05 N.In other words the A+ ions reach temporarily in solution 2 a concentration in excess of that existing in the final true equilibrium state. Under suitable conditions the converse effect will arise-namely a transitory depletion of the concentration of some ionic species in solution 2. Overshooting the depletion effects of 50-85 % of those calculated for the partial equilibrium were observed.2 The overshooting of the equilibrium con-centration reached in some systems several hundred per cent as is evident from the graphs shown on the screen (which are in press elsewhere).2 Whether the overshooting and depletion effects play a significant role in the selective accumula-tion of ions by living cells is an entirely open question.However we feel that these effects should not be overlooked as possible factors. Fourthly the problem of the kinetics of the exchange of ions across membranes of extreme ionic selectivity in the genera1 case in which several species of exchanging ions exist in the two solutions in any arbitrary combination of concentrations can as it seems be attacked successfully along the same line of approach that we have taken in our paper for a very simple case. The kinetic interpretation of the equations for the polyionic potentials arising in such systems 3 seemingly provides the solution of this problem (on which a report will be presented at a later date).Dr. F. Helfferich and Dr. R. Schlogl (Gottingen) said In the derivation of the bi-ionic potential Neihof and Sollner have made the assumption that “ the two species of critical ions are present within the membrane in the same ratio as if the membranes were equilibrated with a solution prepared by mixing equal volumes of the two solutions of the bi-ionic system ”. It has been shown in this discussion that the application of the flux equations leads to a different picture and there is experimental evidence contrary to the above-mentioned assumption. But we wish to emphasize that our criticism of this assumption is not directed against the conclusions drawn by the authors.Both the quasi-thermodynamic treatment and 1 1 1 Donnan Chem. Rev. 1924 1 73. 2 Neihof and SoIlner J. Physic. Chem. (Colloid Symposium Issue 1956) in press. 3 Sollner Dray Grim and Neihof Ion Transport across Membranes ed. Clarke and Nachmansohn (Academic Press Inc. New York 1954) p. 144 ; Electrochemistry in Biology and Medieine ed. Shedlovsky (John Wiley and Sons Inc. New York, Chapman and Hall Ltd. London 1955) p. 62 ; Dray Ph.D. Thesis (University of Minnesota Minneapolis Minn. 1954) ; Dray and Sollner Biochem. Biophys. Acta., in press 134 GENERAL DISCUSSION the flux equation treatment lead without using the assumption in question to an equation for the B.T.P. which is identical with that of the authors except for correction terms. Also the relation given by the authors between the ratio of exchange fluxes #A/#B in system I and the B.I.P.in system I1 may be obtained from the flux equations assuming only constant mobilities constant activity coefficients and ideal permselectivity. The sum of the concentrations of the counterions A B and L in the membrane is equal to the concentration of fixed charges (concentration of co-ions is neglected) : ICi C A + C B + C L = C = const. (1) Z#i +A + +B + #L = 0. (2) The sum of the ionic fluxes is zero (no net transfer of charge) : The Nernst-Planck flux equations are Forming the sum of all fluxes and using (l), (4) In the steady state the left side of (4) is independent of the space co-ordinate x within the membrane. Hence due to C = const. the electric potential gradient is constant ‘ d’ - k = const.RTdx = Substituting (5) in (3) we obtain a linear differential equation for Ci which is readily integrated. By use of the boundary conditions c A = c;; c B = c;; c L = cL=o, at the left membrane surface; CA = c” = 0; c = c; = 0; CL = c” =z- c, at the right membrane surface ; the following solutions are found : c - A [ e x p (k(8 - x)) - 11, c -(6 = membrane thickness), A - kDA [exp {k(8 - x)) - 11 CL =- -[exp #L (- kx) - 11. - kDB kDL Inserting the boundary conditions for x = 0 and x = 6 respectively we obtain the following equations for the fluxes y$ : The exchange flux ratio 2 DACL’DBCi (7) obtained from (6) is identical with eqn. (4) in the paper of Neihof and Sollner (taking their eqn. (1) as a definition of the quantity T~C/T:+).Moreover the equation for the tri-ionic potential in system I is readily obtained from the above calculation. It is identical with that given previously by Wyllie GENERAL DISCUSSION 135 The diffusion potential within the membrane is obtained from (5) when the $i values in (2) are substituted according to (6) and the resulting equation is solved with respect to k6 : Assuming equilibrium at the interfaces membrane/solutions the Donnan potentials are given by The total membrane potential E is This calculation of the exchange flux ratio and of the membrane potential is easily extended to an arbitrary number of univalent counterions ccl cc2 . . . a on the left side and PI P2 . . . Pn on the right-side of the membrane : However this simple approach is not applicable to counter-ions of differing valence, since in this case d$/dx is no longer constant.For the same reason the Henderson formula cannot be used in such systems. Probably the most serious simplification in the above calculation is that the activity coefficients for every ionic species are assumed to be constant throughout the membrane i.e. independent of the mole fractions. This assumption cannot be accepted without some reservations for ion exchangers of pronounced selectivity which in this connection are of special interest. Perhaps the deviations found by the authors in the quantitative comparison of experimental and calculated fluxes can be explained in this way. Dr. R. Neihof (Uppsalu University) said I would like to point out that the use of collodion matrix membranes 1 9 2 in the experiments reported by us has made it possible to avoid certain difficulties which might otherwise have been en-countered with some of the more conventional ion-exchange resin membranes.They have relatively low water contents probably because of the swelling con-straint exerted by the matrix. The concentration of fixed dissociable groups in the membranes is high ; consequently their ionic selectivity is sufficiently great that the leak of non-critical ions can be neglected up to fairly high con-centrations of electrolytes. The ionic conductance of the membranes can be adjusted for the particular experimental conditions at hand so that with only moderate rates of stirring of the surrounding solutions diffusion processes occurring in the system are entirely membrane controlled.Due to the thinness of the membranes the unit-area ion-exchange capacity is small ; this is advantageous where it is important to have low capacities relative to the number of equivalents of ionic constituents in the surrounding solutions. 1 Neihof J. Physic. Chem. 1954 58 916. 2 Gottlieb Neihof and Sollner J. Physic. Chem. 1956 (in press) 136 GENERAL DISCUSSION Dr. R. D. Keynes (Cambridge University) said It is of considerable interest to biologists that Dr. Neihof and Dr. Sollner have succeeded in producing an artificial membrane capable of distinguishing to some extent between the various alkali metal ions. I think I should point out however the degree to which their membranes differ in selectivity both quantitatively and qualitatively from at any rate some cell membranes.The relative passive permeability of resting nerve and muscle membranes to group IA ions may be represented very approximately as Li = Na < K = Rb > Cs ; the difference between Na and K may be as much as 100 times while the membranes seem to be somewhat more permeable to Rb than to K in some cases and slightly less permeable in others. Quite apart from the fact that the selectivity towards Na and K can be suddenly reversed it would seem difficult to explain this complicated sequence by any process as straight-forward as a simple exaggeration of the differences in ionic mobility in free solu-tion arising from the greater hydration of the ions with smaller atomic weights.Prof. Teorell has quoted the relationship first derived by Behn and later by himself and Ussing between the ratio of labelled ion fluxes crossing a membrane in the two directions and the difference in electrochemical potential between the solutions on either side. This may be written as where E is the difference in electrochemical potential between the two solutions for the particular ion whose fluxes $12 and 421 are being measured. The basic assumption on which the derivation depends is that the ions cross the membrane independently ; with a constant potential difference the chances of an individual ion crossing the membrane in a given time interval are not affected by the other ions that are present. It has been shown for the passage of ions across some biological membranes (e.g.iodide and chloride in frog skin 192) that this equation is rather well obeyed but when Hodgkin and I used 42K to examine the passive movements of K+ ions between the inside and outside of Sepia axons,3 we found that the measured flux ratios were appreciably larger than the predicted ones, and that our results were fitted better by h 2 - nEF - exp-, $21 RT where n was about 2.5. We interpreted this deviation from the independence relationship as arising from an interaction between ions moving in one direction and those moving in the other possibly because the ions cross the membrane in single file through very narrow tubes or channels or pass over a bridge or chain of negatively charged sites. I wish to ask whether it has been verified that the movements of ions across artificial membranes of the types being discussed here are independent in the sense required for Behn’s relationship to hold.If any deviation from the predicted flux ratios were found it might throw an interesting light on the structure of these membranes and on the way in which ions move across them. Dr. R. Neihof (Bethesda) said in reply to Dr. Keynes’ remarks it is certainly true that the artificial membranes available now do not have the degree of selectivity for the alkali metal ions which is exhibited by certain biological membranes. The anion selective collodion matrix membranes on the other hand do show a high selectivity for certain anions. The selectivity of these membranes is due to chemical or adsorptive specificity and not to steric restriction of the ions having the larger hydrated size.Improved selectivities for particular alkali metal ions 1 Ussing Acta Physiol. Scand. 1949 19 43. 2 Koefoed Johnsen Levi and Ussing Acta Physiol. Scand. 1952 25 150. 3 Hodgkin and Keynes J. Physiol. 1955 128 61 GENERAL DISCUSSION 137 can be expected when materials having the necessary high chemical specificities become available. Such materials could or course be incorporated not only in microheterogeneous structures like the collodion matrix membranes discussed here but also in homogeneous phase “ oil ” membranes. Prof. A. R. Ubbelohde (Imperial College London) said Modern work in-dicates that the quasi-crystalline structure of liquids such as water or ethyl alcohol may undergo profound changes near a surface especially when the surface con-tains polar molecules as is the case for many membrane walls.One test of such changes of liquid structure arises from measurements of dielectric relaxation, which show that water molecules near the walls are much less free to rotate. In some ways the abnormal orientation imposed by membrane walls on the H20 dipoles nearest to them makes these boundary layers of solvent much nearer to a fluid like H2S than a strongly ionizing fluid like quasi-crystalline bulk H20. For example the effective dielectric constant is lowered. These changes in liquid structure are likely to be particularly important for molecules such as H20 or alcohols of low carbon content that form chains and networks of hydrogen bonds.For bulk water the co-ordination number is about 4 ; a very open structure is maintained by the hydrogen bonds. In the very strong polarizing fields near certain membrane walls a rise in co-ordination number and a decrease in ionizing power would be expected. Other solvents in which the co-ordination number is higher behave more nearly like assemblies of close-packed spheres; for such fluids any structural changes near to or within the membrane are likely to be much less marked. When flow of solvent through a membrane occurs these considerations indicate a number of consequences. For solvents which undergo marked changes of quasi-crystalline structure near membrane walls : (i) The effective viscosity of the modified solvent layers may be markedly different and may involve different entropies and energies of activation.(ii) The ratio of ion mobilities may be quite different from those in bulk solution particularly if ion solvation has a marked effect on the transport number in the bulk solvent. In the “modified” solvent close to the membrane walls, ion solvation is reduced by the competing polarization forces of the walls. These walls orient solvent dipoles along their own force fields which normally conflict with the centric fields due to individual ions. Relative to Kf both the ions Na+ and H3O+ which are very considerably more solvated will suffer substantial changes of mobility in the “ modified solvent ”. On the other hand two ions which are not extensively solvated such as K+ and Rb+ should preserve much the same relative properties in the modified layers.(iii) Ion activities may be appreciably changed in the modified solvent layers near membrane walls. This applies both in the “ diffusion layer” nearest the walls and in “ channels ” whatever their specific structure within the membrane itself. Some of the leading effects can be simply illustrated in relation to the Debye-Huckel expression for the limiting activity coefficient of an ion logf* = - A I z1z2 1 dr with A = 1.8246 x ~ O ~ / ( E T ) ~ / ~ ; I is the ionic strength.1 In the modified layers the effective dielectric constant E will be lowered for reasons described in the preceding section. In comparing the effect for two ions of the same charge a change in E merely leads to proportional changes. At rather higher ionic strengths the expression for log f* must be divided by the term (1 + Bad?) where a is the ionic diameter and B is a constant.At such con-centrations a more important influence may be the decrease in effective ionic radius a+ arising from desolvation in the modified layers. This influence will shift relative thermodynamic potentials of two ions such as K+ and Na+. 1 cf. Robinson and Stokes Electrolyte Solutions (Butterworth 1955) p. 228 138 GENERAL DISCUSSION (iv) On migrating from bulk solvent to modified solvent individual molecules require activation energy which may differ appreciably from the activation energy for migration within the bulk solvent. The change in co-ordination number which accompanies the change in quasi-crystalline structure of the solvent also involves a change in heat content.This change in heat content as the solvent molecules flow from bulk I -+ modified layer -+ bulk I1 must in some cases lead to appreciable heat transfer across the membrane if there is appreciable flow of solvent through the membrane. Ordinarily the thermal conductivity of the mem-brane will equalize any large temperature differences across it. For slow rates of solvent flow no large inequalities of temperature would seem likely. However, if membranes can be found which (i) permit rapid flow (ii) impose substantial modifications of structure on the solvent near the membrane walls appreciable cooling or heating may accompany solvent flow because of the accompanying substantial changes of heat content. Mr. D. Reichenberg (C.R.L.Teddington) said I would like to quote some experimental evidence in support of Prof. Ubbeolohde's view that conditions inside a resin cannot be treated as similar to those in an ordinary electrolyte solution even after the obvious differences due to fixed charges in the resin have been allowed for. At the Chemical Research Laboratory Mr. Selton has measured the equilibrium degree of penetration of HCl from aqueous solutions (0-03 molal up to 2.5 molal) into a commercial carboxylic acid resin Amberlite IRC 50 in the H+ form. Over the whole of this concentration range the molality inside the resin (i.e. mmoles HC1 absorbed per g of water inside the resin) was appreci-ably lower than that in the external solution the ratio rising with concentration from 0.45 0.10 (at 0.03 molal) to 0.67 f 0.03 (at 2-5 molal).The carboxylic acid groups of the resin would be almost completely in the undissociated state. Hence this " salting-out" could arise only from one or more of the following four causes : (i) a dielectric effect due to the hydrocarbon matrix of the resin; (ii) a dipole effect due to the undissociated carboxylic acid groups ; (iii) the water inside the resin being possibly in a different state of aggregation from that in the outside solution; (iv) an osmotic effect arising from constraints due to the cross-linking of the resin. However this last effect can probably be ruled out since it has been shown to be very small with most electrolytes in resins of normal degrees of cross-linking.1 Prof. G. Scatchard (M.I.T.Cambridge Mass.) said After Prof. Ubbelohde reminds me it seems to me that there must be an effect such as he suggests and that this effect must be related to the effect of the breadth of junction on the electro-motive force of cells with transference,2 which depends upon the heat of dilution. This effect at the membrane should also depend markedly upon the efficiency of heat transfer upon the rate of stirring etc. It may well enter into some of the effects of stirring noted in some papers presented at this Discussion. Prof. R. M. Barrer (Imperial College London) (communicated) Dr. Pethica has asked what is the relation between the diffusion expressed in terms of a chemical potential gradient dpldx and that expressed in terms of Fick's law. The relation is derived as follows.The force acting on a molecule at a point x is F cc - dp/dx. Thus the total force acting on all molecules at the point x is FT cc - Cdp/dx 1 Duncan. Proc. Roy. SOC. A 1952,214 344. 2 Scatchard and Buehrer J. Amer. Chem. Soc. 1931,53,574. Hamer J. Amer. Chem. SOC. 1935 57 662 GENERAL DISCUSSION 139 where C denotes the concentration at the point x. If the flux J is now assumed proportional to FT one has for the flux through unit area J = - [BC]dp/dx (1) where B is a coefficient measuring the mobility of the diffusing molecules. Since RT d In a = dp where a is the activity of the diffusing species at point x one may substitute in (1) and obtain BCRT da (2) J = - [4&’ and so J - - [,a]& BCRT da dC (3) But since in the Fick law equation, one has d In a d In C‘ D = BRT- (4) There is of course no reason why B or d In ald In C should not depend in a com-plex way on C or in inhomogeneous media on x.In some polymer systems it has moreover been discovered that on account of slow relaxation times of the polymer network D may for a given penetrant molecule depend also on time t. I would like to make a comment on the rather widespread use of the term “ affinity series ” revealed by the papers given in this Discussion to denote the extent of exchange of a series of ions with a given exchanger. This is a loose application of a term which should have a precise thermodynamic significance. In an exchange equilibrium where has in and Aaq + BZ + Baq + Az, the subscripts aq and 2 denote solution and exchanger respectively one terms of ion activity a, K = aB,qaAZ, aBZaAaq AGO = -RTln K.AGO measures the affinity of the reaction. If the ion B is kept the same and a series of ions A is used then the AGO values for the series will give the true affinity series. This has been measured for some ion pairs exchanging in chabazite.1 I would suggest that the term “ affinity series ” should be retained only in its true thermodynamic sense and should not as at present be incorrectly used to denote ion sequences indicating the extent of reaction. The latter series may not always coincide with the true affinity sequence. Dr. B. A. Pethica (Cambridge University) (communicated) Prof. Barrer’s simplified statement of the relation between the diffusion equations using Fick’s law and the chemical potential gradients is a useful addition to the discussion.The account is similar to that in his earlier publication,2 and should be compared 1 Barrer and Sammon J . Chem. SOC. 1955,2838. 2 Barrer Faraday SOC. Discussions 1948 4 68 140 GENERAL DISCUSSION to the fuller analysis given by de Groot 1 and others. My original remarks on eqn. (1) and (3) in the paper by Lorimer Boterenbrood and Hermans were in-tended to point out a certain degree of thermodynamic arbitrariness about the choice of forces in the flux equations as well as to draw attention to the Fick’s law equation. In the first place the separation of into chemical (p) and electrical potentials ( E ) is open to the well-known criticisms of Guggenheim,2 although since Lorimer et al. consider only small deviations from equilibrium the two sides of the membrane may be considered as of identical composition. In a simple diffusion system obeying Fick’s law it is clear that to write the diffusion in terms of “ chemical ” potential differences will involve a conjugate coefficient which is non-constant. This may be seen by comparing Barrer’s eqn. (1) with Lorimer’s eqn. (1) and (3). In making this point I was bearing in mind a paper by Denbigh 3 in which he considers the same question. Denbigh was principally concerned with the incorrect results obtained by Prigogine 4 on the thermodynamics of the stationary state in an open system involving chemical reaction showing that the errors arose from taking reaction rates as proportional to chemical potentials. In the diffusion case similar considerations will apply where chemical potential gradients are used if the conjugate coefficient is not constant (as when Fick’s law is obeyed). The question of the variation of the coefficients with p is left open by Lorimer et al. who have restricted themselves to small deviations from equilibrium. 1 De Groot Thermodynamics of Irreversible Processes (North Holland Publishing 2 Guggenheim J . Physic. Chem. 1929 33 842. 3 Denbigh Trans. Faruday Soc. 1952 48 389. 4 Prigogine Etude Thermodynamique des Phtnomdnes irriversible (Likge 1947). Co. Amsterdam 1952)

ISSN:0366-9033    

DOI:10.1039/DF9562100117

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

B. PROPERTIES OF PARTICULAR MEMBRANES TRANSPORT PROCESSES IN ION-SELECTIVE MEMBRANES CONDUCTIVITIES TRANSPORT NUMBERS AND ELECTROMOTIVE FORCES BY J. W. LORIMER, (Miss) E. I. BOTERENBROOD AND J. J. HERMANS Laboratory for Inorganic and Physical Chemistry, The University, Leiden Received 1st February, 1956 The thermodynamics of irreversible processes has been applied to the problem of transport of two ions and solvent through a homogeneous membrane. Measurements of transference numbers of potassium ion and water, conductivities and e.m.f.’s as functions of concentration are reported for a new type of cellulose membrane containing a dissolved polyelectrolyte. It is found that the solvent contribution to the e.m.f. is not negligible, and that transference numbers measured directly are in fair agreement with those derived from e.m.f.data. The results indicate large variations in potassium ion mobility in the membrane. Methods for the evaluation of physico-chemical properties of membranes have depended until recently upon some form of the fixed charge theory of Teorell19 2 and Meyer and Sievers.3 This theory contains several restrictive assumptions 2 which make its quantitative application to membrane phenomena rather uncertain. In particular, a number of workers 4-8 have obtained evidence of large differences between ionic mobilities in membranes and in free solution, the explanation of which falls outside the realm of the fixed charge theory. Staverman,% 109 11 in 195 1, and Kirkwood,lZ in 1954, explored the application of the thermodynamics of irreversible processes to ion transport through membranes.The simplest membrane system to which irreversible thermodynamics can be applied consists of a homogeneous membrane separating two homogeneous solutions each containing the same electrolyte. In this case, discussed in the theoretical part, measurement of the specific conductivity, two transference numbers, two diffusion coefficients and mechanical permeability give six relations from which all six phenomenological coefficients of the thermodynamic theory can be obtained. These coefficients are sufficient to describe other phenomena, such as the e.m.f. of membrane cells and streaming potential. For tests of this theory, homogeneous, reproducible membranes which ex- hibited a marked variation in transport properties at electrolyte concentrations below 0.1 N, were prepared in a wide range of dimensions.The specific conduc- tivity, transference numbers of one ion and solvent, and e.m.f. of a membrane cell have been determined for potassium chloride solutions between 0.001 and 0-1 N, and thus form an important part of an extended programme, the aim of which is to obtain all phenomenological coefficients as functions of concentration. THEORETICAL IRREVERSIBLE PROCESSES IN MEMBRANES Consider a membrane separating two homogeneous solution phases I and 11, each containing rz constituents j . This forms a “ discontinuous ” system as defined 141142 TRANSPORT PROCESSES by de Groot,13 for which the flux of constituent j through the membrane at constant temperature and in units of mole cm-2 sec-1 is Here d& is the difference in total thermodynamic potential of constituent j between phases I and 11, and Ljk is a phenomenological coefficient expressing proportionality between the fluxes Jj and the generalized forces d&.There are n(n + 1)/2 of these coefficients, since Onsager 14 showed that they are symmetrical, Ljk = Lkj. (2) Eqn. (1) was used by Staverman 9,1OY 11 in his treatment of membrane pheno- Since the Ljk’s may be functions of F j , it is important to consider only mena. infinitesimal differences in Fj, given by (3) In this equation, dpj is the purely chemical part (4 ) where aj is the activity of constituent j , R is the gas constant in joule mole-1 deg-1 and T is the absolute temperature. The pressure-volume contribution to dFj is given by the product of the partial molar volume vj in cm3 mole-1 and the pressure difference dp in joule cm-3, while the electrical contribution is given by the product of the faraday (96,500 joule equiv.-I), the valence zi of j (including sign) and the potential difference dE in volts.dpj = dpj + vjdp + FzjdE. dpj = RTd (In aj), The total electric current density in A cm-2 is Solution of (1) and (5) for dE gives i FdE = -I/(FLE) - tJ (dpj + vidp) ; j = 1, 2, . . . 12, (6) where tj is the mass transport number of constituent j : and with K the specific conductivity in Q-1 cm-1, and a the membrane thickness in cm. If (6) is inserted into (l), where Relations (6) and (10) are the basic equations for this paper. They are formally equivalent to those of Staverman,g. 10911 but are written in a form particularly useful from an experimental point of view.It is to be noted that Ljk and d j k have the dimensions of (concentration x mobility)/(length x F), with concentration in mole cm-3, mobility in cm2 V-1 sec-1 and length in cm. The relationship between this “ discontinuous system ” and the “ continuous system ” used by Kirkwood 12 is too lengthy to be treated here, and will be discussed elsewhere. 15J. W. LORIMER, E . I . BOTERENBROOD AND J . J . HEKMANS 143 DESIGN OF EXPERIMENTS In the case of interest here, consider a univalent cation 1, a univalent anion 2 and a solvent 0. Eqn. (6) and (10) then become Ji = J2 + IIF = tiI/F - Aii(dp + v dp) - dlo(dpo + vodp), Jo = toZ/F - dlo(dp 4- vdp) - Jloo(dp0 + VO~P), (13) (14) and where and it is found that If anion-reversible electrodes in the solution phases are used to measure potentials, FdE = -FIa/K - tl(dp1 + qdp) - t2(d,u2 + v2dp) - fo(dpo + vodp), p = p1 + p2, v = v1 + v2, and tl - t2 = 1, d l 1 = d l 2 = d 2 2 , d l 0 = d 2 0 .must be added to (14) to obtain the total e.m.f. of the cell. The term +(p) contains the effect of pressure on the electrode reactions. With dp = dp = 0, the specific conductivity and two independent transference numbers can be measured. These transport numbers are sufficient to predict the e.m.f. of a membrane cell with dp = I = 0. For a homogeneous membrane with transference numbers which are single-valued functions of p, the value of this e.m.f is E’ = -(2RT/P) (tl - mMto/lOOO)d In a, s:’ where the Gibbs-Duhem equation -dpo = mMdp/1000 has been used, with m the molality of the solution, and M the molecular weight of the solvent.It must be emphasized that this e.m.f. is a measure of a combination of tl and t0,10, 16 and does not involve any unknown single ion activity coefficients. Tangents drawn to a plot of E’ against In a thus yield values of this transference number combination. At dp = dE = 0, again using the Gibbs-Duhem equation, the quantities 4 1 1 - mMdlo/1000, and d l 0 - mMAYoo/1000, may be obtained by measuring the diffusion rates through the membrane of salt and solvent under steady state conditions. Finally, at dp = dE = 0, measure- ment of the mechanical permeability, gives a sixth independent relation which completes the information necessary for computation of the six phenomenological coefficients.Other phenomena such as the streaming potential may then be predicted readily. numbers, and comparison with measured e.m.f.’s are described below. JOPP = - A l O V - ~oovo., dE’jdp = -tlv - tow0 - $(P) Attempts at verification of eqn. (16) by direct measurement of the transference EXPERIMENTAL AND RESULTS MATERIALS AND soLunoNs.-The sodium carboxymethycellulose (NaCMC) and viscose were samples supplied by the Research Laboratories of the A.K.U. Rayon Co., Arnhem, The Netherlands. A 2 % solution of NaCMC in 40 % ethanol + water was prepared1 44 TRANSPORT PROCESSES and centrifuged at 10,000 rev/min for 30 min to remove undissolved material. The con- centration of the resulting clear solution was determined by evaporation of weighed portions at 110" C.Conductimetric titration 17 of three samples of this partially purified NaCMC gave 2-81 0.02 mequiv." of sodium per g of salt (degree of substitution 0-59) and a completely negligible amount of free carboxyl groups. The viscose was stored at 0" C to slow down decomposition. Analyses of this solution by coagulating three weighed samples by the procedure given below, then drying to constant weight in a dry nitrogen atmosphere 18 at 110" C gave 7.22 &- 0.02 % cellulose by weight. Analyses of the regenerated cellulose by the methods of Ludtke 19 and Neale and String- fellow 20 gave 30 & 2 pequiv. COOH/g cellulose. For conductivities and transport numbers, A.R. KCI was recrystallized from conduc- tivity water and dried thoroughly at 700" C.Solutions were prepared by weighing, using water of conductivity 1 to 1-6 X 10-6 Sz-1 cm-1. Their pH was between 5.8 and 6.0. Solutions for e.m.f. measurements were made by dilution of stock solutions of A.R. KCl with distilled water, in view of the large volumes required. were mixed in amounts sufficient to give a concentration of approximately 0.01 equiv. sodium/l000 cm3 of membrane in its final condition. The solution was mixed thoroughly with a vibrating stirrer. It could be used for three months if stored at 0" C. It was found desirable to make the cellulose concentration greater than 6.5 % for membranes with good resistance to compression. Membranes were formed by pouring the solution into moulds consisting of two glass plates with Plexiglas separator.The separators were rings machined to within 0.02 mm of a given thickness, with small grooves along their radii to allow diffusion of solution into the interior of the mould. The ring was placed on the lower plate, its interior was filled with excess of solution, and the top plate was pressed on firmly. The mould was placed in 15 % ammonium sulphate (iron-free) in distilled water at room temperature. After about two days, agitation caused the glass plates to slide off the mould. The membrane, with a degree of swelling of 17.2 (the same as the original solution), was removed, and was washed in fresh solution for one day. Its degree of swelling had then reduced to 12, and soluble sulphides and sulphur had been washed out.Finally, it was boiled 5 min in 15 % ammonium sulphate solution to complete the conversion to a water-insoluble, highly-swollen cellulose gel (degree of swelling 7.13). Washing and boiling twice in dis- tilled water removed soluble salts, after which the membrane was placed in saturated KCl for one week to convert it to the potassium form. Before making measurements at a given concentration, the membranes were boiled twice in conductivity water, then kept in conductivity water for 12 h at 80" C, and finally placed in the appropriate KCl solution, which was changed several times over a period of 24 h before the membrane was used. It was found that sodium polystyrenesulphonate, and even the potassium salt of Congo Red (with a micelle-forming anion 21) could be incorporated into membranes in this manner.No Congo Red has been leached out of one membrane in contact with water for a period of over 9 months. SWELLING PROPERTIES Membrane thicknesses were measured by means of a micrometer feeler gauge, so that no pressure was applied during measurement. A membrane could be weighed " in air " with a precision of 0-3 % by blotting, placing in a weighed amount of solution and re- weighing. Its volume and density were determined by the buoyancy method 18 to f 0-3 %. The density of dry cellulose was measured by a similar method, using carbon tetrachloride as the buoyancy fluid. Membranes were prepared in the above manner with a range of thicknesses from 0.1 to 3 mm, and uniform in thickness to 5 0.5 %. Measurement of the ratios of the thickness and diameter of the membranes to the thickness and the diameter of the mould showed that the membrane was swollen isotropically to -I 3 %. Further, successive membranes could be made in the same mould with a reproducibility of f 0.5 % in thickness.The degree of swelling was found to be independent of KCl concentrations between 0.001 and 0.1 N. The density was 1.073 i 0.003 g cm-3 at 25" C. From swelling and analytical data, the concentration of potassium carboxymethylcellulose was calculated to be 0.0126 f 0.0003 equiv./1000 cm3 of membrane. * All limits of error are average deviations from the mean. PREPARATION AND CONDITIONING OF MEMBRANES.-viSCOSe and 2 % NaCMC SolutionJ . w. L O R I M E R , E . I . BOTERENBROOD AND J .J . HERMANS 145 RETENTION OF CMC Measurement of the membrane resistance at 0.005 N KC1 before and after passing direct current through it, or before and after pressing solution through it, indicated no measurable losses of CMC. Qualitative tests of the membrane equilibrium solutions with 2 : 7-dihydroxynaphthalene-H2SO417 similarly gave negative results. One membrane was used repeatedly for e.m.f. measurements over a period of two months without any evidence of loss of CMC. It appears safe to conclude, therefore, that this method of incorporating polyelectrolytes into cellulose membranes is quite satisfactory. SPECIFIC CONDUCTIVITY The specific conductivity of the membranes was measured in a cell similar to that described by Manecke and Bonhoeffer,22 and by means of a Philoscope a.c.bridge. A piece of sheet plati- num was soldered to the end of each of two brass plugs A, A' (fig. 1). The plugs were then turned and threaded to fit holes in the two Plexi- glas discs B, B'. These electrodes were screwed into place, the platinum-Plexiglas joint was sealed by cementing with acetone, and the electrodes were coated with platinum black. The two halves of this cell could be lined up reproducibly by means of pins C , C' and corresponding sockets, and brass screws through holes D held the cell together. The cell was supported by a handle E in such a way that the membrane was held horizontally between the two cell halves. In this way, very slight pressure on the membrane was sufficient to prevent leakage. :: F FIG. 1 .-Conductivity cell.The cell was filled through tubes F, F' by means of a capillary pipette. All measure- ments were carried out with the cell in a thin rubber bag in a grounded water thermostat at 25.00 i 0.02" C. Steady resistance readings were obtained within about 1/2 h. FIG. 2.-Resistance as a function of thickness ; 0.01 KCl alone 0 ; with membrane 0. A number of Plexiglas rings of various thicknesses could be used to separate the two halves of the cell by known amounts. This permitted determination of the resistance of the cell as a function of thickness of a layer of KCl solution. The cell resistance with membrane was also measured as a function of membrane thickness. A typical deter- mination is shown in fig. 2.146 TRANSPORT PROCESSES Least-square lines were computed from the data.If the slope of the line with KCI alone is ( R / a ) ~ c l , and with the membrane is (Ria),, the specific conductivity of the mem- brane is where KKCl is the specific conductivity of the equilibrium KCl solution, obtained from data tabulated by Gunning and Gordon.23 The lines had the same intercept at a = 0 within the experimental error of f 2 %. Thus, the effective area for conduction was the same for membrane and solution. Results at both 1000 and 50 c/s were identical at all concentrations to f 0.5 %. Since evaluation of the specific conductivity involves a ratio of resistances, correction for the solvent conductivity was found to be important only at 0.001 N. The good proportionality between resistance and length indicates that any refraction of the current lines 24 in the area between the two Plexiglas plates is negligible, and that the membranes do not show any large inhomogeneous regions.Table 1 gives the specific conductivity of the membranes and for comparison, that of KCl, as a function of the nor- mality of KC1 (C). Each value of K is the average, computed as shown above, for eleven membranes. TABLE l.-SPECIFIC CONDUCTIVITIES (IN f2-l Cm-l) OF MEMBRANES AND OF KCl SOLUTIONS AT VARIOUS CONCENTRATIONS (C) OF KCl C( equiv./l.) 1 0 4 ~ 1 0 4 ~ ~ c 1 0*1000 75.9 129.0 0.04989 39.5 66.8 0.009993 9-02 14.1 0.004968 5.32 7.12 0.00 1068 2.36 1 -57 E.M.F. MEASUREMENTS The e.m.f. of the cell : Ag, AgCl/KCl (Ci)/M KC1 (C2)/AgCl, Ag was measured by means of a Leeds and Northrup type K-2 potentiometer and a Pye portable galvanometer of variable sensitivity. The silver chloride electrodes were prepared by the method of Brown.25 The cell consisted of two identical halves between which the membrane was clamped. Each half (fig.3) had a Plexiglas chamber I into which a glass electrode chamber I1 with a narrow orifice A was cemented with black wax. The area of the membrane through which diffusion could take place was found to affect the depen- dence of the e.m.f. on flow-rate markedly. Consequently, the membrane B was pressed against interchangeable disc C with holes exactly opposite each other. All measurements reported here were made with holes 1 mm in diameter with edges tapered to permit free access of flowing solution to the membrane surfaces. Solutions and cell were kept in separate water thermostats at 25.0 f 0.1" C.A Plexi- glas ring D, slightly thinner than the membrane and greased, prevented electrical leakage between cell interior and thermostat. Solution flowed into the cell from Mariotte bottles at E. The flow was regulated by stopcocks connected to outlet F. The cell was assembled, filled with the appropriate solutions and allowed to stand over- night in order to permit establishment of an approximate steady state in the membrane. Measurement of the e.m.f. as a function of flow-rate then gave constant values for rates greater than about 100 cm3 min-1 (fig. 4) after about 10 min. These values for various ratios CI/C2 are given in table 2, along with average deviations from the mean of several measurements. TABLE 2 C1 (equiv./l.) C2 (equiv./l.) 0.1 0.05 0.05 0.02 0.02 0.0 1 0.0 1 0.005 0-005 0.002 0002 0*001 e.m.f.(mV) 17.6 & 0.1 25.8 h 0.1 22.0 * 0-2 23.6 0.2 37.9 i 0.2 29.9 f 0.3J . w. LORIMER, E . I . BOTERENBROOD AND J . J. HERMANS 147 TRANSFERENCE NUMBERS Experiments were carried out in a cell based upon a design of Remy.26 The membrane was clamped between two Plexiglas flanges cemented to calibrated, closed glass chambers of about 50 cm3 capacity. A silver sheet anode 27 and a fused silver chloride cathode 28 served as electrodes. Calibrated capillary tubes projected from each chamber, and terminated in horizontal sections which carried glass scales. The cell was operated in a water thermostat at 25" C. A rubber ring prevented electrical leakage at the membrane.Current was passed through the cell from a 24 V accumulator supply, and measured by noting the potential drop across a stan- dard resistor in series with the cell. Analyses of the solutions in each chamber were made con- ductimetrically before and after electrolysis, sufficient charge being passed to cause a 10 % change in concentration. Measurement of the displacement of the solution menisci in the capillaries permitted :'i E FIG. 3.-E.m.f. cell. calculation of the solveni transport and the change in volume of each compartment. Passage of one faraday through the cell corresponds to the transfer of ti equivalents of potassium ion and to equivalents of water from anode to cathode compartment. Although 30 - 28 v W 26 24 FIG. 4.-Effect of flow- rate on e.m.f. ; 0*002-0.001 KCl : 0 ; 0.05-0.02 KC1 : 0.100 200 300 FLOW RATE (m'/min) the data obtained should be sufficient to calculate t l with a precision of 0.3 %, the re- producibility of the concentration change at the cathode side was only about 8 %. The anode side gave lower and more irregular results. Possible irreversible reactions at the anode are being investigated, and more complete data will be published later. The cathode results and the solvent transport numbers are given in table 3, together with the mean deviations. TABLE 3 C (equiv./l.) I 1 t0 0.01 0.68 f 0.05 130 & 10 0.005 0.70 & 0.05 170 & 30 0.00 1 0.82 & 0.05 300 & 70148 TRANSPORT PROCESSES DISCUSSION The cellulose-polyelectrolyte membranes described here are similar in principle to the collodion-polyelectrolyte preparations of Neihof.29 The excellent re- producibility in thickness and the possibility of continuous variations in fixed charge concentration make them especially useful models for the investigation of general membrane properties.Comparison of the magnitude of the solvent transference numbers in table 3 with those for potassium ion by means of eqn. (16) shows that the contribution of solvent transfer to the e.m.f. can be as high as 4 %. One other evaluation of this effect has been made by Graydon and Stewart,35 who attributed deviations from ideal fixed charge theory to solvent transfer. Some older work exists, but it is concerned either with ill-defined membranes,26 or solely with electro-osmotic pressure (see summary by Schmid).34 150 50 0.5 1.0 1.5 log a lo /ao.ooc FIG.5.4.m.f. as a function of activity of KC1 By suitable addition of the data of table 2, the e.m.f. for any given concentration difference may be obtained. This has been done in table 4, where for all e.m.f.’s, C2 = 0.001 N. The difference in activity between C1 and 0.001 N is also given,33 and the e.m.f. E’is plotted as a function of loglo(a/ao.ool) in fig. 5. The two straight lines in this figure give the e.m.f. for two ideal cases in which the transference numbers are constant and equal to 1 or 3, and solvent transport is negligible. Differentiation of an empirical function fitted to these e.m.f. data gave the quanti- ties ( t l - rnMto/1000) in table 4. Values of tl were then obtained from the solvent data of table 3.These may be compared with the directly-measured values in table 3. At 0.01 the agreement is good, but the direct values appear to be too low at lower concentrations. The general trend of tl as a function of concentra- tion is similar to that found in oxidized Cellophane by direct measurement and TABLE 4 c.l (equiv./l.) 0.1 0.05 0-02 0-0 1 0.005 0.002 0.001 e.m.f. tmV) 156.8 139-2 113.4 91.4 67.8 29.9 0.0 log10 ta/aoood 1 -902 1-625 1.253 0.969 0.680 0.299 o*ooo I1 t l (direct) 0 1 - 0.52 0.55 0.60 0.66 0-77 0.85 0.87 0.018 mto) (e.rn.f.1 0-68 0.78 0.87 0.68 0.70 0.82J . w. LORIMER, E. J. BOTERENBROOD AND J . J . HERMANS 149 by e.in.f.31 In that case, however, comparisons by Wright 34 showed that the e.m. f. transference numbers were lower than the directly measured values. Further investigation of the equivalence of transference numbers derived from these two methods is being carried out.The specific conductivities resemble those obtained for a more highly selective membrane at higher concentrations by Clarke and co-workers,32 who also found an intersection of the specific conductivity against concentration curves for membrane and solution. On the basis of the fixed charge theory, the membrane conductivity should be greater than that of the solution if the mobilities in membrane and solution are the same.24 Although the internal salt concentration should be known in order to obtain mobilities in the membrane,sy 69 7 estimates based on simple Donnan equilibrium and the data of tables 1 and 4 indicate that the potassium ion mobility for the membranes considered here varies from about 37 at 0.1 N to 18 at 0.001 N, compared with about 73 in free solution.Further interpretation of these variations in transport properties will be reserved until more complete knowledge of the thermodynamic phenomenological coefficients is obtained. The authors wish to thank Miss A. Wijnand and Mr. J. T. Semeyns de Vries van Doesburgh for invaluable assistance with the e.m.f. measurements, and Prof. A. M. Liquori (Rome) for helpful preliminary work during his stay at Leiden. 1 Teorell, Proc. SOC, Expt. Biol., 1935, 33, 282. 2 Teorell, Progress in Biophysics, 1953, 3, 305. 3 Meyer and Sievers, Helv. chim. Acta., 1936, 19, 649. 4 Wright, Trans. Faraday SOC., 1953, 49, 95. 5 Wright, Trans.Faraday Soc., 1954, 50, 89. 6 Manecke and Otto-Laupenmuhlen, 2. physik. Chem., 1954, 2, 336. 7 Hills, Kitchener and Ovenden, Trans. Faraday Soc., 1955, 51, 719. 8 DespiC and Hills, Trans. Faraday, SOC., 1955, 51, 1260. 9 Staverman, Chem. Weekblad, 1951, 47, 1. 10 Staverman, Trans. Faraday SOC., 1952, 48, 176. 1 1 Staverman, Acta Physiol. Pharmacol. Neerl., 1954, 3, 522. 12 Kirkwood, in Ion Transport Across Membranes (Academic Press, Inc., New York, 13 de Groot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 14 Onsager, Physic. Rev., 1931, 37, 405. 15 Hermans and Lorimer, in preparation. 16 Scatchard, J. Amer. Chem. SOC., 1953, 75, 2883. 17 Eyler, Klug and Diephuis, Ind. Etrg. Chem. (Anal.), 1947, 19, 24. 18 Hermans, Contribution to the Physics of Cellulose Fibres, Elsevier (Amsterdam, 1946). 19 Ludtke, 2. angew. Chem., 1935, 48, 650. 20 Neale and Stringfellow, Trans. Faraday Soc., 1937, 33, 881. 21 Robinson and Garret, Trans. Faraday SOC., 1939, 35, 771. 22 Manecke and Bonhoeffer, 2. Elektrochem., 195 1, 55,475. 23 Gunning and Gordon, J. Chem. Physics., 1942, 10, 126. 24 Schmid and Schwarz, Z. Elektrochem., 1951, 55, 295. 25 Brown, J. Amer. Chem. SOC., 1934, 56, 646. 26 Remy, 2. physik. Chem., 1925, 118, 161. 27 Jones and Dole, J. Amer. Chem. SOC., 1929, 51, 1073. 28 LeRoy and Gordon, J. Chem. Physics, 1938, 6, 398. 29 Neihof, J. Physic. Chem., 1954, 58, 916. 30 Neale and Standring, Proc. Roy. SOC. A., 1952, 213, 530. 31 Clarke, Marinsky, Juda, Rosenberg and Alexander, J. Physic. Chem., 1952, 56, 100. 32 Harned and Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, 33 Wright, J . Physic. Chem., 1954, 58, 50. 34 Schmid, 2. Elektrochem., 1951, 55, 229. 35 Graydon and Stewart, J . Physic. Chem., 1955, 59, 86. 1954), p. 119. 1952), p. 54. pp. 200ff. New York, 2nd ed., 1950), p. 369.

ISSN:0366-9033    

DOI:10.1039/DF9562100141

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

ELECTRO-OSMOSIS IN CHARGED MEMBRANES THE DETERMINATION OF PRIMARY SOLVATION NUMBERS BY A. DESPI~ * AND G. J. HILLS Dept. of Chemistry, Imperial College, London, S.W.7 Received 1st February, 1956 Electro-osmosis in highly charged membranes is discussed. The two main ways of investigating electro-osmotic flow in membranes are described and the extensiveness of such measurements necessary to examine current theories of the phenomenon is emphasized. The direct and indirect study of electro-osmosis in membranes of cross- linked polymethacrylic acid in the sodium form is described and its explicit dependence . on the swelling of the membrane is deduced. The validity of the Schmid theory of electro- osmosis in membranes was investigated. From the measurement of total volume flow of solution through a membrane under- going electrolysis and a knowledge of the electro-osmotic contribution to this total flow, the difference, representing the volume of the solvated counter-ions is readily obtained.From this, the solvation number of the sodium ion in the membrane phase has been evaluated. Virtually all forms of membranes in contact with ionic solutions and subject to a potential gradient normal to the membrane exhibit electro-osmosis, The phenomenon arises from a non-uniform distribution of ions close to the walls of the capillaries of the membranes which can occur in two ways (i) by preferential adsorption of one type of ion on the walls of an uncharged membrane, or (ii) by the existence of charged groups in the structure of the membrane itself. In the first case, the distribution is that of a normal double-layer.The ions predominating in the inner or outer Helmholtz planes are considered to be relatively immobile and the electrolytic transport of the other species which predominate in the diffuse part of the double layer give rise to a flow of ions mainly in one direction. The exchange of momentum between the moving ions and the solvent then gives rise to unidirectional flow of solvent. The exact location of the slip-plane in the double layer is not known but the electrical potential in this plane is, by definition, the {-potential and it can be shown1 that the electro-osmotic velocity VE of the solution at a large distance from the walls of the capillaries is given by where e and 7, the dielectric constant and viscosity of the solution respectively are assumed to be the macroscopic values of the solvent (cf., however, ref.(2)), and E is the applied potential gradient.The corresponding volume of solution transported per second for a current density of i A cm-2 through a capillary of constant cross-section is where K is the specific conductance of solution. These equations are ideal and only apply to uncharged membranes of relatively large pore-radius in contact with very dilute solutions where a double layer of significant magnitude is obtained. Even in such systems it is necessary to make a correction for " surface conduction ", i.e. migration of ions in the Helmholtz part of the double layer. * present address : Faculty of Technology, Belgrade University, Yugoslavia.150A . D E S P I ~ AND G . J . HILLS 151 The second type of membrane, consisting generally of sheets of homogeneous or heterogeneous natural or synthetic ion-exchange substances, are characterized by a high concentration of fixed charged and a correspondingly high concentration of counter-ions. The pore radii are usually much smaller than in those of the first type, being often of molecular dimensions. All such systems approximate to the perfectly selective membrane in which there are two charged or ionic species, only one of which, the counter-ion, is mobile. In keeping with the high conductivity of these systems it is assumed that a high proportion of the counter-ions, if not all of them, are free to migrate and that the slip-plane occurs at the surface of each fixed ion or, if it is hydrated, at the surface of its primary hydration sheath. The unidirectional flow of ions will again give rise to unidirectional flow of solvent, i.e.electro-osmosis. For any applied voltage, the net current flow i will be greater than that ( i f ) flowing in a hypothetical, identical system in which there was no electro-osmosis, i.e. no net movement of solvent. Schmid 4 has derived a relationship between i and if for point charges flowing through cylindrical capillaries : (3) i - i f F2X2i-2 - - _ - i 8 T K ’ where F is the faraday and r is the radius of the capillaries. From this equation it might appear that (i - i’)/i -+ co as Y -+ GO but this is not so since K also depends on Y, i.e. increasing with an increasing electro-osmotic effect.A more useful form of this equation is (4) 103 F2Fi-2 A = X + 877 ’ where A and A’ are the equivalent conductances of the counter-ions with and without the electro-osmotic contribution. Both equations suffer from the limi- tations that values of Y are not directly obtainable and that in many cases they are of the same order as the-radii of the mobile ions themselves. The fact that A +co as r -tco at constant Xis in agreement with the concept of increased ionic velocity outlined above since the friction of the solvent with the walls, the sole limiting force, would tend to zero. Neither of these equations has hitherto been experimentally investigated. The direct measurement of electro-osmosis in charged membranes is usually not possible.The total volume of solution transported per faraday is readily observable,69 7 but this is only partly electro-osmotically transported solvent, the remainder, of similar magnitude, being the volume of the transported ions together with that of their solvation sheaths. Since no reliable independent values of these latter volumes are available, this method offers no absolute measurement of electro- osmosis. The contribution of electro-osmosis to ionic velocity in the membrane phase is, however, easily evaluated. The equivalent conductance and, hence, the ionic mobility of the counter ions in the membrane phase, can be determined in a number of ways.39 5.8-16 Where a suitable radioactive isotope of the counter-ion is also available its self-diffusion coefficient D can be determined in the absence of an applied potential gradient and, hence, in the absence of electro-osmosis.The corresponding equivalent ionic conductance and ionic mobility can be evaluated from the Nernst-Einstein equation : where z is the valence of the counter-ion and uf and A’ are the ionic mobility and equivalent conductance in absence of electro-osmosis. The differences between A and A’ (A > A’) in two ion-exchange resins have been recorded by Spiegler and Coryell.14/ mine AA over a wide range of X and of swelling and an 5 - / adequate variation of this last 1 - 2 . 0 / A w o - - a / - / E / - / I - 1 I I I 0 . 2 0 . 4 0 . b 0.8 I or r2) it is necessary to deter- parameter can only be obtained by removing the membrane material from contact with the 1.5 solution and partially dehy- drating it.A similar but more limited variation of swelling could be obtained by alteration of the degree of cross-linking in the membrane material but this ~ was considered undesirable in 6 view of its unknown effect on r . 0- The system, solution + JX’ membrane $ solution, was 0 . 5 only used to study the total electrolytic transport of solu- tion through the membrane. Few values of this transport have been reported 6, 7 for charged membranes and no estimate of how much of the : 1 .O I .OA . D E S P I ~ : AND G . J . HILLS 153 EXPERIMENTAL The preparation and co-polymerization of methacrylic acid with ethylene glycol di- methacrylate in the form of membranes and rods has been described elsewhere.17~ 3 Only 10 % cross-linked polymethacrylic acid was used and the neutralization of the rods with NaOH followed the same procedure as that already described.5 Each rod was equilibrated for several weeks with its appropriate dilute NaOH solution to ensure an even distribution of counter-ions.The variation of swelling of the material and of 2 with degree of neutralization is illustrated in fig. 1. The equivalent conductance and self-diffusion coefficient of sodium ions in each fully swollen rod was determined, after which it was progressively dehydrated, X and D being determined at regular intervals during this process. A section of each rod was retained for analysis 5 and from this, the sodium ion content and the water content for each rod during its dehydration was known. 0.74 0.83 0.94 0-29 0.37 0.48 0.63 TABLE 1 K x 103 ohm-1 cm 4.111 4.065 3.485 0.8 18 8-55 8.13 7.67 4.56 13.81 14.16 13-68 2.182 2-17, 3.261 2.257 6.979 7.546 5.432 18.43 18.99 12.55 20.66 21-97 21.69 25-20 26.25 26-01 17.25 27-35 28.74 3.986 29-56 14.42 7.843 29.05 30.00 28.17 11-17 5.46 31.1 23-88 18-54 13.61 31.96 1 ohm-] cm2 g ion-1 10.07 8.885 6.563 3.397 1.081 14.34 11.90 8.921 3.992 1.709 16.64 14.54 12.30 1.550 0.978 3.911 18.85 15.74 3.07,- 1.935 6.195 17.92 16-20 12.8 1 16.93 13.86 12.53 5.79 0.900 16.15 13.53 11.61 3.908 1.784 15.27 13.30 9.885 2.628 1 so89 14-49 11-70 6.7 1 4.521 3.079154 ELECTRO-OSMOSIS CONDUCTANCE MEASUREMENTS.-These were carried out as described elsewhere 5 9 18 and the.results are recorded in table 1 which gives the ionic concentrations c in g ions/l.of resin phase, the volume ratio VR (see below), the interstitial ionic concentration cj in g ions/l. of interstitial solution in the resin phase, the specific conductance K and the equivalent conductance A, for each degree of neutralization and dehydration. SELF-DIFFUSION rmAsuREMENTs.-The ionic mobility and self-diffusion coefficients of sodium ions in the resin phase were determined by the method of Morgan and Kitchener,lg using 22Na. A detailed description of the diffusion experiments is given elsewhere 18 and in table 2 are given the values of c, VR, Ci, D and A' for 5 different degrees of neutralization, each at various degrees of swelling. TABLE 2 degree of neutralization 0.29 0.8049 0.9388 1.839 0-37 0.963 1.833 0.63 1.461 3.733 0.74 1.678 2.523 6.1 19 0.94 2.132 3.529 4.1 12 2.908 2.02~ VR Cf 1.030 1.234 3.480 1.192 2.893 6.944 1.762 2.656 6.628 2.01~ 3.377 2.562 4.887 15.8 6.082 D X 106 cmz sec-1 3.92 3.50 1.069 4.09 1.918 0.525 3.88 2.72 0.605 3.09 2-12 0.049 3-70 1.734 0-946 1' ohm-1 cm2 g ion-1 14-73 13-17 4.02 7.21 1.97 14-59 10.22 2-27 11.63 7.97 0.184 13-91 6-52 3.56 15-36 TOTAL VOLUME TRANSPORT MEASUREMENTS.-MembraneS of 10 % cross-linked POlY- methacrylic acid were thoroughly equilibrated with 0.01 N NaOH solution and then clamped in the silicone-greased rubber gaskets in the apparatus shown in fig.2, the flanges being I Membrane FIG. 2.-The measurement of total volume transport. ground ends of Industrial Glass Piping held together by the usual bakelite connectors. This apparatus was filled on both sides of the membrane with the same 0.01 N NaOH since under these conditions the transport number of the sodium ion in the membrane isA .DESPIC AND G . J . HILLS 155 close to unity. To prevent ordinary osmotic flow of solvent and diffusion of electrolyte across the membrane, no large concentration changes should occur during the electrolysis. Although it has been observed that neither of these processes occur readily in the mem- branes used in this work, it was decided arbitrarily to restrict the concentration changes to 5 %. Moreover, after the initial experiment the current was reversed so that the time- averaged concentration gradient across the membrane during the subsequent experiments was zero. Such a small concentration change amounts to 0.0005 equiv. or - 50 coulombs/l.of solution. Since the total volume transport was - 200 ml per faraday, the volume of each compartment had to be at least 1 litre in order that a reasonable volume change be observed. The volume increase in the cathode compartment and the volume decrease in the anode compartment were measured by observing the corresponding rise and fall of the menisci in the precision-bore capillary tubes. The electrodes were so placed that most of the gas evolved during the electrolysis escaped up the capillary tubing ; any bubbles clinging to the glass surface and to the electrodes were gently dislodged. The whole cell was immersed in a water thermostat maintained at 25 i 0.005" C and connected in series with a silver coulometer. The membranes used were soft and flexible and any difference in the levels of solution in the two tubes was partly compensated by the bulging of the membrane.It was essential therefore that when the levels of solution in the capillary tubes were being measured before and after each experiment that no net difference in hydrostatic pressure existed. The difference in levels was therefore compensated by the addition of petroleum ether to the lowest side. In table 3, are given the observed volume changes d Y in the cathode and anode compartments. TABLE 3 expt. no. no. of coulombs d Y (cathode) d V (anode) passed ml ml 1 72 0- 180 0-184 2 74 0.174 0.182 3 72 0.151 0.156 4 72 0.150 0.157 Conductance and self-diffusion measurements were also carried out on rods equilibrated irz tlze same soZution as used in the transport experiments.The results are listed in table 4. TABLE 4 C K X 103 1 D x 106 A' 2.39 32.1 13-43 2-68 10.09 2.36 31.3 13-26 2.89 10-87 2.39 32.0 13.38 2.74 10.30 2-39 31.8 13.31 2-76 10.37 2.37 31-9 13-43 2-64 9-92 mean 13-36 & 0.46 % mean 10.31 i 2.4 % DISCUSSION EVALUATION OF THE INTRINSIC DEPENDENCE OF CONDUCTANCE ON Ci AND ON SWELLING The decrease of equivalent conductance of the sodium counter-ions with inter- stitial ionic concentration was attributed to an increase in overall viscosity and a structural parameter was sought which would reflect directly the viscous effect of the resin matrix. For this system always having the same distribution of compon- ents, the same degree of tortuosity etc., the viscous effect of the matrix was taken t o be directly proportional to the fractional volume content or relative volume content of organic matter V R .~ VR values for each rod are readily evaluated 5 and are included in tables 1 and 2. Since VR and Ci change simultaneously, the intrinsic dependence of h on VR or on ci can be isolated only if one of the variables is kept constant, e.g. by interpolating from vertical lines drawn on graphs of X against ci and h against VR respectively. Fig. 3 and 4 show the variation of equivalent conductance with Cj at constant VR and the variation of X with VR at constant ci.156 ELECTRO-OSMOSIS The corresponding curves for the equivalent conductance derived from the self- diffusion coefficients are shown in fig. 5 and 6. Finally, in fig.7 and 8 are shown the corresponding relationships for AA, the electro-osmotic contribution to A, obtained by comparison of fig. 3 and 5 with fig. 4 and 6. I 2 3 4 5 c i q-ions titre-’ FIG. 3.-The variation of equivalent conductance with interstitial ionic concentration at various constant VR values. 0-2 0-3 0-4 0.5 V, FIG. 4.-The variation of equivalent conductance with VR at various constant Cj values. DEPENDENCE OF ELECTRO-OSMOSIS ON THE INTERSTITIAL CONCENTRATION The form of Schmid’s equation given by eqn. (4) suggests that the electro- osmotic contribution to h should be a function of two variables, x(= ci) and r2. The interstitial viscosity 7 is assumed to be constant and approximately equal to that of water. Keeping VR constant is equivalent to maintaining constant r values, and therefore from (4), i.e. (AA)VR should be a linear function of ci.A .D E S P I ~ : AND G . J . HILLS 157 It is evident from fig. 7 that this is not so. The inapplicability of the Schmid theory to highly cross-linked and highly charged membrane materials might be expected. If the membrane material consists of a cross-linked linear polymer the pores are probably those through the polymer spirals, the diameters of which are of the same order as that of hydrated sodium ion. The annulus of " free water " c , q-ions litre-' FIG. 5.-The variation of A' with Ci at various constant VR values. 1 I I I I I 0.10 0.20 0.30 040 0.50 vR FIG. 6.-The variation of A' with VR at various constant ci values. surrounding such an ion is therefore only a few molecular diameters in thickness and it is questionable whether the relationship between diffusion coefficient, pore radius and solvent viscosity used in the theory is admissible.For a particular Y value, the retarding influence of the walls increases with the ionic concentration, i.e. as the annulus of " free water " decreases, contrary to eqn. (4). The effect increases with the degree of primary solvation of the counter- ion and it would appear therefore that eqn. (4) and (6) are only applicable to mem- branes of large pore size.158 ELECTRO-OSMOSIS The present system could be modified by using a smaller, less hydrated counter- ion. Although corresponding conductance values are available for the potassium system,s in the absence of a convenient radio-isotope, direct determination of h’ and Ah’ for potassium has not yet been possible.It is, however, possible to deduce A’ for this system,lg and the derived Ah as a function of ci at various VR values is A X ci 9-ions litre-’ FIG. 7.-The variation of AA with ci at various constant VR values. FIG. 8.-The variation of AA with VR at various constant Ci values. shown in fig. 9. The potassium ion is apparently small enough for the wall-effect described above to be insignificant below 3 N and for each VR value a linear section of the (Ah), against ci relation is observed. The slope of the linear section for the smallest VR value, where 7 is approximately equal to that of water, is 7.5 ohm-1 cm2 mole-2 which from eqn. (10) gives a value for Y of 7 A.A . D E S P I ~ AND G .J . HILLS 159 THE DEPENDENCE OF ELECTRO-OSMOSIS ON VR According to eqn. (4), AA is also a linear function of the square of the pore radius. The pore radius as used by Schmid was based on an earlier definition of this quantity by Bjerrum and Manegold,*o i.e. where W is the volume of solution per ml of membrane material and N is the number of pores per cm2. Schmid eliminated N in terms of r2 but, in the present work, it was found more convenient to eliminate r2 in terms of Nand to express N in terms of VR. r2 = W/rN, (7 ) c , q-ions l i t r e - ’ FIG. g.-The variation of AA for potassium counter-ions with ci at various constant VR values. The number of pores NO per cm2 of membrane organic material is a constant determined only by the structure of the matrix, and the number per cm2 of swollen material is thus where AR is the relative area of organic material, i.e.V R ~ . Since W is by definition equal to (1 - VR) N = NoAR, ( 8 ) and, therefore, eqn. (4) becomes In the absence of No values, eqn. (10) does not permit absolute values of the electro- osmotic contribution to be calculated but the dependence of (AA)cj on VR is un- ambiguously expressed. From fig. 10 it can be seen that for the potassium system eqn. (10) is obeyed. ELECTRO-OSMOTIC TRANSPORT AND PRIMARY SOLVATION NUMBERS The observed volume changes during electrolysis AVO,, must be corrected for volume changes at the electrodes. From the corrected volume change per faraday the total transport of solvent (both free and solvating) AV,,~,,,~ is obtained by subtracting from AV:E:hode and adding to AVZZde the partial molar volume of NaOH, nv,,,.160 ELECTRO-OSMOSIS The number of moles of water transported in each case is given by A Vsolvcnt/ is the partial molar volume of H20 in dilute NaOH solution.ATH20, where The mean net values of AVs,,,,,t/fiH,O are shown in table 5. TABLE 5. cathode 21 8 - 6 18 242 13.5 anode - 222 - 6 18 246 13.7 FIG. 10.-The variation of with (=)for the potassium system. VRQ The electro-osmotic contribution to this solvent transport can also be evaluated. If a current i A cm-2 flows through the membrane under a potential gradient E V cm-1, (1 1) UCjEF ciAE 1000 1000 a i - - = - The corresponding current in absence of electro-osmosis is given by ., u'c~EF - CiX'E I = - - - 1000 1000 * Eliminating E, and iji' = ulu' = X/h', Ai = i - i' = AAijA.For any time t the quantity of current passed through the two systems would be Q = it and Q' = i't respectively, where Q - Q' or AQ represents that part of Q which is transported electro-osmotically i.e., Where Q is one faraday, AQ is a number of g equiv. sodium ions transported electro-osmotically per equivalent of total transport, and, assuming all the solution AQ = Q AA/A. (15)A . D E S P I ~ AND G . J . HILLS 161 inside the membrane phase is transported, the volume of solution per faraday transported elec tro-osmo tically is and the number of moles of water transported electro-osmotically is V' = AQ/ci litres, (16) moles, AQ 1000 AA 1000 M E = - -=-- mi 18 h iiii 18 where /?li is the interstitial molality (in these experiments, 2-75).fore given by The primary solvation number of sodium ions in the membrane phase is there- This value is regarded as accurate only to & 1 and more precise work has since been carried out.22 Three criticisms of the method are (1) that possibly only part of the interstitial solvent is transported, (ii) that there may be ion-association in the membrane phase and (iii) that SNa is not a primary solvation number as such but a related parameter appertaining to the membrane phase. With respect to (i), some solvent may be primarily solvated to the fixed charges.21 The evidence for primary solvation of large anions is not convincing although Oda and Yawatawa 7 claim to have observed a degree of " trapped " solvent in their recent studies of solvent transport through cation-selective membranes, because the total concentration of the transported solution, i.e.[total Na+]/[total H20], is greater than the interstitial ionic concentration. This must always be so when the counter-ions move faster than the water but the implication that the instantaneous concentration of moving solution is also greater is fallacious, since the latter remains constant throughout the electrolysis. Although therefore there is no direct experimental evidence for trapped water in cation-selective membranes, it still remains a possibility. It would, however, lead to higher values of ci and mi in eqn. (16) and (17), to lower of VE and ME and hence to higher values for the primary solvation numbers. If ion-pair forma- tion were appreciable in the membrane phase it would increase VE and ME and hence reduce SNa but, contrary to earlier suggestions, there is no evidence of ion association in cross-linked polymethacrylic acid + alkali metal ion systems.' 8 The third criticism has two aspects : (a) the special effects the membrane phase has on solvation number and its determination and (b) the significance of primary solvation numbers.The special effects could involve (i) the high ionic concentration in the membrane phase, (ii) "pumping action" of ions in close fitting pores, or (iii) frictional stripping of part of the solvation sheath. There is no evidence that the degree of primary solvation is concentration dependent ; (ii) and (iii) can be investigated by studying SNa as a function of current density and extrapolating it to zero current density.This has been done22 and a more precise value of SN~(= 8) has been obtained. A discussion of primary solvation numbers is outside the scope of this work. There is no doubt that, in water, small cations at least have associated with them significant number of solvent molecules which move with them whether they migrate in an electric field or simply by diffusion. It is this number which migrates in this sense which has been determined in the present work. It is distinct from the additional solvent transported by an ion in an electric field. The steady migration of an ion, solvated or not, gives rise to movement of the '' free " solvent about it, the magnitude of which will be proportional to the viscosity of the solvent, the radius of the ion and to the velocity of the ion.This movement is not generally observed in solutions because the resultant of the motion in opposite directions of cations and anions is small and would invariably be balanced by an opposing F162 SPECIFIC TRANSPORT ACROSS MEMBRANES hydrostatic pressure. It is observed in any system where one type of ion is im- mobilized and is called electro-osmosis. In any such system therefore the solvent is divided into that moving with the velocity of the ion, i.e. as its solvation sheath, and that moving with a velocity limited by the frictional resistance offered by the membrane structure and considerably smaller than that of the ion. 1 Kruyt, Colloid Science, vol. 1, pp. 198 et seq. (Elsevier, 1951). 2 Elton, Proc. Roy. SOC. A, 1948,194,259,275 ; 1949,197,568. Elton and Hirschler, 3 Hills, Kitchener and Ovenden, Trans. Faraday SOC., 1955, 51, 719. 4 Schmid, 2. Elektrochem., 1950, 54, 424. Schmid and Schwarz, 2. Elektroclzem., 1951,55,245,684. Schmid, Z. Elektrochem., 1952, 56, 181. Schmid and Schwarz, 2. Elektrochem., 1952, 56, 35. 5 Despib and Hills, Trans. Faruday SOC., 1955, 51, 1260. 6 Despik, Thesis (London), 1955. 7 Oda and Yawatawa, Bull. SOC. Chem. Japan. 1955, 28, 263. 8 Manecke and Bonhoeffer, 2. Elektrochem., 1951,55,475. 9 Sober and Gregor, J. Colloid Sci., 1952, 7, 37. 10 Moulton, Diss., Abstr., 1952, 12, 321. 11 Ishibashi, Seyama and Sakai, J , Electrochem. SOC., Japan, 1954,22, 684. 12 Manecke and Otto-Laupenmuhler, 2. physik. Chem., 1954,2, 336. 13 Juda, Rosenberg, Marinsky and Kasper, J. Amer. Chem. SOC., 1952, 74, 3736. Clarke, Marinsky, Juda, Rosenberg and Alexander, J. Physic. Chem., 1952, 56, 100. 14 Speigler and Coryell, J. Physic. Chem., 1953, 57, 687. 15 Wyllie and Kanan, J. Physic. Chem., 1954, 58, 73. 16 Hills, Kitchener and Jakubovic, J. Polymer SOC., 1956, 19, 382. 17 Howe and Kitchener, J. Chem. SOC., 1955, 2143. 18 Despid and Hills, (in preparation). 19 Morgan and Kitchener, Trans. Furaday SOC., 1954, 50, 51. 20 Bjerrum and Manegold, Kolloid-Z., 1927, 43, 5. 21 Glueckauf and Kitt, Proc. Roy. SOC. A , 1955,228,322. 22 Hills, Jacobs and Lakshminaryan (in preparation). Proc. Roy. SOC. A, 1949, 198, 581.

ISSN:0366-9033    

DOI:10.1039/DF9562100150

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

162 SPECIFIC TRANSPORT ACROSS MEMBRANES SPECLFIC TRANSPORT ACROSS SULPHONIC AND SELECTn7E MEMBRANES CARBOXYLIC INTERPOLYMER CATION- BY HARRY P. GREGOR AND DAVID M. WETSTONE Dept. of Chemistry, Polytechnic Institute of Brooklyn, New York Received 23rd May, 1956 The specific uptake of calcium over potassium by new types of sulphonic and car- boxylic cation-selective Interpolymer membranes was measured ; the molal selectivity coefficient was one to two orders of magnitude greater than that found for non-specific divalent-univalent cation systems. The specific conductance of calcium in the membranes was found to be half of that for potassium. Bi-ionic potentials for calcium against potassium indicated a larger membrane transport number for calcium ; rates of stirring up to 400 cm/sec did not produce maximum potentials.Transport determinations carried out with mixed potassium + calcium solutions gave T ~ / T K values of about 3/1 at lower (0-1-1 mAcm-2) current densities, the ratio decreasing to less than unity at high (10-100 mA cm-2) current densities. These results show that specific binding of a cation by a polyelectrolyte does not necessarily preclude its mobility, and is related to the free energy of binding. Copper 11 was found to be bound so firmly that its conductance and transport numbers were extremely low.H . P . GREGOR AND D . M. WETSTONE 163 The general characteristics of ion-selective membranes, i.e. membranes which are seIectively permeable to ions of one sign as opposed to ions of the opposite sign, have been established for a number of different membranes and membrane types by the work of Teorelll and of Sollner,2 and by the work of Marshall,3 Kressman and Kitchener,4 Wyllie,s Juda,6 Manecke,7 Kunin,S Graydon and Stewart9 and others.It has been established that the transport number of the permeable ion species approaches unity at low concentrations, decreasing with increasing concentration, and that the electrical conductivity of permeable ions in the membrane phase is somewhat concentration independent in dilute soh- tions ; for alkali metal cations it is proportional to the ionic conductivity in solu- tion. The significance of solvent transport has been pointed out by Staverman l o and by Scatchard ; 11 solvent transport is appreciable, particularly with resin-type membranes of high specific conductivity.This contribution is particularly concerned with ion-specific phenomena, i s . those in which one ion possesses a significantly higher mobility than other per- meable ion species in the membrane phase. The occurrence of these phenomena in bioIogical systems is well documented; 12 the preparation of synthetic ion- specific systems and the elucidation of their mechanism constitutes a major scientific problem. This contribution presents some preliminary results on the specific transport of calcium over potassium by new types of carboxylic and sulphonic cation- selective membranes. The preparation of the membranes is described and their general characteristics are summarized. These systems were further characterized by selectivity coefficient studies and measurements of electrical conductivity, bi-ionic potentials and transport numbers.EXPERIMENTAL PREPARATION OF MEmRANES.-Detaik of the preparative procedures for the membranes used in this study are given else~here.13~14 The general procedure used for these Inter- polymer membranes involves the dissolution of a polyelectrolyte or an ionogenk polymer and an inert, film-forming polymer in a suitable solvent or mixed solvent system to form a homogeneous solution, the casting of this solution upon a plate or a matrix material, and finally evaporation of the solvent under controlled conditions. For example, the Interpolymer carboxylic acid membranes described herein were prepared from a solution of the ionogenic copolymer polyvinylmethylether + maleic anhydride (PVM/MA, General Aniline and Film Co.) and the film-forming copolymer polyacrylonitrile 4- vinylchloride (Dynel, Carbide and Carbon, Bakelite Division, NYGL) in N, N-dimethyl- formamide (DMF, duPont).The sulphonic Interpolymer membranes were prepared from a solution of linear polystyrenesulphonic acid, Dynel and DMF, and also from solutions in dimethylsulphoxide (DSO, Stepan Chemical Co.). The casting solutions were made up to about 12 % total solids, filtered, and then the films were formed upon glass plates by drawing a “doctor blade” (Boston-Bradley Blade) across the plate. A blade opening of 0.5 mm gave a membrane having a thickness of about 25 p. The solvent was allowed to evaporate in an oven, the film soaked in water and lifted from the plate.These membranes are quite strong, and when properly pre- pared the polyelectrolyte molecules are so intertwined with molecules of the film-forming polymer that they cannot be separated without dissolving the fiIm entirely. GENERAL CHARACTERIZATION PROCEDURES The procedures for obtaining fundamental characterization data on these membranes has been described in detail elsewhere.13 Characterization included measurement of thickness, ohmic resistance, and concentration potential. The average thickness of a membrane in 0.1 M KCl was taken with a micrometer. The electrical resistance was that of the membrane in equilibrium with 0.1 M KCl. It was obtained by clamping the membrane between the chambers of a simple cell which contained fixed platinum elec- trodes, the resistance of the cell with its solution being subtracted from the result obtained when the membrane was interposed. An a.c.bridge at 1000 c/sec was employed.164 SPECIFIC TRANSPORT ACROSS MEMBRANES The characterization concentration potential was that resulting from the chain : SCE I 0.2 M KC1 [ memb. [ 0.1 M KC11 SCE corrected for the asymmetry of the saturated calomel electrodes (SCE) and the salt-bridge liquid junctions, and for the ambient temperature to 25" C. The membrane was clamped in a small plastic cell that provided air-bubbling over the membrane surface to reduce the unstirred film. Potential readings were taken with a Leeds and Northrup type K-2 potentiometer. SELECTIVITY COEFFICIENTS This study reports the results of four experimental procedures : (i) determination of selectivity (distribution) coefficients for calcium and potassium ions ; (ii) measurement of membrane resistance when in the calcium, potassium and various intermediate states ; (iii) measurement of bi-ionic potentials as a function of liquid movement at the membrane surface (i.e.stirring) ; (iv) determination of electrical transport numbers for calcium and potassium. Procedures for the selectivity coefficient determinations followed those of Gregor, Abolafia and Gottlieb 15 with certain modifications. A number of 330 cm2 samples of each of four different membrane types was used, the membranes having been prepared for the selectivity determination by several hours' immersion in distilled water. Each sample was then brought to equilibrium with a solution, of some desired strength, con- taining calcium chloride and potassium chloride in a concentration ratio previously estimated to yield the desired distribution of cations in the membrane phase.A sample of each of the four membranes was subjected to a different solution concentration ratio. The establishment of the above equilibrium was accomplished by subjecting each sample to successive 1-1. portions of its solution or, at least initially, to solutions somewhat richer in calcium. This was necessitated by the fact that, in some cases, the total equivalents of calcium contained in a 1-1. portion was less than the capacity of the membrane. Accordingly, the membrane had to be brought up to approximately its required calcium content before equilibration with the solution at its desired concentration ratio could result.That such was the case was established by employing the proper number of changes of solution, and where the highest capacity membrane was subjected to the lowest calcium concentrations, the composition of the final equilibrating solutions was checked by analysis. After equilibration, all samples were blotted quickly with filter paper to remove surface solution ; this procedure yields accurate and reproducible " wet weights ".I6 Each sample was then treated with 25.0 ml of 1 M HC1 for elution for a period of at least 10 times the equilibration time; the excess of acid over capacity was at least 1000-fold. The analytical procedure for the eluting solutions differed, in part, for the carboxyl and sulphonate membranes.Total capacity was readily determined for the sulphonate membranes by eluting the membrane in the hydrogen state with an excess of potassium chloride and titrating the eluate. For the carboxyl membranes, where the capacity is pH dependent, a portion of the acid eluting solution was analysed for calcium using ethylenediamine tetra-acetate and ammonium purpurate murexide indicator.17 Since the indicator is very sensitive to pH (a somewhat alkaline medium is required) modifications in the procedure were necessitated by the high acid and low calcium contents of the sample. A 5-ml aliquot of the unknown (1 M in HCl) was treated with 0-55 ml 9 N NaOH, followed by ap- proximately 20 mg of indicator powder, then titrated with approximately 0.001 M ethylenediamine tetra-acetate.The colour change from pink to purple at the end- point is subtle at these concentrations and the use of a freshly prepared colour blank was necessary. The eluting solutions were in all cases analysed for potassium by flame photometry employing a Perkin-Elmer model 52A instrument. The direct reading procedure with careful control of gas pressures was employed, using standards containing calcium. However, it was established that at SOOOA calcium emission with a propane flame was negligible. Potassium could be determined to f 1 %; the calcium content of the sulphonate membranes was calculated by difference. CONDUCTIVITY The conductivity of membranes in the combined calcium-potassium state was measured in the resistance cell as previously described ; the selectivity coefficient samples were used here in their respective, final equilibration solutions.H .P. GREGOR AND D . M. WETSTONE 165 BI-IONIC POTENTIALS For the purpose of obtaining bi-ionic potentials at different rates of flow across the membrane face, a new cell was designed as shown schematically in fig. 1. The essential feature of this cell was that it provided for the extremely rapid movement of solution directly across the membrane surface, accomplished by flat paddle stirring at high speed, the paddle closely conforming to the vertical cross-section of the circular membrane chamber. In the cell assembly, the membrane was positioned so as to be part of the periphery of both circular chambers. Constant temperature coils were set in the lower portion of each membrane chamber and maintained the temperature to $.0.1" C even at extreme stirring rates. For example, stirring speeds which produced liquid flows of over 400 cm/sec did not raise the temperature of the solution appreciably. The small salt-bridge chamber (for the calomel electrodes) was connected to the membrane chamber by several small holes drilled near the top, and was stoppered tightly when the salt bridge was employed. This served to minimize hydrodynamic movement which could carry diffusing KCl from the salt bridge to the membrane chamber. As with the character- ization data, these potentials were taken with the K-2 potentiometer and the usual accessories. Each of the cell compartments could be drained individually.FIG. 1 .-Cell for measurement of membrane potentials at variable rates of stirring. The assembly is symmetrical. The speed of liquid movement at the membrane surface was calculated by assuming that the solution within the circular portion of the membrane chamber which contained the paddle stirrer was rotating at the same angular velocity as the stirrer itself. The diameter of the chamber at the membrane was 5.1 cm ; accordingly, the circumference velocity was (in revlmin) and (16/60) in cm/sec. This calculation assumed that there was no angular velocity gradient between the end of the paddle and the membrane face. TRANSPORT Transport data were taken in the conventional fashion. The membrane was clamped between two large (375-ml capacity) plastic chambers, designed for bath immersion. Each face plate was flanged and covered with &-in.gum rubber to seal the system. A 1.2-cm diameter opening and a 3.6-cm opening were used. Each chamber was provided with a stirring propeller (about 1000 rev/min) and a silver/silver chloride electrode. Each electrode consisted of a sheet of perforated h e silver, wound closely around a silver wire, and then electrolyzed in HCl. Current for the transport process at high densities was supplied by a Heath variable voltage-regulated power supply ; at low densities, dry cells and a variable resistor were used. The circuit consisted of the power source, variable resistance and meter, coulo- meter and two transport cells, all in series. With 0.2 N solution in the cells, the resistance of each cell was about 200 ohms ; at 0.02 N the resistance was roughly 1500 ohms.An iodine coulometer was employed, patterned after the technique of Washburn and Bates9 An M-shaped drainable glass assembly was fitted with a 5 by 5-cm cylindrical166 SPECIFIC TRANSPORT ACROSS MEMBRANES platinum electrode at the base of each foot. The assembly was filled with 10 % KI solution, with a 50 % KI solution introduced at the anode foot so that it rose above the electrode. Similarly, a concentrated iodine + potassium iodide solution was introduced at the cathode electrode. Upon the completion of a run, the anode compartment was drained and used to titrate standard arsenious acid.19 Diffusion of iodine up the feet of the M to cross-over at the centre arms (about 23 cm) was found to be insignificant.After 66 h of one run (the longest) the centre arms were drained and the solution treated with starch indicator. The colour developed was less than that taken as endpoint for these titrations. The electrical transport numbers were calculated from the number of equivalents of each cation transported. Initially, both chambers of the cell were filled with equal volumes (375ml) of the same solution of CaC12 and KCI at 05 equivalent fraction of each and at a total concentration of 0.2 or 0.02N. Approximately one-fourth of the number of equivalents of cations in the anode chamber was transported to the cathode. At the conclusion of the run both chambers were drained and analysed for both cations as before. For each cation, half the difference in concentration between anode and cathode com- partments was taken as the equivalents transported.No corrections were applied for water transport which was found to be small across these membranes. Also, water transport would not appreciably affect the relative cation transport numbers reported herein. RESULTS Table 1 summarizes the characterization data for the membranes used in this study. The carboxyl membranes were prepared from a mixture of one part of polyelectrolyte to three parts of Dynel, etc. As prepared, about 50-75 % of the ionic groups present in the membrane were titrable. The maleic anhydride polymer hydrolyzed to the acid when the dry films were wetted. TABLE 1 .-CHARACTERIZATION DATA FOR CARBOXYL AND SULPHONATE INTERPOLYMER MEMBRANES membrane polyelectrolyte polyelectrolyte solvent thickness resistance Co .P * % P ohm cm2 mV c- 1 PVM/MA 25 DMF 60 15 15.1 1 c-2 PVM/MA 25 DMF 18 5 14-53 s-1 PSA (30,000) 33 DMF 11 4 15.53 s-2 PSA (70,000) 25 DSO 12 42 15.55 16.11 ** * chain : 0.2 1 memb. I 0.1 M KCI. ** theoretical maximum. Two carboxyl films of the same composition but different thickness (C-1 and C-2) were used because previous work had shown that the B.1.P.s for the chain 0.0033 M CaC12 I memb. 10.01 M KCl were much larger for thick membranes of this type than for thin films. This effect was not a function of anion “ leak ”, for it was present in membranes which showed nearly ideal concentration potentials at these ionic strengths. With the chain, 0.02 M KCl I memb. I 0.01 M- KC1, membrane C-1 had a potential of 16-70 mV and C-2 a potential of 16.71 mV in the dilute solutions ; the theoretical maximum here is 16.87 mV.Similarly, the sulphonate membranes showed differences when cast from different solvents which apparently gave homogeneous casting solutions. The selective uptake of calcium over potassium by the carboxyl and sulphonic mem- branes is shown in fig. 2, where the equivalent cation fraction (equivalents of one cation species divided by total cation equivalents present in the phase) due to calcium (XFa) in the membrane phase is plotted against the corresponding fraction in the solution phase (Xka). The molal selectivity coefficient for this system is where rn is the molality, n the number of moles. Table 2 gives calculated molal selectivity coefficients.The moles of water (nw)m in the membrane phase was calculated from theH . P . GREGOR AND D. M . WETSTONE 167 difference in weight of the " wet " and dry states of each membrane. It was assumed that the water content was proportional to the equivalent cation fraction for each mem- brane, since determinations were made for only the potassium and calcium states. The molalities in the potassium and calcium states were as follows : C- 1, mz = 1.2, 2mza=2.0; C-2, mE=0-6, 2mEa=2.1; S-1, m2=2.0, 2m,Ta=2*8; S-2, mE = 3.3, 2mEa = 3.3. The cation activities in the solution phase were calculated by utilizing the single-ion activity coefficients calculated by Conway 20 from the Debye-Huckel equation, inter- polating where necessary. 0.00 I 001 I x:.a FIG. 2.-Equivalent fraction of calcium in the Interpolymer membrane phase as a function of the equivalent fraction of calcium in the solution phase for Werent KCI + CaC12 mixtures.Black symbols are for 0*2N (total normality) solutions, open symbols for 0.02 N solutions. Membranes : C-1 (0) ; C-2 (0) ; S-1 (A) ; S-2 (v). On the assumption that Kd = 1, values of Xza could be calculated as a function of the solution phase composition. The total molality of active sites enters into this calculation ; it was assumed to be 2.0. TABLE 2.-sELECTIVITY COEFFICIENTS FOR CALCIUM-POTASSIUM EXCHANGE WITH CARBOXYLIC AND SULPHONTC INTERPOLYMER MEMBRANES membrane C - 1 membrane C - 2 membrane S - 1 membrane S -2 - total ambient 0.2 N 0.25 11.2 0.22 14-1 0.23 2.0 0.58 2-2 0.47 10.0 0.42 16.0 0.46 2.2 0.78 6.7 - 0-94 20.4 0.87 73 0.92 12.8 - 0.02 N 0.41 8.0 0.35 13.0 0.10 2.6 0.24 1.83 0-51 9.6 0.45 16.3 0-24 2-2 0-52 2.6 0.74 13.5 0-68 27 0.74 5.2 0.65 6-2 In table 3 are listed the specific conductivities K of membranes in both the pure potas- sium and pure calcium states for three different solution concentrations.At 0-002N the resistance of the solution contained in the resistance cell was so large in comparison to that of the membrane that the sensitivity of the bridge precluded greater accuracy. The data of 0.2 N and 0.02 N are plotted in fig. 3 , together with results at intermediate168 SPECIFIC TRANSPORT ACROSS MEMBRANES values of XE for each membrane. The specific conductivity of membrane C-1 in equilibrium with a 0.01 M solution of copper11 chloride was found to be 1.14 x 10-6 ohm-1 cm-1.2ol 6 ' 5 - of Interpolymer membranes in 0.2 N (black symbols) and 0.02N (open symbols) solu- potassium and calcium 3 chloride. Data expressed as membrane phase, X z . Membranes : C- 1 (0) ; c - 2 (0); s--1 (A); s--2 (v). 4 - K x 10' /O - I m V E l 01 I I I I I x: 0 - 2 - 4 -6 - 8 1.0 2 0 E 10- 0 Bi-ionic potentials (B.I.P.) are shown in fig. 4 for the membranes in the chain, 0.0033 M CaC12 I memb. I 0-01 M KCI. Here the potential in mV is plotted against liquid flow at the membrane surface, calculated as previously described. In general, - I I I I I I I I I I F l o w r a t e c m / r e c FIG. 4.-Bi-ionic potentials at different flow rates measured across Interpolymer mem- branes for the cell : SCE 1 0.0033 M CaC12 I memb. 1 0.01 M KC1 I SCE ; temperature, 263" C.Membranes: C-1 (0); C-2 (0); S-1 (A); S-2 (V). potentials at lower rates of flow evidenced the greater experimental error, which became quite large at rates approaching zero. One membrane (C-1) was studied in greater detail, exploring the effects of the addition of a small amount of calcium to the potassiumH . P. GREGOR AND D . M . WETSTONE 169 solution, and also determining B.1.P.s for potassium against lithium and copper. These results are listed in table 4. At the bottom of each column is given the potential which would be exhibited by a boundary obeying the Henderson conditions but in which anion movement was barred (i.e. free diffusion with uc1 = 0). TABLE 3.-sPECIFIC CONDUCTIVITIES OF CARBOXYL AND SULPHONIC INTERPOLYMER MEMBRANES IN THE POTASSIUM AND CALCIUM STATES membrane N .;; x 104 Kzfa x 104 c- 1 0.2 2.1 5 0.863 c- 1 0.02 1.715 0.592 c- 1 0.002 2.20 f 0.5 0.55 rfT 0.03 c-2 0.2 6.0 0.812 c-2 0.02 2.17 0-730 c-2 0402 1.13 i 0.4 0-30 5 0.03 s-1 0.2 4.8 1.17 s-1 0.02 2.89 1 *20 s- 1 0.002 1-60 f 1.5 1-20 & 0.6 TABLE 4.-BI-IONIC POTENTIALS WITH CARBOXYLIC INTERPOLYMER MEMBRANE c- 1 FOR POTASSIUM AGAINST LITHIUM, CALCIUM AND COPPERIL Temp.26.2" C 0.0033 M CaClz 0.0033 M CaC12 I memb. I rate of flow I memb. I 0.01 M KC cm/sec 0.01 M KCl +0.001 M 350 290 240 160 80 free diffusion u- = 0 - CaClz mV mV 21.0 4.2 19.3 4.0 16-6 3.7 14.2 3.4 2.9 - 26.2 - 27 0.01 M LiCl I memb. I 0.01 M KCI mV - 37.0 - 36.9 - 37.0 - 37.0 - 36.4 - 19.1 0.0033 M CUCIZ I memb.I 0.01 M KCl mV -13.5 -13.0 - 13.0 - 7.5 - 0.5 - 29 Table 5 lists the results of transport experiments. Runs at 100, 10 and 1 mA cm-2 were made across a membrane area of approximately 1 cm2, while one at 0.1 mA cm-2 employed a membrane area of 10cm2. The quantity 1 - TC, - TK represents the fraction of charge presumed to be carried by the chloride ion or resulting from transport of water. TABLE 5 .-TRANSPORT NUMBERS ACROSS INTERPOLYMER MEMBRANES FOR EQUINORMAL (INITIALLY) SOLUTIONS OF POTASSIUM AND CALCIUM CHLORIDE Temp. 25.0" C membrane 2%;; mA cm-2 c-1 100 10 1 0.1 c-2 loo 10 s-1 100 10 1 0.1 5-2 100 10 total initial concentration N 0.2 0.02 0.02 0.02 0.2 0.02 0.2 0.02 0.02 0.02 0.2 0.02 running time h 6 6 60 60 6 60 6 6 60 60 6 6 T c a TK 0-28 0.36 0.42 0.57 0.61 0.32 0.76 0.19 0.20 0.25 0.40 0.53 0.39 0.53 0.47 0.53 0.72 0.20 0.67 0.22 0-36 0.52 0.43 0.55 1 - TCa - TK 0.36 0.0 1 0.07 0.05 0.55 0.07 0.08 0.00 0.08 0.1 1 TCalTK 0.78 0.74 1.9 4.0 0.79 0-76 0.74 0.89 3-6 3.1 0.12 0.69 0.02 0.78170 SPECIFIC TRANSPORT ACROSS MEMBRANES DISCUSSION Since other papers 139 14 contain a detailed discussion on the general properties of Interpolymer membranes, only those properties which may be related to specific transport require comment here.These membranes may be viewed as a tangled network of coagulated Dynel fibres which serves as the matrix, with the hydro- philic polyelectrolyte gel held (in large part) in the network openings. Part of the polyelectrolyte is so enmeshed by the hydrophobic Dynel fibres that an appreci- able fraction (25-50 %) of the groups is not available for exchange.While it is possible that the polyelectrolyte is not fastened to the matrix directly but is simply contained in its interstices, this does not appear likely because the poly- electrolyte is not diffusible. Further, very thin membranes (1 p) have been pre- pared; here, too, the polyelectrolyte did not diffuse out. Several membranes of these types have been allowed to soak in water for periods in excess of three years without loss in capacity. Some indication of the effective pore sizes in these membranes can be obtained from studies on the rate of diffusion of non-electrolytes of different molecular weights across them.21 The membranes are permeable to urea, not to sucrose. On this basis, one can estimate the effective pore diameter as being about 5A.Since the thickness of a 1 ,U film is about 2000 times the pore size, it is evident that the membrane is homogeneous on a microscopic (but, of course, not on a molecular scale). The percentage of water in the thick carboxyl membrane (C-1) was less than that for the thinner (C-2) carboxyl membrane, particularly in the potassium state; the potassium molality of the thin membrane was 0.6 while that of the thicker membrane was 1 a 2 as described previously. Since both membranes were cast from the same solution, this difference was the result of greater swelling on the part of the thinner membrane, presumably because its matrix was less able to withstand the osmotic swelling pressure of the polyelectrolyte.The resulting larger average distance between fixed exchange groups in the C-2 membrane may be responsible for the lower mobility of divalent calcium across it. The lower water content of the sulphonated polystyrene membranes compared to the carboxyl membranes and the correspondingly higher molality of active groups (2.0 for S-1 and 1.2 for C-1 in the potassium state) probably reflects differences in the equivalent weights of the polyelectrolytes (184 to 80). Further, it is interesting to note that the carboxyl membrane shrinks and loses from one-half to one-third of its water on going from the potassium to the calcium state. The sulphonate membranes are little affected. This may reflect differences in the binding mechanism. The selectivity coefficient data is quite enlightening.Previous work with an 8 % cross-linked polystyrenesulphonic acid resin showed a selectivity coefficient for magnesium over potassium of 0.16. Since for ideal solutions the molal selectivity coefficient would be approximately unity, the lower value is presumably due to a relatively lower activity coefficient for potassium than for magnesium in the resin phase. This effect is probably the result of electrostatic binding, since there is no Q priori reason to expect specific binding in either case. The selectivity coefficient for calcium and magnesium over ammonium (com- parable to potassium) with a phenolsulphonic cation exchange resin was measured by Kressman and Kitchener.22 From their data and water content data for a similar resin,23 it may be shown that their value of K s 4 is comparable to that for the polystyrenesulphonate resin,ls while the value of K;h4 is three times as large.With the membranes, this difference is larger by an order of magnitude, probably because of the greater flexibility of the linear polymer chain. An examination of table 2 and fig. 2 shows that the sulphonate membrane sorbs calcium strongly over potassium, the average selectivity coefficient beingH . P . GREGOR AND D . M. WETSTONE 171 approximately 3 or an order of magnitude greater than for the sulphonate resin and magnesium. This larger (than for magnesium) selectivity coefficient is attri- buted to some form of specific binding between the calcium ion and the fixed sulphonate groups. The selectivity coefficient with the S-1 and S-2 membranes is singularly constant over the concentration range and the wide composition range examined.The sharp increase at very low calcium concentrations in the resin phase is not explained. The selectivity coefficient for calcium over potassium in the carboxyl mem- branes varies, on the average, from about 10 to 50. These values, being an order of magnitude greater than for the sulphonate membranes, reflect complexing with formation of oxalato-type complexes. The binding of metals to polymeric acids has been studied by Gregor,24 who observed formation constants which were several orders of magnitude greater than those found with monomeric acids. These effects appear to be the result of the large chain potential found with polymeric acids and bases. For carboxyl membranes, the selectivity Coefficient was about the same for the relatively dilute C-2 membrane as for the more concentrated C-1 membrane, validating the selectivity coefficient calculation.It is concluded that the sulphonate membranes sorbed calcium specifically, i.e. to a greater extent than that found for doubly charged ions as compared with single charged ions. This is evident from fig. 2, where it is seen that the experi- mental values are considerably above those calculated on the basis of the con- centration effect alone, even assuming that Kd was equal to unity. The poly- carboxyl membranes show considerably enhanced specific sorption. The results of electrical resistance measurements are particularly significant. The conductance values for 0.02N solution are more reliable because the con- tribution of non-exchange or diffusible electrolyte is negligible 23 and the values are more accurate than those in the more dilute solution.The specific con- ductivity of potassium in the carboxyl membranes is 1-72 x 10-4 for the thicker (C-1) membrane compared to 2.17 x 10-4 for the thinner membrane. This difference may readily be a reflection of differences in the degree to which the polymer acid is neutralized, since Donnan effects act to decrease the degree of neutralization of the polymeric acid. The sulphonate membrane S-1 has a significantly higher potassium conduc- tivity than does the C-1 carboxyl membrane, but this is undoubtedly a reflection of its higher fixed ion and diffusible ion concentrations.For example, K;; equals 2.89 x 10-4 for membrane S-1 with a molality of 2.0; for membrane C-1, K;; is 1-72 x 10-4 for a molality of 1-2. Here the conductivities are directly propor- tional to the capacities. The equivalent ionic conductivity of the calcium ion at infinite dilution is approximately 0.8 that of the potassium ion. As an approximation, it can be assumed that the calcium ion has a hydrated volume which is about 25 % greater than that of potassium. In the membrane phase the specific conductivity of calcium varies from 5 to 3 of that for potassium. This effect appears surprising because calcium is bound by the polyelectrolyte of the membrane. For example, a simple calculation 24 would serve to show that about 90 % of the calcium present in membrane C-1 was bound.Nevertheless, the conductivity of the calcium ions in the membrane phase is high. It must therefore be concluded that accumula- tion of an ion by a membrane phase, presumably as the result of binding or complexing, does not preclude a high mobility for that ion. Tt is evident that the calcium ion, whatever the mechanism by which it is ac- cumulated by the membrane phase, is quite mobile in the membrane phase. This leads to the conclusion that the binding is largely electrostatic and that the ions can migrate from one exchange site to the other. These phenomena are clarified further upon consideration of the fact that the conductivity of copperI1 ion in the carboxyl C-1 membrane is only 1/100 that for calcium or potassium. The binding of copper to polycarboxylic acids172 SPECIFIC TRANSPORT ACROSS MEMBRANES is quite strong; Gregor reports24 a formation constant of 106 for copper" and polyacrylic acid compared to a value of 102 for calcium.Both formation con- stants are sufficiently large to result in a marked preference of the membrane for the divalent ion over potassium, but evidently the binding with copper is so strong that the metallic ion is substantially immobilized. These differences may be largely ones of degree rather than kind. It should be noted from fig. 3 that the specific conductivities of carboxyl and sulphonate resins are approximately linear functions of the equivalent cation fraction in the membrane phase. Some of the deviations shown in fig. 3, namely, those cases where there is a maximum in the curve, cannot be explained at this time.They may reflect differences in the concentration of diffusible cations as a function of composition. The bi-ionic potential measurements emphasize the importance of flow rate where abnormal concentration gradients are known to occur in the membrane phase, and, as a result, in the solution phase adjacent to the membrane. Even at flow rates as high as 400 cm sec-1 it was evident that a limiting experimental situation had not been attained. A previous study by Tetenbaum and Gregor 25 with resin particles has shown that at these higher flow rates film thicknesses of 1 p exist. A detailed mathematical analysis of the bi-ionic potential data will be deferred to a later paper. An application of the Henderson equation, which postulates linear gradients such as do not exist in this case, leads to values for bi-ionic potentials as functions of relative mobilities of cations for the following chain: 0.0033 M CaC12 I memb.I 0.01 M KCl, using concentrations rather than activities. Bi-ionic potentials in mV as a function of UC&K are : 0.76 (as in free solution), - 26.5 ; 1, - 20.7 ; 2, 2.4 ; 5, 8.8 ; 7, 14.3 ; 10, 23.4, providing ucl is assumed zero. The bi-ionic potential measurements therefore suggest that the mobility in the membrane of the calcium ion may be as high as 10 times that of potassium ion. When a small amount of calcium is introduced into the potassium chloride solution, the bi-ionic potential is decreased sharply. The calculated free solu- tion value for this chain, again on the basis of the Henderson equation with UCI = 0, is - 27 mV; a result of 3.4mV corresponds to a cation mobility ratio of 7.The bi-ionic potential for lithium against potassium shows that the transport number of potassium is approximately three times that for lithium if t- is assumed zero. This effect is presumably largely a steric effect, reflecting differences in the hydrated sizes of these cations. The bi-ionic potential for the chain 0.0033 M CuC12 I memb. I 0.01 M KCI indicates that the copper ion has approximately the same transport number as the potassium ion. These data are again consistent with the conductivity data, showing that most of the copper present in the membrane phase is immobilized. Results of transport experiments show that at low current densities the transport number of calcium is approximately 3-4 times that of potassium.The sulphonate membrane S-1 reaches this limiting value at current densities as high as 1 mA cm-2; the carboxyl membrane may still show a greater specificity at even lowcr current densities. Since the current density which arises from dissipative processes occurring during the measurement of bi-ionic potentials is very much smaller than 0.1 mA cm-2, measurements shouId be made at lower current densities. At high current densities (10-100 mA cm-2) the membranes are virtually non- specific. This effect is not the result of selective hydrolysis of water and the resulting hydrogen and hydroxide transport, because the pH effects observed were small. They might have resulted from concentration gradients at the membrane interface but a simple calculation shows that this is unlikely.For example, assuming that the unstirred film has a thickness of 10 p as is reasonable inH . P . GREGOR AND D . M . WETSTONE 173 view of the rapid stirring, and that the concentration at the membrane surface is one-half that in the bulk solution, the flux due to diffusion for a 0.01 N solution would be 0.005 - 0.01 1 Q~ = --DJC/JX = - 2 x 10-5 ( 1000 )m = The current flux at 10 mA cm-2 is 0.01 coulombs sec-1, or 10-7 F or equivalents per second. Therefore, diffusion alone would supply the membrane surface with ions. These membranes demonstrated good ion-selective properties (see 1 - Tca - TK values in table 5) at current densities as high as 10 mA cm-2, but their ion-specific properties were demonstrated only at 1 mA cm-2 and below. A plausible ex- planation is that the high field strengths dissociate the calcium complexes and destroy the specificity. Wien effects are particularly strong in polyelectrolyte systems. This study was supported in part by the Office of Saline Water, United States Department of the Interior. 1 Teorell, see, e.g., in Progress in Biophysics, vol. 3, ed. Butler and Randall (Academic 2 Sollner, see, e.g., J. Electrochem. SOC., 1950, 97, 139C. 3 Marshall and Bergman, J. Amer. Chem. Soc., 1941, 63, 191 1. 4 Kressman and Kitchener, J. Chem. SOC., 1949, 1190. 5 Wyllie and Patnode, J . Physic. Chem., 1950, 54, 204. 6 Juda and McRae, J. Amer. Chem. SOC., 1950,72, 1044. 7 Manecke, 2. Elektrochem., 1951, 55, 672. 8 Winger, Bodamer and Kunin, J. Electrochem. Soc., 1953, 100, 178. 9 Graydon and Stewart, J. Physic. Chem., 1955, 59, 86. 10 Staverman, Trans. Faraday SOC., 1952,48, 176. 11 Scatchard, J. Amer. Chem. Soc., 1953, 75, 2883. 12 see, e.g., Zon Transport Across Membranes, ed. Clarke (Academic Press, New York, 13 Gregor, Jacobson, Shair and Wetstone, J. Physic. Chem., in press. 14 Gregor and Wetstone, J. Physic. Chem., in press. 15 Gregor, Abolafia and Gottlieb, J. Physic. Chem., 1954, 58, 984. 16 Gregor and Sollner, J . Physic. Chem., 1946, 50, 53, 17 Betz and Noll, J . Amer. Water Works Assn., 1950, 42, 49. 18 Washburn and Bates, J. Amer. Chem. Soc., 1912, 34, 1341. 19 Pierce and Haenish, Quantitative Analysis (John Wiley and Sons, New York, 1948). 20 Conway, ElectrochemicaZ Data (Elsevier Publishing Co., New York, 1952), p. 102. 21 Gregor and Jacobson, to be published. 22 Kressman and Kitchener, J. Chem. Soc., 1949, 1190. 23 Gregor, Gutoff and Bregman, J . Colloid Sci., 1951, 6, 245. 24 Gregor, et al., J. Physic. Chem., 1955, 59, 34, 366, 559, 990. 25 Tetenbaum and Gregor, J. Physic. Chem., 1954, 58, 1156. Press, New York, 1953). 1954).

ISSN:0366-9033    

DOI:10.1039/DF9562100162

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

ELECTRICAL POTENTIALS ACROSS POROUS PLUGS AND MEMBRANES ION-EXCHANGE RESIN-SOLUTION SYSTEMS BY K. S. SPIEGLER, R. L. YOEST AND M. R. J. WYLLIE Gulf Research and Development Co., Pittsburgh, Pennsylvania Received 1st February, 1956 An electrical potential difference arises in a manner analogous to that for a glass elec- trode when a solid membrane made from an ion-exchange resin or a plug composed of ion-exchange resin particles separates two solutions of the same electrolyte. The potential difference depends on the activities of those ions in the two solutions which can exchange with the resin. While ion-exchange membrane potentials can be used to determine ionic activities in many solutions, the simple relationship between membrane potentials and ionic activity is limited to a definite concentration range.Porous plugs made from particles of ion-exchange resin act as “ leaky ” membranes. Both the electrical potentials across ion-exchanging plugs and the electrical conductance of the latter can be quantitatively interpreted if the plug is represented by a simple resistor model. This model consists of three elements in parallel, namely, (i) alternating layers of solution and conductive solid, (ii) ion-conductive solid and (iii) solution. Thus plug potentials can be estimated from conductance data. The implications of this work for the interpretation of pH measurements in ionic suspensions are discussed. When a calomel and a glass electrode are inserted into an ionic suspension or gel, the potential difference between them may be interpreted as the algebraic sum of (i) the potential of the glass electrode in the equilibrium solution of the suspension, (ii) the potential of the calomel electrode, and (iii) the plug potential between equilibrium solution and potassium chloride solution in the calomel electrode.The latter is a plug potential like those studied in this investigation and explains the “ suspension effect ”. SYMBOLS a&, al, a2 mean activity of NaCl in general and in soln. 1 and 2 respectively, UNaCl a, b, c, 4 E E’ EJ E M f l , f 2 , f3, F K KO KR K W N Q R T t+, t- X , Y cc PO, P activity of NaCl = a:, geometrical factors as shown in fig. 2, plug potential (V), potential measured between two solutions separated by a porous plug with a pair of Ag/AgCl eIectrodes (V), junction potential between two sodium chloride solutions of different con- centration, potential of an ideally cation-selective electrode (V), Faraday ’s constant (coulomb equiv.-I), fraction of current carried by resistor elements 1, 2 and 3 respectively (fig.2), specific conductance (mho cm-I), specific conductance of resistor model, specific conductance of solid, specific conductance of solution, expression defined in eqn. (17), expression defined in eqn. (19), gas constant (watt sec deg.-1 mole-I), absolute temperature (“K), transport numbers of cation and anion respectively, geometrical factors equal to (1 - d)/a and d/a respectively, proportionality factor relating the specific conductance of a NaCl solution to the mean activity of NaCl (eqn. (lo)), standard chemical potential and chemical potential respectively (watt sec mole-1).174K . S. SPIEGLER, R . L. YOEST AND M. R. J. WYLLIE 175 It is well-known that electrical potential differences arise when two different solutions are separated by a permselective membrane or plug. These potential differences are termed membrane potential or plug potential respectively. They are different from the potential differences between the two solutions in the absence of the permselective membrane or plug. They depend on the nature of the solutions as well as the material separating them. Permselective materials are defined as media which transfer certain types of ions in preference to others. Cation and anion-exchange resins transfer preferentially cations or anions respectively.This property can be used in industrial electrodialysis.1 Membrane potentials across natural shale bodies containing cation -exchanging clays are very important in the electrical logging of oil wells.2 Membrane potentials across synthetic resinous ion-exchange membranes have been studied extensively in the recent past.3-9 For solutions of the same salt, it was found that the membrane potential EM is roughly proportional to the logarithm of the ratio of the mean activities q of the electrolyte in the solutions separated by the membrane : EM = 0.0592 loglo (u2/al) (at 25" C)* This relationship can be predicted by quasi-thermodynamic reasoning 10 for ideally permselective membranes. It holds over a limited concentration range, depending on the nature of the membrane and the solutions.Examples of such plots for mem- branes made from synthetic ion-exchange resins are shown in fig. 1. Our measure- ments with dilute NaCl solutions are compared to those of Kressman7 with KCl solutions over a wider concentration range. The membranes used were different. The points fall roughly on the line predicted for ideally cation-selective membranes. Similar potentials have been observed previously with certain thin clay films 11 and collodion membranes.12 The relationship shown in fig. 1 between the electrical potential and the ratio of the activities of the solutions is entirely analogous to that between the potential of a glass membrane and the difference of the pH of the solutions separated by it. Glass electrodes act as if they were permeable only to hydrogen ions.Ion exchange membranes are usually permeable to all cations or all anions. Therein lies an ad- vantage and a disadvantage. The resin electrodes are versatile because they do not only measure pH, but also pNa, pCNS and the like. But reliable measurements of the activities of electrolytes can only be made in solutions containing one single electrolyte. The glass electrode measures acidity irrespective of the presence of other electrolytes (unless these are present in abnormally high concentrations when the salt-error is observed), whereas ion-exchange resin membranes develop potentials dependent on all the electrolytes present in the solutions. The interpretation of potentials across membranes separating solutions of different electrolytes is com- plex.13~ 14 No resinous membranes have been described which are specifically permeable only to one particular kind of cation or anion.A further complication results from diffusion processes across the membrane which may cause complex distribution patterns of ions in the membrane and in the adjacent solution layers. This is usually indicated by a variation of the measured potential difference with the rate of stirring of the solutions.9 All ion-exchange membranes lose permselectivity with increasing concentration of the solutions which they separate. This loss is due to the increasing penetration of anions and cations into cation- and anion-exchange resins respectively, and also to water transport.s. 8.13 The loss of permselectivity is often termed ion leakage.Membranes or plugs containing ion-exchange resins are permselective. * This relationship holds for 1 : 1-electrolytes and if the activities of the cation and anion are equal. When reversible electrodes are used, as in almost all experiments reported here, no assumptions about the relationship of the ion activities are necessary. When calomel electrodes are used, the " single " cation or anion activities are conventionally substituted for cation and anion exchange membranes respectively.176 ELECTRICAL POTENTIALS Its source may be two-fold. One is the fact that even mechanically perfect, homo- geneous solid membranes take up electrolytes from solutions in contact with them. The amount of electrolyte taken up increases rapidly with increasing solution con- centration.This phenomenon may be considered as a " Donnan " effect. Theories of the change of membrane potential with solution concentration based on the Donnan effect have been worked out independently by Teorell15 and by Meyer and Sievers.16 These theories apply only for membrane materials which may be con- sidered as single phases. 0 I 2 3 4 loqio ( a ' / a l ) FIG. 1 .-Membrane potential EM against logarithm of activity ratio. Circles represent measurements of Kressman 7 with KCI solutions at 19-20" C. Homogeneous synthetic cation-exchange membrane ; solution concentration on one side of the membrane electrode was kept constant at 0.002 M and varied on other side. Squares represent our measurements with NaCl solutions at 25" C. Hetero- geneous synthetic cation-exchange membrane containing 64 % weight finely powdered Amberlite IR-100 ( R o b and Haas Co., Philadelphia, Pennsylvania) and 36 % polystyrene powder.Solution concentration on one side constant at 0401 M and varied on other side. Electrodes : saturated calomel. In porous plugs of ion-exchange material or in defective membranes, a different type of leak exists in addition to the leak caused by Donnan ions. This additional leak is due to a continuous connection between the two solutions through the liquid phase in the pores. If the specific conductance of the ion-exchanger is high and the solutions are very dilute, this leak does not affect the membrane potential appreciably. But in the reverse situation, the larger proportion of the ion transport phenomena takes place in the conductive liquid phase and the effect of the leak overshadows the effect of the ion-exchange material.Thus porous plugs of many ion-exchange materials give rise to membrane potentials which are almost perfect when the plugs separate very dilute solutions. On the contrary, if the solutions are con- centrated, the solid acts as if it were an inert material and the potential difference between the two solutions approaches the liquid junction potential.K . S . SPIEGLER, R . L . YOEST AND M. R. J . WYLLIE 177 Plug potentials have been studied by a number of investigators in the recent past.17 Their interpretation concerns the soil scientist and petroleum technologist. It is believed that they are of general importance in membrane theory, for there exists hardly a membrane that is mechanically perfect and acts strictly as a single phase.Most membranes show to some extent the characteristics of a porous plug. For an understanding of plug potentials, it is useful to have an electrochemical model for an ion-conducting plug. We have recently postulated such a model l8$ and found that it explains quantitatively the change of the specific conductance of the plug with the specific conductance of the saturating solution. The model is shown in fig. 2. It consists of three conductance elements in parallel represent- ing (1) conduction through alternating layers of resin and solution, (2) conduction A FIG. 2.--Electrochemical model of porous plug composed solution Solution Solid of conducting spheres and A.Schematic representation of current path through plug. (1) represents current through solution and spheres in series, (2) through spheres in contact with each other, (3) current through solution. B. Simplified model representing situation shown in A. a + b + c = 1 cm. through the resin and (3) conduction through the solution. A first attempt has been made to apply this model to plug potentials across a column flushed with solutions, and in some cases containing oil, with a view to interpreting electric logs in shaly sands.20 It was the purpose of the present investigation (i) to measure the potential differences between stationary sodium chloride solutions separated by a plug of cation-exchange resin, (ii) to relate these measurements to the plug conductance, (iii) to develop further the theory of plug potentials based on the proposed model and (iv) to compare the measured potential differences to those predicted from the theory. EXPERIMENTAL AND RESULTS PREPARATION OF msIN.-l000 g Dowex-50 (cross-linked by 8 % divinyl benzene), a cation-exchange resin made by the Dow Chemical Company of Midland, Michigan were used.The resin particles were spherical and represented the size fraction between 100 and 200 mesh (U.S. Standard Screen). The resin was placed in a column, backwashed and " conditioned " by a number of alternating regeneration cycles with 6 % HC1 and 4 % NaOH solutions respectively. The resin was finally treated with 8 % NaCl solution and leached. DETERMINATION OF PLUG CONDUCTANCE A Plexiglas cell was used for the measurement of the conductance of the resin plug, saturated with solutions of sodium chloride of different concentrations.The resins were178 ELECTRICAL POTENTIALS placed between a pair of perforated platinum electrodes, flushed with the solution of the desired concentration until equilibrium was reached and the a.c. conductance of the plug determined at 60 c/s. Then a solution of different concentration was introduced into the column and the procedure repeated. A detailed description of the apparatus and experi- mental procedure for plug conductance measurements has been presented elsewhere.19 The results are plotted as specific conductance of the saturated plug against the specific conductance of the saturating solution (fig. 3). Comparing the results to those of previous experiments 19 with the cation-exchange resin Amberlite IR-120 (a product of the Rohm and Haas Company, Philadelphia, Penna.), it is seen that the points fall approximately Q v) Specific conductance of the interstitial solution (mho c 5 ' ) FIG.3.-Specific conductance of resin] plug saturated with solution against specific conductance of solution Circles represent experimental data with small-size Dowex-50 cation- exchange resin (100-200 mesh, U.S. Standard Screen). Squares represent data from a previous investigation 19 for coarse Amberlite IR-120 (32-35 mesh). Solid line is calculated from theory based on 3-component model (fig. 2) ; cross mark shows isoconductance point ; temp. 25-28" C. on the same line, although the particle size of the latter resin was much larger (32-35 US.Standard Screen). This shows that the amount of current carried by the solid and inter- stitial liquid in a bed of spherical particles is a geometrical effect independent of the particle size ; it is worth remembering that the porosity of a bed of particles of uniform size is also independent of the particle size provided the geometry is the same. From the con- ductance data, the following geometrical parameters for the plug model (fig. 2) were calculated : The specific conductance KR of the resin was found from the isoconductance point, viz. the point where the specific conductance of plug and the solution are equal. KR = 0.030 mho cm-1. LI = 0 6 3 , b = 0.01, c = 0.34, d = 0.95. These parameters are identical with those found for the larger particles,l9 except for KR which was 0.029 mho cm-1.The present value seems to fit the results somewhat better. This slight difference is probably due to the fact that the resins came from different batches and manufacturers. In previous experiments,ls a different batch of resin was used and KR was 0.019 mho cm-1. DETERMINATION OF PLUG POTENTIALS A junction between two resin plugs saturated with NaCl solutions of different concentra- tion was produced in a Tiselius cell (American Instrument Company, Silver Springs, Maryland) and the potential difference was measured between two silver/silver chloride electrodes dipping into the supernatant solutions. The Tiselius cell was selected because the boundary is highly reproducible. It was found that after an initial period of slight change of the order of minutes, the potential differences remained constant for many hours.K .S . SPIEGLER, R . L. YOEST AND M . R . J . WYLLIE 179 The Tiselius cell consists simply of a glass U-tube divided into three sections, of which the top two are held stationary. The bottom section rests on a sliding platform and when the bottom section is slid to one side, the continuity of the U-tube is broken (fig. 4). E : 5 0 4 0 3 0 v W 20 10- 0 Resin t Solutron I Resin t Solution 2 - 1 _-____------ ------- ---- -------- -- - - _ _ _ _ _ _ _ _ _ _ -r - - Inert membrane - I I 1 1 I I l l 1 1 I I I I I I I I I I I I l l ( - 0 0 3 .O I .03 - 1 . 3 FIG. 4.-Schematic representation of the formation of a plug boundary in the Tiselius cell.The solutions used in these experiments were 2-02, 0.673, 0.205, 0.062, 0.0192, 0.00605, and 0.00195 molal NaCl. This corresponds to 1-35, 0.45, 0.15, 0.05, 0.0167, 0.00557, and 0.00186 mean activity. In each experiment, two consecutive solutions were used so that I d e a l membrane a FIG. 5.-Potential difference E' against average activity Z of sodium chloride in solutions separated by ion-exchange resin plug Solution activity ratio 1 : 3. Vertical lines represent potential difference measured between Ag/AgCl electrodes at 25" C ; solid line calculated from theory. the activity ratio between the two solutions was always 3 : 1. The solutions were titrated with silver nitrate after their preparation and corrections made for minor deviations of the activity ratio from the value of 3.Silver/siIver chloride electrodes made by Beckman Instruments, Inc., Pasadena, Cali- fornia, were used. In a number of preliminary experiments, calomel electrodes made by180 ELECTRICAL POTENTIALS the same manufacturer were tried, but it was found that the leakage of saturated potassium chloride solution caused appreciable concentration changes in the dilute solution systems, whereas in concentrated solutions the uncertainty of the junction-potential difference hampers the evaluation of the results. It was verified that the potential difference was less than 0.2 mV when the electrodes were immersed in the same solution. To obtain a continuous record of the potential difference against time, the electrodes were connected to a Leeds and Northrup no.7664 pH Indicator whose output was fed into a Brown Electronik recorder. The accuracy of these measurements is estimated to be 0.5 mV. The recorder trace showed that a few minutes after the formation of the boundary, the potential difference remained constant. The electrodes were then dis- connected and a more accurate reading carried out by means of a Leeds and Northrup manual potentiometer (accuracy 0.2 mV). The potential differences remained almost constant for many hours. Comparing the measured potential differences to those predicted by the theory, a number of additional possible sources of error have to be noted. The ratio of the mean activities of the solutions was 3 f 0.02 corresponding to an error limit of about 0.3 mV. The response of the silver/silver chloride electrodes to the chloride activity may not be ideal over the whole concentration range investigated here.Considering all these possible sources of error, we estimate a limit of error of rt 0.8 mV for the potentials. Each experi- ment was carried out several times and corrections were made for the small fluctuations of the prevailing temperature. At first the junction potential (also called diffusion potential) between pairs of solutions of activity ratio 1 : 3 was determined. The transport number t- can be determined from these measurements (eqn. 20). The resins were equilibrated with the solutions by stirring for at least 30min prior to introduction into the Tiselius cell. The results of the total potential measurements are shown in fig. 5 which also shows the potentials expected from a theory based on the model shown in fig.2. DISCUSSlON DERIVATION OF EQUATION FOR THE PLUG POTENTIAL Consider an equivalent resistor system as shown in fig. 2. This system is defined by three parameters; namely, by either two of the group a, b, c and by d. (The sum a + b + c is theoretically unity.) It is often convenient to use also the parameters x and y derived from a and d : x = (1 - d)/a, y = d/a. This model provides a good explanation for the conductance data obtained in the past 18-19 and in the present investigation (fig. 3). It is now applied to the calcula- tion of the plug potential. The plug is supposed to separate two solutions of activities al, a2 and specific conductances K1 , K2, respectively.It is assumed that the concentration difference between the two solutions is infinitesimal and a2 > al, and also that the boundary layer is large compared to the size of the solid particles. In general, there exists a potential difference between the two solutions. Suppose that we insert silver/ silver chloride electrodes and allow 1 P to pass from solution 2 to solution 1 under reversible conditions. (It is assumed that the plug and the solution volumes are so large that no appreciable concentration change occurs as a result of this current transfer.) We determine the fraction of the current passing and the results produced by the passage of the current through each of these elements. In general, the fractionfof the current passing through an element is equal to f = K/KO, where K and KO are the specific conductances of the element and the total plug respectively.KO is given byK . S . SPIEGLER, R . L . YOEST A N D M . R. J . WYLLIE 181 ELEMENT I.-KI is given by (3) where a, d, x and y are geometrical parameters (fig. 2). KR is the specific resin conductance and KW the average specific conductance of the solution. KRKW - aKRK W K1 = - XKR + p w d K w + (1 - ~ K R ' Hence, the fraction of current carried by element 1 equals When 1 F passes through the whole plug, only f l F coulomb passes through element 1. This element consists of a succession of components alternately of true resin micromembranes and solutions. If the micromembranes are ideally cation-selective, and the dimensions of the plug sufficiently large, then no concentra- tion changes occur in the intermediate solution compartments and the results of the passage of f1F coulombs is the transfer of fi moles NaCl from solution 2 to 1.ELEMENT 2 also acts as an ideal membrane. f2 is the proportion of current carried by element 2 : The fraction of current carried by ELEMENT 3 is f 2 = bKR/KO. ( 5 ) - f 3 = CKWIKO. (6) The sodium chloride transfer through this element is t+ moles per faraday passing through it 10 or f3t+ moles NaCl per faraday passing through the plug. The transfer is from solution 2 to 1. The total amount of sodium chloride transferred is, therefore, f 1 + f2 -I- f 3 t + moles and since the free energy p of sodium chloride is given by (7) it follows that the total free energy change equals (8) dp has been set equal to the reversible electrical work obtainable from this process.If the difference of the activities of the solutions separated by the plug is finite, the plug may be considered as an assembly of infinitesimal elements in series. The activity difference across each of these elements is infinitesimal and so is the potential difference. This reasoning is strictly applicable only if the particle size of the resin is itself infinitesimal. However, the results are reasonably accurate for particles of finite size provided the boundary zone is large by comparison with the size of a resin particle. In the following it will be assumed that this condition is satisfied. To obtain the total potential difference between the electrodes, eqn. (8) is in- tegrated over the whole length of the plug : p = Po + R T h aNaC1, dp = (fi + f 2 + f3t+) RTd In a N a c i = Fa'.This is the complete equation for the potential between two silver/silver chloride electrodes in solutions of activities a1 and a 2 , respectively, separated by the conducting plug. As shown previouslyf1,f;! and f 3 are given in terms of geometrical parameters determined from conductance measurements of the same plug and are functions of the specific conductance. To integrate eqn. (9), a functional relationship between the specific conductance KW and the activity aNaC1 must be found. A plot of KW against the mean activity, ah = (aNaCI)*, shows that KW is roughly proportional to (fig. 6) : KW = aaf, (10) where 0: = 0.126 mho cm-* at 25" C.182 ELECTRICAL POTENTIALS Thus eqn.(9) may be integrated without any assumptions about the magnitude of single ion activity coefficients. However, for the sake of convenience and convention, we shall now split the activity aNaCl into two ion activities aNa+ and aci-. The final result, in terms of E', is independent of the manner in which this separation h - I 5 .-4 I s 0 E z Y v a* FIG. 6.-Spec%c conductance KW against mean activity a& of NaCl solutions, temp. 25" C. The mean activity a& is defined by aNaCl (aNa+>(aCl-) = 6 (1 1) The ionic activities are arbitrarily defined equal to the mean activity : d In aNa+ = d In acl- = d In a&. Hence It is customary to ascribe the first term of this potential difference to the silver/ silver chloride electrodes. The remainder is the plug potential, E : Substituting forfl,.f2 andf3 in eqn.(14) from eqn. (4) to (6) and replacing K W by a a&, we obtain KRCC[I f by f (t- - t + ) C X ] ( l / N ) da* + b X K R 2 - c p 2 (t- - t+) (a*/N) dq}, (16) 0 1 where = cyx2a$ + KRCC (1 + by + cx) a& + bxKR2. (17)K. S. SPIEGLER, R . L. YOEST AND M. R. J . WYLLIE 183 The integrals in eqn. (16) may be found in standard tables.21 The integration yields the following result : E = (RT/F) In (az/al) RT cya2az2 4- KRU(~ + by + cx)a:! 3- bXKR2 - - '- In Cya2a12 $- KRCC(~ + by C X ) q + bXKR2 where Q [(l + by + C X ) ~ - 4 b ~ ~ y ] * . (19) The first term of eqn. (18) represents the potential of an ideally cation-permeable membrane (on the assumption of equal ion activities, aNa+ and acl-).When the plug is in equilibrium with extremely dilute solutions (KW= aka < KR), the algebraic sum of the second and third terms vanishes and the first term alone represents the plug potential. As the concentration of the solution increases, the plug potential drops and the second term approaches -2(RT/F) t- In (a2/al), while the third term vanishes. Thus the plug potential approaches (20) This is the junction potential of the two solutions in the absence of a permselective plug. This value was not reached in our experiments. If we use the numerical values of the geometrical parameters and of KR listed in the previous section, the total potential difference of the cell when using silver/ silver chloride electrodes is obtained from eqn. (14) and (18). For (a2/a1) = 3 at 25" C, E = (1 - 2t-) (RT'F) In (a2/a1).040814 a22 + 0-00395 a2 + 7-65 (10-7) 0.00814 a12 + 0.00395 a1 + 7.65 (10-7) E' = 118.4 log10 3 - 59.2 (t-) log10 ] (21) a2 + 6.18 (10-0 0.129 a1 + 0.0626 0.129 a1 + 6.18 (10-6) I[ 0.129 a2 + 0.0626 + 55.9 (t-) log10 The numerical values in eqn. (21) hold only for the particular materials and con- ditions chosen in our experiments. The computation of the potential differences E' from eqn. (21) is illustrated in table 1 where the values thus calculated are compared with the measured ones. The results are also plotted in fig. 5, using a logarithmic activity scale. TABLE COMPARISON OF OBSERVED AND COMPUTED POTENTIAL DIFFERENCES, E' Solutions of sodium chloride, activity ratio 3 : 1 ; electrodes, Ag/AgCl ; plug, " Dowex-50 " ; temp., 25" C ; t- computed from junction potential mean activity ~~ a2 a1 1.35 0.45 0.45 0.15 0.1 5 0.05 0.05 0.01 67 0.0167 0.00557 0.00557 0.00186 potential computed from eqn.(21), mV I- 1st term 2nd term 3rd term total 0.63 56.5 - 28.7 6.5 34.3 (0.63)* 56.5 - 24.0 10.9 43.4 0.63 56.5 - 20.5 14.2 50.2 0.62 56.5 - 18.3 15.5 53.7 0.61 56.5 - 17.2 15.8 55.1 0.61 56.5 - 16.2 15.9 56.2 * estimated potential obs., mV 34.0 42.9 48.5 51.4 52.9 55.5 It is seen that the agreement between the observed and computed values is within 2.3 mV. In the concentrated solutions the observed potential differences agree well with the theory, whereas in the dilute ones, the observed values are lower.electrode X The potential difference across Xis a plug potential like the potentials described in the present investigation and is the cause of the suspension effect.Jenny et al.22 measured similar potentials before we did and related them to transport numbers across the resin plug. Their investigation gave rise to discussions and other investigations ; these have recently been summarized by Overbeek.17 The potential across X has often been considered as a liquid-junction potential. Since the resin or gel are solids, we prefer to call it a plug potential and have treated it above as the potential of a leaky membrane. Our application of the resistor model (fig. 2) to this problem may perhaps shed some additional light on these earlier investigations. * In a previous publication 20 experiments were reported on plug potentials measured with calomel electrodes in a resin column in which an interstitial solution of sodium chloride was flushed out by another solution of higher activity.The observed potential differences were compared with values computed from a simplified theory, based on average solution conductance values rather than the completely integrated equation presented here. In the equations based on average conductance it is relatively simple to alIow for the non- ideal permselectivity of the resin proper. It was found that the observed potentials agreed fairly well with the measured ones, when such allowance was made. + solution c1 i + saturated KCl KClsolution electrode.K. S. SPIEGLER, R. L . YOEST AND M. R. J . WYLLIE 185 1 Kressman, Ind. Chem., 1954,30, 99. 2 Wyllie, The Fundamentals of Electric Log Interpretation (Academic Press, New York, 3 Juda, Marinsky and Rosenberg, Ann. Rev. Physic. Chem., 1953, 4, 373. 4 Winger, Bodamer and Kunin, J. Electrochem. SOC., 1953, 100, 178. 5 Spiegler, J. Electrochem. SOC., 1953, 100, 303C. 6 Wyllie and Kanaan, J. Physic. Chem., 1954, 58, 73. 7 Kressman, J. Appl. Chem., 1954, 4, 123. 8 Scatchard, in Ion Transport Across Membranes, ed. Clarke (Academic Press, New 9 Helfferich, Thesis (Gottingen, 1955). 10 Spiegler and Wyllie in Physical Techniques in Biological Research, ed. Oster and 11 Marshall, The Colloid Chemistry of the Silicate Minerals, 1st ed. (Academic Press, 12 Sollner, J. Electrochem. SOC., 1950, 97, 139C. 13 Scatchard, J. Amer. Chem. SOC., 1953, 75, 2883. 14 Wyllie, J. Physic. Chem., 1954, 58, 67. 15 Teorell, Proc. SOC. Expt. Biol. Med., 1935, 33, 282. 16 Meyer and Sievers, Helv. chim. Acta, 1936, 19, 649. 17 Overbeek, J. Colloid. Sci., 1953, 8, 593. 18 Wyllie and Southwick, J. Pet. Tech., 1954, 6, 44. 19 Sauer, Southwick, Spiegler and Wyllie, Ind. Eng. Chem., 1955,47, 2187. 20 McKelvey, Southwick, Spiegler and Wyllie, Geophysics, 1955,20, 913. 21 Hodgman (editor), Handbook of Chemistry and Physics (Chemical Rubber Publishing 22 Jenny, Nielsen, Coleman and Williams, Science, 1950, 112, 164. 1st ed., 1954), chap. 2. York, 1st ed. 1954), p. 128. Pollister (Academic Press, New York, 1st ed., 1956). New York, 1949), p. 172. Co., Cleveland, 35th ed., 1953).

ISSN:0366-9033    

DOI:10.1039/DF9562100174

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

K . S. SPIEGLER, R . L . YOEST A N D M . R . J . WYLLIE 185 THE EFFECT OF CURRENT DENSITY ON THE TRANSPORT OF IONS THROUGH ION-SELECTIW MEMBRANES BY T. R. E. KRESSMAN AND F. L. TYE The Permutit Co. Ltd., Gunnersbury Avenue, London, W.4 Received 6th February, 1956 Hitherto, transport numbers of ions through ion-exchange membranes have mostIy been obtained indirectly from measurements of membrane potentials under conditions of zero current. A method is now described for measuring the transport numbers directly with current densities and concentration differences similar to those prevailing in a multi- compartment electrodialysis cell. At high current densities and in an unstirred system the ions can be transported through Permaplex C-10 and A-10 membranes at a faster rate than they can diffuse and be transported through the solution and up to the membrane faces.When, as a result, the interfacial layer has become sufficiently depleted in ions the current is carried by H+ and OH- ions (derived from the water) and lower transport numbers result. Stirring the solution results in normal transport numbers. At low current densities the transport numbers of Na+ and Cl- are independent of stirring, and their dependence upon current density and upon the difference of concentra- tion between the two sides of the membrane can be explained on the hypothesis that both concentration diffusion and electrical transport occur simultaneously through the mem- brane. The straight lines obtained on plotting transport number against the reciprocal of the current density indicate that the decrease of transport number with current density is due to concentration diffusion.Extrapolation to infinite current density gives the values 0.98, 0.95, 0.95 and 0.95 for the true transport numbers of Na+ through Permaplex C-10 at concentrations of 0-1, 1.0, 2.0 and 2.95 N NaCl (all against 0.1 N), and the slopes of the lines enable the concentration diffusion coefficient of NaCl to be calculated. For Permaplex C-10 this is 8.1 x 10-8 cm2 sec-1.186 EFFECT OF CURRENT DENSITY The use of ion selective membranes in multicompartment cells to remove salt from brackish waters by electrodialysis has been described by several authors.1-5 An important property in this process is the selectivity of the membranes. The degree of selectivity is a function of the transport number of the counter ion through the membrane, e.g.cation transport number through a cation-exchange membrane. The rate at which salt is removed on passing through a multicom- partment electrodialysis cell depends directly on the quantity tA + tc - 1, where tA and tc are the anion and cation transport numbers through the anion- and cation-exchange membranes respectively. This quantity, expressed as a per- centage of unity, is termed the cell efficiency. The membrane area required to desalt a given water to a given level, at a fixed current density and output rate, is controlled by the cell efficiency. Alternatively, if the size of the cell is fixed then current density and, hence, power consumption are determined by the cell efficiency.Membrane transport numbers are, therefore, extremely important quantities in the design and operation of multicompartment cells. Of particular interest are the transport numbers of sodium and chloride ions through cation and anion exchange membranes respectively, since these ions are the ones encountered most frequently in the treatment of brackish waters. Most workers have determined membrane transport numbers by measuring membrane potentials and applying a modified Nernst equation.6-8 The procedure is simple, but is indirect and bears little relation to the processes taking place in multicompartment cells. For example, it is a null method and the potential is recorded when no current is passing through the membrane. This method obviously could not be used in the present study to investigate the effect of current density on membrane transport numbers. For this reason another procedure has been devised to measure transport numbers with current densities and con- centration differences similar to those prevailing in multicompartment electro- dialysis cells.As in these cells also, electrical transport is from the more dilute to the more concentrated solution. EXPERIMENTAL MATERIALS.-PermapkX c-10 and A-10 membranes (The Permutit Co. Ltd.) were used. These are heterogeneous ion selective membranes of nominal thickness 0-02 in. In the fully swollen state they contain 30-40 % moisture and will shrink by about 10 % in each linear dimension if allowed to dry out. Permaplex C-10 is a unifunctional cation-exchange membrane containing highly ionized sulphonate groups to the extent of about 2 mequiv.per wet g. It is permeable to cations and substantially impermeable to anions. Permaplex C-10 was used in the sodium form and its electrical resistance in an ambient 0-1 N sodium chloride solution was approximately 30 ohms/cmz. Permaplex A-10 is a unifunctional anion-exchange membrane containing highly ionized quaternary ammonium groups to the extent of about 1-3 mequiv. per wet g. Permaplex A-10 was used in the chloride form and its electrical resistance in an ambient 0.1 N sodium chloride solution was approximately 12 ohms/cm2. The aqueous suspension of finely divided cation-exchange resin used in the deter- mination of individual transport numbers was prepared by ball milling 1000 g (wet) of washed, sodium form Zeo-Karb 225 with 500 ml of distilled water for 48 h.The average size of the particles in the resulting viscous mixture was 4p. The particles tended to settle out so the mixture was always thoroughly stirred before use. An aqueous suspension of finely divided anion-exchange resin was prepared in a similar manner from washed, chloride form De-Acidite FF. APPARATUS.-The apparatus used for the measurement of transport numbers is shown in fig. 1. It consists of three T-pieces and two elbows of &in. bore Pyrex industrial glass piping, separated by two anion- and two cation-exchange membranes to form five com- partments. Four standard clamping units hold the compartments together. Platinum electrodes are inserted into the end compartments (the anode into A and the cathode into E) and connected via an iodine coulometer, variable resistance, and milliammeter to a 1OOV d.c.supply. Compartments A and E are filled with approximately 0.1 N sodium chloride solution.T. R. E. KRESSMAN AND F. L. TYE 187 The centre compartment C is bounded by an anion-exchange membrane on the side nearest to the anode and by a cation-exchange membrane on the side nearest to the cathode. The transport determination gives the sum of the transport numbers of the counter-ions in these two central membranes. The outer anion and cation membranes are guards that prevent the electrode products, chlorine and caustic soda, from affecting the nature of the electrolyte in the three central compartments and interfering with the transport processes.FIG. 1 The apparatus was placed in a thermostat bath regulated to 25" 0.1" C with the open ends of the elbows and T-pieces above the level of the water. That part of each membrane that extended outside the piping was isolated from the water in the bath by placing the membrane in a sealed rectangular polythene envelope. Matched circular holes in the two faces of the envelope, of diameter equal to the bore of the pipes, exposed the membrane to the electrolyte in the compartments on either side. The polythene also acted to some extent as a gasket between the membrane and the piping. Once the membranes had been clamped into position they were not allowed to dry out. In those experiments in which the compartments were stirred two streams of air were directed close to the membrane faces.The iodine liberated at the anode of the coulometer was titrated with 0.04 N sodium thiosulphate solution. Chloride estimations were carried out volumetrically with standard N/30 silver nitrate, potassium chromate being used as indicator. DETERMINATION OF f N a + tc1 t N a is the transport number of the sodium ion through the cation-exchange membrane and tc1 is that of the chloride ion through the anion exchange membrane. Compart- ments B and D were filled with 1-ON sodium chloride and the centre compartment C with 15 ml of standardized 0.1 N NaCl. A constant electric current, adjusted to the current density required, was then passed until about one-half of the electrolyte had been removed from compartment C.The centre compartment was emptied and rinsed out with water, and the total amount of chloride present in the compartment estimated. The sum of the transport numbers is then obtained by simple application of the laws of electrolysis, no. of equiv. of C1- lost from compartment C no. of coulombs of electricity passed tA .+ t , = 1 + F ( and values of this sum were determined at current densities from 2-5 to 43 mA/cm*. DETERMINATION OF INDIVIDUAL TRANSPORT NUMBERS To justify the method, determinations oft^^ + tc1 were carried out with compartment €3 filled with an aqueous suspension of ground anion-exchange resin and compartment D filled with a suspension of ground cation-exchange resin. Compartment C again con- tained 15 ml of standardized 0.1 N sodium solution. This solution was stirred in some experiments and not stirred in others.The duration of each run was approximately 24 h and the current density was 5 mA/cm2. Fresh ground resin suspension was used for each determination. Values of t N a were obtained by retaining the suspension of anion-exchange resin in compartment B, and replacing that in compartment D with sodium chloride solution. t N a values were determined at current densities from 0.75 to 5 mA/cm2 for each concentra- tion4.1, 1.0, 2.0 and 2.95 N-of sodium chloride solution in compartment D.188 EFFECT OF CURRENT DENSITY RESULTS AND DISCUSSION The variation of tNa and fC1 with current density is shown in fig. 2. These results were obtained with compartments B and D filled with 1.0 N sodium chloride solution. The initial rise of transport number between 2.5 and 5 mA/cm2 will be referred to later.For the moment attention will be focused on the second part of the curve which shows a decrease in fNa + fC1 as the current density increases from 7 to 43 mA/cm2. In this range of current density, compartments C and D were found to be acidic (pH m 2.0) and compartment B alkaline (pH m 10) at the end of a transport-number determination. This contrasts with the range 2.5 to 5 mA/cm2 in which the pH of compartments B, C and D remained unchanged at 5.5 throughout the determinations. - U c + 0 Z 4- I I I I I I I I 5 10 15 20 2 5 3 0 35 4 0 C u r ren t d en si,t y, m A / c m FIG. 2.-Variation of transport number with current density. 0 unstirred, x stirred. Consider the layer of electrolyte in the centre compartment C immediately adjacent to the anion-exchange membrane.Chloride ions are removed from this layer by electrical transport through the membrane at a rate controlled by the transport number tcr, which has a value of 0.9 or greater. Chloride ions enter the layer by electrical transport at a rate controlled by the transport number of the chloride ion in free NaCl solution, viz. about 0.6. Thus the rate of removal exceeds the rate of replacement. The chloride ion concentration in this layer will decrease and become lower than that in the bulk of the solution. The rate at which chloride ions enter the layer will then be augmented by concentration diffusion from the bulk of the solution. If, however, the amount entering by concentration diffusion is small then the concentration of chloride ions in the layer may fall to a level approaching the hydroxyl ion concentration, i.e.g equiv./l. (PH 5.5). In this circumstance, hydroxyl ions will compete with chloride ions for transport through the membrane and the value of tC1 will fall. A con- sequence of the hydroxyl ion transport is that the equilibrium 2 H20 + H3O+ + OH- will move to the right and so increase the concentration of hydrogen ions in the layer and these ions will migrate through the rest of the compartment. At low current densities, the diffusion rate is sufficiently high in relation to electrical transport to maintain the chloride ion concentration in the layer at a level that precludes any hydroxyl ion transport. As the current density is increased, however, the amount of diffusion becomes relatively less, and the abnormal effects just described come into operation.Similar considerations apply to the cation exchange membrane. On this basis a decrease in the value of tNa + tcl would be expected with increas- ing current density. Further, in the region of current density where abnormalT . R . E . KRESSMAN AND F . L . TYE 189 transport is occurring, compartments B and D should become alkaline and acid respectively and, depending upon the extent of the abnormal behaviour at the two membranes, compartment C should develop a high or low pH. These pH changes, in fact, occurred, as described above. Three experiments were carried out to test the explanation. First, with a current density of 19 mA/cm2, which is in the region of abnormal behaviour, a transport experiment was carried out with 1.0N sodium chloride solution in the compartment C.The higher concentration of the centre compartment would be expected to increase the rate of concentration diffusion into the layer sufficiently to prevent any abnormal behaviour. In fact, the pH of compartments B, C and D remained unchanged at 5.5 throughout the experiment. In the second test, a normal transport experiment was carried out with 0.1 N sodium chloride solution in the compartment C. A few drops of screened methyl orange indicator were added to compartments B, C and D. A current of 40 mA/cm2 was passed and as the run proceeded, acidic and alkaline layers were seen to develop in compartment C, adjacent to the anion- and cation-exchange membranes, respectively, while alkaline and acidic layers, respectively, formed on the outer sides of the membranes.Finally, an attempt was made to eliminate the depleted layers and their effects by stirring the centre compartment C. The run was carried out with 0.1 N sodium chloride in the centre compartment and at a current density of 35 mA/cm2. At the end of the experiment the pH of the compartments B, C and D was un- changed at 5.5. This point is shown on fig. 2 by a cross. The figure obtained without stirring was 1.55. The possible existence of depleted electrolyte layers adjacent to the membranes is of importance in the design and operation of multicompartment electrodialysis cells. The above experiments have indicated that depleted electrolyte layers are more likely to form in 0.1 N than in 1.0 N sodium chloride solution.The effluent from multicompartment desalting cells is generally of the order of 0.01 N and the range of current densities used is roughly from 4 to 30 mA/cm2. Thus, de- pleted electrolyte layers are almost certain to occur in these cells unless a deliberate attempt is made to prevent their formation. More important than the reduced cell efficiency that results from their presence is an increased electrical resistance.5 The electrical resistance may well increase by a factor of five, and power con- sumption will be multiplied by a similar amount. The remedy is to design and operate the cells so that the linear flow rate through the compartments is high enough to ensure turbulent flow.5 This is quite feasible and it is possible to observe a decrease in electrical resistance as the linear flow rate in a multicompartment cell is increased through the critical rate at which turbulence sets in.The above discussion has been confined to values of the sum, tNa + tcl. Individual values for either of the two terms could be obtained if the other could be assumed to be unity. The transport number of a counter ion through a selective membrane is less than unity because there is some transport of ions of the opposite charge in the opposite direction. For example, the transport of sodium ions from compartment B to compartment C results in tcl being less than one. If, however, the cations in compartment B were so large that they could not pass through the pores of the membrane then the value of fcl would be unity and a figure for fNa could be obtained.Large soluble cations, possibly of the polymeric type, could be used. However, an aqueous suspension of finely ground anion-exchange resin is very suitable; it is easily washed free from soluble ionic impurities and, by its very nature, is unlikely to be transported through the anion exchange membrane. Similarly, individual tC1 values can be obtained by using a suspension of cation exchange resin in compartment D to make tNa unity. The method was tested by placing suspensions of anion- and cation-exchange resins in compartments B and D respectively. Under these conditions the sum The measured value of tNa + tcl was 1.86.190 EFFECT OF CURRENT DENSITY of fNa 4- tcl should be two.Several measurements gave the sums 2-00, 2-00, 2-01, 2.00, 1.99, 1-98, 1-99, 1.99. The accuracy of the method, within f 0.02, is limited by the iodine coulometer. With an improved coulometer an accuracy of I 0.005 can be expected. That portion of fig, 2 between 2.5 and 5.0mA/cm2, showing an increase in transport number with current density, was investigated more thoroughly by determining individual values of tNa with the method just described. The results can be explained on the hypothesis that concentration diffusion and electrical transport occur simultaneously through the membrane. Let QT g equiv. be the quantity of sodium ions electrically transported from compartment C to compartment D in t sec. Then 'Na where A is the membrane area, in cm2, separating compartments C and D, i the current density in A/cm2, and iNa the true transport number.From Fick's law, the rate dQD/dt at which sodium ions move from D to c by diffusion is where D is the diffusion constant, C1 and Cz the concentrations in g equiv./ml. of sodium chloride in compartments C and D, respectively, and s the thickness of the membrane in cm. Integration gives the quantity of sodium ions (QD g equiv.) moving from D to C in t sec : Total loss of sodium ions = total loss of chloride ions, dQo/dt = DA(C2 - Ci)/s, QD = DA(C2 - C1)f/s. = QT- QD - Ait DA(C2 - C1)t = tNaI; - S The apparent transport number, as measured, is given by tNa = (QT - Qd-F/Ait* b o u - u Hence Thus, if C2 - C1 is kept constant in a series of experiments a graph of tNa against the reciprocal of the current density should be a straight line and t ~ , , the true transport number, will be one intercept. In all the present experiments Ci was initially 0-1 N and was depleted to approximately 0.05 N.Four values of C2 were used : 0.1, 1.0, 1.0 and 2.95 N, and these values remained almost constant in each run. Fig. 3-6 show the variation of transport number with the reciprocal I 1 I 1 '-9'0 d.2 0!4 Of6 0 ! 8 1.0 1.2 1.4 Reciprocal of current density, cm2 mA-' FIG. 3.-Variation of tNa with current density; C' = 0.1 N of the current density for the four values of C2. The straight lines indicate that the decrease of transport number with current density is, in fact, due to con- centration diffusion through the membrane. The true transport numbers obtained from the intercepts are 0.98, 0.95, 0.95, 0.95 at concentrations of 0.1, 1.0, 2.0 and 2-95 N NaCl (all against 0.1 N).T. R.E. KRESSMAN A N D F. L. TYE 191 Eqn. (1) predicts that the gradients of the lines in fig. 3-6 should be proportional to C2 - C1. This is confirmed in fig. 7 where the gradient is plotted against the mean of the initial and final concentration differences. From the slope of I I I I I I * I I 0 0.2 0 . 4 0.6 0.8 1-0 1.2 1.4 Reciprocal of c u r r e n t d e n s i t y , cm2 mA-l FIG. 4.-Variation of t~~ with current density; Cz = 1-0 N. 0 unstirred, x stirred. I .o I I I I I I 0 . 8 - 0.1 - I I I 1 I I 0 0.2 0.4 0.6 0 . 8 1.0 1.2 1 ' 0 . b Reciprocal of current density. cm2 mA-' FIG. %-Variation of tNa with current density; C2 = 2.0 N.0 unstirred, x stirred. I .o I I 1 I I I - - 0 . 1 - 0 . b - Reciprocal of current density, cm2 mA-l FIG. 6.-Variation oft^^ with current density; C;! = 2.95 N. 0 unstirred, x stirred. the line in fig. 7, the diffusion constant of sodium chloride in a Permaplex C-10 membrane can be calculated. The value obtained is 8.1 x 10-8 cm2 sec-1. The method described here for measuring transport numbers is quite general and can, of course, be used for ions other than sodium and chloride. An192 MEMBRANE ELECTRODES interesting feature of the determination is that, since the total amount of chloride is estimated before and after the experiment, transport of water does not affect the results as it would do if only concentrations were measured. Mean concentration difference (C, - C,) 9 equiv./ ml FIG. 7,-Diffusion constant data; thickness of membrane 0.057 cm. The experimental work was performed by Miss Anne M. Jones and Mr. H. R. Bott. We thank the Directors of The Permutit Co. L,td. for permission to publish the paper. 1 Meyer and Straus, Helv. chim. Acta, 1940,23, 795. 2 Langelier, J. Amer. Water Works ASSOC., 1952, 44, 845. 3 Kressman, Ind. Chem., 1954, 30, 99. 4 Wegelin in Ion Exchange and its Applications (Society of Chemical Industry, London, 5 Winger, Bodamer, Kunin, Prizer and Harmon, Itid. Eng. Chem., 1955, 47, 50. 6 Bodamer, Kunin and Winger, J. Electrochem. Soc., 1953, 100, 178. 7 Juda, Rosenberg, Marinsky and Kasper, J. Arner. Chern. SOC., 1952, 74, 3736. 8 Clarke, Marinsky, Juda, Rosenberg and Alexander, J. Physic. Chem., 1952, 56,100. 1959, p. 122.

ISSN:0366-9033    

DOI:10.1039/DF9562100185

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

192 MEMBRANE ELECTRODES SOME USES OF ION-EXCHANGE MEMBRANE ELECTRODES BY D. HUTCHINGS AND R. J. P. WILLIAMS The Inorganic Chemistry Laboratory, South Parks Road, Oxford Received 16th January, 1956 The equilibrium potentials established across a permiselective cation exchange membrane have been examined in the presence of several cation chlorides. The cations include sodium, potassium, magnesium, barium as well as those of several organic bases. The quantitative behaviour of the membranes has many unsatisfactory features when considering the possibility of their use in accurate analysis even of the simplest cations. The rate of penetration of the membrane by different cations has also been examined. The application of ion exchange membranes to analytical problems involving the use of membrane electrodes, has been proposed many times.1 If the method could be made sufficiently reproducible and sensitive such electrodes would be ofD .HUTCHINGS AND R . J . P. WILLIAMS 193 great value in the study of complex formation particularly of the alkali metal cations. The procedure would parallel the use of the glass electrode in the study of proton complexes i.e. weak acids. Here a further examination of the possible uses of these membrane electrodes is described. THE MEMBRANE ELECTRODE AND CELL The membranes used were made from poIymerized sulphonated styrene and were cast in the form of sheets, thickness - 2.0 mm. They are manufactured by Permutit Ltd., London. In the hydrogen form they have a resistance of - 100 ohms/cm3, they take up 55% of their own weight of water and there are 1.5 m-equiv.of exchangeable protons per gram of wet resin. They are approxi- mately equivalent to a 1 -5 M solution of a strong electrolyte.2 For use as membrane electrodes such membranes, prepared in the desired cation form (see later), and cut into discs of 2-0 cm diam., were held in brass plumbers’ unions by rubber washers coated with silicone grease. The holder is very similar to that described by Wyllie and Kanaan.3 For the measurement of membrane potentials the membrane holder, inside which there was a silver/silver chloride electrode and a stirrer immersed in a metal chloride solution, concentration c1, was dipped into a solution of the metal chloride, concentration c2. Also in the latter solution there was a silver/silver chloride electrode, a stirrer and a dip-type Ag/AgCl electrode assembly. This dip-type assembly was a Ag/AgCl electrode in a solution of the metal chloride, concentration c1, i.e.the same concentration as in the membrane holder, and made contact with the solution through a rough ground glass sleeve, J. Two cell potentials were measured in this assembly, EA and EB : 9 1 I I cell A Ag/AgCl MCl(c1) 1 MCl(c2) MCl(c1) AgCl/Ag I t ‘ k I J Here X represents the membrane. Now EA is given by the sum of the junction diffusion potential Ej, and the membrane diffusion potential EM as the simple Nernst potentials cancel at the two junctions. + Ej = At, RT 2 In (:)+ E,. EA = EM + Ej = where a1 and a2 are the activities of solutions c1 and c2, u and v are the mobilities of the positive and negative ions in the membrane, assumed independent of activity, At, is (t+ - t-), the difference in transport number of the negative and positive ions.E,, the liquid junction diffusion potential at the sleeve junction J, takes the same form as the membrane diffusion potential except that u and v are now the ionic mobilities in the aqueous solutions. The value of EB is RT d(ln a) - Ej = niF In e) - EJ. Now a cation-exchange membrane is permiselective and t+ might be expected to approach unity. Thus the sum of EA and EB should give a potential 2RT __ In (2) . nF In general, however, the sum does not equal this value, but falls short of it due to (i) transport of negative ions, (ii) transport of water. G194 MEMBRANE ELECTRODES EXPERIMENTAL Experiments consisted of measurements of EA and EB.EB was measured separately for it should give a known potential of a concentration cell with liquid junction. In this way it was hoped to determine directly the ratio a1/a2, in the cell after assembly, in order to test whether the membrane holder leaked. In practice, the values found for this potential were close to the theoretical potentials providing that neither the solution c1 nor c2 was very dilute. However, if either solution was dilute, < M/250, the potential E, was in- variably too small. After ensuring that the membrane holder did not leak, by tests with coloured ions, it was found that the dilute solution was altered in strength through the release of salt from the membrane. This deviation from ideal behaviour is inherent in the method.The membranes were obtained from the manufacturer in the acid form and before use the hydrogen ion had to be displaced by the metal ions of the solution under study. This was done by equilibrating the membrane with N/lO metal chloride solution until the washings were not detectably acid by pH measurements. The membrane so obtained is really a strong metal sulphonate solution plus some metal chloride held in a gel phase. On placing such a membrane " solution " in a dilute metal chloride medium some of the ions leave the membrane and enter the solution. EB was changed in this way. Washing the membrane twice with distilled water before use was not sufficient to remove this effect. Prolonged washing was not considered desirable as the amount of metal chloride absorbed by the membrane was altered and the membrane was no longer strictly in equilibrium with N/10 metal chloride.4 The value taken for the potential EB was that reached after prolonged equilibration over many hours.EB was then used to find values of al/a;! of dilute solutions and to check them in stronger solutions. The membranes were re-equilibrated with N/10 metal chloride after every measurement. This pre- caution is not usual but we believe that it is essential if results are to be'reproducible. The problem of the diffusion of ions from the membrane into the solutions can be avoided if flowing solutions are used. We did not adopt this expedient as we wished to investigate the behaviour of membranes in conditions similar to those which would be practical in a titration cell as employed in the determination of stability constants of complex ions.5 The measurement of EA was sometimes more difficult.In measurements with cations other than those of the alkali metals and some organic cations, equilibrium between solution and membrane phases was not achieved rapidly. For several divalent or more highly charged ions and for many large organic cations, it was frequently necessary to wait as long as 24 h for equilibrium. Such slow equilibrations have been found in the study of the behaviour of ion exchange granules.6 In all cases the potentials were measured at intervals over periods up to 24 h to ensure that equilibrium potentials were observed. EQUILIBRIUM MEMBRANE POTENTIALS OF SOME SALT SOLUTIONS In fig.1 the values of log (al/a2) are plotted against (EA + E,) where the metal chloride in the cells is sodium chloride or potassium chloride. Over the linear portion of the plot the slope is 1.10 volts/log unit. The transport numbers tNaand t~ must be somewhat less than unity, - 0.95, perhaps due to the transfer of water. The fact that there is a linear portion of the plot suggests that the transport number of the ions is constant over this region and that the membrane electrodes could be used analytically. The departure of the slope of this plot from that given by t, = 1-00 (v = 0) is nevertheless disturbing.7 The grosser deviations at higher concentration of the salts is probably due to saturation of the membrane with positive ions, the further uptake of both positive and negative ions, and gross changes of the values of the transport n~mbers.7~8 Deviations from linearity at low concentration are harder to explain.There appears to be considerable risk in the use of the membrane electrodes for quantitative analytical measurements even with the alkali-metal cations. Similar experiments were made with barium chloride. The results are plotted in fig 2. Although the plot for the barium solutions is like that for the sodium and potassium salts, tga is apparently 0.90 over the shorter linear portion of the plot. The deviations at higher concentrations are much greater and it is suggested that the chloride ions are carrying part of the current, perhaps as BaCl+. It is known that the larger group 2~ cations form associated halides especially in organic solvents amongst which we must include the poly- styrene of the membrane.The results we obtained in the study of the magnesium ion were most unsatisfactory ; t~~ appeared to be close to 0.50. They suggest that the magnesium ion does not readily enter the membrane, i.e. it finds difficulty in displacing the proton or it is too large to enter the pores of the membrane. Kressman and Kitchener 6 observed, asD . HUTCHINGS AND R. J . P. WILLIAMS 195 we do, the order of affinity Ban > SrII > Ca" > Mgn and comment upon the weak affinity of sulphonated resins for magnesium ions as compared with hydrogen ions. Gregor and Frederick 9 compared the affinity of similar exchangers for the four alkali-earth cations with the solubility products of their respective sulphates and found an almost linear relationship.This implies an affinity for barium of many powers of ten greater than that E.H.F o-201 FIG. 1.-The relationship between the membrane potential and the ratio of the activity of potassium chloride on one side of the membrane to that on the other. +, c1 = M salt; 0, CI = M/10 salt; 0, CI = M/100 salt E.H.F. FIG. 2.-The relationship between the membrane potential and the ratio of the activity of barium chloride on one side of the membrane to that on the other. a, c1 = MjlO salt; 0, c1 = M salt for magnesium. Gregor, Cutoff and Bregman 10 in an analysis of the swelling of ion- exchangers by cations concluded that whereas barium ions formed ion pairs with the sulphonate groups losing water of hydration the magnesium ion entered the resin fully hydrated.We are not entirely satisfied that some error is not present in our experiments with magnesium chloride although we have repeated the observations. The pH of the solutions excluded hydrolysis. The same results are not obtained with weak acid exchange resins containing carboxy- late anions in place of sulphonate groups.11 The order of affinities here is MglI > Car1 >196 MEMBRANE ELECTRODES Sru > Ban. The magnesium ion membrane potential is now of the expected size, i.e. t~~ approaches unity. The parallel between solubility, complex ion formation, activity coefficients in strong solution of salts of weak and strong acid anions and cation exchange affinity is now obvious.12 The parallel can be illustrated from data of Schwarzenbach, Willi and Bach,l3 given in table 1.TABLE l.-STABILITY CONSTANTS K FOR SOME COMPLEXES OF THE GROUP 2A CATIONS log K ligand M grI Car1 Sr" BaII Ph.N(CH2C02H)2 1-15 0.6 small small oxalate 3.43 3.00 2-54 2-33 nitrate 0-00 0.28 0.92 sulphate 2-1 5 2.28 Other examples are given in ref. (12). A carboxylic acid substituted vinyl compound polymerized into an exchange resin will behave as a ligand in a manner similar to an acetate group. In table 1, di-N-acetyl aniline, is given as an example and shows that the affinity order is MgII > Ca" > Sr" > Ba", as with the weak acid exchangers. The differences between the behaviour of anions of weak acids and of strong acids in their affinities for group 2~ cations have been previously discussed in terms of the hydration of the cations 12 (cp. table 1).The discussion is sup- ported by the behaviour of the two kinds of anion exchange resins in their affinity for the same cations and in so far that the swelling of strong acid resins follows the order MgII > CaII > SrII > BaII, while that of weak acid resins is BaIl > SrII > CaII > MgII. It is difficult to explain such observations except in terms of the uptake of hydrated cations in the first series and bare ions in the second. In order to examine the supposition that the magnesium ion had little affinity for the membrane because of its strong hydration, we looked for a cation of similar size to that of the hydrated magnesium ion but which would not exchange its immediate coordinated ligands readily.In this respect the ammines of CoIII are ideal. The radius of the hydrated magnesium ion and that of the roseocobaltic ion, Co(NH&H203+, for example, are very similar - 2.0 A. The latter ion exchanges its ligands exceedingly slowly and does not hydrolyze readily. The membrane potentials of the trichloride [CO(NH~)~H~O]CI~, were therefore studied in the usual manner. In this case no activity or liquid junction potential data are available. When the sum of the potentials EA and EB is plotted against log (cI/c~) the slope of the plot is very close to that found for magnesium chloride despite the fact that a trivalent ion would be expected to have lower mobility than a divalent ion. We concluded at this stage that the cobaltic ion, and possibly the magnesium ion, did not enter the membrane readily, i.e.they did not totally displace the proton under the conditions used to prepare the membranes. It was considered that the reluctance to enter the mem- brane might be due to the large size of these ions. A study of the rates of establishment of the cobaltic ion potential confirms this suggestion. Again the roseocobaltic ion is coloured and it has proved possible to follow the extremely slow diffusion of this ion from the membrane into strong potassium chloride. EQUILIBRIUM MEMBRANE POTENTIALS OF LARGE CATIONS The chlorides of diethyl ammonium, cetyl pyridinium? quininium and p-chloro-anilinium ions have also been examined. Their membrane potentials show clearly that the last three ions hardly enter the membrane.Kressman and Kitchener observed similar effects in the study of absorption of large cations by ion exchange granules. The diethyl ammonium ion behaved like the potassium ion. An application of the membranes as selective sieves is now clear. Thus they could be used in the analysis of small cations in the presence of much larger ones just as anion exchange resins can be used to estimate concentrations of small anions in the presence of very large ones. This would appear to be the only safe analytical application of these membranes. So far selectivity in the use of ion-exchange membranes as discussed here depends simply upon (i) sieve effects, (ii) ion-pair formation with the fixed charges. We believe that " solubility " is also important.By " solubility " we refer to the differences in free energy between ions in water and in the lattice polymer, which forms the basic membrane net- work for the fixed charges, even in the absence of the charges. In other words we think inD. HUTCHINGS AND R. J . P . WILLIAMS 197 terms of a partition coefficient between water and polystyrene. For an ion such as silver which interacts powerfully with unsaturated residues we believe that a " solubility term " is important and produces the anomalies observed by Gregor, Cutoff and Bregman,lo which were considered to arise from adsorption. A similar approach will be used in the subsequent discussion of the rate of replacement of one ion by another in a membrane. THE RATE OF EQUILIBRATION OF IONS WITH THE MEMBRANE If the ion-exchange membranes are to be used as electrodes for the analytical deter- mination of given cations they must come to immediate equilibrium.An examination of the change of membrane potentials with time was therefore undertaken. If a membrane, pretreated with N/10 potassium chloride is transferred to the cell unit containing two solutions of potassium chloride of different strengths c1 and c2 the final equilibrium potential is achieved in under 5 min (fig. 3). To test the rate of equilibrium with other ions the mem- branes were soaked in a given metal chloride (concentration M/10) before transferring to the cell unit containing the same potassium ion solutions c1 and c2. To reach equilibrium the metal ion must diffuse from the membrane and this diffusion, if slow, is rate-determining. A number of cations have been studied in this way.Equilibrium is established very rapidly when the membrane is pretreated with sodium or magnesium ions (fig. 3, curve I), but the rate of change of potential is slow with a barium ion membrane (fig. 3, curve 11). "'I0' 3 FIG. 3.-The rate at which the potential reaches a steady value after pretreatment of the membrane with I, potassium chloride ; 11, barium chloride ; 111, di-ethyl ammonium chloride ; IV, roseocobaltic chloride. These and other observations suggest that there is an order of affinity of the membrane anions for the cations BaII > KI > NaI > MgII.6 Pretreatment of the membrane with cetyl pyridinium and quininium ions had no effect upon the rapid attainment of the potassium ion potential.It has already been suggested that these ions are too large to be appreciably absorbed by the membrane. After pretreatment with roseocobaltic ion, equilibrium was not established after several days, the pink ion diffusing slowly from the membrane. Thus although the roseocobaltic ion and the magnesium ion behave similarly with regard to their equilibrium membrane potentials there is a dissimilarity in the rate of achievement of these potentials. We are unable to explain these differences. During the further study of changes in potassium ion potential of the membrane after pretreatment with one or two organic cations a peculiarity in the potentials was noted. The potential recorded rose very rapidly to a value greater than that of the simple potassium ion membrane and then fell slowly (fig.3, curve 111). The behaviour suggests that the organic cation is taken up by the membrane in a manner different from that of the simple potassium ion. That is to say that the organic cation apparently finds sites in the resin phase from which it cannot be displaced by potassium. This type of effect could be described as a difference of solubility in the membrane. Our experiments did indicate that there were two rate-controlling stages in the entry of ions into the membrane, one at the membrane surface and one in the interior of the mem- brane. As far as we were capable of analysing our results they could be expressed in terms of a very rapid equilibrium at the surface of the membranes followed by the diffusion of ions from the interior. Our discussion of the rate of change of potassium ion potential has been limited accordingly to the discussion of effects in the membrane rather than at its surface.198 GENERAL DISCUSSION As a whole the study of both equilibrium potentials and the rate at which they are estab- lished suggests that the present membrane electrodes have little to recommend them for quantitative use. 1 Sollner, Ann. N. Y. Acad. Sci., 1953, 57, 177. 2 Kressman, Nature, 1950, 165, 568. 3 Wyllie and Kanaan, J. Physic. Chem., 1954, 58, 73. 4 Manecke and Otto-Laupenmiihlen, 2. physik. Chem., 1954, 2, 336. 5 Irving and Griffiths, J. Chem. SOC., 1954,213. 6 Kressman and Kitchener, J. Chem. Soc., 1949, 1201 7 Juda, Marinsky and Rosenberg, Ann. Rev. Physic. Chem., 1953, 4, 373. 8 Graydon and Stewart, J. Physic. Chem., 1955, 59, 86. 9 Gregor and Frederick, Ann. N. Y. Acad. Sci., 1953, 57, 87. 10 Gregor, Cutoff and Bregman, J. Colloid Sci., 1951, 6, 245. 11 Gregor, Luttinger and Loebl, J. Physic. Chem., 1955, 59, 990. 12 Williams, J. Chem. SOC., 1952, 3770. 13 Schwarzenbach, Willi and Bach, Helv. chim. Acta, 1947, 30, 1303.

ISSN:0366-9033    

DOI:10.1039/DF9562100192

出版商:RSC    

年代:1956

数据来源: RSC

摘要:

198 GENERAL DISCUSSION GENERAL DISCUSSION Dr. P. W. M. Jacobs (Imperial College London) (communicated) The pro-gramme described by Lorimer Boterenbrood and Hermans is similar to our own in that one of our aims has been to establish experimentally values for the pheno-menological coefficients. Using the form of the theory applicable to discontinuous systems they obtain eqn. (16) which can be tested by calculating t+ from dE’/d In a, allowing for solvent transport and comparing the calculated values with those measured directly. Since our results using membranes of polymethacrylic acid in KOH solution cover a wider concentration range than those recorded in their paper it is perhaps of interest to quote the results here. rn 0.00562 0-0 1 125 0.05624 0.1005 0.2010 0.4025 0.8078 1.013 f + (calc.) 0.998 0-991 0.988 0-986 0.957 0-90 1 0.794 0.765 t+ (obs.) 0.954 0.941 0-925 0.914 0-875 0.820 0.740 0-705 The calculated results are from 4-9 % too high whereas the observed values were reproducible to better than 1 %.Some of the discrepancy may be due to the errors inherent in the graphical differentiation of the plot of E’ against log (urr/ax), but there remains the suspicion that some more fundamental factor has been over-looked. This is not likely to be due to the authors’ use of the form of theory required for discontinuous systems for the same equation can be derived from pseudo-thermostatic arguments 1 and also by applying the thermodynamics of irreversible processes when the membrane is regarded as a continuous system.2 At least for membrane potentials there are no inherent theoretical difficulties, and one feels fairly safe in applying eqn.(16). The discrepancies observed are therefore all the more puzzling. Dr. J. W. Lorimer (Leiden University) (communicated) Two new techniques applicable to membranes which can be made in strip form are under development 1 Scatchard Ion Transport Across Membranes ed. Clarke (Academic Press 1954), 2 Hills Jacobs and Lakshminarayanaiah unpublished work. p. 134 GENERAL DISCUSSION 199 in our laboratory. The same cell (fig. 1) is used both for d.c. conductance and e.ni.f. measurements. It consists of two Plexiglas blocks B with electrode chambers C C’ D D’ and a channel A just slightly smaller than the membrane.For d.c. conductance measurements the membrane is placed in A and its equilibrium KCl solution in C and C’. A known current is passed through reversible electrodes in C and C’ and measurement of the potential between two reversible probe electrodes in D and D’ permits calculation of the cell re-sistance. Preliminary experiments using H FIG. 1. membranes of the type described earlier in this Discussion showed Ohm’s law was valid and gave conductance values agreeing within experimental error with those obtained from ax. measurements. For e.m.f. measurements a membrane is cut into two sections each of which is equilibrated in a different KC1 solution. The sections are placed in the cell, and meet at the dotted line. The appropriate equilibrium solutions and silver chloride electrodes are placed in C and C’.For 0.05-0.001 N KCI an e.m.f. of 134.8 mV was recorded at 15” C in excellent agreement with the value 134.4 mV obtained from flowing-junction cell experiments (8 B). Dr. K. S. Spiegler (Pittsburgh U.S.A.) (communicated) In their excellent discussion of transport processes across membranes Lorimer Boterenbrood and Hermans mentioned the experimental difficulties encountered as a result of un-wanted electrode reactions. Mr. J. G. McKelvey and I have met with similar difficulties and found a way to overcome them at least for certain systems. In the past our study dealt with transfer phenomena across commercial cation-exchange membranes (e.g. Permaplex C- 10 product of The Permutit Company Ltd., London).Our work too is based on the fundamental paper by Staverman.1 Since the transport numbers depend on the concentrations of the solutions separated by the membrane we determine the transport without changing appreci-ably the total solution concentration. No stirring is required. This is achieved by : (1) adding a radioactive tracer to one solution and (2) adding small amounts of appropriate ion-exchange resins to the solutions in the anode and cathode compartments. The resins act as “ concentra-tion buffers ” removing the unwanted products of the electrode reactions and balancing the ion concentrations in the two compartments. For instance in the determination of transfer phenomena in the Permaplex C-1 + sodium chloride system we used the following arrangement I NaCl + solution HR I Pt-cathode I membrane Pt-anode 1 + Na*:R Na*Cl solution where R represents the negative radical of the weakly acid cation-exchange resin Amberlite IRC-50 (product of the Rohm and Haas Co.Philadelphia Pennsylvania). The sodium ion in the anode compartment is traced with 2.6 y Na22 both in solution and on the resin. Upon passage of the electric current the platinum anode generates hydrogen ions which are immediately taken up by the resin since the solution in the electrode compartments is vigorously agitated by magnetic stirrers. At the same time the resin releases sodium ions most of which migrate through the membrane. At the cathode NaOH is formed and promptly adsorbed by the resin thus removing excess sodium ions approximately in the same amount as they migrated through the membrane.As a result the total concentrations of the solutions change 1 Trans. Faraday Soc. 1952 48 176 200 GENERAL DISCUSSION very little during current transfer. The transport numbers are calculated from the increase of the specific radioactivity of the solution and/or the minor change of the chloride concentration in the cathode compartment. The cell is made of Plexiglas. The gases produced by the electrode reactions escape through burettes inserted at the dome-shaped ceilings of the cell com-partments. The solvent transfer is calculated from the change of level in the burettes. Allowance is made for the small amount of water decomposed by electrolysis. This method might also be suitable for salts other than chlorides since it does not depend on the supply of anions from the cathode.With chlorides some chlorine evolution occurs at the anode but this does not seem to affect the results to any appreciable extent. A different method aimed at keeping the solution concentrations constant was used by Murakoshi 1 who measured ion and water transport in systems of KCl solutions and cation-exchange membranes. In these experiments potassium amalgam and mercury were used as anode and cathode respectively. Dr. F. L. Tye (The Permutit Co. Ltd. London) said Dr. Lorimer Miss Boterenbrood and Prof. Hermans write “ The good proportionality between resistance and length indicates that any refraction of the current lines in the area I I I / I I oo 0.1 0 - 1 0.3 a tcm, FIG.1. between the two Plexiglas plates is negligible . . .”. This statement is question-able and the evidence for it in their fig. 2 can be interpreted as being indicative of considerable current distortion between the Plexiglas plates. In fig. 1 cell resistance with membrane is plotted against membrane thickness and a smooth curve drawn through the points. The points are a repeat plot of the open circles shown in the authors’ fig. 2 except for the point at a = 0 1 private communication see also Kosaka J . Electrochem. SOC. Japan 1955 23 659 GENERAL DISCUSSION 201 which is shown in the authors’ fig. 2 as a half-filled circle. The curve convex to the resistance axis is the type one would expect if the effective area of conduction were increasing as the thickness of the membrane increased.Such an increasing area of conduction would of course result from distortion of current lines between the Plexiglas plates. An estimate of the effective area of conduction at any particular membrane thickness e.g. a = a1 can be obtained from the ratio of the slope of the tangential line at a = 0 to the slope of the line joining points a = 0 and a = a1 on the curve. This ratio gives the value of A/Ao where A is the effective area of conduction for a membrane of thickness al and A0 is the internal cell area. A plot of A/& against membrane thickness is shown in fig. 2. I I A/A I I I 1 a ( c m ) FIG. 2. The magnitude of the A/Ao values in the range of membrane thicknesses em-ployed demonstrates that distortion of current lines is far from negligible.The rather small internal diameter of the cell used by the authors has of course, emphasized the effect. The cell diameter is only four times greater than the thickest membrane used. It follows that had the internal cell area been used to calculate specific con-ductivities the results would have been considerably in error. However the authors have employed a comparative method which necessitates measurement of the resistance of KCl solution as a function of thickness. If it can be assumed that the amount of current distortion is the same for the KCl solution as it is for the membrane the final error in the specific conductivity results should be fairly small. It should be made clear that for this procedure to be at all justifiable the Plexi-glas rings inserted between the two halves of the cell to measure KCl solution resistance as a function of thickness must have internal diameters larger than the internal diameter of the cell so that full distortion of current lines is possible.The Plexiglas rings used by the authors did have much larger diameters than the internal bore of the cell.1 1 J. W. Lorimer private communication 202 GENERAL DISCUSSION Dr. J. W. Lorimer (Leiden University) (communicated) Dr. Tye’s remarks on the distortion of current lines in the conductance cell used in our research seem to demonstrate the importance of such effects. However two points must be settled before his method for finding the effective area of conduction proves acceptable. First the magnitude of the effect depends upon the slope of the tangent drawn at a = 0 in Dr.Tye’s fig. 1 and it is somewhat difficult to locate this line accurately. Secondly because there will always be some curvature of current lines in the solutions bathing the membrane there will be a refraction effect 1 at the membrane-solution interface. This effect should result in greater distortion in a KC1 solution layer than in a membrane layer of the same thickness, since the solution conductance is greater than that of the membrane. Our plots of resistance against thickness however all gave better straight lines for solutions than for membranes. This may indicate that distortion effects in the solutions next the cell electrodes are also important. Since this method for measuring membrane conductance is convenient and widely used an accurate analysis of the situation is highly desirable.Prof. G. Schmid (KoeZnlRhein Germany) said I cannot subscribe to the opinion of Dr. Hills when he says “The Schmid theory of electro-osmosis in charged membranes does not appear to be valid for this membrane system.” In its main deductions this theory makes a minimum of arbitrary assumptions. It is therefore hard to understand why it should not be valid for the membrane system under consideration. To be sure the basic formulae of my theory contain no information on pore radii or pore numbers these being obtainable only on the basis of quite arbitrary assumptions. Bjerrum and Manegold assume incorrectly of course a’system of random cylindrical pores and give the pore radius r as r = (24D~dv/W)# where DH is the water permeability of the membrane d its thickness and Wits water content.By use of the formula rrr2N = W the number of pores N can be calculated from the above assumption which is certainly incorrect. The basic formulae in my papers contain only the empirical quantities DH and W. To make them more comprehensible however I have also calculated “ pore radii ”. But here I have stressed that the pore radius r may be understood only as a numerical value which strictly speaking has no real meaning. The same is of course true for the number of pores N. The primary values which alone have a quantitative meaning are the water permeability DH and the water content W (or the resin content VR). Eqn. (6) of Dr. Hills is 1 0 3 ~ 2 ~ 2 (g) vR =-* ‘71 Dr.Hills is of the opinion that the right side of the expression is constant. He assumes that membranes with the same water content have also the same pore radius r and that if the water content or the resin content is kept constant, the pore radius must also be constant i.e. independent of ci. This idea seems plausible and may be valid to a certain extent for pore systems containing a great deal of mobile water. However for pore systems in which, due to fixed or mobile ions the amount of bound water is appreciable compared with that of unbound water the assumption certainly is not true. Even if the organic matrix and the water content remain unaltered an increase in fixed ion concentration can immobilize so much water that both the pore radius and the pore number are greatly altered.In general as the Bjermm-Manegold formula shows r is only constant provided not only VR but also DH is kept constant. In the system with which Dr. Hills works it is likely that the value DH decreases sharply with increasing ci even if the structure of the matrix and the value VR 1 Jeans The Mathematical Theory of EIectricity and Magnetism (Cambridge 5th ed., 1925) p. 346 GENERAL DISCUSSION 203 are kept constant. In the calculation of pore radii a decrease of r with increasing ci would then appear. The expression (g) VR must therefore decrease with increasing ci as has in fact been observed by Dr. Hills and Dr. Despi; and was represented in fig. 7. Furthermore I would like to say that I consider it somewhat unfortunate that the definition of the term electro-osmosis used by Dr.Hills does not include the transport of water of hydration. I would suggest that the term electro-osmosis should be defined purely phenomenologically and with no hypotheses from the total amount of transported water or solution as has nearly always been done until now as far as I am aware. For the treatment of electro-osmosis according to the thermodynamics of irreversible processes an unphenomenological definition would certainly be unsuitable. The distinction which Dr. Hills has made is of course completely correct in practice and indispensable for a theoretical inter-pretation of electro-osmosis. However the term electro-osmosis as such should not be encumbered with the uncertainties of theoretical interpretations as for example with hydration numbers.Prof. G. Scatchard (M.I.T. Cambridge Mass.) said If we consider the water as stationary the determination of primary solvation from the measurements of Despic and Hills is equivalent to the assumptions with ordinary solutions that self-diffusion gives the ‘< true transference ” number that from the difference between “ true ” and “ Hittorf ” transference the “ hydration ” of the ions may be de-termined and that this “ hydration ’’ is entirely the “ primary solvation ” of the cation. Many of us would be unwilling to make these assumptions. Dr. P. Meares (Aberdeen University) said When considering the change with concentration of equivalent conductance and self-diffusion coefficient of the counter-ions in an ion-exchange resin Despic and Hills include only the effects due to electro-osmosis and the c‘viscous effect of the matrix”.At constant volume fraction of resin they consider that the latter effect will be the same for conductance as for diffusion so that the difference between mobilities obtained by the two methods will give the electro-osmotic contribution. It appears however that a relaxation effect may also contribute to this difference. Confining attention for the present to the simple Onsager treatments neglecting the finite size of the ions the fractional decrease in the applied field A X / X caused by the relaxation effect in conduction is AX Z122e2K (1) X 3ckT 1 + l/q’ where z1 and z 2 are valencies e the electronic charge E the dielectric constant, k the Boltzman constant T the absolute temperature and K the Debye reciprocal length q for univalent ions is 3.Under the conditions of a self-diffusion experi-ment the reduction in the virtual force arising from the concentration gradient of tracer ions AFIF due to the relaxation effect is for univalent ions - - _ ~ ~ AF 1 + 2t F 3 ~ k T here t is the transport number of the ion of sign opposite to the tracer ions. For an ion-exchange resin t = 0. reduce to ~ _ _ Hence for the case here considered (1) and (2) e2K - 0.293 __ A x X 3 ~ k T AF e2K - = 0.500 --F 3&T (3) (4 204 GENERAL DISCUSSION Since (3) and (4) are not identical in the range of validity of the Onsager equations, the difference between and A’ of Despic and Hills will be due partly to electro-osmosis and partly to the relaxation effect.At higher concentrations such as were encountered in the resin phase the calculation of the relaxation effect in conduction can be improved by taking into account the finite size of the ions, as has been done by Falkenhagen Kelbg and Leist. No similar extension has been given for the self-diffusion theory but it seems necessary to admit the possibility that at high concentrations the difference between X and A’ may not give an uncomplicated measure of the electro-osmotic effect. Dr. A. DespiC and Dr. G. J. Hills (Imperial College London) said Prof. Schmid contends that constant VR does not imply a constant value for the Y or r2 because this is a hypothetical quantity introduced into his equations from DH, the hydrostatic diffusion coefficient which is dependent on concentration even at constant VR.This apparent anomaly emphasizes the need to consider the finite volume of the ions transported through the membrane. In Schmid’s equation where pe is the electro-osmotic pressure Df the electro-osmotic coefficient and i the current density the volume of solvent transported under a hydrostatic pressure is equated to the volume of solution transported electro-osmotically. This is only so on the basis that ions are point charges. Whenever the need arises to consider ions of finite size the appropriate form of this equation is peDs = Dii (1) where Ds is the hydrostatic diffusion coefficient of the solution notwithstanding the fact that this coefficient cannot be obtained in the same way as DH.Apart from the effect of concentration on the viscosity of the interstitial solution which we have neglected DS is not dependent upon ionic concentration but only upon r. We regard r2 as a purely geometrical quantity which on the basis that NO is con-stant is given unambiguously by eqn. (9) of our paper. On either argument constant VR does imply constant 9. It is this previous neglect of the finite volume of solvated ions which also leads to the anomaly in the definition of electro-osmosis. We agree with Prof. Schmid that the phenomenon of electro-osmosis has always referred to the total quantity of solvent transported through a membrane. In any consideration of the mechan-ism or theory of electro-osmosis however a distinction must be made between the water transported by the electro-osmotic mechanism and that migrating with the ions.Even if no experimental distinction were possible a distinction in principle should be made e.g., electro-osmosis = electro-convection + ionic solvation. pe DH = Dii , On this basis the mechanism and the various theories of electro-osmosis strictly refer to electro-convection. We used the word “ electro-osmosis ” and “ electro-osmotic transport ” in relation to the mechanism not the phenomenon. It is worth noting that where the electro-convection is very large and/or the solvation nil the anomaly disappears. In reply to the remarks of Dr. Meares we agree that the difference in the two relaxation effects could give rise to part of the difference between the observed mobilities or conductances but there is experimental evidence that this is apparently not so.As we pointed out earlier the variation of ionic mobility with ionic con-centration at constant VR obtained from self-diffusion coefficients is in accord with the equation (2) where A& is the limiting equivalent conductance of the counter-ion species in aqueous solution A is a constant equal to ( V R ) ~ = ~ and a* is the Onsager relaxation u’ = ( x ~ ~ / F ) ( I - a*dii)(A - I+) GENERAL DISCUSSION 205 parameter applicable to normal ionic conductance. Further if to this equation is added an equation similar to (10) of our paper the expression is obtained where B is the value of VR as AA -+ 0 and K = 103P/877-7No. A value for NO must be found from one experimental observation on the membrane material.Eqn. ( 3 ) which contains only terms for the normal conductance relaxation effect and electro-osmosis expresses the equivalent ionic conductance of all the alkali metal ions over a wide range of ci and VR values. It therefore does appear that the difference between u and u’ is due solely to electro-osmosis. Dr. G. A. H. Elton and Dr. D. I. Stock (Battersea Polytechnic London) (com-municated) We should like to raise some points concerning the work of Despik and Hills on electro-osmotic transport. The nature of the electrodes used is not stated but whether these were reversible or not the value of ANsolvent (anode) in table 5 is incorrect; if the electrodes were reversible to OH- the value of A Vsolvent (cathode) is also incorrect.With inert irreversible electrodes the result of the passage of 1 faraday is in respect of water the loss of 1 mole in the cathode compartment and a gain of 0.5 mole in the anode compartment. With reversible electrodes (e.g. Hg/HgO) the corresponding result is the loss of 0.5 mole in the cathode compartment and the gain of 0.5 mole in the anode compartment. In their calculations DespiL and Hill have assumed implicitly that 1 mole is lost in the cathode compartment and that 1 mole is gained in the anode compartment, Table 5 should then read : irreversible cathode 218 - 6 18 242 13.4 reversible cathode 218 - 6 18 233 12-9 electrodes {anode - 222 - 6 18 - 237 - 13.2 electrodes {anode - 222 - 6 18 - 237 - 13.2 These alterations lead to values of S N a of 8.7 (irreversible electrodes) and 8.5 (reversible electrodes).Dr. A. Despi; and Dr. G. J. Hills (Imperial College) (comniunicuted) In reply to Dr. Elton and Dr. Stock we should like to add that the electrodes were irre-versible (Pt) a fact which might have been deduced from our remarks concerning gas evolution. The need to use the appropriate correction for the volume of solvent lost at the electrodes was appreciated and the original typescript of our paper contained the following two equations which summarize the remarks of Dr. Elton and Dr. Stock : A Vcathode cathode solvent = Avobserved - ATNaOH f A/H,O 3 Nevertheless they are right in pointing out the arithmetical error in table 5 A Vszt should certainly be - 237 ml and A V s o ~ v t / A ~ ~ 2 0 - 13.2 and we thank them for making this clear.Dr. G. A. H. Elton (Buttersea Polytechnic London) (communicated) I should like to raise a few points concerning the paper by Despic and Hills The viscosity (va) of water in the narrow capillaries present in the ion-exchange material will probably differ considerably from the normal “ bulk ” viscosity (7). An approxim-ate estimate of y,/~ can be obtained from the equation 1 1 Elton and Hirschler Proc. Roy. SOC. A 1949 198 581 206 GENERAL DISCUSSION For solutions in the concentration range used by the authors the double layer will be compact and we may write (2) where Q is the surface charge per cm2 d is the effective thickness of the gegen-ion layer and the other symbols are defined by Despic and Hills.The value of d at 25" C is given by (3) €5 = 4 ~ 0 d = 2 x 10-3 Fcjrd, d = 3 x 1 O - S ~ i - i 19 whence 2% I + h' rl (4) For ci Q= 1 eqn. (4) should be fairly accurate for r > 25 A and should give a reasonable approximation for capillaries of rather smaller radii. (The equation cannot be used for low concentrations since in this case the double layer is not compact and d is not small compared with r.) Applying eqn. (4) to the values of ANa given by Despic and Hills we obtain the values of y,/r) shown in the table. TABLE 1.-vALUES OF '/,?a/q FOR VARIOUS VALUES OF Ci AND VR (FROM XNa DATA) VR ci = 1 C i = 2 C i = 3 C i = 4 0.2 2.0 2.2 2.5 2.9 0.3 2.4 2.7 3.0 3 *4 0-4 3.2 3.5 3.8 4.3 It might perhaps be argued that A' should be used in eqn.(4) instead of A, but this would lead to even higher values of y,/y (since A' < A). It would therefore appear that it is incorrect to assume that ~ ~ / r l is approximately unity for VR = 0.2 as Despid and Hills do in interpreting their results for A,. The values of q,/y in this system will be lower than those shown in the table (since A > ANJ but I think that the appropriate value should be calculated, and used in the estimation of r. As a result of the use of this correction a rather higher value of Y will be obtained; the correction will become more important as VR is increased. Since ya varies with Ci the author's eqn. (6) should be (5) A linear relation between (Ay)v and ci will therefore be obtained only if 1 O'P2r' 3(ci/y,) (%) = B ( T & is constant.This is not the case for the Na' system; the variation VR of (AA) v with Ci should therefore be described more satisfactorily by eqn. (5) above than by the authors' eqn. (6). In general a linear variation of (Ah), with ci will indicate that ci/ya varies linearly with ci over the range of ci studied and not necessarily that qa = The authors list three possible criticisms of their method of calculation of S N ~ ; a further point should also be considered. For a compact gegen-ion layer the electro-osmotic velocity of the more dilute solution further from the capillary wall may be greater than that of the more concentrated solution near the wall, so that a relatively greater amount of solvent may be transported ci being kept constant by osmotic forces.In this case the value of SNa calculated by the authors will be too high. Finally I should like to suggest that an investigation be made of the dependence of X on the a.c. frequency for systems of this type. It is to be expected that the electro-osmotic contribution to h will decrease fairly rapidly with increasing frequency due to inertial effects. If it should be found that the electro-osmotic contribution can be virtually eliminated by the use of a suitable frequency while = constant GENERAL DISCUSSION 207 leaving the electrolytic contribution practically unchanged this would provide a method of determining A’ independent of the use of radioactive species. Dr. A. Despi; and Dr. G. J. Hills (Imperial College) (communicated) We are grateful to Dr.Elton for his comments on the probable variation of the inter-stitial viscosity with ci and VR. Our elementary investigation of Schmid’s theory of electro-osmosis does not depend upon the assumption that 7 w ~ H ~ O but only that ( 7 ) ~ ~ m constant or (&; M constant (cf. Dr. Elton’s table 1). The value of Y = 7 A evaluated on the basis that 7 = ~ H ~ o was put forward simply to show that the value of (3X/JCi) vR = 0.2 was at least sensible. Dr. J. A. Kitchener (Imperial College London) said With a view to inter-preting membrane properties in terms of molecular structure it is desirable to work with homogeneous cross-linked polyelectrolyte gels rather than with hetero-geneous membranes or even deposited films of insoluble polymer with incorporated ionic substance (e.g.modified collodion membranes). Probably the best material of this class is the transparent polymethyl-methacrylate resin developed by Howe,l which seems to be ideal for fundamental studies. This is the material for which Dr. DespiC and Dr. Hills have now provided some remarkably accurate data covering conductivity self-diffusion and water-transport. Such data should give valuable information about the resin structure but some of the models at present proposed for treating electro-osmotic flow seem unrealistic-for example the treatment of pores as cylindrical capillaries. -. - ‘c / * # . 0 C a r b o n a t o m s COO- a n i o n s @ E r c h a n q o b l c c a t i o n s @ M o b i l e a n i o n s - i - ‘\ Diagrammatic representation of the structure of a pore in a polymethacryIate ion-exchange resin of about 10% cross-linking.The chains are nearly fully extended and the water-content is about 30 molecules of water per cation. Probably the best model for ion-exchange resins is a tangled network of flexible polymer chains permeated by a kind of 3-dimensional electrical double-layer, as shown schematically in the accompanying figure. It should be emphasized that the disposition of the counter-ions will depend on such factors as (i) charge density along the chains (e.g. higher with polymethacrylate resins than in sulphon-ated polystyrenes) (ii) valency and structure of the counter-ions (iii) presence of hydrophobic groups (e.g. aromatic nuclei) (iv) presence of non-ionic hydrophilic groups (e.g.-OH groups in phenol-sulphonic acid resins). An instantaneous picture would show a certain proportion of the counter-ions associated with the fixed charges (probably a minority with alkali-metal ions, varying of course with ionic radius but the majority in the case of the Ba2f salt of Howe’s resin 1). The remainder would be distributed in the pore-volume, 1 Howe and Kitchener J. Chew. SOC. 1955,2143 208 GENERAL DISCUSSION according to the potential gradient. The centre of a pore would be least concentrated in counter-ions and most concentrated in any diffusible " nebenions " present. An interesting piece of evidence in support of this model is provided by the work of Tetenbaum and Gregor 1 on self-diffusion of Kf counterions and C1-nebenions in a sulphonated polystyrene resin the latter moved almost twice as fast as the former whereas in water their mobilities are practically identical.The measured diffusion coefficient and equivalent conductivity of the counter-ions are clearly mean values for the ions in the different situations. Dr. DespiC and Dr. Hills have evaluated from their results a mean velocity of electro-osmotic transport of the counterions-i.e. a streaming of the medium superimposed on the electro-migration of the ions. This seems unobjectionable but it does not seem to be valid to assume that the mobile phase as a whole is moving with this velocity. When a field is applied the counterions in the centres of the pores will move most rapidly and impart momentum to the medium in their vicinity but those near the chains will be retarded and will transport less water.Thus the mean velocity of the water molecules cannot be identified with the quantity men-tioned above and it is not surprising to find cases where more water is transported than that assumption would indicate; in fact this is the result to be expected on the model suggested. Extension of these studies to other types of well-defined membrane should be extremely illuminating. Mr. D. K. Hale and Mr. D. J. McCauley (Chemical Research Laboratory, Teddington) said We have been investigating the properties of a series of ion-exchange membranes of the heterogeneous type containing sulphonated polystyrene resins of different degrees of cross-linking. The membranes were prepared by moulding a mixture of the finely divided ion-exchange resin (2 parts) and poly-ethylene powder (1 part).To obtain an intimate mixture of the two components, the ion-exchange resin and polyethylene were mixed in the presence of xylene which was subsequently removed by vacuum distillation. The powder obtained was then moulded into discs at a pressure of 2000 Ib.jsq. in. and a temperature of 140" C. The membranes swelled readily in water and had a high electrical conductivity (a membrane containing a resin cross-linked with 10 % divinyl-benzene (DVB) had a specific resistance of 136 ohm cm in 0.1 N NaCl solution). The permselective behaviour of these membranes has been studied by both direct and indirect methods. The e.m.f. of the cell has been measured using a technique similar to those described in the papers of Lorimer Boterenbrood and Hermans and Scatchard and Helfferich.The e.m.f. obtained was compared with that of a similar concentration cell without the membrane and the apparent transport numbers of the ions in the membrane calculated from the ratio of the two e.m.f.s and the transport numbers in solution. The results obtained with a mean sodium chloride concentration of 1.ON (c1 = 0.667 equiv./l. ; c2 = 1.333 equiv./l.) are given in table 1 and show the marked effect of the degree of cross-linking on the apparent transport number. TABLE 1 .-APPARENT TRANSPORT NUMBER OF SODIUM ION IN MEMBRANES CONTAINING RESINS OF DIFFERENT DEGREES OF CROSS-LINKING divinylbenzene content apparent transport of cation-exchange number of resin sodium ion 2 % 0,675 10 % 0-854 1 Tetenbaum and Gregor J.Physic. Chern. 1954 58 11 56. 5 % 0.808 15 % 0.88 GENERAL DISCUSSION 209 The apparent transport number (t;) should be equal to t+ - 0.018 mto where t+ is the true transport number nz the molality of the solution and to the transport number of the water.1 We are therefore determining the transport numbers of both the sodium ions and the water by a direct method. A known quantity of electricity is passed through a cell which contains sodium chloride solution and which is divided into two compartments by the membrane. The amounts of sodium ion and water which pass through the membrane are determined and the transport numbers calculated. Results obtained with a commercial membrane (Permaplex C-10) and a laboratory-prepared membrane (2 % DVB resin) and 1 N sodium chloride solutions are given in table 2 which also includes values for t+ calculated from the values of tl and fg.TABLE 2.-TRANSPORT NUMBERS OF SODIUM ION AND WATER IN CATION-EXCHANGE MEMBRANES Membrane f0 (moles per Faraday) t+ direct method ti-(calc. from t i and to) Permaplex C-I0 8 0-9 1 0.95 laboratory prepared membrane 12 0.8 1 0.89 (2 % DVB resin) The agreement between the values of f+ obtained by the two methods is not very good. The discrepancy in the results may be due to the approximate nature of the calculation of t + from the e.m.f. measurements or to errors which arise in the direct method because of concentration gradients which develop during the course of the experiment. FIG.1 .-Relationship between weight-swelling and resin content of heterogeneous membranes (a) expected (6) observed. We have also determined the weight-swelling in water and the density of a series of cation-exchange membranes containing different proportions of a sulphon-ated cross-linked polystyrene resin (5 % DVB) and polyethylene. At the higher resin contents the weight-swelling is greater than would be expected from the 1 Staverman Trans. Faraday SOC. 1952 48 176 210 GENERAL DISCUSSION weight-swelling of the resin alone (fig. l) and the density is less than would be expected from the densities of the wet resin and polyethylene (fig. 2). These results indicate that the swollen membranes contain interstices which are filled with water ; the interstices presumably develop when the dry membrane is allowed to swell in water.At the lower resin contents the weight swelling is lower and the density is higher than would be expected. This suggests that when the membranes contain a high proportion of polyethylene complete swelling of the resin is prevented. 0 2 5 5 0 7 5 100. Resin c o n t e n t b y v o l u m e ( % I FIG. 2.-Relationship between density and resin content of heterogeneous membranes, (a) expected (b) observed. These effects are likely to lead to considerable difficuIty in the detailed inter-pretation of results obtained with heterogeneous membranes and it will probably be necessary to interpret their electrochemical behaviour in terms of a model similar to that described in the paper by Spiegler Yoest and Wyllie.Dr. J. E. Salmon (Battersea Polytechnic London) (communicated) In a reply to my comment on the papers by Bergsma and Staverman and by Scatchard and Hemerich Prof. Scatchard suggested that since the porous plug described in the paper by Spiegler e f al. behaves like a membrane in some respects differences in behaviour between heterogeneous membranes which he likens to the porous plug and homogeneous membranes are not to be expected. Reference to the left diagram of fig. 2 in this paper shows however that there is little similarity between the heterogeneous membranes and porous plugs. The shaded region in this diagram (fig. 2) would for a heterogeneous membrane correspond to the hydro-phobic non-conducting matrix. Hence the alternative paths of conduction through bulk liquid with normal properties (of dielectric constant etc.) are not available in the heterogeneous membrane for which as I pointed out earlier electrical conduction between the beads is through films which are likely to have abnormal properties.Thus although the porous plug resembles the heterogeneous mem-brane in being " leaky " in other respects it is probably more like a " homogeneous " membrane. It still seems to me very doubtful if it is correct to assume that the behaviour of heterogeneous membranes is similar to that of " homogeneous " ones. Indeed the comments of Prof. Gregor Dr. Tye and others (in discussion) suggest that important differences in properties have already been observed GENERAL DISCUSSION 21 1 Dr. G. Scatchard (M.I. T. Cambridge Mass.) (communicated) When I said that the porous plug serves as an approximate model of a heterogeneous mem-brane and that there is no membrane which is not somewhat heterogeneous I was not using the term “ heterogeneous membrane ” in the sense of Dr.Salmon as a membrane with a non-conducting matrix but as what I will hereafter call a “ non-uniform membrane ”. Non-uniformity means a variation in “ pore size ” charge density etc. within the conducting region if the membrane is heterogeneous. I believe that non-uniformity is much more important than heterogeneity and that a heterogeneous membrane may be very uniform or a homogeneous membrane may be very non-uniform. If all the shaded area in fig 2 were non-conducting matrix the plug would represent a very uniform heterogeneous membrane.The original high pressure membranes of Wyllie and Patnode are probably of this type. If the matrix does not fill all the shaded area leaving conducting solution regions at the surfaces of the beads these regions will behave like large pores or cracks in a homogeneous membrane. For either one the model has to be modified to make the properties of the conducting solution different from that of the external solution. Although the mixed path (1) passes through a series of Donnan equilibria, they alternate in sense and the concentrations are so little different between two adjacent ones that all but the first and last are nearly cancelled out. Many of the properties of a very non-uniform membrane average out to appear much like those of a uniform membrane if the regions of non-uniformity are small relative to the thickness of the membrane.Dr. R. Schlogl (Guttingen) said The discussions on porous plugs and similarly constructed membranes are of particular interest to me as Herr Koschel 1 from our research group has recently completed physical measurements on ion exchangers of phenolsulphonic resins from which it is evident that even these optical clear materials possess an inhomogeneous granular structure. This conclusion follows both from recordings of stress-strain diagrams and from light-scattering measurements. According to these investigations the denser granular regions must in any case be smaller than about 10-5 cm i.e. roughly of the order of magnitude of normal colloids. Each of these dense regions is surrounded by electrical double layers and separated from the others by channels of lower density and lower membrane charge.This agrees well with the view put forward by Spiegler et a/. that even membranes which are apparently homogeneous show characteristics of porous plugs. Mr. W. D. Stein (King’s College London) said I should like to consider to what extent the porous plug system of Dr. Wyllie and Dr. Spiegler can be considered as a model for the membrane of the red blood cell. It is well known that the red cell manifests a high permeability towards certain anions e.g. chloride and bicarbonate and a far lower permeability (of the order of 104 lower) towards cations. Hence as a first approximation the red cell membrane may perhaps be regarded as a positively-charged ion-exchange membrane with a slight leakiness towards cations.In the first place it may be possible to compare the behaviour of the red cell membrane with that of cationic ion-exchange membranes of different charge density and containing different types of charged ions. In this way it may be possible to estimate the number and types of charged groups present in the red cell membrane and to compare this with the known molecular architecture of the membrane. Thus, insight into the nature of the cell membrane may be gained as well as possible confirmation of the cation-exchange model. Second studies on permselective membranes show that the selectivity between ions of opposite charge of such systems decreases with increasing concentrations of the bathing ions.It would be of interest to study the selectivity of cell membranes at varying concentrations of 1 publication being prepared. Several possibilities arise from this viewpoint 212 GENERAL DISCUSSION bathing electrolyte since such a study may confirm the proposed model. Finally, since the cations are here considered to be leaking through the ion-exchange membrane any selectivity between cations that the cell membrane manifests should be considered as a selectivity of leakiness rather than the conventional selectivity between readily permeating ions. Hence better models for cell membranes may be developed if the differential leakiness of synthetic ion-exchange membranes is considered rather than their differential Permeability. It is likely however, that such a model is far too simple and that we should regard the cell membrane, as far as its ion permeability is concerned as a mosaic of cationic and anionic permselective membranes.Dr. G. A. H. Elton (Battersea Polytechnic London) (communicated) The values of plug potentials calculated by Spiegler Yoest and Wyllie show greater deviations from the observed values at low concentrations than they do at high concentrations; this fact is contrary to the authors’ expectations. It seems to me that the deviations are due to the fact that it was assumed implicitly in deriving eqn. (21) that KR is a constant independent of uW. This seems unlikely as the specific conductance of an ion-exchange resin is usually a function of the activity of the solution with which it is in contact.It would appear likely therefore, that the value of KR will be 3.0 x 10-2 ohm-1 cm-1 only at the isoconductance point where the mean ion activity is 0.24 and not as the authors have assumed, over the whole activity range. It is seen from the authors’ table 1 that the difference between the observed and calculated potentials is within experimental error for the activity range 0.1 5 to 0.45 (which includes the isoconductance point) and also for the higher range 0.45 to 1-35. Although KR may not be 3.0 x 10-2 ohm-1 cm-1 in the latter range the error in potential introduced is small as most of the current is carried by the solution (element 3 in fig. 2 ~ ) . For moderately low activities (below the isoconductance point) errors in K~ become more important since an appreciable fraction of the current is carried by the resin.Finally at very low activities where uW becomes very small the plug potential approaches that of an ideally cation-permeable membrane; the actual value of KR then becomes unimportant so that the difference between the observed and calculated potentials should decrease again. These conclusions are confirmed by the results given in the authors’ table 1, which show that for activities below the isoconductance point the difference be-tween the observed and calculated plug potentials increases to a maximum and then falls again as very low activities are reached. To obtain agreement between the observed and calculated potentials it would be necessary to use values of K~ which decrease as K~ decreases although this might make the integration of eqn.(16) very diffcult. Although the experimental values of KO shown in fig. 3 agree with the line obtained by a calculation based on the assumption that KR is constant this does not justify the assumption as the equation used in the calculation (eqn. (2)) contains thee independently adjustable parameters while the form of the equation ensures that the line must pass through the isoconductance point. In order to interpret fully the data on plug conductance and plug potentials it will be necessary to know K~ as a function of K ~ . The required relationship could be determined experimentally e.g. by a method similar to that of Despic and Hills,l or might perhaps be obtainable from the existing values of KO and K ~ if suitable assumptions are made.For example it should be possible (except perhaps for very low values of K ~ ) to neglect the contribution to KO from element 2 ( fig. 2B) in view of the very low area of contact of the resin particles (actually equal to zero for perfect spheres). To do this b is set equal to zero so that only two independent constants (viz. c and d ) characteristic of the plug have to be determined. From eqn. (2), it is seen that c is equal to the limiting value to which the ratio K O / K ~ tends at high 1 DespiC and Hills this Discussion GENERAL DISCUSSION 21 3 values of K ~ . The constants c and d are related in a way which depends on the tortuosity factors for elements 1 and 3 (fig. 2 ~ ) so that d may be determined from c if the geometry of the plug packing is known (e.g.for close-packed spheres). Hence eqn. (2) can be used with b = 0 to determine KR as a function of K~ (and hence of activity in the solution) using the experimental values of KO shown in Dr. K. S. Spiegler (Pittsburgh) (cornrnunicated) In reply to Dr. Salmon in-asmuch as plugs of ion exchange resins have appreciable conductance even when they are immersed in distilled water (fig. 3 and ref. (5) (18) and (19) of our paper) it must be assumed that counter-ions alone can migrate from one bead to another at the point of contact and that the presence of mobile co-ions is not necessary to effect electrical conductance in this case. This mechanism of migration is also borne out by the phenomenon of " contact exchange " ; viz. the relatively rapid exchange of counterions between solid particles of an ion-exchange resin when the latter are stirred together in distilled water.It is believed that the small amounts of hydrogen and hydroxyl ions in distilled water play no important part in this transport. Ing. J. Straub (Utrecht) said Much work has also been done in the Nether-lands on transport numbers of ions in membranes in connection with the electro-dialysis of brackish water. These numbers are ratios of mobilities. Absolute numbers are given by experiments in which only one ion permeates. This can be effected by placing electrodes specific to the particular ion in front and behind the membrane and passing a constant direct current through the system. When a steady state has been reached only the specific ion moves and its concentration difference is a measure of its mobility in the membrane.Complications arise, if the concentrations are not sufficiently low. Such complications however, caused by lower activities or complex building are in themselves interesting in connection with specific phenomena occurring at membranes in living organisms. 1 Dr. F. Helfferich (Cuttingen) said As an explanation for the decrease in efficiency with decreasing current density encountered when current density is low Kressman and Tye suggest a " concentration diffusion " of NaCl across the membrane according to the equation (1) Eqn. (1) gives a linear relation between the diffusion flux QD and the concentration difference (Cl - C2) between the two solutions which is not obtained from the corresponding equations derived by Mackie and Meares,2 and Manecke and Heller.3 There are two possible mechanisms for electrolyte diffusion across a charged membrane.Mackie and Manecke deal with a single phase (" homo-geneous ") membrane in which the diffusion must occur through the resin itself; the rate is governed chiefly by the diffusion constant of the anion and the con-centration gradient within the membrane and should decrease faster than (C1- C,) with decreasing C1. For " heterogeneous " membranes consisting of resin par-ticles embedded in an inert binder an alternative mechanism is a diffusion which takes place through pockets of solution between resin and binder being thus unobstructed by fixed charges. The latter mechanism which is evidently assumed by the authors leads to a linear relationship as in eqn.(1). Actually both mechanisms should be effective in a " heterogeneous " membrane but the con-stancy of the quantity D (as seen from the linear plot in fig. 7) indicates that the second prevails in the membranes used by the authors. It is suggested however, that the quantity D be called a permeability constant rather than a diffusion constant the latter being defined conventionally by an equation similar to (1) but containing the fraction of area available for diffusion and a tortuosity factor. fig. 3. Q D = DA(C1 - C ~ ) / S . 1 Straub Chem. Weekblad. 1941 47 1041 ; 1956 52 in press. 2 Mackie and Meares Pruc. Roy. SOC. A 1955 232 510. 3 Manecke and Heller this discussion 214 GENERAL DISCUSSION Prof.Karl Sollner (Bethesda Maryland U.S.A.) said The conclusions of the paper by Hutchings and Williams seem to me to go too far. I refer to the state-ment " The study of both equilibrium potentials and the rate at which they are established suggests that the present membrane electrodes have little to recommend them for quantitative use ". While I certainly do not want to contend this con-clusion as far as it applies to the membrane electrodes with which the authors have worked I feel that no such sweeping statement applies to the various types of permselective collodion matrix membranes that were developed in our laboratory. If used judiciously these membranes are rather useful as membrane electrodes. 1 Of course I must also refer to the excellent quantitative pioneering work by Marshall and collaborators which was carried out with clay membranes,:! and Dr.Wyllie I hoped would make some remarks about his experience with membrane electrodes. In particular I should like to draw your attention to a fairly detailed study by Dr. Gregor and myself in which we have evaluated many points of interest in the practical use of membrane electrodes.3 The usefulness of these membranes as membrane electrodes seems to me evident also from such papers as those by Carr Johnson and Kolthoff,4 Chandler and McBaine,s Snell,6 and particularly the extensive studies by Carr and collaborators on the binding of ions by protein,7 and also from the recent similar work of Lewis.8 The ionic selectivity of the permselective collodion matrix membranes is ex-tremely high-with the most recent types of the order of 10,000 1 to 50,000 1 in 0-01 N KCl solution and 500 1 to more than 1500 1 in 0.1 N KCl solution.9 Their water permeability is so low as to cause seemingly no complications which would not be well within the range of normal analytical accuracy.The problem of gross leakage of bulk solution does not arise with the test-tube-shaped mem-branes which we use ; likewise contamination of the experimental solutions with material released by the membrane does not occur because of the rather low water content and the low exchange capacity of our membranes-about 1 p-equiv.lcm2. With properly prepared membranes final stable concentration potentials (at least with univalent ions) are obtained regularly within a few minutes in many instances virtually instantaneously.That these potentials very closely approach the theoretically possible value over wide ranges of concentration was shown in numerous papers. The current limitation of the ready applicability of permselective collodion matrix membranes as membrane electrodes aside from those inherent in any such electrometric measurements,3 lies in our inadequate knowledge of their behaviour with divalent polyvalent or very large ions. Nevertheless Carr has used such membranes extensively with good success in the study of the binding of alkali earth metal ions and so also did Lewis.* 1 Sollner J . Amer. Chem. SOC. 1943 65 2260. 2 Marshall J. Physic. Chem. 1939 43 1155 ; 1944 48 67. Marshall and Bergman, J.Amer. Chem. Sac. 1941 63 191 1 ; 1942 64 1814 ; J. Physic. Chem. 1942 46, 52 325. Marshall and Ayres J. Amer. Chem. SOC. 1948 70 1797 et seq. 3 Gregor and Sollner J. Physic. Chem. 1954 58 409. 4 Cam Johnson and Kolthoff J. Physic. Chem. 1947,51,636. 5 Chandler and McBaine J . Physic. Chem. 1949 53 930. 6 Snell Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York Chapman and Hall Ltd. London 1955) p. 284. 7 Carr and Topol J. Physic. Chem. 1950 54 176. Carr Arch. Biochem. Biophys., 1952 40 286; 1953 43 147; 1953 46 417 424. Electrochemistry in Biology and Medicine ed. Shedlovsky (John Wiley and Sons Inc. New York; Chapman and Hall Ltd. London 1955) p. 266. 8 Lewis Ph.D. Thesis (Georgetown University Washington D.C.1955). 9 Neihof J. Physic. Chem. 1954 58 916. Gottlieb Neihof and Sollner J. Physic. Chem (Colloid Symposium Issue 1956) in press GENERAL DISCUSSION 21 5 I think that commercial-type ion-exchanger membranes (which after all are prepared in general for different purposes to fulfil different requirements) are not nearly as suitable as membrane electrodes as are the permselective collodion matrix membranes. Anyone interested in the solution of problems which might be solved by means of membrane electrodes should explore the usefulness of this latter type of membranes. Incidentally the word “ permselective ” which we coined quite some years ago,l has been used by now in a goodly number of papers ; it is not trade marked ; maybe we do not need the very similar term “ permiselective ”.Dr. T. R. E. Kressman (The Permutit Co. Ltd. London) (partly communicated) : I would like to correct two errors made by Hutchings and Williams in their interpretation of some statements in previous papers of Dr. Kitchener and myself. In their experimental section they refer (their ref. (6)) to our paper2 and state that we observed slow equilibrations between ion exchange granules and bivalent ions. A few lines below fig. 2 they quote the same reference as providing evidence for the weak affinity of sulphonic resins for Mg2+ as compared with H+. In fact both these effects were observed with a resin specially prepared to contain very few sulphonic groups which were consequently spaced widely apart. With normal resins including a sulphonated polystyrene (of composition virtually identical to the membrane used by Hutchings and Williams) rapid reaction and high affinity were observed with bivalent ions.A few lines above their fig. 3 they quote our same paper as giving the order of affinity Ba2+ > K+ > Na+ > Mg2+ in fact the order we observed was Ba2+ > Mg2+ > K+ > Na+ in the concentrations relevant to Hutchings and Williams’ work. All the evidence of our work is that Mg2+ behaves quite normally both as regards affinity and rate of attainment of equilibrium and does not support the apparent abnormality observed by Hutchings and Williams. Hutchings and Williams attempt to explain the abnormalities on the basis of the large size of the magnesium ion. However they state that the diethyl-ammonium ion behaves like the potassium ion (i.e.normally) yet the diethyl-ammonium ion is considerably larger than Mg2+ its major diameter 4 being 7.2A. Consequently their explanation does not appear to be valid. The ab-normal behaviour might be due to the unusual manner in which they have used the membrane viz. soaked with 0.1 N metal chloride solution which must inevitably diffuse out into the ambient electrolyte solutions and so affect the membrane potential. Hutchings and Williams remark upon the peculiar shape of curve I11 in their fig. 3. This is most probably due to the fact that the potential was measured with the membrane in the diethylammonium form and immersed in KC1 solution. Thus they had the system referred to by Scatchard and Helfferich in their paper as an “ abnormal cell ” whose potential is strongly dependent upon stirring among other factors.The shapes of the curves I I1 and IV are probably also influenced by this factor. I agree with Dr. Sollner that Hutchings and Williams are not justified from the results of their work in stating that “ the present membrane electrodes have little to recommend them for quantitative use ”. I believe their experimental technique is responsible for their disappointing results since other workers using membranes of this type and more orthodox techniques have obtained more satisfactory results. Dr. N. Krishnaswamy (India) said According to Dr. D. Hutchings and Dr. R. J. P. Williams there is a discrepancy noted for the membranes in the sodium magnesium forms when their equilibrium potentials and the rate of attain-ment of equilibrium are considered.Taking into consideration ionic size they This was supported by other work.3 1 Carr and Sollner J. Gen. Physiol. 1944 28 119. 2 J. Chem. SOC. 1949 1201. 3 Faraday SOC. Discussions 1949,7 90. 4 Kressman and Kitchener J. Chem. SOC. 1949 1209 216 GENERAL DISCUSSION studied a membrane with roseocobaltic ion comparable to the hydrated mag-nesium ion. They find that while the magnesium form of the membrane attained equilibrium quickly the membrane in the roseocobaltic form did not. This may be due to the inability of the potassium ion from the solution to displace the com-plex ion while it can easily displace sodium or magnesium ions. Working with salts of different valency an " abnormal cell " is set up as explained by Prof.Scatchard and Helfferich. Experiments with membranes of different porosity will help in explaining the influence of ionic size of the bound ions (simple and complex ions). Fig. 1 and 2 of the authors show the relationship between the membrane potential and ratio of the activity of potassium chloride on either side of the membrane. The larger deviations obtained with barium chloride are explained on the basis that the chloride ion is carrying part of the current perhaps as BaClf. It has been shown already 1 that cation-exchange membranes in different forms (i.e. with different bound cations) absorb different quantities of chloride ion, Thus for the same external concentration the barium form of the membrane absorbs more chloride ions than when it is in the lithium or sodium forms.In the alkali metal series the uptake is found to be in the order Cs > Rb > K > NH4 > Na > Li and in the alkaline earth group the order is Ba > Sr > Ca > Mg. An explanation for this difference in uptake in terms of the hydrated ionic radius of the bound cations has been provided.2 This study was conducted to predict how far the ideal permselective property of the membrane would be affected by different bound cations. The results obtained by Hutchings and Williams have confirmed our findings. Dr. F. Helfferich (G~ittingen) said The conclusions of Hutchings and Williams concerning the analytical application of ion exchange membranes seem somewhat too pessimistic when compared with numerous publications in which more encouraging results have been reported.Reference may be made to Schindewolf and Bonhoeffer,3 who discuss in detail the advantages and limitations of this method. The deviations found by the authors could be due at least partly to (i) the use of membranes primarily designed for other purposes (ii) the intro-duction of the liquid junction not necessary for potential measurements and (iii) the equilibration with 0.1 N solution previous to measurement. In the derivation of the theoretical potential values two assumptions are made equi-librium between the solutions and the adjacent membrane surfaces and steady state within the membrane. Generally this stage is reached faster and with less concentration change in the solutions when the membrane is equilibrated previous to measurement with a mixture of both solutions or when a twofold membrane sandwich is used each membrane being equilibrated previously with the solution with which it is in contact during the measurement.Dr. R. J. P. Williams (Oxford) said I am not sure that I understand the remark of Dr. Helfferich that the membranes we have studied were primarily designed for other purposes. Introducing these particular membranes Kressman 4 claimed that they were useful for the very purposes we had in mind during the experiments. The membranes were obtained from Dr. Kressman. I believe that the second point made by Dr. Helfferich is also misleading. The cell we described has three electrodes. It is possible to measure three poten-tials and one of these the membrane potential from direct measurement does not include a liquid junction.It is equivalent to a proper sum of the other two possible potentials. The use of the concentration cell potential which we measured also and which does include a liquid junction was that it enabled us to study any changes in the concentration of the solution bathing the membrane at the 1 Krishnaswamy J . Sci. Ind. Res. (India) By 1954 13 722 ; J . Physic Cliem. 1955 59 2 Krishnaswamy communicated for publication. 3 2. Elektrochem. 1953 57 216. 187 ; Current Sci. 1955 24 234. 4 Nature 1952 170 150 GENERAL DISCUSSION 217 same time as we measured the membrane potential. We found this precaution advisable although it is unusual. In all measurements we read the values of the three potentials in order to check the electrodes.The third point also raised by Dr. Kressman concerns the preparation of the membranes. Very little has been said on this topic in the discussion and yet I believe it is an important factor in the.study of membranes if high accuracy and reproducibility of potentials is wanted. We did not require to understand the origin of the potentials we obtained. We wished to have an analytical method. We could not prepare membranes by bathing them in very strong salt solutions for this leads to the absorption of neutral salt. Our method which appears to be very similar to that of many others was to treat the membranes with 0.1 molar salt until the washings were free from hydrogen ions. With the alkali metal cations this leads to the establishment of potentials very little different from those observed by many others but the method was still not analytically satisfactory.Dr. Helfferich is correct when he points out that it is advantageous to treat the membrane with mixtures of the salts under study but even in this case one side of a membrane in a bi-ionic cell will come to equilibrium before the other. It is easy to demonstrate slow rates of establishment of potentials even under the very rapid stirring we used throughout our measurements. I think that this also answers another of Dr. Kressman’s questions. If a membrane does not establish a potential rapidly it is unlikely to be of great practical value for the type of study we had in mind. I feel that there is not such a difference between our statements and those of Dr.Kressman as he would suggest. First we do not find slow equilibrium with magnesium ions. Secondly we make no comment on the absolute affinity of the resin for magnesium but we suggested that it is bound weakly (as compared with other cations) as an explanation of the peculiarities of the magnesium mem-branes. We used the reference to Dr. Kressman’s work as an illustration of parallel findings. Thirdly there is the point about the relative affinity for mag-nesium and sodium ions. The equilibrium constants which Dr. Kressman quotes in his paper were used as measures of affinity of ions for his exchangers. There is an arbitrary character in such a comparison but it does give the order we give. It must be remembered that we did not make a thorough study of exchange rates under different concentration conditions ; we only wished to know if a potential was established instantaneously.I do not understand Dr. Kressman’s remark about the concentration conditions relevant to our work for the concentration of magnesium ion in the membrane and in the solution were not measured by us. In the discussion of size factors and their effect on the uptake of cations Dr. Kressman has left out the fact that magnesium is divalent and diethyl ammonium ion univalent. It is readily shown that for ions of the same size the one of higher charge comes into equilibrium more slowly. This is made clear by the study with the cobaltic ion. Finally we have no comment to make upon the suitability of Dr.Sollner’s membranes. We have had no chance of studying them and they have many properties different from those of the membranes with which Dr. Kressman supplied us. We are quite convinced however that the latter membranes are not suitable for an accurate determination of activities of ions in solution. The data we have plotted in fig. 1 of our paper are very like those obtained by other workers in this field and are unsatisfactory. The data in fig. 3 were obtained under conditions of rapid stirring and they can be compared with the observations quoted by Dr. Helfferich under these conditions. Prof. Dr. K. F. Bonhoeffer (Giittifzgen) said I would like to mention some experiments carried out recently by Dr. Woermann in our laboratory. Since we are interested in membranes which show selectivity with respect to different alkali metal ions D.Woermann prepared membranes from an ion exchanger described In many cases it was not 218 GENERAL DISCUSSION by Skogseid,l which adsorbs K+ in preference to Na+. This ion exchanger con-tains a group with a configuration similar to dipicrylamine a precipitating agent for K+. Woermann prepared the membranes by embedding the powdered ex-changer in polyethylene ; the weight ratio exchanger/polyethylene was 6 4. The membranes are red opaque and brittle. In these membranes the self-diffusion coefficient for diffusion of K+ with the suggestion of K+ is-smaller than that of Na+ and the activation energy larger than that of Na+ (fig. 1). These results are consistent that K+ is more firmly held by the exchanger than Na+.FIG. 1. The experimental bi-ionic potential across these membranes between 0.1 N NaCl and KC1 solutions is 20 mV the NaCl solution being positive. If only the diffusion potential within the membrane would be responsible for the total mem-brane potential the higher mobility of Na+ within the membrane would lead to a potential of the opposite sign. However the total membrane potential is the sum of this diffusion potential and the difference of the two Donnan potentials at the phase boundaries. The preference of the membrane for K+ (which is equivalent to an activity coefficient within the membrane lower for K+ than for Na+) results in a Donnan potential on the side of the KC1 solution which is con-siderably smaller than that on the other side.The sign of the experimental potential is thus explained. Potentials across these membranes were also measured between a 0.1 N KC1 solution and KC1 + NaCl mixtures total concentration 0.1 N. The results are given below. They are compared with theoretical values calculated from the equation for multi-ionic potentials 2 assuming &a/& = const. = 1.2 (obtained from self-diffusion measurements) and r N a / r K = Const. = 2.7 (estimated from equilibrium data). potential (mV) expt. calc. left side right side 5 x 10-2 N KCl 5 x 10-2 N KC1 0 0 4 3.0 5 x 10-2 , 4 x 10-2 N KCl 1 x 10-2 N NaCl 10 8-4 5 x 10-2 , 2.5 X 10-2 N KCl 2.5 x 10-2 N NaCl 18 15.1 5 x 10-2 )) 1 x 10-2 N KCl 4 x 10-2 N NaCl 5 x 10-2 , 5 x 10-2 N NaCl 20 20.8 1 A.Skogseid Thesis (Oslo 1948), 2 R. Schlogl and F. HeHerich contribution to this Discussion GENERAL DISCUSSION 219 Prof. Dr. K. F. Bonhoeffer (Giittingen) (partZy communicated) G. Richter in our laboratory has recently succeeded in preparing membranes which behave very differently with respect to chlorine and bromine ions. The difference is so obvious that it may be observed without the aid of any measuring device. When the membranes contain chlorine ions they are voluminous soft, mechanically unstable and have a high water content and when they contain bromine ions they are dense rigid and stable and have only a small water content. Richter made use of the fact that soaps or generally speaking, amphipatic substances show a 6o remarkable power of discrimi- 2o H20 nation for similar ions.For example the different solubility of the ordinary potassium and 'O sodium soaps is very well known. The simplest way to prepare membranes containing amphi- 2o patic substances is to equilibrate a loosely cross-linked ion ex-changer with soap solution. For example we prepare a cation ex-acid with a small amount of P H 100 " 2 0 changer by polymerizing acrylic 2 . 0 4 . 0 6.0 divinylbenzene SO that the Pores FIG. 1.-The dependence on pH of water content of the exchanger are large enough of polyacrylic acid exchanger in a solution of to take up soap molecules such cetyltrimethylammonium chloride (CTAC) and as cetyltrimethylammonium cetyltrimethylammonium bromide (CTAB) resp. chloride or bromide.Now if we take this cation exchanger in the sodium form and immerse it in a solution of chlorine or bromine soap the sodium cations are exchanged by soap cations. In addition to these more soap molecules are adsorbed due to the van der Waals forces exerted by the soap ions already taken up by the exchanger and by the exchanger network itself. These newly adsorbed soap molecules carry halide anions with them for reasons of electroneutrality. As the soap cations are big and immobile compared with these anions the former cation exchanger is trans-formed into an anion exchanger. The new character of the exchanger can be shown by a reversal of the membrane potential between two alkali halide solutions of different concentration. This new anion-exchanger shows the above-mentioned discrimination between chlorine and bromine ions.It is intimately connected with the critical pheno-menon of micelle formation in soap solution. We have reason to assume that there exists in the interior of the exchanger a sort of critical concentration for the formation of soap micelles which is different from that in the external solution and lower for chlorine soap than for bromine soap. We may vary the soap concentration in the exchanger by varying the concentration of fixed charges, which in our case are carboxyl groups; this is easily done by varying the pH of the solution. Thus by altering the pH we alter the soap concentration in the exchanger. We believe that the two above-mentioned membrane types the one with high and the other with low water content differ from each other in that the mem-brane with low water content has shrunk due to the formation of soap micelles.I should like to show the results of some experiments of Richter in which an original cationic exchanger on a base of polyacrylic acid is transformed by 220 GENERAL DISCUSSION cationic soap namely cetyltrimethylammonium halide into an anionic exchanger. In the range of pH = 3 to pH = 4.5 this new anionic exchanger discriminates very remarkably between bromine and chlorine ions. The diagram shows the abrupt change in the water content at a critical pH, that is at a critical soap concentration different and characteristic for each halide ion. Here the water content changes from about 90 % to 25 % and we know other systems where the change is still greater.I need not mention that the change of water content means a change of all properties of permeability and conductivity, which will now be investigated. As the soap is firmly held by the exchanger the discrimination is found not only when the exchanger is immersed in soap solutions but also in salt solutions, provided these contain a small amount of soap. We believe that it is possible to synthesize corresponding membranes which behave differently with respect to sodium and potassium ions. Research is being made along these lines. Prof. H. Thiele (Kid University) (communicated) An important factor seems to be structure since artificial membranes are made up of disordered particles, but natural membranes have well-ordered particles in a particular type of fine structure as can be shown by electron micrographs.Gels with ordered particles could be built up by diffusion of gegenions into a solution of polyelectrolytes. These ionotropic gels represent a synthetic micellar structure and behave like gels in tissues. Since membranes are plate-shaped gels, this gives a method of preparing artificial membranes with well-ordered particles. A further step has been made by preparing gels and membranes with pores and capillary tubes of uniform size and shape. The gel formation formally follows the equation : 2 Na alginate + CuC12 $ Cu (a1ginate)z + 2 NaCl + water first phase second phase. polyelectrolyte + ions $ gel ionotrope + 2 reaction product. Na alginate and CuC12 yield the ionotropic gel or membrane-this gel now forms a special phase. The NaCl and water of dehydration form the second phase. The two phases are separated from another by a demixing of droplets. The water of dehydration arises from the transition from sol to gel. Now in the growing gel the second phase in the shape of droplets gives rise to a structure of many fine round tubes lying parallel to each other starting in a zone near the ions and ending in the sol. The gel forms the walls of the tubes and the second reaction product gels; the second phase as droplets gives rise to a structure of many fine round tubes lying parallel to each other starting in a zone near the ions and ending in the sol. The gel forms the walls of the tubes the second reaction product with the water of dehydration form the contents of the capillary tubes as shown in fig. 1 and 2. If our explanation is right then the pore size must depend on the concentra-tion of the second reaction product NaCl -t water. ' Indeed we found a strong de-pendence the diameter growing with increasing concentration of NaCl. The size of the pores depends on the gegenions giving the series C1 < Br < NO3 < SO4 < formate < acetate the other ions not being so important. Non-electrolytes and detergents have no effect on the pore size. H-ions and non-electrolytes do not yield pores at all. The diameter was found to vary between about 3 and 300 micron depending on the concentration of the polyelectrolyte. One can get tubes with a length varying from a few microns to 10 rnm. The membranes can be obtained simply by means of a Graham dialyser FIG. 1. FIG. 2. Capillary tubes of uniform size and shape by a droplet demixing from diffusing counterions in a polyelectrolyte during gel formation FIG. 1.-In directions of the diffusing FIG. 2.-Vertical section showing the ions x 25. uniform diameter and the parallelism, of the many thin tubes x 25. [To face page 220

ISSN:0366-9033    

DOI:10.1039/DF9562100198

出版商:RSC    

年代:1956

数据来源: RSC