摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 105- 1 13 Kinetics of Heterogeneous Nitration in Emulsions BY JOHN E. CROOKS* AND JOHN M. CHISHOLM Chemistry Department, King's College, University of London, Strand, London WC2R 2LS Received 1 st December, 1983 The two-phase nitration of aromatic hydrocarbons has been studied in a model system consisting of a solution of toluene in hexane dispersed as an emulsion in aqueous sulphuric acid, in the concentration range 63-76 wt%. Reaction half-lives were found to range from 400 to 0.4s over this acid concentration range. The progress of the reaction was monitored by spectrophotometric determination of the nitrotoluenes produced ; a stopped-flow apparatus was used for the faster runs. The experimental results are compared with those calculated from a theoretical model.The aqueous acid phase around each organic droplet is subdivided into a number of concentric spherical shells. The change in the amount of toluene in each shell owing to diffusion in and out and to reaction is calculated for a large number of short time intervals, during each one of which the concentration is assumed constant. Good agreement between theoretical and experimental results is obtained except for the fastest runs. For these, diffusion is faster than predicted for stagnant conditions, showing that stirring is occurring within 1 pm of the liquid/liquid interface. The nitration of benzene is a reaction of great technical importance, being the first step in the production of aniline dyes. The nitration of benzene and its methyl derivatives has thus been the subject of much research.The reaction is between two immiscible liquids, the aromatic hydrocarbon and the nitrating mixture, which is a solution of nitric acid in aqueous sulphuric acid, of approximate composition 60 wt% acid. Reaction occurs in the aqueous phase in a surface region closely adjacent to the interface with the organic phase.' The mechanism involves attack on the aromatic molecule by the nitronium ion, NO,', which is insoluble in the organic phase, whereas the aromatic hydrocarbon is sparingly soluble (ca. lop3 mol dmp3) in the aqueous phase. The reaction scheme may be represented by k ; HN03 +H' NO; +H20 Xr; NOl+ArH ArHNOi kLI k 12 ArHNOl A HArNO; HArNOl __* H4+ArNO2 where [ArHNO,]' and HArNO,' indicate reaction intermediates whose nature has been the subject of much research.It is fairly well established3 that HArNO; has the Wheland structure. The nature of ArH NO,' is less certain. It could be a simple encounter complex4 (ArH, NO:) or an ips0 ~omplex.~ If [NO,'] is assumed to be 105106 HETEROGENEOUS NITRATION IN EMULSIONS constant, i.e. the steady-state assumption is made, the overall rate of nitration is given by (1) -d[ArH] - ki kikj [ArH][HNO,](H+) - d t kL, (H,0)(kL2 + k : ) + k;k;[ArH] where (H,O) and (H') are the activities of H 2 0 and H', respectively. In concentrated aqueous sulphuric acid the activities of these species cannot be assumed to be equal to their concentration, not even as a first approximation. However, since (H20) and (H') may be considered to be constant during the course of the reaction, eqn (1) may be simplified by the substitutions k , = k',(H') (2) k2 = kl(H')k/k~/[k'l(H20)(k;+kS)] (3) to give -d[ArH] d t = kl k,[HNO,][ArH]( kl + k,[ArH]).(4) There are two limiting cases, depending on the relative magnitudes of k , and k2[ArH]. Ih solutions of high concentration in sulphuric acid, (H20) is low and (H') is high, so that k2[ArH] >> k , . First-order kinetics are observed, since eqn (4) reduces to ( 5 ) -d[ArH] d t = kl[HN03]. In solutions of relatively low concentration of sulphuric acid, k,[ArH]<< k , and second-order kinetics are observed: -d[ArH] d t = k,[HNOJ[ArH]. For toluene, the transition from first-order to second-order kinetics occurs at ca. 78% sulphuric acid. In aqueous sulphuric acid of this composition, k2= 1500 dm-' mol-' s-l, [ArH] = 5 x low4 mol dm-, for a saturated solution and kl = 0.6 s-I.Benzene, being less reactive than toluene, has k2 values too low for first-order kinetics, and nitration of benzene is second-oider for the whole range of sulphuric acid concentrations. The nitration of toluene has been studied thoroughly6 in homogeneous solution in aqueous sulphuric acid in the concentration range 52.5-80 wt% acid. However, the nitration of aromatic hydrocarbons in bulk is a two-phase process, so the interfacial kinetics must also be studied. Various theoretical models of stirred reactors have been produced, but these are semi-empirical and they introduce quantities which may only be evaluated from the kinetic measurements themselves, such as a mass-transfer coefficient7 or the volume and surface area of an eddy in a rapidly stirred mixture.* The aim of this study is to produce a theory for which all the parameters may be evaluated by non-kinetic experiments and which may be tested by comparison with experimental results for a well defined system.THEORETICAL DESCRIPTION The organic phase is considered to consist of a set of spheres of uniform radius, stationary in a continuous aqueous medium. A small proportion of ArH and ArNO,J. E. CROOKS AND J. M. CHISHOLM 107 is present in the aqueous phase but no NO,’ is present in the organic phase. Nitration occurs when the ArH molecules diffuse away from the surface of the spheres and meet NO: in the aqueous phase. The ArN02 produced diffuses back into the organic phase.An ArH molecule can only diffuse a short distance into the aqueous phase before reaction; the more concentrated the sulphuric acid, the shorter this distance is. The reaction zone thus consists of a spherical shell, across which [ArH] falls from its maximum value immediately adjacent to the organic phase to zero on the outside. The thickness of this shell depends on the relative magnitudes of the diffusion rate and the reaction rate. The differential equation describing the con- centration gradient is extremely difficult to solve analytically but it lends itself to solution by numerical methods. The organic sphere and its aqueous surroundings are split into a number of concentric spherical shells, of thickness Sr, whose centre is the centre of the sphere.The interface separating the organic and aqueous phases is between the outermost shell of organic liquid and the innermost shell of aqueous liquid. The solute concentration, [ArH], is considered to be uniform across each shell at all times. The system as a whole has radius rB ; there are S elements of thickness containing the organic phase A, surrounded by a further S elements of thickness SrB containing the aqueous phase B. The progress of the reaction is considered to take place in a series of short time intervals, each of duration S t . During each time interval the concentration change due to diffusion and reaction in each spherical shell is con- sidered negligible in comparison with the concentration, [ArH], in each shell.This enables the amounts diffusing in and out across the boundaries of the shell to be calculated by simple linear equations, based on Fick’s second law: amount of solute crossing interface of unit area = D times the concentration gradient (7) where D is the diffusion coefficient. For diffusion out from shell ( i - 1) to shell i, the concentration gradient is taken as the difference in concentrations in these shells divided by Sr. Diffusion out from shell i to shell ( i + 1) also affects the concentration in shell i, unless the shell is shell S, the outermost in the model system. The change in concentration in shell i due to diffusion in and out, Sc,(diff), is given by 3DSt(r,-6r/2)2(ci-1 +cj)-(ri +6r/2)2(c,-Ci+1) ( 6r)2[ 3 rf + ( S r / 2)2] Sc,(diff) = (8) Eqn (8) is true for any shell i, except the outermost of phase B and also the shell I of phase B, the innermost, whose inner boundary is the interface with phase A.Since ArH is much more soluble in the organic phase A than in the aqueous phase B, free energy equal to the difference in solvation energy between the two solvents must be supplied to enable ArH to move out from phase A to phase B. This reduces the rate of diffusion out. The required free energy can be estimated from the partition coefficient, K, where (9) K = ([ArH] in phase A)/([ArH] in phase B) at equilibrium. A detailed study of the rate of flow of ArH molecules across the interface in both directions shows that the net rate of diffusion out is given by where c,,~ and c ~ , ~ are the concentrations of ArH in the outermost shell of A and the innermost shell of B, respectively, and D A B is the diffusion coefficient which108 HETEROGENEOUS NITRATION IN EMULSIONS would be observed if A and B had the same viscosity and K was unity.For shell 1 in phase B, eqn (10) is used to modify eqn (8). For all the shells in phase B the concentration is also changed by chemical reaction, by an amount Sc, (reaction) in the time interval S t Sci (reaction) = cB.i{l -exp (-k2[HN03] S t ) } . This assumes that the sulphuric acid concentration is <78%, so that eqn (6) applies and HN03 is in excess over ArH. At the end of time St, the flows are 'frozen' and all the concentration changes given by eqn (8), (10) and (1 1) are calculated. New values of ci in phases A and B are calculated and substituted into eqn (8), (10) and (1 1) and the flows re-start and continue for another time interval St.Calculations for a large number of steps, performed by a Fortran IV program run on the University of London's CDC 7600 computer, gave a complete picture of the conversion of ArH to ArN02. The computation was subject to computer time constraints which limited the number of spherical shells and the number af time intervals considered. If the subdivision was too coarse, it was no longer true that the concentration changes were negligible by comparison with the standing concentrations. This had the effect of sending the diffusion pattern into oscillation, c,,, being alternately less and greater than ci in successive time intervls. Experience showed that, to prevent this occurring, 6t and Sr should be chosen so that D8t/(8r)2 < 0.45.Results from the theoretical model can be compared with experimental data from a system in which nitration is initiated by mixing an emulsion consisting of droplets of toluene dispersed in aqueous sulphuric acid with a solution of nitric acid in aqueous sulphuric acid of the same composition. The theoretical treatment must be extended to take account of the polydispersity of the emulsion; the spheres are of a range of radii. The droplet-size distribution is represented by five sets of spheres, each of a single radius, and the total amount of ArH reacted at any time is the sum of that reacted from each of the five sets of spheres, weighted according to the particle-size distribution. In order to calculate the amount of toluene nitrated at any time, various data, independent of the experimental kinetic data, are required.The radius of the sphere of the toluene phase, rA, were chosen for each of the five sets from photomicrographic measurements. The radius of the outer sphere of aqueous sulphuric acid, rB, was calculated from the phase volume ratio, I?, the ratio of the volumes of toluene and acid phases. This was kept at 0.0076 throughout. The value of r B is hence 5.9 rA. Values of DA and DB, the diffusion coefficients in the two phases, were calculated using the Stokes-Einstein equation D = kT/6.rrqr. Values of D for toluene in a solvent of known viscosity, namely hexaney were used to obtain a value of r, 250pm, then values of the viscosity of the aqueous sulphuric acid solutions" were used to calculate DB.Values of Sr and S t were chosen so that eqn (12) was valid. The total number of steps was chosen to allow time for nitration of almost all the toluene. Typically a few thousand steps were required. Values of k2 were taken from the literature? Fig. 1 shows some typical results of the calculation. Each circle shows the calculated concentration of toluene at the mid-point of each spherical shell in the aqueous acid phase. The number of circles on the concentration gradient curve shows the fineness of subdivision of rBJ. E. CROOKS AND J. M. CHISHOLM 8 1 (0 m - 109 ( i i l I -0 E - 2 4 - I 0 --. - u a -. 81 (iii) 81 (iv) (a) 3 - 1 n " V E U - z - 0- 0 - (4 I \ - u " (4 - (c) - ' - " " a e (=I - - P.A - u V " I I I 1 I I 1 0 distance from interface/pm c: I E -a 0 2 distance from intetface/pm Fig. 1. Concentration of toluene in aqueous sulphuric acid at various times and distances from the interface, at 25 "C. (i) 63.2% Sulphuric acid, r, = 0.94 pm: (a) 20 s after mixing, (b) 400 s after mixing and (c) 980 s after mixing. (ii) 67.6% Sulphuric acid, rA = 1.63 pm: ( a ) 0.8 s after mixing, (b) 8.0 s after mixing and (c) 24.0 s after mxing. (iii) 7 1.9% Sulphuric acid, rA = 2.22 pm: (a) 0.1 s after mixing, (6) 2.5 s after mixing and (c) 4.9 s after mixing. (iv) 73.6% Sulphuric acid, r, = 1.21 pm: ( a ) 0.02 s after mixing, (b) 0.4 s after mixing and (c) 0.98 s after mixing. required to obtain a reasonable representation of the reaction. The higher the acid concentration the faster the reaction and the larger the number, S, of subdivisions necessary. For systems in which the reaction is much slower than diffusion, e.g.as for 63.2% acid in fig. 1, the observed rate of nitration depends only on k, and not on D or rA. However, the observed rate constant is not k2 since most of the toluene is held in the organic spheres and is not available for reaction until the toluene in the aqueous acid phase has reacted. If the ratio of the concentrations of toluene in the organic phase to that in the aqueous acid phase is K at all times then where kobs is related to the total number of moles of toluene in the whole system, n ~ r ~ , by110 HETEROGENEOUS NITRATION IN EMULSIONS EXPERIMENTAL PREPARATION AND C H ARACTERI SAT1 0 N OF EMU LS I 0 NS The emulsifying agent used was a blend of Brij 30 and Brij 35, supplied by Sigma Chemicals and used without further purification.These surfactants are non-ionic polyoxyethylene lauryl ethers, C12H25(OC2H4)nOH, for which n =4 for Brij 30 and n =23 for Brij 35. A blend of 43 wt% Brij 30 with 57 wt% Brij 35 had the correct HLB number, 14, for emulsifying hydrocarbon in aqueous sulphuric acid. In order to keep the droplet radius constant during the reaction, the organic phase was not pure toluene but a solution of toluene in hexane. To prepare an emulsion, 5 cm3 of toluene and 2.15 g brij 30 were dissolved in 10 cm3 hexane; 1.14 g of Brij 35 were dissolved in 200 cm3 aqueous sulphuric acid of known concentration and the hexane solution was dispersed in this in a tissue grinder using three strokes of the plunger.The emulsions produced were stable for >24 h. The size distribution was obtained by photomicrography. Droplet sizes were measured from projections of the photomicrographs, which included a graticule scale. A total of at least 250 droplets was measured for each emulsion. MEASUREMENT OF THE PARTITION COEFFICIENT, K A solution of toluene in hexane was carefully added to an equal quantity of aqueous sulphuric acid of known concentration, in a separating funnel, with minimum agitation. The funnel was placed in a thermostat tank at the required temperature for 48 h. Samples were taken from the two layers and the concentration of toluene determined spectrophotometrically at 260 nm. If the layers were mixed by shaking, droplets of the organic phase, rich in toluene, were formed in the aqueous phase and could not be removed.The value of K so found, 1700* 150, was independent of sulphuric acid concentration in the range 61.2-76.1 wt%. KINETIC MEASUREMENTS To initiate the reaction, the emulsion was mixed with an equal volume of aqueous sulphuric acid containing 1 moldm-3 HN03. The concentration of sulphuric acid in the reacting mixture took into account the water necessarily introduced by the addition of HN03 (66 wt%) to the stock aqueous sulphuric acid. For runs of duration >50 s, the increase in absorption at 300 nm from nitrotoluene formation was monitored using a conventional spectcophotometer (Perkin-Elmer Lambda 5). For faster runs, a stopped-flow spectrophotometer (Hi-Tech Scientific SF-3A) was used.The slower runs were made more complicated by the slow breaking-up of the emulsion. Although the emulsion in sulphuric acid was stable this was not so if nitric acid was also present. This had the effect of reducing the absorbance, as the emulsion droplets disappeared. A correction factor was obtained by repeating the runs with emulsions containing hexane only in the organic phase. In a typical run, in 60.4wt% sulphuric acid, the absorbance at 370 nm for a 10 mm pathlength cell increased by 0.17 units for complete nitration, after 5700 s, even though the absorbance had been as high as 0.24 at 1500 s. The absorbance of a 10 mm cell containing the blank of emulsified hexane decreased by 0.25 units at 1500 s and by 0.65 units at 5700 s.The true absorbance increase for complete reaction was thus 0.82 units. Fortunately the theoretical progress of reactions proceeding this slowly is unaffected by droplet size, since the slow runs are kinetically controlled. Emulsion break-down was negligible for the fast runs, whose kinetics are partly diffusion controlled. The infinity values for the slow runs were calculated using the Swinbourne extrapolation," which was permissible as the runs are first order. RESULTS AND DISCUSSION The experimental data for a representative range of a sulphuric acid concentration are shown in fig. 2, together with predicted results from various theoretical models.J. E. CROOKS AND J. M. CHISHOLM 100 - 80- 2 6 0 - 2 .- * m ,,LO- 20 - 1 I I LOO 800 I 0 0 2 t / s L I I I 0 10 2 0 30 t l s 0 0.5 1'0 1'5 t / s 111 Fig.2.Experimental and computed plots of '/o toluene nitrated as a function of time, at 25 "C. (a) Experimental data; (b) computed, assuming stagnant conditions; (c) computed, assuming fast diffusion; ( d ) computed, assuming stirred aqueous acid phase. (i) 63.2% Sulphuric acid; a, = 0.94 pm, u, = 1.68 pm. (ii) 67.6% Sulphuric acid; ug = 1.63 pm, ug = 1.59 Fm. (iii) 71.9% Sulphuric acid; ug = 2.22 p m , ug = 2.01 pm. (iv) 74.8% Sulphuric acid; ag=2.00pm, up= 1.99pm. For each acid concentration, curve ( a ) shows the experimental data. Curve ( 6 ) shows the curve produced by the calculation described above, using the photomicro- graphically determined droplet-size data. Observed values for the geometric mean radius, a,, and geometric standard deviation, u,, are given for each system.These quantities are defined by In a, = C (n, In ai)/C ni In2 ag = C (In a, - na,>2/z n, where there are ni particles of radius ai. These statistical parameters are useful measures of the particle-size distribution, which to a good approximation is given by the log normal distribution12 ni/C n, = [hai/(a,27r) In ug] exp [-(In ai -In ~ , ) ~ / ( 2 ln2 u,)]112 HETEROGENEOUS NITRATION IN EMULSIONS Table 1. Values of Robs and K for various temperatures T/"C kobs/ s-' K 25.0 2.76 700 30.0 9.76 655 40.0 19.1 564 50.3 30.8 470 67.4 200 3 14 where there are n, droplets in the range (ai - Aai/2) to (ai +Aai/2). Curve (c) shows the limiting behaviour if diffusion is so fast, or reaction so slow, that the equilibrium concentration of toluene is maintained in the aqueous acid phase at all times.In acid concentration of 63.2 wt%, the nitration rate is entirely kinetically controlled and independent of droplet size. The points for curve (c) were calculated using eqn ( 14). Unfortunately a discrepancy between theoretical and observed nitration rates was found even for this simple limiting case. This was ascribed to an incorrect value of the partition coefficient, K. If K was taken as 700 rather than 1700, the good agreement seen in fig. 2 is found. The discrepancy may be explained by the presence of surfactant in the solutions used for kinetic studies. The toluene is partially solubilised by the surfactant, so the toluene concentration in the aqueous phase is greater than for the surfactant-free solutions used in equilibrium studies.It was not possible to test this theory by measuring K directly for systems with added surfactant because the two phases could not be separated. At high acid concentration where nitration is diffusion controlled, there is a large discrepancy between curves (a) and (b). This is attributed to a failure of the diffusion model. It has been assumed that the liquid for a few p m around each droplet could be regarded as stagnant, especially considering that the viscosity was around ten times that of water. However, the comparatively high nitration rates observed suggested that stirring was occurring. A representation of stirring is easily achieved in the mathematical model used in this study.At the end of each time interval St, the total amount of toluene present in the aqueous phase, phase B, is calculated, and divided by the volume of phase B to obtain the concentration of toluene in each shell of phase B, which is used to calculate rates of change in the next time interval. Curve ( d ) shows the rate of nitration calculated by this technique. The observed rates lie between curves ( b ) and ( d ) , showing that some stirring is occurring, but not right up to the interface. The temperature variation of the first-order rate constant for the nitration in 64.4% sulphuric acid was used to calculate the activation energy parameters. Values of K were calculated by applying the temperature variation of K found for surfac- tant-free solutions (1700 at 25 "C, 970 at 57 "C) to the kinetically determined value of 700 at 25 "C. The results are shown in table 1. From these data a value of 66*7 kJ mol-' was calculated for AH$ and a value of -37* 5 J K-' mol-' was calculated for AS'. We thank I.C.I. for the award of a CASE grant to J.M.C. 1 J. Giles, C. Hanson and H. A. Ismail, Inddstrial and Laboratory Nitrations, A.C.S. Symp. Ser. No. 22, ed. L. F. Albright and C. Hanson (A.C.S., Washington D.C., 1976), chap. 12, p. 190. ' G. F. Sheats and A. N. Strachan, Can. J. Chem., 1978, 56, 1280. K. Schofield, Nitration (Cambridge University Press, Cambridge, 1980).J. E. CROOKS AND J. M. CHISHOLM 113 C. P. Perrin, J. Am. Chem. SOC., 1977, 99, 5516. J. W. Barnet, R. B. Moodie, K. Schofield and J. B. Weston, J. Chem. SOC., Perkin Trans. 2, 1975, 648. R. B. Moodie, K. Schofield and P. G. Taylor, J. Chem. SOC., Perkin Trans. 2, 1979, 133. J. W. Chapman, P. R. Cox and A. N. Strachan, Chem. Eng. Sci., 1974, 1247. F. Nabholz and P. Rys, Helv. Chim. Acta, 1977, 60, 2937. Pin Chang and C. R. Wilkie, J. Phys. Chem., 1955, 59, 592. l o J. H. Ridd, Adv. Phys. Org. Chem., 1978, 16, 1. ” E. S. Swinbourne, J. Chem. SOC., 1960, 2371. ’* E. Shotton and S. S. Davies, J. Pharm. Pharmacol., 1968, 20, 430.

ISSN:0301-7249    

DOI:10.1039/DC9847700105

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 1 15-126 Use of Microemulsions as Liquid Membranes Improved Kinetics of Solute Transfer at Interfaces BY CHRISTIAN TONDRE" AND ARISTOTELIS XENAKIS Laboratoire de Chimie Physique Organique, ERA CNRS 222, Universite de Nancy I, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France Received 28 th November, 1983 When the volume fraction occupied by the dispersed phase of a microemulsion is small, the microglobules making up this dispersed phase can be viewed as mobile carriers permitting the transport of substances which are either insoluble or very poorly soluble in the continuous phase. In this paper water-in-oil microemulsions composed of decane, water, tetraethylenegly- col dodecylether (TEGDE) and hexan-1-01 are used as liquid membranes and the micro- globules are shown to transport alkali-metal picrates between two aqueous phases.The effect of changing the initial picrate concentration in the source compartment has been investigated and the resulting flux can be adequately described by a classical model of facilitated transport (fast transfer and 'chemical reaction' coupled with slow diffusion), as has been observed previously for the transport of lipophilic substances by oil-in-water microemulsions. The presence of dicyclohexano- 18-crown-6 (DC 18C6) in the liquid membrane brings about an increase in the flux of alkali-metal picrates. At optimum conditions, the transport of K' picrate by the microemulsion alone is 5.1 times faster than with DC18C6 in pure decane, but it is 12.6 times faster when DC18C6 is added to the microemulsion.Although drastically reduced, selectivity for ion transport still exists in the latter situation. Liquid membranes have long been used as models of biological membranes for studying the transport of different solutes (salts, metabolites, drugs etc.) either facilitated by a carrier or not.'-9 Numerous applications have also been found in separation techniques which take advantage of their ability to perform selective permeations. * The transport of substances in such experiments is usually facilitated by the incorporation of a carrier molecule in the liquid membrane. Macrocyclic compounds which are either naturally occurring (antibiotics)2 or synthetic (crown ethers or cryptands for have often been used for this purpose.On the other hand, the use of liposomes or vesicles as carriers for intracelluIar delivery of drugs constitutes an active area of re~earch.'"'~ We have developed experiments to demonstrate that the very small microemul- sion droplets may behave like the mobile carrier molecules commonly used in studies of facilitated transport. In these experiments a microemulsion is used as a liquid membrane separating two liquid phases in thermodynamic equilibrium with it. We have previously examined the transport of lipophilic substances by oil-in-water microemulsion droplet^,^'-^^ but only very preliminary results have been given for the transport of hydrophilic solutes by water-in-oil microemulsions. " This paper will give a full account of the results obtained when water-in-oil microemulsion systems involving a non-ionic surfactant are used to transport alkali-metal picrates.The role of carrier of the microemulsion droplets has implications regarding the liquid-liquid extraction of metal ions as it can be responsible for an improvement 115116 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER DECANE 34 H E x ANOL VL Fig. 1. Composition (filled circles) of the initial mixtures in the diphasic region of the pseudo-ternary diagram n-decane/ water/ tetraethyleneglycol dodecylether (3/4), hexan- 1-01 (1/4). Phase separation occurs according to the tie-lines joining the water apex to the open circles indicating the composition of the water-in-oil microemulsions. The dashed line delimiting the monophasic domain was drawn approximately according to ref. (22).in the kinetics of solute transfer at interfaces, as observed when surfactants are added to the extracting medium.18-20 For this reason we have also investigated the transport of alkali-metal picrates by a crown ether, which can be considered as a model sjstem, both when the membrane is a pure organic solvent and when the membrane is a water-in-oil microemulsion. Two alkali-metal cations with different stability constants2' for complexation with the crown ether have been tested in order to compare the selectivity of ion transport in both media. EXPERIMENTAL CHOICE OF CHEMICAL COMPOUNDS For these experiments, we required a water-in-oil microemulsion in thermodynamic equilibrium with an aqueous phase of composition as close as possible to pure water, i.e.a diphasic system of the so-called Winsor I1 type. In addition, the hydrophilic substance to be transported had to be able to be detected spectrophotometrically; this led us to choose the alkali-metal picrates. Because of the nature of the chosen hydrophilic solute we preferred to use a microemulsion system containing no salt, although most known diphasic systems of the Winsor I1 type require a salt in their formulation. This was intended to avoid an exchange of ions during the transport process. For this reason we sought a system involving a non-ionic surfactant and finally found a quaternary system meeting all the above requirements: decane/water/ tetraethyleneglycol dodecylether (TEGDE)/hexan- 1-01. The monophasic region of the pseudo-ternary phase diagram obtained when keeping the ratio of TEGDE to hexanol constant (TEDGE/hexanol = 3) has previously been described by Friberg et aLZ2 We found that the systems, the compositions of which are indicated in fig.1, separate into two perfectly clear phases according to the tie-lines indicated. Unfortunately we could not find a simple ternary system having such a property: if there was no hexanol the system did not produce clear phases even after several weeks. It thus seems that it is easier to obtain Winsor I1 systems by adding an alcohol, as previously observed by Winsor himself in the case of ionic surfactants in the absence of salt.23C. TONDRE AND A. XENAKIS 117 Table 1. Compositions (in wt%) of initial mixtures and microemulsion phases initial mixture & (water-in-oil microemulsion) d 7 7 system H 2 0 C10H22 C6HI30H TEGDE H 2 0 C10H22 C6HI30H TEGDE /gcmP3 /cp I 50 47 0.75 2.25 1.83 92.28 1.47 4.42 0.742 1.06 I1 53 42 1.25 3.75 3.40 86.32 2.57 7.71 0.753 1.30 I11 53 40 I .75 5.25 4.80 81.03 3.54 10.63 0.762 1.55 IV 54 38 2 6 5.76 77.85 4.10 12.29 0.770 1.77 V 50 40 2.5 7.5 6.47 74.82 4.68 14.03 0.771 1.81 VI 52 37 2.75 8.25 8.05 70.96 5.27 15.82 0.781 2.37 VII 50 37 3.25 9.75 10.20 66.45 5.84 17.51 0.789 2.8? Our choice of dicyclohexano- 18-crown-6 (DC 18C6) for the experiments in the presence of a classical extractant was for the following reasons: (i) it has good solubility in decane and poor solubility in water, and will thus stay in the liquid membrane, and (ii) it complexes both K+ and Na+ ions with different stability constants,21 which makes it convenient for testing the influence of the microemulsion on the selectivity of transport of alkali-metal ions.ORIGIN OF CHEMICALS Tetraethyleneglycol dodecylether (Nikko Chemicals, 'Japan), n-decane and dicyc- lohexano-l8-crown-6 (Fluka purum) and hexam- 1-01 (Fluka puriss.) were used as supplied. Potassium and sodium picrates were prepared from picric acid (Merck) according to the procedure described in ref. (24). The salts were recrystallized three times and the extinction coefficients measured in tetrahydrofuran were in agreement with previously published value^.^ CHARACTERIZATION OF BIPHASIC SYSTEMS Biphasic systems with the compositions shown in fig. 1 and table 1 were prepared by weighing the components directly in a separating funnel which was then placed in a thermostat- ted bath regulated at 20 "C (*0.2 "C) until separation into two clear phases was achieved (this took 3 days to 3 weeks, depending on the system). The compositions of the initial mixtures were chosen so as to give approximately equal volumes of the two separated phases.Analysis of these phases was performed by the Karl Fisher method for the water content and by gas-phase chromatography for decane, hexan-1-01 and TEGDE, using columns 1 m long and in. in diameter containing 3% SE30 on chromosorb WAW 80/ 100 mesh with a linear variation of temperature from 50 to 280 "C. The composition of the superior phase & is given in table 1. The inferior phase is essentially water (no other component could be detected by gas-phase chromatography).For this reason the representative points of both phases can be shown in the same pseudo-ternary diagram (fig. 1). Densities and viscosities of & (table 1 ) were measured with a digital Anton Paar DMA 10 densimeter and with an Ubbelohde-type viscometer (Schott-Gerate with automatic timing), respectively. TRANSPORT EXPERIMENTS The setup used for the transport experiments is similar to that previously described when investigating oil-in-water microemulsions,'6~1 except that the shape of the cell used in the reverse of the previous one. As shown in fig. 2, it resembles an inverted U tube with the two arms filled with the aqueous phase and the microemulsion phase at the top. The volumes were 14.8, 18.6 and 35 cm3 for the source (S), receiving (R) and membrane (M) compartments,118 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER ----- PECTAOMETER Fig.2. Schematic diagram of the apparatus used for the transport experiments. respectively. The light absorption of the receiving phase was measured continuously at 357 nm for K+ picrate and at 351 nm for Na+ picrate, thus allowing us to calculate from a standard curve the number of transported molecules at any time (Beer's law was found to be valid in the concentration range used). Peristaltic pumps (Masterflux) were used to ensure fast homogenization in both branches of the transport cell.9 The microemulsion compartment was stirred using a magnetic stirrer whose rotation speed was regulated at 120 r.p.m. The whole cell was thermostatted at 20 "C.RESULTS AND DISCUSSION TRANSPORT OF PICRATES BY PURE MICROEMULSIONS The transport of K' or Na+ picrates by the microemulsion systems referred to as I to VII in table 1 was first studied without adding a classical extractant to the membrane. Fig. 3 shows a plot of the number of moles of K' picrate transported against time for different initial concentrations of picrate in the source compartment, using system V. The curves look very much like those obtained for the transport of pyrene by oil-in-water microemulsions, with a time lag attributed to the time required for the picrate to reach an equilibrium concentration inside the membrane. The flux of picrate, calculated from the slopes of the straight lines observed when a steady state is established, is shown in fig.4 as a function of the initial picrate concentration. Blank experiments carried out with pure decane instead of the microemulsion in compartment M did not reveal any transport of picrates after 24 h. We chose a picrate concentration of 2 x mol dmP3 to study the influence of the composition of the microemulsion on the transfer rate of K' and Na' picrates. As can be seen in table 1 , the composition of the microemulsion was varied by changing the amount of amphiphile compounds in the initial mixture: the larger the amount of amphiphiles, the larger the amount of water incorporated in the microemulsion phase. Fig. 5 shows the variation of the flux of K' and Na+ picrates when increasing the volume fraction of water. The flux increases linearly up to a volume fraction of 0.05 and then decreases.Only a very small difference is observed between K+ and Na+ picrates, with the latter always giving a slightly lower value for the flux (table 2). The maximum observed in the variation of the flux was unexpected because when the corresponding experiments had been conducted with oil-in-water micro- emulsions (increasing percentage of oil), instead of a decrease, a dramatic increase of the flux of pyrene occurred for a certain volume fraction of Such aC . TONDRE AND A. XENAKIS 119 20 I I I I I f/min Fig. 3. Plots of the number of moles of K+ picrate crossing the second interface against time in microemulsion system V. The numbers indicate the initial picrate concentratbn in the source compartment S (mol dm-3).Cross-section of interface = 3.14 cm2. Fig.4. Plot of the flux of K+ picrate against the initial picrate concentration in the source compartment S. The curve is calculated from eqn (9) with the values of parameters given in fig. 6 . phenomenon was attributed to the percolation threshold of oil droplets. In the present situation a structural change of the microemulsion is probably responsible for the maximum observed. A possible interpretation is as follows: when the amount of water in the microemulsion is < 5 % , there is just enough water to hydrate the ethylene oxide groups constituting the hydrophilic part of the surfactant (we have between 2 and 2.4 water molecules per ethylene oxide group, in agreement with120 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER 3 - - I .C E - 2 - z I 2 \ 4 0 2 4 6 a H,O(% V/V) Fig.5. Plots of the flux of K+ picrate ( X ) and Na+ picrate (0) against the percentage of water (v~E.‘) in the microemulsion phase. Initial picrate concentration = 2 x mol dmP3. previous e~timations’~,~~); at >5% water there is enough water to start forming water pools (the sudden increase in the ratio-of H20 to TEGDE can be seen in fig. 1 : it occurs when the representative points of the microemulsion phases depart from a straight line originating from the oil apex). In the first situation, only agregates of TEGDE and hexanol would exist, as previously postulated in comparable systems in the absence of a l c ~ h o l . ~ ’ Real water droplets (with unknown shape) with a palissade layer of amphiphile molecules would occur in the second situation.I3C n.m.r. relaxation time measurements currently in progress should enable us to say whether the mobility of the hydrophilic chains is in agreement with such a In this hypothesis it is clear that the equilibrium constant characterizing the interac- tion (solubilization or complexation) of the alkali-metal picrate with the ‘carrier’ will be very different if this carrier is an aggregate or a water droplet (in the latter case the ethylene oxide groups lining the inside of the droplet could act as a kind of crown ether towards the alkali-metal cations and make the releasing process more difficult). We will not attempt to speculate further on the maximum observed in fig. 5, but will merely try to interpret the results obtained in the linear part of the figure, i.e.where we can assume that there is only one sort of carrier (the exact structure of which does not matter). According to fig. 1 and table 1, the ratio between water and the amphiphile molecules is constant for all the systems containing <5% (v/v) water. Increasing the amount of amphiphile molecules (or water) can be considered as equivalent to increasing the concentration of carrier, which results in a linear increase of the flux. In the previous case of oil-in-water microemulsions we tested different possible mechanisms in order to determine which step was rate controlling: transfer of solute across the interface, solubilization inside the droplet or diffusion through the non-stirred layers. The results were consistent with a model in which the diffusion of the droplet having solubilized the probe is much slower than transfer andC.TONDRE AND A. XENAKIS 121 Table 2. Fluxes of transported picrates as a function of the nature of the liquid membrane and the presence or absence of a classical extractant flux"/ mol h- ' nature of water solute with DC 18C6 liquid membrane ("/o v/v) transported without DCl8C6 ( mol dm-') pure decane z microemulsion I microemulsion I1 microemulsion 111 microemulsion IV microemulsion V microemulsion VI microemulsion VTI ,O 1.36 2.55 3.63 4.41 4.98 6.27 8.1 1 KPi NaPi KPi NaPi KPi NaPi KPi NaPi KPi NaPi KPi NaPi KPi NaPi KPi NaPi 0.74 x 0.61 X 1.37 x lop6 0.87 x 1.48 X 2.15 X 1.33 x I 0-6 1.06 x 0.94 x 2.1 1 x lop6 - 4.21 x 1 0 - ~ 8.6 X 2.42 X lop6 0.85 X loy6 4.74 x 2.28 x 5.30 X 2.80 x lop6 2.61 x lop6 1.56 X lop6 " Cross-section of interface = 3.14 cm2. solubilization reactions.Similar treatment permits a satisfying description of the present results. The different steps involved in the transport process can be written as follows: interface I : Mesf + Pi, s Me', Picontinuous phase o f M Me+, Picontinuous phase of M +(c) (c, Me+, pi-) (2) diffusion of (C, Me+, Pi-) across the non-stirred layers (3) (c, Me+, pi-) * Me', Picontinuous phase of M +(c) (4) ( 5 ) where the subscripts M, S and R refer to membrane, source and receiving compart- ments, respectively, Me' is the alkali-metal ion, Pi- is the picrate ion and Me', Pi- is the ion pair, and (C) and (C, Me+, Pi-) are the 'carrier' and the carrier-solute complex, respectively.Steps (1) and ( 5 ) correspond to the formation of the ion pair through the interfaces characterized by an equilibrium constant k. Steps (2) and (4) are governed by the equilibrium constant K for the solubilization (or complexation) of the metal picrate in (with) the carrier. Step (3) is characterized by a diffusion coefficient 0, the thickness of the diffusion layer being L=2Z, where Z is the non-stirred layer on the organic side of both interfaces (as previously observed with oil-in-water microemulsions, changing the rotation speed of the magnetic stirrer influences the transfer rate, but changing the rotation speed of the peristaltic pumps does not affect the result). membrane: interface 2: Me', Pi~,ntinuous phase of == Me& + Pi; I122 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER Solving the continuity equations for all the species present in the membrane with the assumptions that (i) the steady-state approximation is valid, (ii) the equili- brium characterizing steps (2) and (4) is always established and (iii) the unfacilitated transport of picrate is negligible, and with the following boundary conditions: [Me', Pi-]M = k[Me'],[Pi-1, = k[Pi-]: on interface 1 (6) [Mef, Pi-]M = k[Me+I2[Pi-l2 = k[Pi-]: on interface 2 (7) where [Pi-], and [Pi-]* are the concentrations outside the membrane but right beside it in compartments S and R, respectively, at the beginning of the steady state, leads to the following equation for the flux: As the concentration [Pi-I2 is practically zero at the beginning the equation reduces to the first term: DKk[(C)] [Pi-]: F = L 1 + ~ k [ ~ i - ] : ' (8) of the steady state, (9) The essential difference from the previously developed treatment comes from the ion-pair formation equilibrium, which introduces a squared term in the con- centration dependence of the If the model is suitable for describing the experimental results, a plot of 1/F against l/[Pi-]: should give a straight line with intercept L/D[(C)] and slope L/DKk[(C)].The concentration [Pi-], is not known and must be calculated first. It can be shown to be given by where [Pi-l0 is the initial picrate concentration in the source compartment, k' is the partition coefficient of the picrate ion between the aqueous phase and the microemul- sion phase as a whole (k' is a number without dimensions, not to be confused with k ) and the V are the volumes occupied by the different phases.k' was experimentally measured in system V and found to be equal to 0.84, so the complete correcting factor is 0.44. Fig. 6 shows that very good agreement exists between the theoretical prediction according to the proposed model and the experimental data. Combining the values of the intercept and slope enables us to determine the value of the product Kk= (0.98 f 0.2) X lo6 dm6 mol-'. It is difficult to discuss this value on a quantitative basis. Unfortunately we have no estimate of the equilibrium constant k, which could in principle be obtained from the solubility of picrate in water and in decane if one assumes that the continuous phase of the microemulsion is pure decane (it may also contain hexanol and TEGDE): we failed to detect any solubility in decane by measuring the absorption of an aqueous solution of picrate before and after shaking with decane. On the other hand, the only results we know concerning the dynamics of solubilization of a picric acid probe in reversed micelles are consistent with an equilibrium constant of 2.3 x lo6 dm3 mol-', i.e.of the same order of magnitude as123 0 5 10 15 20 25 ( I / [ P ~ - ] , ) ~ / I O ' ~ cm6 molP2 Fig. 6. Plot of the reciprocal flux of K+ picrate against the square of the reciprocal concentra- tion of picrate at steady state in the source compartment S. Intercept=L/D(C)= 0.225 x 10" mol-' cm2 s; slope = L/DKk(C) = 2.29 x lo-' mol cmP4 s.the above value. This result was obtained by Tamura and Schelly2g in the system Aerosol OT+ benzene + water. TRANSPORT OF PICRATES BY MICROEMULSIONS CONTAINING A CLASSICAL EXTRACTANT When dicyclohexano- 18-crown-6 is added to the microemulsion being used as a liquid membrane, an increase in the flux of transported picrates is observed for both Na+ and K' salts. The results obtained with the different microemulsion systems containing mol dm-3 DC 18C6 are shown in fig. 7 and table 2, in which are also given for comparison the fluxes obtained when the liquid membrane is either pure decane containing 1 OP2 mol dm-3 DC 18C6 or the microemulsion alone. All the experiments in which a microemulsion is involved show a maximum in the flux for the same volume fraction of water. At this maximum (system V) the transport of K+ picrate by the microemulsion alone is 5.1 times faster than with DC18C6 in pure decane, but it is 12.6 times faster when DC 18C6 is added to the microemulsion.For the Na' picrate, the corresponding values are, respectively, ca. 245 and 325 because of the very weak flux obtained with DC18C6 in pure decane (the flux was so small that it was difficult to determine it accurately, which explains why the preceding values are approximate). A comparison of the results obtained for K' and Na' cations shows that, although drastically reduced, some selectivity for ion transport still exists in the presence of the microemulsion. This is of importance when considering the use of microemul- sions for liquid-liquid extraction of metal ions.124 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER H20( O/o V/V) Fig.7. Plots of the flux of K+ picrate (X, -) and Na+ picrate (0, - - -) against the percentage of water (v/v) in the liquid membrane containing (or not containing) dicyclohexano- 18-crown- 6. Initial picrate concentration = 2 x 1 0-3 mol dm-3 ; concentration of DC 18C6 = 1 0-2 mol d ~ n - ~ . Note also that when the system contains both the classical extractant and the microemulsion globules, the resulting flux of K' as well as Na+ picrates is not equal to the sum of the fluxes obtained with the individual carriers. The accelerating effects of microemulsions on the kinetics of the extraction of metal ions by a classic extractant have been reported by Fourre and Bauer,I8 who used a two-compartment cell of the type described by Lewis29 and Allen3' to study the extraction of gallium by Kelex 100.They suggested that the reason for the improvement in the extraction kinetics could be found in the fact that the micro- globules of the microemulsion act as a relay between the aqueous phase and the extractant contained in the organic phase. According to this explanation the follow- ing simplified mechanism can be proposed for the present results: A Pi(aqueous phase S ) * Pi(microemu1sion 'carrier') - Pi(aqueous phase R) @ 11 + ether carrier) * If there were no coupling between the two carrier complexes a simple additive effect would be expected on a first approximation. The coupling between the two species has the result of reducing the effective membrane thickness L and thus it improves the transfer rate according to equations similar to eqn (9).The detailed mechanism can be regarded as follows: the diffusion of DC18C6 in the non-stirred layer is certainly much faster than the diffusion of the microemulsion globule, so when the empty macrocycle diffuses back towards interface 1 it will meet microemulsion globules carrying a picrate ion, and if exchange occurs the driving force will pull it towards interface 2 before it has reached interface 1. The effective layer is thus decreased for both carrier species.C. TONDRE AND A. XENAKIS 125 CONCLUSIONS We have attempted to give a clear demonstration of the carrier properties of water-in-oil microemulsion globules by studying the transport of hydrophilic solutes (alkali-metal picrates) through an oil continuous phase.The behaviour observed is very similar to that previously reported for the transport of lipophilic substances by oil-in-water microemulsions. A quantitative interpretation is nevertheless more difficult because, contrary to the case of oil-in-water microemulsions, very little is known concerning the structure of the microemulsion systems used here, which involve a non-ionic surfactant. This work also tries to clarify the mechanisms by which microemulsions can improve the kinetics of the liquid-liquid extraction of metal ions. It has been shown that transfer through a liquid membrane can help to test for the optimum conditions, such as the optimum water content of the organic phase.Nevertheless, when there is enough water to form water pools, the non-ionic detergent molecules present in the microemulsion system probably act as a strong chelating agent, and other systems will have to be found in order to investigate further the role of microemulsions in the mechanism of ion-extracting processes. We thank J. L. Fringant and J. L. Vasseur for their technical assistance in the building of the experimental apparatus. ' H. L. Rosano, P. Duby and J. H. Schulman, J. Phys. Chem., 1961, 65, 1704. R. Ashton and L. K. Steinrauf, J. Mol. Biol., 1970, 49, 547. W. I. Higuchi, A. H. Ghanem and A. B. Bikhazi, Fed. Proc., Fed. Am. SOC. Exp. Biol., 1970,29,1327. K. H. Wong, K. Yagi and J. Smid, J. Membr. Biol., 1974, 18, 379. J. D. Lamb, J.J. Christensen, S. R. Izatt, K. Bedke, M. S. Astin and R. M. Izatt, J. Am. Chem. SOC., 1980, 102, 3399. Y. Kobuke, K. Hanji, K. Horiguchi, M. Asada, Y. Nakayama and J. Furukawa, J. Am. Chem. Soc., 1976, 98, 7414. M. Kirch and J. M. Lehn, Angew. Chem., Int. Ed. Engl., 1975, 14, 555. E. Pefferkorn and R. Varoqui, J. Colloid Interface Sci., 1975, 52, 89. l o N. N. Li and A. L. Shrier, in Recent Developments in Separation Science, ed. N. N. Li (CRC Press, Cleveland, 1972), vol. I, p. 163. I ' N. N. Li, Ind. Eng. Chem., Process Des. Deu., 1971, 10, 215. l 2 N. N. Li, AIChEJ., 1971, 17, 459. l 3 J. N. Weinstein, Pure Appl. Chem., 1981, 53, 2241. l4 J. H. Fendler and A. Romero, Li$e Sci., 1977, 20, 1109. I s C. Tondre and A. Xenakis, Colloid Polym. Sci., 1982, 260, 232. '' A. Xenakis and C. Tondre, J. Phys. Chem., 1983, 87, 4737. l7 C. Tondre and A. Xenakis, in Surfactants in Solution, ed. K. L. Mittal (Plenum, New York, 1983), '' P. Fourre and D. Bauer, C.R. Acad. Sci., Ser. B, 1981, 292, 1077. l 9 P. Fourre, D. Bauer and J. Lemerle, Anal. Chem., 1983, 55, 662. 2o J. Komornicki, Thesis (UniversitC de Paris, 1981). '' J. Lamb, R. M. Izatt, J. J. Christensen and D. Eatough, in Coordination Chemistry ofMacrocyclic ' C. F. Reusch and E. L. Cussler, AIChE J., 1973, 19, 736. vol. 3, p. 1881. Compounds, ed. G. A. Melson (Plenum Press, New York, 1979). S. Friberg, I. Lapczynska and G. Gilbert, J. Colloid Interface Sci., 1976, 56, 19. 22 23 P. A. Winsor, Trans. Faraday Soc., 1948, 44, 376. 24 M. Coplan and R. Fuoss, J. Phys. Chem., 1964, 68, 1177. G. Mathis, J. C. Boubel, J-J. Delpuech, J. C. Ravey and M. Buzier, in Magnetic Resonance in Colloid and Interface Science, ed. J. P. Freissard and H. A. Resing (D. Reidel, Dordrecht, 1980), p. 597. 25126 MICROEMULSIONS TO IMPROVE KINETICS OF SOLUTE TRANSFER 26 M. Buzier, Thesis (Universitk de Nancy, 1979). 27 C. Tondre, A. Xenakis, A. Robert and G . Serratrice, to be published. 2R K. Tamura and Z. A. Schelly, J. Am. Chem. Soc., 1981, 103, 1018. 29 J. B. Lewis, Chem. Eng. Sci., 1954, 3, 260. 30 K. A. Allen, J. Phys. Chem., 1960, 64, 667.

ISSN:0301-7249    

DOI:10.1039/DC9847700115

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 127-137 Solute Transport and Perturbation at Liquid/ Liquid Interfaces BY RICHARD H. GUY," ROBERT S. HINZ AND MICHAEL AMANTEA School of Pharmacy, University of California, San Francisco, California 94 143, U.S.A. Received 23 rd November, 1983 Solute transfer kinetics across aqueous-solution/organic-liquid interfaces have been measured by two techniques. First, a new method based upon the capillary-tube procedure for self-diffusion has been developed. A short capillary containing radio-labelled solute dissolved in one phase is immersed in a large stirred volume of the second liquid phase, into which the movement of marker is followed. Demonstration and validation of the approach has been performed with a number of systems including the transport of salicylic acid (SA) at a water/isopropyl myristate (IPM) interface. In the second procedure, a rotating diffusion cell has been used to determine whether the rate and energetics of the transfer process are altered by the presence of dissolved anaesthetic alcohols.SA and methyl nicotinate (MN) transport across an aqueous-solution/IPM interface has been studied with various concentra- tions of different alcohols dissolved in the aqueous phase. The effects of alcohol are solute dependent: SA is not affected by any of the anaesthetics studied whereas 100 mmol dm-3 ethanol retards MN transfer by a factor of 2. For MN, furthermore, the favourable entropic contribution to the free energy of activation for interfacial transfer (which is observed in the absence of ethanol) is negated by the presence of 100 mmol dmP3 ethanol.This change may reflect a destabilization of interfacially ordered water molecules by the alcohol and appears similar to the effect of poly(ethy1ene glycol) on the same system. The objectives of the work described in this paper were two-fold: (1) to develop a new procedure for the determination of solute transfer kinetics at liquid/liquid interfaces and (2) to investigate, using the physical chemistry of interfacial transport, the effect of anaesthetic alcohols at a model biomembrane interface. The study of interfacial transport at liquid/liquid boundaries is important for its own sake, in terms of contributing to the understanding of a complex solution chemistry problem, and has relevance to numerous situations in industrial and biological processes (e.g.separation technology and membrane transport). Precise and reliable measurement of interfacial transport kinetics, however, is difficult and prone to artefact. The development of an alternative experimental approach is therefore both fundamentally useful and of value as a means with which to verify independently data from a single different technique. We describe here a novel application of the capillary-tube procedure for self-diff usion.' A capillary containing a radio-tagged solute dissolved, for example, in an organic liquid is immersed into a large stirred volume of aqueous buffer. Transport of the solute is followed by measuring the radioactivity lost from the capillary as a function of time.The solution to Fick's second law of diffusion with the appropriate boundary condition for the interface at the mouth of the capillary enables the phase-transfer coefficient of the solute to be evaluated from the data. The correlation of anaesthetic potency with lipid solubility among the alcohols and other structurally unrelated small molecules has resulted in their biological effect being generally interpreted as a non-specific action (e.g. increasing fluidity) 127128 TRANSPORT AT LIQUID/LIQUID INTERFACES in the hydrophobic regions of membranes2 rather than at discrete receptor sites.3 However, the functional significance of anaesthetic-induced membrane fluidization has not been demonstrated absolutely. Furthermore, although alcohols do change the interfacial interactions between water and both surfactant and phospholipid mono1ayers4-6 spread on an aqueous solution, the possibility that at least some of these molecules' effects on membranes could be due to interfacial events had, until recently, received little consideration.In 1976 Eyring et a1.' proposed that interfacial water structure and its alteration by anaesthetic agents may determine the state of membrane activity. This work has been developed8 and expanded by showing ( a ) the dehydration of micelle surfaces by anaestheticsY3lo (6) a decreased tendency for inhalation anaesthetics to penetrate cell membranes" and ( c ) a growing body of theoretical and experimental evidence for the interfacial activity of these molecule^.'*-'^ In the study reported here we have chosen to use the kinetics and thermodynamics of solute transfer at a model biomembrane interface as a means to probe the interfacial influence of anaesthetic alcohols.The membrane surface is simulated with an aqueous-solution/isopropyl myristate liquid/liquid boundary, and the movement of two solute molecules has been considered. Experiments have been performed with a previously described rotating diffusion ce11,16 which has been used extensively in recent years for the measurement of interfacial transport kinetic^.'^^^ EXPERIMENTAL CAPILLARY TECHNIQUE A schematic diagram of the initial experimental configuration most often studied in this work is shown in fig. 1. A small glass capillary was first filled carefully with a solution of radio-labelled solute in isopropyl myristate (IPM) ensuring that the liquid surface was flush with the open end of the capillary.Over-filled capillaries were discarded. Generally, the capillaries used were 1.1-1.2 cm long with an internal diameter of 0.84 mm (corresponding to a volume of ca. 5 mm3). Most experiments have been performed with salicylic acid (SA) (14C-labelled in the carboxy position) as the solute. The specific activity was 56.5 mCi mmoi I, which was equivalent to ca. 23 000 *800 counts min-' per 5 mm3 of IPM solution. The initial SA molar concentration in IPM was ca. 40 pmol dm-3. The filled capillary was placed in a simple wire support and lowered into an aqueous receptor phase contained within a scintillation vial. The vial and contents were pre-positioned in a water bath held within a glass jacket through which thermostatted water at 25 "C was pumped.To allow the capillary to attain thermal equilibrium it was not fully submerged immediately but allowed sufficient time to reach 25 "C by being immersed to ca. 90% of its length into the receptor-phase. The receptor-phase volume was 2 cm3 ( i e . ca. 400 times the entrapped volume in the capillary) and was stirred thoroughly by a small magnetic bar spinning at 800 r.p.m. We have found our results to be independent of stirring speed between 400 and 1000 rpm. Below 400 rpm it appeared that solution was not moved adequately across the mouth of the capillary and transport is impeded. Above 1000 rpm there was vortexing of the receptor phase and the possibility of convective removal of the liquid within the capillary.At time zero the capillary was fully immersed into the receptor phase to a depth of ca. 0.5 cm below the surface and transport commenced. The duration of the experiment depends upon the system but was generally between 1 and 10 min, at the end of which the capillary was quickly and carefully removed from the receptor phase. We had found by experiment that the circumspect method of capillary submersion and retrieval did not induce a perturba- tion resulting in a burst of activity from the capillary. We therefore believe that the solute, which had exited from the entrapped phase, had done so according to the transport equation described below. The receptor phase was now mixed with an appropriate volume of scintilla- tion fluid and the percentage of initially entrapped radioactivity, which had been transportedR.H. GUY, R. S. HINZ AND M. AMANTEA I29 Fig. 1. Diagram of the most frequently considered experimental configuration for the capillary technique. For the sake of clarity, the thermostatting part of the apparatus has been omitted. A, wire support for capillary ; B, glass capillary containing radio-labelled solute dissolved in IPM; C, aqueous receptor phase into which solute movement is followed; D, magnetic stirrer bar; E, scintillation vial. Table 1. Initial experimental configurations of the systems studied with the capillary technique system soluten capillary-entrapped phase receptor phase ~~ C l salicylic acid isopropyl myristate C2 salicylic acid isopropyl myristate C3 salicylic acid 60 mmol dmP3 pentan- 1-01 C4 salicylic acid isopropyl myristate in isopropyl myristate C5 acetic acidb 10 mmol dm-3 hydrochloric C6 acetic acidb I0 mmol dm-3 hydrochloric acid (aq) acid (aq) water 20 mmol dm-3 pentan-1-01 in water 20 mmol dm-3 pentan-1-01 in water 0.15 mmol dm-3 sodium dodecyl sulphate in water isopropyl myristate dodecane Solutes were 14C-labelled. Specific activity of acetic acid was 56 mCi mmol-', equivalent to ca.19 000 counts min-'per 5 mm3 of 10 mmol dm-3 HCl solution. out of the capillary, was determined. The other information required for the interpretation of the data consists of (i) the capillary dimensions, which were known or measured, and (ii) the solute diffusion coefficient in the capillary-entrapped phase, the values of which (for the systems reported here) have been previously determined. All chemicals used (for these and the rotating-diff usion-cell studies) were purchased commercially and aqueous solutions were prepared with water distilled from an all-glass apparatus.The initial experimental configurations studied are given in table 1. ROTATI NG-DI FFUSION-CELL TECHNIQUE The rotating-diff usion-cell (r.d.c.) procedure for the measurement of interfacial transfer kinetics has been described in detail.16 In the systems reported in this paper (see table 2)130 TRANSPORT AT LIQUID/LIQUID INTERFACES Table 2. Initial configurations of the systems studied by the rotating-diff usion-cell procedure system inner compartmentn filter outer compartment T/"C R1 5 mmol dm-3 salicylic acid IPM' (SA) in 10 mmol dmV3 HCl (as) 10 mmol dm-3 HC1+ 100 mmol dm-3 ethanol (aq) 10 mmol dm-3 HC1+ 20 mmol dm-3 pentan- l-ol (aq> 10 mmol dm-3 HCl + 10 mmol dm-3 benzyl alcohol (aq) R5 100 mmol dm-3 methyl I PM nicotinate (MN) in water 100 mmol dm-3 ethanol (aq) R2 5 mmol dm-3 SA in I P M ~ R3 5 mmol dm-3 SA in I P M ~ R4 5 mmol dm-3 SA in I P M ~ R6 100 mmol dm-3 MN in I P M ~ 10 mmol dm-3 HCl (as) 10 mmol dm-3 HCl + 100 mmol dm-3 ethanol (aq) 10 mmol dmW3 HCl + 20 mmol dm-3 pentan- l-ol (aq) 10 mmol dm-3 HC1+ 10 mmol dm-3 benzyl alcohol (aq) water 100 mmol dm-3 ethanol (as) 20,25,30,37 20,25,37 20,25,30,37 20,25,30,37 20,25,30,37 20,25,37 a Volume 40 cm3; volume 250 cm3; isopropyl myristate; IPM was pre-equilibrated with the appropriate alcohol before impregnation into the r.d.c.filter. the inner and outer compartments of the r.d.c. contained aqueous phases, while the rotating filter was impregnated with IPM. The choice of the organic phase reffects its use in previous work to model the characteristics of a biomembrane.16~17*22~23~25-27 Liquid/liquid interfaces were thereby established on both sides of the spinning disc. The filters used were Millipore GS type 0.22 pm pore size. The porosity and thickness of these membranes were 0.75 and 150 pm, respectively, values that have been independently verified by an electrochemical technique.28 Solute flux in the r.d.c. was followed by periodic spectrophotometric assay, of the outer aqueous phase. Experiments were conducted at three or four temperatures between 20 and 37 "C.Data analysis for this procedure requires knowledge of the solutes' diffusion coefficients in the aqueous and organic phases and the partition coefficients of the substrates. Diffusion coefficients in the control systems (no alcohol) were known.'6y22*23*29 In the presence of alcohol, the change in solute diffusion coefficient was assessed from the alteration induced in solvent viscosity. These relatively minor effects were determined using an Ostwald vis- cometer. Partition coefficients were found by shaking an aqueous solution of substrate with an equal volume of IPM (in the presence and absence of alcohol) for 48 h and then assaying for the solute spectrophotometrically. Diffusion and partition coefficients are reported in table 3. THEORY CAPILLARY EXPERIMENTS Fig.2 shows schematically the capillary system and defines the physicochemical and geometric parameters. The diagram assumes that an organic phase is contained within the capillary and that the receptor phase is aqueous (although this need not necessarily be the case).Table 3. Diffusion" and partition coefficients R 1 -R4 R5 and R6 Do Da Do Da K b T/OC /10-9rn2 s-l rn2 s-' rn2 s-' rn2 s-I R1 R2 R3 R4 R5 R6 20 0.37 0.83 0.37 0.8 1 36.6 36.9 45.5 37.6 2.08 2.17 25 0.42 0.96 0.41 0.88 33.2 33.1 41.2 33.7 2.22 2.27 37 0.58 1.37 0.5 1 1.20 26.0 25.7 30.5 26.2 2.56 2.50 30 0.49 1.16 - - 30.5 30.6 37.0 31.0 2.38 - Diffusion coefficients for the control systems (Rl and R5) have been reported in ref. (16), (22), (23) and (29). Within experimental error ( f 3%), addition of any of the alcohols at the level used did not cause solvent viscosity to change.Hence D, and Do values for R2-R4 and R6 are the same as the respective controls (R1 and R5). Each value is the mean of at least 3 determinations. Standard deviations were not greater than 2%. 2 z N132 TRANSPORT AT LIQUID/LIQUID INTERFACES I C0(cO=caat t = ~ ) I o ( t = O ) I DO I I i X-I x-11 solute concentration diffusion coefficient distance normalized distance interfacial transport cross-sectional area A I Fig. 2. Schematic representation of the capillary system and definitions of the relevant physicochemical and geometric parameters. To describe the loss of solute from the capillary as a function of time requires that we solve Fick’s second law of diffusion ac,/at = Do(a2co/ax2) (1) with the appropriate boundary conditions.The mathematics are clarified by the use of the normalized variables u = co/c, x = x / l r = Dot/12 K = k,,l/D0 such that eqn (1) becomes au/aT = a2u/ax2. ( 6 ) The boundary conditions, in terms of the normalized variables, are ( a ) f o r O < x < l , a t T = O , u = l (7) ( b ) at x = 0, (au/ax)o = 0 (8) (c) at x = 1, = - K U ~ = ~ . (9) The boundary condition given by eqn (7) shows that the initial solute concentration in the capillary is c,. Eqn (8) indicates that there is a finite supply of solute in the capillary (i.e. there is no replenishment at x = 0). Lastly, eqn (9) describes the flux of solute across the aqueous/organic interface at the open end of the capillary. The heterogeneous-interfacial-transfer rate constant for this process ( koa) is related to the corresponding parameter for transport in the opposite direction (itao) by the solute’s bulk organic/aqueous partition coefficient ( K = kao/ koa).Eqn (6) is solved by the method of Laplace transformation following a similar procedure to that described for the calculation of drug release from controlled- delivery systems.30 The transform of eqn (6) with boundary condition eqn (7) is su - 1 = a2ti/ax2 (10)R. H. GUY, R. S. HINZ AND M. AMANTEA 133 the general solution of which is ii = Cl cosh s ] / ~ x + C2 sinh s ' / ~ x +s-' (1 1) where C, and C2 are constants. capillary after a time t is The cumulative amount ( M t ) of material which has transported out of the Mt = AZc, 1; - K U ' d r and AZc, is simply M,, the total amount of solute in the capillary at t = 0.Hence to evaluate M, requires that we find u,. This is achieved by using eqn (11) and the boundary conditions given by eqn (8) and (9) to yield, on substitution into eqn (1 2), M, = M , ~ - ' { K tanh s ~ / ~ / [ s ~ / ~ ( s ' ' * tanh s ' / ~ + K ) ] } (13) where the integration with respect to r has been achieved by division by the Laplace variable s. A simple inversion of eqn (13) cannot be found. At short times ( T < . 1 , s >> I), however, we can approximate the hyperbolic term tanh s'/* --+ 1 and eqn (13) reduces to M,/M,= . = ! ? ? - ' { K / [ s ~ / ~ ( s ' / ~ +K)]} which on inversion gives3' M,/M,=2(~/.rr)'/~+K-'[exp(K~r)erfc(Kr~/~)- I]. (15) (16) If K == 1, then for r << 1 eqn (14) can be further approximated by M I / M, = 2 - ' ( K / s 2 } = KT i.e.the release rate of solute from the capillary becomes a zero-order process. to the diffusion equation is the classic ('burst') tIi2 f~nction:~' If no interfacial barrier exists at the interface at x = I ( K + a) then the solution Mt/ M , = 2 ( r / ~ ) " ~ . (17) Eqn (15) is plotted in fig. 3 for various K values and is compared with the t ' / 2 equation, eqn (17). For the smallest K values eqn (16) provides a reasonable description of the release process. At long times ( r >> 1, s << 1 ; tanh s " ~ - s eqn (1 3) can again be inverted to give M,/M,= 1 - e x p ( - ~ r ) . (18) However, Hadgraft3' has shown that this expression is likely to be of value experi- mentally only if K = 0.1 or less.The kinetics in our systems fall outside this range and hence attention is focussed upon the short-time approximation and solution. R.D.C. EXPERIMENTS Flux measurements in the r.d.c. yield an overall solute transport coefficient ( P ) (bulk inner aqueous phase -+ bulk outer aqueous phase) given by'' P-' = 2(0.643 W-'/*) + h / a K D , + 2 / a k , , . (19)134 TRANSPORT AT LIQUID/LIQUID INTERFACES 0.050r 0 100 200 1 0 ~ ~ Fig. 3. Solute transport from the capillary as a function of time (7<< 1). Predicted profiles [eqn (IS)] for different interfacial barriers are compared with the release expected when no resistance to phase transfer exists [eqn (17)]. Each profile corresponds to a different value of K : (A) 250, (B) 100, (C) 25, (D) 75, (E) 20, and (F) 5.The first term describes substrate movement through aqueous diffusion layers on either side of the rotating filter (v is the kinematic viscosity of aqueous phase and W the cell rotation speed). h/aKD, is the barrier to diffusion through the IPM- impregnated filter of thickness h and porosity a. The third contribution to P-' is the interfacial transfer resistance. Experimentally we measure P-' as a function of W-Ii2 and force the theoretical slope through the data to obtain the intercept terms in which k,, is the only unknown. Since the partition coefficient (K) is determined independently, interfacial-transfer rate constants may be obtained for both aqueous + organic and organic + aqueous processes. RESULTS AND DISCUSSION The results from the capillary-technique experiments are summarized in table 4.The values of K were deduced from the experimental data using eqn (15). Interfacial transfer coefficients could then be obtained by application of eqn (5) with the values of the capillary length and either Do (systems Cl-C4) or 0, (systems C5 and C6). Rate constants spanning two orders of magnitude are reported. For the systems and times studied, between 0.3 and 2.5% of the capillary entrapped counts reach the receptor phase. Transport kinetics determined using the r.d.c. procedure are given in table 5. The manner in which the raw r.d.c. data are handled to obtain these parameters has been discussed.'6-21 In table 6 the kinetics and partition coefficients are analysed in the normal way'6918*20*21 to yield the thermo- dynamic parameters describing the phase-transfer processes.The capillary-derived data suggest that the technique has potential for the measurement of interfacial transfer kinetics. Fig. 3 shows that an upper bound on the rapidity of the measurable range exists but also implies that, in our studies, we have considered systems for which transport is slower (in some cases much slower) than this theoretical maximum. Most of the systems investigated have been pre- viously or concurrently studied by the r.d.c. technique. In most cases the capillaryR. H. GUY, R. S. HINZ AND M. AMANTEA 135 Table 4. Capillary technique:" experimental results experiment koa kao system duration/s 104rb 102M,/M,E K b / l P m s - * /lO+ms-' c1 200 c 2 200 c 3 75 150 200 c 4 200 c 5 200 500 C6 1500 8.40 8.40 3.15 6.30 8.40 8.40 24 60 180 1.40 f 0.04 1.40 f 0.12 1.41 kO.11 2.13 f 0.34 2.45 f 0.22 1.17 f 0.10 0.39 0.76 f 0.16 0.33 f 0.04 27 27 125 110 95 20 1.7 1.4 0.2 1.14d - 1.14' - 5.27' - 4.62' - 3.97' - 0.84 - - 0.204f - 0.1 68f - 0.024g a T = 25 "C for all systems. T and K are defined in eqn (3) and (9, respectively.Diffusion coefficients for the various systems (except C5 and C6) are given in table 3. For C5 and C6, T = Dat/ZZ and K = kaoZ/Da because the capillary holds the aqueous phase. ' Except for system C5 at 200 s, all values of M,/ M, are the mean ( f standard deviation) of at least 5 determinations. r.d.c. value found in this work was 1.54 x m s-', R.d.c. value found in this work was 1.68 X m s-' for this system; 0, = 1.2 x lo-' cm2 s-'.16 m s-' for this system; D, = 1.2 x I o - ~ cm2 s-'.16 m s-'.Ref. (16) gives koa = 0.28 x Ref. (18) gives koa = 0.086 x Table 5. Interfacial transfer kinetics determined with the rotating diffusion cell kao/ m s-' koa/ m s-' T/"C: 20 25 30 37 20 25 30 37 R1 51 51 56 63 1.39 1.54 1.84 2.42 R2 56 62 - 69 1.52 1.87 - 2.68 R3 52 57 64 65 1.14 1.38 1.73 2.13 R4 52 51 57 61 1.38 1.51 1.84 2.33 R5 17 24 38 86 7.9 11 16 34 R6 9.1 12 - 22 4.2 5.1 - 8.8 Table 6. Thermodynamic parametersa (at 298 K) of phase transfer and partitioning for the systems studied with the rotating diffusion cell' R1 R2 R3 R4 R5 R6 k,, AG' AS' koa AG' AS' K AG AH AS AH' AH' 35.9 9.9 44.6 25.0 -87 -66 -8.7 -15 -2 1 35.4 8.9 44.1 24.8 -89 -65 -8.7 -16 -25 35.6 10.3 -85 44.8 28.2 -56 -9.2 -18 -30 35.9 8.0 -92 44.6 24.0 -69 -8.7 -16 -25 37.8 69.8 39.7 61 .O 71 -2.0 9.3 38 107 39.5 39.1 -0.1 41.6 33.2 -2.0 6.3 28 -28 a AG and AH in kJ mol-', A S in J mol K-'.Deduction of the thermodynamic parameters from the kinetic constants has been described in detail elsewhere [e.g. ref. (16), (1 8) and (21)].136 TRANSPORT AT LIQUID/LIQUID INTERFACES procedure yields slightly lower values. Relatively speaking, the two methods do show reasonable agreement; for example, both techniques find that the acetic acid systems (C5 and C6) have the slowest kinetics and that the transport into IPM from water is the more rapid of the two. The reasons why the capillary measurements are consistently lower, though, remain unclear. It is noted that systems C l and C2 and systems Rl and R3 give identical k,, values and that the agreement here between procedures is good.Specifically loading the IPM phase with pentan-1-01 in C3, however, facilitates the transport process and yields a rate constant faster than that found with the r.d.c. Again, the reason for this discrepancy is not yet understood. In system C4 we attempted to populate the interface with a surfactant to hinder solute transport. A 26% reduction in k,, was observed and the difference is significant. The concentration of sodium dodecyl sulphate used is below the critical micelle concentration (c.m.c.). We found that above the c.m.c. the surfactant was able to solubilize some of the IPM (and dissolved radioactivity) out of the capillary, producing an inflated value of M,/Mm in excess of that predicted by eqn (17).For the r.d.c. experiments alcohol concentrations were chosen on the basis of previous investigations considering anaesthetic-membrane interaction^.^^-^^ It is first observed that the interfacial transport of salicylic acid (systems Rl-R4) is not affected by ethanol, pentan- 1-01 and benzyl alcohol. In these systems the activation free-energy barrier to transport is primarily entropic (table 6), AS* being large and negative in every case. This observation has been reported for a number of alkanoic acids traversing the dodecane/water interface'* and appears to be the effect of the carboxylic acid group. For methyl nicotinate the introduction of 100 mmol dm-3 ethanol does perturb the transfer behaviour.AGf for this solute in the absence of alcohol is enthalpic in origin and a positive AS* contribution of some magnitude exists (the size of AS* in the system has been reported to be slightly higher in earlier The AS* value has been attributed in part to the disruption of a structured interfacial c o n f i g ~ r a t i o n ' ~ - ~ ' ~ ~ ~ by the transporting solute. The implication of the results of the ethanol system (R6) is that the alcohol destabilizes this orientation (presumably of ordered water molecules) such that ASs decreases significantly. The observation is consistent with the hypotheses and results of Ueda et aL8-I5 and very similar to recent studies in our laboratory in which the effect of poly(ethy1ene glycol) (PEG) on the same system was ~onsidered.~' In the latter work PEG 400 concentra- tions of 10,25 and 40% v/v reduced the AS* terms from ca.100 J mol-' K-' to zero. Thus we have described a new procedure for studying liquid/liquid transfer and we have probed the action of various agents upon the interfacial region. Differences are identified between the procedures and between the effect of different perturbants on two different solute molecules. Because of the importance of interfacially related events to many biomembrane phenomena, it appears that further work is required in this area before an adequate physicochemical understanding is attained. We thank Drs F. C. Szoka and C. A. Hunt for advice and comments and the U.S. National Institutes of Health (AA-05781-01) and the Donors of the Petroleum Research Fund administered by the American Chemical Society (PRF- 13860-G5) for financial support.M. A. is a recipient of a President's Undergraduate Fellowship from the University of California, San Francisco. The expert typing of Andrea Maze1 is gratefully acknowledged. R. A. Robinson and R. H. Stokes, in Electrolyte Solutions (Butterworths, London, 2nd edn, 1959), chap. 10, pp. 261-264. ' K. W. Miller, Anesthesiology, 1977, 46, 2.R. H. GUY. R. S . HINZ AND M. AMANTEA 137 N. P. Franks and W. R. Lieb, Nature (London), 1982,300,487. F. A. Vilallonga, E. R. Garett and J. S. Hunt, J. Pharm. Sci., 1977, 66, 1229. D. A. Cadenhead and J. Osonka, J. Colloid Interface Sci., 1970, 33, 188. H. L. Booij and W. Dijkshoorn, Acta Physiol. Pharmacol. Neerl., 1950, 1, 631.H. Eyring, J. W. Woodbury and J. S. D'Arrigo, Anesthesiology, 1976, 38, 415. I. Ueda, H. Kamaya and H. Eyring, Proc. Natl Acad. Sci. USA, 1976, 73, 481. S. Kaneshina, I. Ueda, H. Kamaya and H. Eyring, Biochim. Biophys. Acta, 1980, 603, 237. S. Kaneshina, H. Kamaya and I. Ueda, J. Colloid Interface Sci., 1981, 83, 589. 10 I ' A. Shibata, Y. Suezaki, H. Kamaya and I. Ueda, Biochim. Biophys. Acta, 1981, 646, 126. l 2 A. Shibata, H. Kamaya and I. Ueda, J. Colloid Interface Sci., 1982, 90, 487. l 3 S. Kaneshina, H. Kamaya and I. Ueda, Biochim. Biophys. Acta, 1982, 685, 307. l4 S. Kaneshina, H. Kamaya and 1. Ueda, J. Colloid Interface Sci., 1983, 93, 215. l 5 Y. Suezaki, S. Kaneshina and I. Ueda, J. Colloid Interface Sci., 1983, 93, 225. W. J. Albery, J. F. Burke, E. B. Leffler and J. Hadgraft, J. Chem. Soc., Faraday Trans. I, 1976, 72, 1618. 16 l7 W. J. Albery and J. Hadgraft, J. Pharm. Pharmacol., 1979, 31, 65. l 8 N. H. Sagert, M. J. Quinn and R. S. Dixon, Can. J. Chem., 1981, 59, 1096. R. H. Guy, T. R. Aquino and D. H. Honda, J. Phys. Chem., 1982, 86, 280. R. H. Guy, D. H. Honda and T. R. Aquino, J. Colloid Interface Sci., 1982, 87, 107. R. H. Guy, T. R. Aquino and D. H. Honda, J. Phys. Chem., 1982, 86, 2861. 22 M. Ahmed, J. Hadgraft and 1. W. Kellaway, Int. J. Pharmaceut., 1982, 12, 219. R. Fleming, R. H. Guy and J. Hadgraft, J. Pharm. Sci., 1983, 72, 142. 24 M. Ahmed, J. Hadgraft and I. W. Kellaway, Int. J. Pharmaceut., 1983, 13, 227. 25 B. J. Poulsen, E. Young, V. Coquilla and M. Katz, J. Pharm. Sci., 1968, 57, 928. 27 N. Barker and J. Hadgraft, Znt. J. Pharmaceut., 1981, 8, 193. ** W. J. Albery and P. R. Fisk, in Hydrometallurgy '81 (SOC. Chem. Ind., London, 198 l), FS/ 1-FS/ 15. 30 J. Hadgraft, Int. J. Pharmaceut., 1979, 2, 177. 3 ' J. C. Metcalfe, P. Seeman and A. S. V. Burgen, Mol. Pharmacol., 1968, 4, 87. 32 P. Seeman, Pharmacol. Rev., 1972, 24, 583. 34 J. H. Chin and D. B. Goldstein, Science, 1977, 196, 684. 3s D. A. Johnson, N. M. Lee, R. Cooke and H. H. Loh, Mol. Pharmacol., 1979, 15, 739. 36 E. S. Rowe, Biochemistry, 1983, 22, 3299. 37 R. H. Guy and F. C. Szoka, J. Membr. Biol., submitted for publication. 19 20 21 23 N. A. Armstrong, K. C. James and K. C. Wong, J. Pharm. Pharmacol., 1981,31, 627. 26 A. D. Cadman, R. Fleming and R. H. Guy, J. Pharm. Pharmacol., 1981, 33, 121. 29 J. H. Chin and D. B. Goldstein, Mol. Pharmacol., 1977, 13, 435. 33

ISSN:0301-7249    

DOI:10.1039/DC9847700127

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 000. GE N E M L DISCUSSION Prof. P. Meares (University of Aberdeen) said: The introduction of the rotating diffusion cell has been a major advance in the study of interfacial kinetics of reactions involving two liquid phases. It is necessary, however, to be satisfied that the postulated hydrodynamic conditions are fully met in practice. Three questions arise in this connection. The surface area available for transport of solutes is a function of the shape of the menisci at the open ends of the pores and so will be a function of the interfacial tensions, which will not, in general, be equal on opposite sides of the membrane. The theory of Levich deals with a solid disc rotating in a liquid. It has to be considered whether the shear forces between the liquid in the disc and in the bulk phases are sufficient to induce circulatory motion within the pores which could make a convective contribution to the total mass flow, i.e.reduce the effective diffusional length of the pores. Thirdly, the possibility of interfacial turbulence at the pore mouths, driven by the disequilibrium between the liquids in contact, has to be borne in mind. Prof. W. J. Albery (Imperial College, London) said: Prof. Meares has frightened us all by drawing attention to the problems created by interfacial turbulence. What experimental methods are there for determining if interfacial turbulence is present or not? Dr. M. A. Hughes (University of Bradford) replied: Interfacial turbulence is a common phenomenon observed in liquid-liquid extraction systems.It is especially common when high concentrations of solutes in either phase are present. Simple direct observation is possible using a microscope,‘ but a more sophisti- cated technique is that of Schlieren photography. This system is described in ref. (2) and (3). M. A. Hughes, Int. J. Hydrometallurgy, 1978, 3, 85. A. Orell and J. Westwater, AIChE J., 1962, 351. H. R. C. Pratt, in Handbook ofSolvent Extraction, ed. H. I. Baird, C. H. Nanson and T. C. Lo (Wiley, New York, 1982), chap. 3. Dr. M. A. Hughes (University of Bradford) said: My first remark concerns the site of the reaction proposed in this work. It is suggested in Prof. Albery’s paper that according to other workers [ref. (S)] ‘The reaction takes place entirely in the aqueous phase.’. Actually, these workers did not say that: instead they suggest a thin reaction zone on the aqueous side of the interface where the interface is taken to mean a unimolecular layer of extractant/ diluent molecules.Liquid/liquid inter- faces are likely to be more diffuse than the air/liquid interface; thus the previous workers have considered ‘interface zones’ rather than ‘unimolecular layers’ as the site of reaction. If the site of reaction was a unimolecular layer, as suggested by the present authors, it might be expected that these commercial processes would be much more sensitive to surface-active impurities ; this is not the general experience. (1) I have two questions for Prof. Albery. The model proposed in this paper does not appear to have the protonated ligand as a species.There is some evidence 139140 GENERAL DISCUSSION from interfacial tension and acid-base titration measurements to show that oximes do protonate. However, the extent of this protonation relates to the structure of the oxime.' Would the authors comment on this aspect of the mechanism, which would be important in the stripping process. (2) There appears to be a fair amount of scatter in the points recorded in certain of the graphs. In particular, could the authors say (1) if the lines drawn through the points in fig. 3 are theoretical Levich lines or estimates of the best straight line through the points, (2) if the lines drawn through the points in fig. 5 could also be drawn as curves passing through the (0,O) and (3) if the line drawn through the points in fig.6 should not intercept the vertical axis, otherwise it implies that copper could be stripped under zero acid conditions. I believe the technique described here is a useful contribution to the study of liquid-liquid extraction processes for metals. The other techniques, used to study the rate of mass transfer, are all complicated by hydrodynamics which are difficult to account for. ' T. A. B. Al-Diwan, M. A. Hughes and R. J. Whewell, J. Inorg. Nucl. Chem., 1977, 39, 1419; J. S. Preston and R. J. Whewell, J. Inorg. Nucl. Chem., 1977, 39, 1675. Dr. B. H. Robinson (University of Kent) said: I have three questions for Prof. Albery. (1) Have you studied the extraction of any other reactive metal ions in addition to Cu2+(aq), e.g. Mg2+ or Co2+? Would a correlation be expected between transfer rates ( j , values) and the corresponding rate constants for complexation in bulk aqueous solution? (2) Have you considered varying the alkyl chain length of the ligand, which should enable you to distinguish between k , and k,? (3) Have the authors considered adding a kinetically inert charged surfactant, e.g.C8H17S04, to the system? This should serve to concentrate the Cu2+ at the interface and facilitate the complexation rate. F .ve you carried out any experiments which support this? Dr. A. Steinchen (Universiti Libre de Bruxelles, Belgium) added: I do not under- stand what is the actual surface of reaction. Indeed, in Millipore pores the surface of the meniscus may vary under the experimental conditions (pH and surfactant concentration), as may the interfacial tension.Prof. A. Sanfeld ( Universitk Libre de Bruxelles, BeZgium) remarked: When dealing with surface kinetics one needs to know details of the evolution of interfacial tension with the concentrations of reacting species. Prof.-M. M. Kreevoy ( University of Minnesota) said: DjugumoviC, Skerlak and I' have determined the profile of copper concentration in working membranes similar to those discussed by Albery and coworkers. As shown in fig. 1 of this comment, there is measurable accumulation of copper in a 5-layer, 0.3 mm thick, Gore-Tex2- supported membrane transferring Cu" from an acetic acid-acetate buffer of pH 4, to 2 mol dmP3 H,SO,. The active carrier was 2-oximinobenzoyl-4-nonylphenol (LIX- 65N3) [0.11 mol dm-3 in decahydronaphthlene (97% cis)]. Our apparatus was a modified dialysis cell4 in which the hydrodynamic resistances have been previously determined as a function of pumping rate.4 Experiments were interrupted at various40 30 m I E a - 2 20 U 6 v, I 2 --.n - I 10 0 0 Fig. 1. Cu" concentra GENERAL DISCUSSION I I t,*03 s 10 15 141 ion in the feed (0), in the strip solution (O), and the sum of the tw (0) plotted as a function of time. times, the membrane layers separated, and the Cu" concentration determined in each layer. Several of the resulting profiles are shown in fig. 2. From the slopes of these profiles it is evident that the internal resistance never becomes negligible in our experiments. Between 30 and 90 min the Cu'' content of the membrane is relatively constant, as shown by fig.1, and the CU" profile within the membrane is also relatively invariant, so the flux of Cu" out of the feed, into the strippant, and across the membrane should be about the same. From fig. 1 this common flux, J, is ca. 1 x 10-lomol cm-2 s-l. Within the membrane J is given by Fick's first law, eqn (1). A concentration near the interface with the feed is indicated by subscript f, i and a concentration near the interface with the strippant is indicated by subscript s, i: Since all the other quantities in eqn (3) are known, D', the apparent diffusion coefficient of the LIX-65N complex with Cu", can be calculated. A value of 5 x cm2 s-' for the migration of didodecylamrnonium picrate through a Gore-Tex-supported membrane with phenyl ether as solvent at 25 O C 4 At that temperature phenyl ether has a viscosity of ca.4 CP while the viscosity of cis-decalin at 40 "C is 1.9 cP.' Assuming that D' is inversely proportional to the viscosity of the solvent leads to cm2 s-' is obtained. A value of D' can also be estimated from our previous value of 1.9 x142 GENERAL DISCUSSION I I I I 0 1 2 3 4 5 Fig. 2. Cu" concentration profiles in 5-layered membranes at various times. The time of interruption, in minutes, is as follows: 0, 15; 0, 15 +30; a, 60 and 8, 120. Profiles similar to the 60 min profile were also obtained at 30 and 90 min. The profile marked 15 +30 was obtained from an experiment interrupted after 15 min, but the membrane layers were not separated for a further 30 min, to evaluate the possible distortion introduced by the operational delay in the other experiments (ca.2 min). a value of 4.0 x cm2 s-' for the present D'. Considering the uncertainties involved in the various estimates and assumptions, the agreement is respectable. Our internal resistances are higher than Albery's, and our D' value lower by about a factor of 10. However, most of the difference can be accounted for by physical differences between the two systems. Our Gore-Tex support has a void volume only around 0.5,4 while Albery's membranes are supported on Millipore filters, which have void volumes close to unity. The tortuousity of the Gore-Tex- supported membranes is also probably greater than that of those supported on Millipore filters. Finally, the viscosity of heptane, Albery's solvent, is only 0.4 CP at 25 O C 6 In order to compare the Cu" concentrations close to the interfaces, obtainable from fig.2, with those which would be at equilibrium with the feed and stripGENERAL DISCUSSION 143 solutions, given by [-I[ H +I2 [m]2[cu2+] * Ko/a = was evaluated in separator-funnel experiments. RH is LIX-65N and R,Cu is its copper complex. Brackets indicate concentrations and the over-bar indicates a concentration in the organic phase. Activities were assumed to be proportional to concentrations. Complexing of Cu2' with SO',- and with acetate, and dimerization of LIX-65N were taken into account. A value of 2 was obtained for KO,,. Using this value of KO,., the concentrations of R2Cu which would be in equili- brium with the feed and the strip solutions were calculated for the Cu" concentrations prevailing at the time the experiments were interrupted for Cu" profile determination. On the feed side, the Cu" concentrations obtained by extrapolation to the interface ranged from 0.23 to 0.43 of the calculated values.However, on the strip side, the observed values exceeded the calculated values by factors between lo4 and lo5. The latter require a substantial interfacial barrier at the stripping interface, in agreement with the conclusions of Albery and coworkers. The results for the feeding interface, however, imply that there is little or no interfacial barrier there, contrary to the conclusions of Albery and coworkers. This discrepancy may be due to the efficiency of acetate present in our feeds but absent from Albery's, in catalysing the interfacial transport of metal ions.Fig. 1 shows that the flux of Cu" into the strip solution is nearly constant for over 120 min, while fig. 2 shows that the concentration of R2Cu near the stripping interface varies considerably over this period. These observations support the contention of Albery and coworkers that rate of transport across the stripping interface is independent of [ R2Cu]. S. DjugumoviC, M. M. Kreevoy and T. Skerlak, J. Phys. Chem., to be published. Gore-Tex is a registered tradesmark belonging to W. L. Gore Associates, Inc. LIX is a registered trademark belonging to Henkel-America, Inc. L. A. Ulrick, K. D. Lokkesmoe and M. M. Kreevoy, J. Phys. Chem., 1982,49, 3651. F. Nauwelaers, L.Hellemans and A. Persoons, J. Phys. Chem., 1976, 80, 767. Lunge's Handbook of Chemisrry, ed. T. A. Dean (McGraw-Hill, New York, 12th edn, 1979), pp. p. T. Wasan, 2. M. Gu and N. N. Li, Faraday Discuss. Chem. SOC., 1984, 77, 67. 1 0- 1 09. Dr. R. D. Noble (N.B.S., Boulder, Colorado) said: I would like to make the following comments. (1) Stability theory shows that there would not be convective cells present in supported liquid membranes. The wavelength of the instability is much larger than the membrane pore size. (2) Concern over the size of the reaction zone at the interface depends on: ( a ) how one models the system and (6) what one wishes to calculate (flux or chemical reaction mechanisms). Can Prof. Albery estimate the size of the reaction zone at the interface? If so, would he provide an example.Dr. C. Tondre (University of Nancy, France) said: I would like to address a question to Prof. Albery concerning the different ways of monitoring the rate of interfacial reactions in the rotating diffusion cell. If the ring-disc method appears to be well suited to provide a continuous record of the rate of reaction without perturbing the kinetics, I do not understand how a titration of the acidic or basic144 GENERAL DISCUSSION products of the reaction using the pH-state method can be performed directly in one of the cell compartments without influencing the measured flux. Prof. W. J. Albery (Imperial College, London) said: First I must take issue with Prof. Astarita on the difference between an interfacial reaction and a reaction that takes place in a thin reaction layer in the aqueous phase.Prof. Astarita suggested in an unrecorded remark that this distinction was only a semantic one. In our view this is not the case. The distinction is real and, as discussed in our paper, will lead to different rate laws for the variation of the observed rate with the concentration of aqueous reactant. For an interfacial reaction the transition state must be located within a few hgstrom of the interface. The reactants are partially solvated by the two different solvents. For the reaction layer, the transition states are entirely in the aqueous phase and are located all over the reaction layer. In answer to Dr. Noble, the thickness of this layer can be as large as 10-2cm. Its thickness, 6, is determined by the balance between the diffusion of the oxime and the rate of its reaction with Cu2+: s = ( D / k[Cu2']) 1'2.( 1 ) The thickness of the layer varies with [Cu"], and this is why a different rate law will be observed. For very fast reactions the thickness S can approach molecular dimensions of 2 A or so; under these circumstances the distinction between the reaction layer and the interface becomes blurred. However, such a thin reaction layer requires k[Cu2'] to be as large as 10" s-'. Such a large value can only be found if the homogeneous reaction is diffusion controlled and the concentration of Cu2' is larger than 1 mol dmV3. These conditions are not found for our system. Hence in our system (and most similar systems) the reaction layer would have to be at least several pm thick and the distinction between the interfacial reaction and the reaction layer is a real one.I agree with Dr. Hughes that in his paper' he and his coworkers locate the reaction in a thin reaction layer in the aqueous phase. They discuss how the reaction-layer thickness depends on 'the balance between the rate of reaction and the rate of transfer of the species concerned'. This balance is given by eqn (1) above. Hence there is no doubt that these authors' are suggesting that the reaction takes place in a reaction layer. As argued above, the thickness of this layer must be at least several pm. In that case, as stated in our paper, all the transition states must be 'entirely in the aqueous phase'. The diffuseness of the liquid/liquid interface can only extend over a mater of Angstroms and therefore cannot really affect the distinction between the interfacial reaction (Angstrom) and the reaction layer (> pm).We do not claim that an interfacial reaction takes place in a simple unimolecular layer. The reorganisation of the solvents must extend through several layers, but the reaction zone is nevertheless much smaller than 1 pm. As regards surface impurities and surface-active agents Dr. Fisk and Mr. Choudhery have found that Teepol completely blocks the reaction, while traces of sodium lauryl sulphate can increase the rate by up to 100°/~. Prof. Kreevoy has found the same effect with octyl sulphate.2 We have examined the data on the protonation of the oxime ligand~.~ In the pH range 0-5 there is very little alteration in the interfacial tension for our P50 ligand.The authors3 themselves conclude that the protonation of this oxime is slight. We agree. Answering Dr. Hughes' questions about our experimental plots, first the gradients in fig. 3 of our paper are calculated Levich gradients allowing for the diffusion ofGENERAL DISCUSSION 145 both Cu2' and of the oxime ligand. The lines in fig. 5 cannot pass through zero. In fig. 5 we are plotting a reciprocal flux. So a value of zero corresponds to an impossible flux of infinity! As stated in our paper, the intercepts are in reasonable agreement with a term describing rate-limiting diffusion of the ML2 complex through the membrane. The experimental points in fig. 6 are perfectly clear; there is hardly room to stop the line before the y-axis.The results of Djugumovid et al. are most interesting. It is particularly gratifying that the same conclusions have been reached by two different groups using quite different experimental techniques. Taken tbgether these results should settle the controversy as to where the reaction takes place. Answering Dr. Robinson's questions, first we are studying other metal ions besides copper. Preliminary results on Ni2+ show that the reaction rates are an order of magnitude slower. We would expect a correlation between the rate constant for a homogeneous reaction in solution and the corresponding process taking place on a liquid/liquid interface. Indeed we have found such behaviour in our studies of modified electrodes. However, there are experimental difficulties in measuring the homogeneous reaction when the ligand is very insoluble.The idea of varying the alkyl chain length to distinguish between kl and k3 is a good one. Thank you. We have described above some results with surfactants. More interesting work remains to be done with such systems. In answer to Dr Tondre, the great advantage of the pH-stat method is that the pH of the outer compartment does not change, and hence has no effect on the flux. The two methods are complementary. For extraction the copper concentration is large but the effect of the release of H+ on the pH can be followed. For stripping the H' concentration is large, but the flux of Cu2' can be followed with the ring electrode. Dr. Steinchen, Prof. Sanfeld and Prof.Meares raise the question of the surface area, its curvature and the effect of surface tension on the area. We agree that these are interesting questions, but at the moment the experimental data are not sufficiently precise to enable one to see any effects arising from such variations in the surface area. The maximum possible difference is a factor of 2 between a flat disc of m2 and a hemisphere of 27v2. In practice the variation of the area with the composition of the solution will be much less than this. We therefore believe that these are second-order effects compared with the variation of the rate with the concentration of reactants. At the present state of the art we should concentrate on the first-order effects and establish the mechanisms of reaction. Turning to the second point raised by Prof.Meares, as to whether the rotating-disc motion can introduce circulatory motion in the pores, we agree with Dr. Noble that this is impossible. The thickness of the hydrodynamic boundary layer for the rotating disc is of the order of several mm. This is much larger than the radius of the pores of the Millipore filter (ca. lop5 cm). Hence the Millipore surface will appear to be uniform. Finally, we are intrigued by the problem of interfacial turbulence. At present we have no evidence for such effects, but it may be sensible to look for these effects with systems which are known to suffer (or enjoy?) large Marangoni instabilities. ' R. J. Whewell, M. A. Hughes and C. Hanson, in ISEC'77 (Canadian Institute of Mining and ' M.M. Kreevoy, personal communication. Metallurgy, 1979), vol. 21, p. 185. T. A. B. Al-Diwan, M. A. Hughes and R. J. Whewell, J. Inorg. Nucl. Chem., 1977, 38, 1419.146 GENERAL DISCUSSION ORGANIC AQUEOUS X i I Ph-7 Fig. 3. Concentration profile about an interface. Dr. R. D. Noble (N.B.S., Boulder, Colorado) asked whether Dr. Hughes could estimate the size of the reaction zone at the interface for his model? Could he provide an example? Dr. M. A. Hughes ( University ofBradford) replied: The definition of the thickness of the zone is somewhat arbitrary, since the model predicts an asymptotic concentra- tion profile of the extractant HR in the aqueous film, as shown in fig. 3. The interfacial flux NHR can be expressed as follows. (i) For the organic side N H R , ; = L R ( C H R - CHR,;).(ii) for the aqueous side By eliminating cHR,i from these equations we obtain the distance A’, e.g. We define the thickness of the reaction zone as A, = 3 A ’ ; hence Now the thickness of the diffusional film is related to the mass transfer coefficient by A d = DHR/kHR ( 5 )GENERAL DISCUSSION 147 so the relative thickness is given by which is our eqn (18) in the original paper. We can now estimate the thickness, A,, using the following typical values: DHR= m2 s-l, P H R = lo4, C‘HR=O.l kmol m-3 NHR,~ = lop8 kmol mP2 s-’, k,, = 1 0 - ~ m s-’ A, = %( - -&-) =r 3 x m. If the ‘solubility’ of the extractant in the aqueous phase is very low and the extraction rate is high even at low extractant concentrations then a very small thickness is predicted.Thus in the case of a substituted 8-hydroxyquinoline, used for copper extraction, it was found that P H R z lo5. NHR,i = kmol mP2 s-’ and cHR= 0.02 kmol mP3. Then Prof. W. Nitsch (Technische Universittit Miinchen) asked: Can the model be altered to incorporate a surface reaction which occurs simultaneously with a reaction in the zone? Dr. M. A. Hughes ( University ofBradford) replied: The model could be extended to incorporate a reaction occurring at an interface simultaneously with the reaction taking place in the reaction zone. However, this would require additional parameters in the model and these parameters are difficult to estimate from the experimental results. Thus a surface chemical reaction rate and surface concentrations are required.We are not sure if it is feasible to determine directly what reacts at the interface and what reacts in the film. Prof. M. M. Kreevoy ( University of Minnesota) said: Can the model accommodate the observation in the stripping of copper where the flux is independent of chelate concentration at the interface? Dr M. A. Hughes (University of Bradford) answered: We understand this to mean the proposal by yourself and Prof. Albery that CUR, accumulates at the interface during the stripping process. It is well known that with certain extractants a product can accumulate at the interface during extraction. Thus we have seen ‘films’ of copper-LIX complex formed at interfaces in diffusion cells and it is clearly demonstrated (by direct observation) that solid product precipitates at the liquid/ liquid interface when oxime is contacted with aqueous copper under high- concentration conditions.In other words the rate of complex formation can exceed the rate of its removal from the interface by diffusion into the organic phase. It is difficult to see how CUR, accumulates at the interface during the stripping process since conditions at the interface are favourable for the reverse reaction, whereby this component is consumed.148 GENERAL DISCUSSION The basic formulation of our model in the form of differential equations describ- ing concentration profiles is the same for both extraction and stripping processes. In the case of stripping the aqueous proton concentration is particularly high and the reverse extraction reaction equation can be neglected.The resulting relationships for flux calculations are quite simple in this case. Dr. A. Steinchen (Uniuersite‘ Libre de Bruxelles, Belgium) said:, I have two questions for Prof. Nitsch. (1) Could he comment on the instabilities observed in the uranyl nitrate extrac- tion from water to hexane with tributylphosphate at very low stirring rate. Has he observed surface motion with these reactants on non-stirred system (kicking of drops or emulsification) and under what conditions? (2) When the surface is covered by a surfactant how does one explain the formation of a rigid region in the centre of the interface after a critical threshold of the stirring velocity? Prof. M. M. Kreevoy (University of Minnesota) said: Komasawa et al.’ have reported a solubility in water of 3 x lop6 mol dm-3 for 2-oximinobenzoyl-4- nonylphenol (LIX-65N).* This implies a much larger distribution coefficient than the one reported in Prof.Nitsch’s table: lo7 might be a good guess; since LIX-65N is very soluble in most organic solvents. This observation strengthens the argument. I. Komasawa, T. Otake and A. Yamada, J. Chem. Eng. Jpn, 1980, 13, 130. LIX is a registered trademark belonging to Henkel-America, Inc. Prof. W. J. Albery (Imperial College, London) said: It is interesting that the shapes of the curves in the paper by Barker et al.’ are similar to those in our work2 and that the same type of double.reciproca1 plot is found in their fig. 7 for the variation of flux with substrate concentration. Mr Choudhery and I have also 0.02 - I I h N E E - I c 3 0.01 8 \ 5 v 0.OC / I I 1 I -0 0.1 0.2 { [(3)]/mmol dn~-~}-’ Fig.4. Variation of flux with substrate concentration for compound (3), N,N-bis(2-hydroxy- buty1)octadecylamine.GENERAL DISCUSSION 149 analysed the data in fig. 4 and 5 of the paper for the variation of flux with carrier concentration according to the same double reciprocal plot. Results for N7N-bis(2- hydroxybutyl) octadecylamine, compound (3), are presented in fig. 4. A reasonable straight line is found with a definite intercept that corresponds to a flux of 300 pmol h-' mmF2. Whereas the intercept in fig. 7 of ref. (1) could be caused by rate limiting transport through the membrane, the intercept in our figure, corresponding to infinite carrier concentration, cannot be caused ,by such rate-limiting transport.We suggest that it must be caused by rate limiting interfacial kinetics. Does Dr. Hadgraft agree? ' N. Barker, J. Hadgraft and P. K. Wotton, Furaduy Discuss. Chem. Soc., 1984, 77, 97. ' W. J. Albery, R. A. Choudhery and P. R. Fisk, Furaduy Discuss. Chem. SOC., 1984, 77, 53. Dr. J. Hadgraft (University of Nottingham) replied: I was interested to see that the transport kinetics in Prof. Albery's work contained a significant interfacial barrier. At present we have no conclusive evidence to suggest that our facilitated transfer scheme is limited by a slow interfacial term. However, I agree with Prof. Albery and, in the light of previous work,' think that the intercept is caused by rate-limiting interfacial kinetics. ' W.J. Albery, J. F. Burke, E. B. Leffler and J. Hadgraft; J. Chem. SOC., Furuday Truns. I , 1976, 72, 1618. Dr. D. Leahy (ICI Pharmaceuticals, MaccZesJield) said: There are a few points that I would like Dr. Hadgraft to elaborate. (1)Did he attempt any analysis of the intercept terms from ( k-', w - ' ' ~ ) plots? This might give interesting information on the diffusion coefficients and the size of the specie moving within the IPM-saturated membrane support. (2) Has he any other evidence to support the ion-pair transport mechanism? Could the RBR be partially neutralised as it moves within the membrane, the amine then acting as a proton sburce? (3) Has he any thoughts on an explanation for the large differences in rate- enhancing ability between amines of such similar structure? (4) He mentions that ionic strength changes modify transport rates. I would be grateful for an elaboration of this point.Dr. J. Hadgraft (University of Nottingham) replied: (1) The intercept in the ( k I , w plots comprises two terms, diffusion through the membrane and interfacial transfer. In the absence of knowledge concerning the latter it is not possible to calculate the diffusion coefficients. An effective diffusion coefficient could be measured but this would be meaningless. (2) We have conducted partitioning studies over a range of pH which suggest that the mechanism of transport is governed by ion-pair formation. (3) We have observed that interfacial kinetics are modified in the presence of phospholipids such as distearoylphosphatidylcholine.Small changes in the alkyl chain length alter the magnitude of the interfacial kinetic term.' The exact mechanism for this is not understood. (4) At an early stage we found that ionic strength altered the transport rates. However, we did not investigate this further. We chose in the experiments to maintain a constant strength. ' M. Ahmed, J. Hadgraft and I. W. Kellaway, Int. J. Phurm., 1983, 13, 227. Dr. B. H. Robinson ( University of Kent) asked: What is the thickness of the IPM lipid layer and has Dr. Hadgraft any idea of the concentrations in the membrane?150 GENERAL DISCUSSION Is the permittivity of IPM such that dissociation of ion pairs or proton transfer will occur. Dr J. Hadgraft (University of Nottingharn) replied: The thickness of IPM layer is 150 pm.We have not attempted to calculate absolute concentrations of the ion pairs in the membrane. In view of the complex sets of equilibria possible which are not fully understood it would be difficult to do at this stage. The permittivity of IPM is such that we would not expect ion-pair dissociation to be significant. Dr. M. Spiro (Imperial College, London) said: In discussing the transport- controlled rates obtained in high-concentration sulphuric acid media, Crooks and Chisholm concluded that diffusion is faster than predicted for stagnant conditions, with stirring taking place within $I p m of the liquid/liquid interface. i n aqueous 71% sulphuric acid . - --' Fig. 5. Schematic representation of toluene droplets moving through the sulphuric acid medium.I would like to show that this is what would be expected from a hydrodynamic analysis of the situation and that there is no need to invoke Marangoni effects. In a medium of ca. 74% sulphuric acid at 25 "C (see fig. 5), where the viscosity, q, is ca. 125 x kg m-' s-',' the Stokes-Einstein equation gives the diffusion coefficient D of toluene as 0.70 x lo-'* m2 s-'. In this medium the authors dispersed droplets of hexane containing toluene and emulsifying agent, and I estimate their density p as ca. 0.76 g ~ m - ~ . The mean radii r of the droplets is given as 1.21 p m in 73.6% H2S04 (fig. 1 of the paper) and as 2.00 p m in 74.8% H2S04 (fig. 2). The thermal velocity of these spheres is therefore 1.48 x m s-' (for r = 1.21 pm) 0.70 x m s-' (for r = 2.00 pm) u = (3kr/rn)'l2= ( 9 k ~ / 4 .r r p r ~ ) ' / ~ = where rn is their mass, k is Boltzmann's constant and T is the absolute temperature. That their motion is streamlined and not turbulent is shown by the small size of the Reynolds number (ca. 2 x low4). To obtain the diffusion layer thickness we have first to evaluate two dimensionless hydrodynamic parameters for this system. The first is the PCclet number, given by 25.6 (for r = 1.21 pm) 19.9 (for r = 2.00 pm). P e = r U / D = The second parameter, the Nusselt number Nu, follows from the equation of Brian and Hales2 2.27 2.13 (for r = 1.21 pm) (for r = 2.00 pm). Nu = J( 1 + 0.4802 Pe2'3) =GENERAL DISCUSSION 151 This leads directly3 to the effective thickness of the diffusion layer around the spherical droplets: 0.53 p m (for r = 1.21 pm) 0.94 pm (for r = 2.00 pm).aeff = r / Nu = Although no allowance has been made here for disturbance by Brownian motion: these values should be of the right magnitude. Both aeff values are < I pm, which nicely explains the findings of Crooks and Chisholm. ’ J. H. Ridd, Ado. Phys. Org. Chem., 1978, 16, 1. ’ P. L. T. Brian and H. B. Hales, AIChE J., 1969, IS, 419. M. Spiro and P. L. Freund, J. Chem. SOC., Faraday Trans. I , 1983, 79, 1649. W. B. Russel, Annu. Rev. Nuid Mech., 1981, 13, 425. Dr. C . Tondre (University of Nancy, France) said: I wish to put two questions concerning the work on kinetics in emulsions presented by Dr. Crooks: (1) He said that the reaction between the aromatic molecule and the nitronium ion, NO;, occurs in the aqueous phase because the last one is insoluble in the organic phase, whereas toluene can partition between the two phases, A comparable situation has been reported to occur for the reaction of oxygen with cobalt(I1)-L-histidine complex in perfluorotributylamine emulsion,’ where the complex is presumably in the water- continuous phase and the oxygen partition between the two phases with a marked preference for the perfluorinated phase. In this case the reaction kinetics are observed to be slower in emulsion in comparison with the homogeneous reaction in water and this result can be simply explained by considering a fast partition equilibrium of oxygen in addition to the reactions taking place in the homogeneous situation.Could Dr. Crooks say how his nitration reaction compares with the corresponding homogeneous reaction and would it agree with the preceding explana- tion? (2) Would Dr.Crooks think that changing the emulsifier in his experiments (the non-ionic Brij’s) to an anionic surfactant would increase the rate of reaction owing to the expected increase of the local concentration of NO,’ around the electrically charged emulsion droplets? ’ A. Berthod and J. Georges, Anal. Chim. Acta, 1983, 147, 41. Dr. J. E. Crooks (King’s College, London) said: In answer to the first question I draw attention to curves ( c ) in fig. 2 of my paper. These show the computed rates of nitration for an emulsion in which diffusion is infinitely fast, which are the same as for the homogeneous system making due allowance for the partition of toluene between the two phases.If the system were homogeneous, the nitration would be faster still. In answer to the second question, note that, as shown in fig. 1 of my paper, the reaction zone is quite large in terms of molecular dimensions. I would only expect the increase in NO: concentration due to adsorption at an anionic interface to extend over a small portion of the zone, The effect would be small unless the effect of the anionic surfactant was to drastically reduce the thickness of the zone. We have no experimental data. Prof. W. J. Albery and Dr. P. R. Fisk (Imperial College, London) (partly cornrnuni- cared): We have used the rotating diffusion cell to study the nitration of toluene.152 GENERAL DISCUSSION The reaction scheme is as follows: +----- ------- x - - - _ - _ _ _ _ + D In this scheme XD is the thickneis of the diffusion layer and can be calculated from the Levich equation.’ We obtain the following expression for the rate of reaction, J/mol s-*: J = ADco coth (XD/Xk)/Xk X, = (D/k)”’ (1) where and co is the concentration of toluene at the aqueous side of the liquid/liquid interface.The reaction was followed by measuring the increasing concentration of nitrotoluene in both the organic and the aqueous phases. Typical results for two different acid mixtures are shown in fig. 6 and 7. For the aqueous phase we find that the number of moles of nitrotoluene, naq, is given by: (2) n,, = Vco[ 1 - exp (-AD?/ mD)]. The ‘rate constant’ in the exponential term describes the supply of nitrotoluene across the diffusion layer into the volume, V, of the aqueous compartment.The steady-state concentration of nitrotoluene in the bulk aqueous phase matches that of the toluene at the liquid/liquid interface, co. This is because in the steady state the sum of the concentrations of toluene and nitrotoluene must be constant throughout the aqueous phase. In the bulk the concentration of toluene is negligible because it is destroyed by the reaction, and at the interface the concentration of nitrotoluene is negligible because it is being back-extracted into the toluene phase. The shapes of the aqueous curves in fig. 6 and 7 show the exponential approach to the steady state described in eqn (2). Analysis of these results therefore allows us to determine the diffusion coefficient for nitrotoluene in the aqueous phase and the vital parameter co.Unlike other workers we do not have to assume that there is local equilibrium at the interface and that co is simply determined by the partition coefficient. In fact we find that co is close to its equilibrium value. The number of moles of nitrotoluene in the organic phase norg is given by norg = J? = naq (3) where J is given by eqn (II). The results in fig. 6 and 7 show that the total number of moles of nitrotoluene increases linearly with time. From the gradient J can be found, and then using eqn (1) and the values of co and D determined from eqn (2) one can find k. Results obtained by this technique are compared with those of other a ~ t h o r s ~ - ~ in fig. 8. Reasonable agreement is found.The behaviour of norg in fig. 6 and 7 is different. In fig. 3 the nitrating mixture is strong (75% H2S04 by weight) and the rate constant is large enough for X , <XD.GENERAL DISCUSSION 153 2 - E" E ---. E 1 0 0 200 40 0 600 tlmin Fig.6. Variation of norg (0), naq (x) and ntota, (+) with time for a nitrating mixture (by weight) of 74.5% H,S04, 1.7% HN03 and 23.8% H 2 0 . Note that naq<< norg. Fig. 7. Variation of norg (0), naq (x) and ntotal (+) with time for a nitrating mixture (by weight) of 56.8% HZS04, 2.3% HN03 and 40.9% H 2 0 .154 GENERAL DISCUSSION 0 A X + A X + 0 0 X 0 60 70 80 [ H2S04]( wt '/o ) Fig. 8. Comparison of results for the second-order rate constant, kZ, where k2 = k/[HNO,] for different nitrating mixtures: A, ref. (2); +, ref.(3); X, ref. (5) and 0, this work. Hence the nitrotoluene is made in a thin reaction layer close to the interface. Most of it is therefore back-extracted into the toluene phase so that norg>> naq. In fig. 7, on the other hand, the nitrating mixture is weaker (57% H2S04 by weight). Here xk> X,,. Much of the reaction takes place in the bulk of the aqueous phase. Hence to start with there is no back-extraction. When the nitrotoluene has built up to its steady-state value in the bulk it diffuses back across the diffusion layer and then appreciable quantities appear in the organic phase. Results such as those in fig. 6 and 7 therefore confirm the accepted view that this reaction takes place in the aqueous phase. The rotating-diff usion-cell technique is particularly powerful in allowing one to control the balance between xk and XD so as to obtain the different partition behaviour of the product seen in fig.6 and 7. V. G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, N.J., 1962), p. 69. R. B. Moodie, K. Schofield and P. G. Taylor, J. Chem. SOC., Perkin Trans. 2, 1979, 134. G. F. Sheats and A. N. Strachan, Can. J. Chem., 1978, 56, 1280. A. N. Strachan, in Industrial and Laboratory Nitrations, A.C.S. Symp. Ser. No. 22, ed. L. F. Albright and C. Hanson (A.C.S., Washington D.C., 1976), p. 210. ' J. W. Chapman and A. N. Strachan, J. Chem. SOC., Chem. Commun., 1974, 293.GENERAL DISCUSSION I55 Dr. B. H. Robinson (University of Kent) said: Has Dr. Tondre any idea of the droplet sizes and concentrations in the microemulsion phase and how these vary with composition? At Kent we have made some size measurements using the technique of photon correlation spectroscopy on the CI2E4+ H 2 0 + alkane system in the single-phase region of the phase diagram and it was found that the droplet sizes varied with water content in a complex way because of surfactant partitioning between the interface and the continuous oil phase.Dr. Tondre’s transport mechanism involves an initial transfer of the metal-ion picrate as an ion-pair into decane. Has he considered the possibility of an interface reaction with the droplet and, in this connection, could I invite him to speculate on what happens to a droplet when it diffuses to the interface? For example, does it open up or bounce back elastically? Does Dr. Tondre think it would be possible to transfer water (or T20) between his aqueous compartments? Is the position of the maximum in fig.5 of the paper at 5% water independent of the picrate concentration? Dr. C . Tondre (University of Nancy, France): Concerning the first question of Dr. Robinson relative to droplet sizes and concentrations in the microemulsion phase, we unfortunately have little information available for the moment. We have tried to avoid the use of the word ‘droplet’, because it may be that spherical reversed micelles (as was found for instance with AOT systems) do not exist in the non-ionic systems investigated here, at least for low water contents. Some structural informa- tion is available for the system TEGDE + decane + water in the absence of hexanol. The addition of hexanol was found to be necessary in order to obtain Winsor I1 systems separating into two perfectly clear phases.When there is no hexanol present in the system, neutron scattering data’y2 have been shown to be consistent with ‘hank-like’ or ‘lamellar’ structures incorporating from 20 to 1000 surfactant molecules at low water content, and with oblate ellipsoids incorporating ca. 1500 surfactant molecules at high water content (the longer axis of the ellipsoid would be of the order of 200 A). The free surfactant concentration in the continuous phase was found to decrease rapidly on increasing the water ont tent.^'^ We do not know what is the effect of hexanol, but our results, on varying the water content of the system, do not seem in contradiction to such structural changes and we have not attempted to interpret these results other than in a very qualitative manner.The theoretical interpretation has been restricted to the case where the water content, and thus the structure of the dispersed phase is fixed. Assuming then ‘hank-like’ or ‘lamellar’ aggregates (for system V, which was used for these experiments, the ratio of the number of water molecules per ethylene oxide group is 2.3, which should be just sufficient to hydrate the surfactant heads) one can speculate on an aggregation number ranging between 100 and 1000, giving, respectively, aggregate concentrations of ca. 3 x mol dm-3. If the latter were to be true the assumption made in our model that there is one alkali-metal picrate molecule by aggregate (or droplet?) would become questionable, but how could we understand then the linear dependence shown in fig.6 of our paper? I come now to the second question concerning the transport mechanism that we have postulated. Adopting an interfacial reaction between the metal-ion picrate and the droplet, instead of a reaction involving the transfer of the picrate as an ion-pair into decane, would not change the form of the flux equation as long as both mechanisms are considered to be fast compared with diffusion [see ref. (4) by Wong et al. in the paper under discussion]. The problem in the case of direct transfer is to define the correct boundary conditions in order to derive the dependence of and 3 x156 GENERAL DISCUSSION the flux with the initial picrate concentration.In fact, considering that the interface is probably constituted of a layer of surfactant molecules, the situation is very similar to what happens when transfering pyrene or pyrene derivatives between two neutral vesicles. The solubility of pyrene in water is very poor, as is the solubility of picrates in decane. It seems nevertheless well established4 that the transfer always occurs through the aqueous phase. It is not easy to speculate on what happens to a droplet when it diffuses to the interface, but because there probably exists a layer of surfactant molecules at the interface I cannot imagine how the droplet could easily come in contact with the water phase in order to deliver some quantity of water or conversely to pick up a certain amount of water which could include picrate ions. On the other hand, the dynamic nature of these systems may be favoured by the presence of hexanol and perhaps should we not neglect the possibility of formation of 'holes' in the surfactant layer at the interface if Marangoni effects as described in Dr. Nakache's paper can take place? I would think that the transfer of water between the two aqueous compartments is certainly possible, but checking it with tritiated water does not appear to be easy to do for different experimental reasons: (i) the simple fact of introducing T20 in one compartment only will create a concentration gradient which initiates the transport by itself; (ii) iri the present state of our experimental set-up it is not easy to devise a way of measuring the radioactivity, unless extremely small volume samples can be used. Unfortunately we do not have enough results to give a definite answer to the third question concerning the position of the maximum when changing the picrate concentration. The transport experiments are not easy to perform and the effect of the water content was investigated at only one picrate concentration. Nevertheless we think that the position of the flux maximum is probably characteristic of the microemulsion structure and not of the picrate concentration: '3C-n.m.r. relaxation times of the surfactant head groups also show a characteristic change at 5% water.5 ' J. C . Ravey and M. Buzicr, in Surfactunfs in Solution, ed. K. L. Mittal (Plenum Press, New York, ' J. C. Ravey, M. Buzier and C. Picot, J. Colloid Interface Sci., 1984, 97, 9. 1983). M. Buzier, Thesis (University of Nancy I, 1984). H. J. Pownall, D. L. Hickson and L. C . Smith, J. Am. Chem. Soc., 1983, 105, 2440. A. Xenakis, Thesis (University of Nancy I, 1983); C. Tondre, A. Xenakis, A. Robert and C. Serratrice, to be published.

ISSN:0301-7249    

DOI:10.1039/DC9847700139

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 157-168 The Variational Principles of Onsager and Prigogine in Membrane Transport BY GERHARD DICKEL Institut fur physikalische Chemie der Universitat Miinchen, SophienstraBe 1 1, 8000 Munchen 2, Federal Republic of Germany Received 28th November, 1983 Whilst Onsager’s principle of least dissipation of energy and Prigogine’s principle of minimal entropy production both refer to the extremum value of a space integral, Hamilton’s principle refers to a definite time integral. With the help of cyclic variables, Onsager’s theorem can be transformed into a space-time variational problem. Using a method of Hilbert, a field of extremals can be obtained, composed of potential gradients pi and the coordinated geodesic slopes ji. Only these field quantities furnish the validity of linear thermodynamics ; the choice of arbitrary fluxes and forces, however, requires the introduction of excess terms resulting from a theorem of Weierstrass.1. INTRODUCTION In his first paper concerning reciprocal relations’ Onsager pointed out that they may be understood as a consequence of Rayleigh’s principle of least dissipation of energyS2 Later, following Prigogine’s recognition of the principle of minimal produc- tion of e n t r ~ p y , ~ Ono made attempts to clarify the relationship between these different principle^.^ Ono’s conclusions provoked a widespread reaction, and finally Gyarmati’ showed that Prigogine’s principle is not independent, but rather a special case of Onsager’s principle, valid for stationary states only. The energy of dissipation E can be obtained from an expression of the form f d2E/dVdt= C XiJi i = I where Xi are the forces and Jj the conjugated fluxes.’ In order to obtain further statements concerning the behaviour of such a system, further presumptions are necessary.Assuming a linear relation between fluxes Ji and forces Xi given by f Ji= C LikXk ( i = I 9 2 , . - . , f l j: 1 where Lik are indetermined coefficients, and introducing this into eqn (1), we obtain f u, called the local entropy production, is a quadratic expression of the forces Xi. Analogously, 0 can be expressed by a quadratic expression of the fluxes. A simple example concerning the diffusion of a binary gas mixture in the presence of a temperature gradient should demonstrate the principle of minimal entropy production as used by Prigogine.In this case the boundary conditions of the force 157158 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT Xi and X2 are given by XI (fixed force) = A T = constant; X2 (free force) = Ac (unknown). (4) Therefore eqn (1) and (2) can be differentiated with respect to X, but not X,. The minimum condition with respect to the unique variable force X2, given by A c in eqn (3), Le. d a dX2 -- -0 yields, considering eqn (3), and further, regarding LI2 = Lzl and eqn (2), J 2 = 0. (7) This means that in the minimum of entropy production the diffusion fluxes vanish. In this case we speak of free boundary conditions, because in contrast to AT the demixing effect Ac resulting from an unknown, ‘kinetic’ potential is not fixed by boundary conditions.Therefore Ac can be eliminated by differentiation. Any statement, however, concerning the demixing effect Ac itself cannot be obtained in this way. Free boundary conditions, playing an important role in open systems, can be taken into account using Hamilton’s theory of variation of the endpoint.6 Hamilton’s ‘eiconal’ is the base and the beginning of the potential theory. The term ‘potential’ was coined by Gauss later. Independent of this idea, Weierstrass founded the theory of fields of extremals by introducing the concept of field into the calculus of variations. Finally, this idea leads to Hilbert’s independence theorem, which is the core of our considerations in the next section. With the help of the boundary conditions resulting from the rigorous causal connection between forces and fluxes (potentials and extremals) in the general field theory, we turn in section 3 to an open system whose interfacial kinetics is ruled by free boundary conditions.The application of Routh’s method will be successful in solving this problem. In section 4 this theory is applied to a membrane problem (isotonic osmosis) investigated earlier. Finally, in section 5 the difference between an arrangement involving arbitrary forces and fluxes, as used in the thermodynamics of irreversible processes, and an arrangement using the forces and fluxes resulting from the theory of fields of extremals is discussed. 2. THE THEORY OF FIELDS OF EXTREMALS The calculus of variations starts out from a definite integral. According to a statement of Gyarmati’ the ‘integral principle of thermodynamics refers to the stationary (extremum) value of a space integral, whereas the Hamilton principle refers to a finite time integral’.Fig. 1 explains the latter principle. Assuming At is the interval, if a ray runs from A to B along the straight line in fig. 1, we ask how the air-lens interface must be formed in order that all other rays, represented by broken lines, need the same At. This time law is not immediately evident using geometrical optics. Similar difficulties arise in the case of other time integrals, e.g. the principle of least action. The success, however, also suggests the introductionG. DICKEL A 159 A. Fig. 1. Hamilton's principle of a system of rays. The condition that all rays pass from A to B in the same interval A t can be fulfilled by varying the air/glass (lens) interface.of a Hamiltonian form into thermodynamic transport problems. This can be perfor- med with the help of a cyclic variable, a term coined by Helmholtz.' A cyclic variable can be obtained by replacing fluxes by the number of objects or particles passing a fixed line or a cross-section. For example, a stream of cars will always be expressed by the number of cars passing a fixed line in unit time. Analogously a flux Ji of particles of type i will be measured by the number of moles dni/dt passing a cross-section q = 1 in unit time. The quantity ri, = dni/dt, rather than Ji, is the correct variable in a variational problem. rii is called a cyclic variable if the integrand of the variational problem depends on rii but not explicitly on ni.To replace Ji in eqn (1) by a cyclic variable, let us start from a frictional model where N types of particle i are moving with a velocity vi relative to the flux of the solvent, jL. We obtain f; is the frictional coefficient between the particle i and the solvent L. Considering (9) dni = ciq dx and ri, = ciqq ( i = 1,2, . . . , N, L) we obtain after integration of eqn (8) the integral form of eqn (1): E = IOA' joAx d L dt where N ~ L ( J , ci, f i i ) = 1 f;/ci(rii/q-riLci/qcL)2q dx (1 1) i = 1 is the Lagrangian in the volume d V = q dx and ri, represent cyclic variables. The remark that dL is a homogeneous function of second degree with respect to rii and riL and of degree -1 with respect to ci is useful, because it results in essential statements to follow.E represents the energy dissipated in order to maintain a stationary state of motion of N types of dissolved particles i and solvent L in a volume A V = q Ax over the interval At.160 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT According to the principle of least dissipation of energy we postulate a minimal value of the definite integral (10). This means the variation Sf6,E = S,S, loAf loAx dL d t = 0. Sf joAf d E = Sf IOAf dL( ril, ri?, . . . , riNl tiL) = 0. (12) According to Hilbert’ a solution of the double integral (12) can be obtained in two steps. In the first step we restrict ourselves to a volume element q dx and obtain the variational problem (13) The right-hand-side integral represents a line integral between the points t, = 0 and t, = At, whose value depends on the functions n , ( t ) .The solution of a variational problem requires one to choose the function n , ( t ) in such a way that integral (13) assumes its minimal value in comparison with those values which would be obtained by using instead of n,( t ) other functions n: ( t ) with the same values t, = 0 and t, = At. The functions n,( t), called extremals, can be conceived as integrals of the differential equation dnJq d t = j , ( i = 1,2,. . . , N, L) (14) where any j , represent the slope at the point (t, n,) of the unique extremal of the field of extremals. Generally j , is called the geodesic slope, in contrast to any arbitrary slope, j : , which does not furnish the extremum eqn (13).The geodesic slope j , can be obtained from the differential equation of the slope function. The latter is merely the Euler-Lagrange differential equation. However, we will adopt a different method. Let us assume we have found the geodesic slope. Taking the line integral (1 3) along the integral curves n,( t ) of the differential equation (14), according to Hilbert’s independence theorem we can transform the line integral (13) in an integral independent of the path of integration. Hilbert’s theorem is given by L dL(Gl, 62,. . ., GL)dt= dL(jl,j2,. . . , j L ) + C (ri,-qj,)[dL,,],,=,,, , = I L in the upper limit of the sum means that the sum must be taken over all particles N and the solvent. Whilst the integral on the left-hand side must be taken along the integral curves iii of eqn (14), the right-hand-side integral is independent of the path n( t ) .An intuitively geometric interpretation of the independent integral will be given at the end of this section. The right-hand side can be conceived as a Taylor series of dL in the neighbour- hood of the geodesic slopesj,, where all terms of higher order are zero. The remainder of this series is called the Weierstrass excess function,””2 the meaning of which is as follows. Taking the left-hand-side integral in eqn (15) not along the integral curves iii of eqn (14) but along arbitrary paths, the difference between the left-hand- side integral and the independent integral is given by Weierstrass’s excess function. This theorem will play a fundamental role in the last section of this paper.To obtain the connection between Hilbert’s theorem and Hamilton’s theory let us introduce the canonical variable^'^*'^ defined byG. DICKEL 161 Bearing in mind that we have restricted, in the first step, the variation with respect to time [eqn (13)] to the volume element d V = q dx, the canonical variable 7~ depends on the position x of the ‘strip dx’. The question now arises as to how the functions T , ( x ) must be chosen in order to furnish the minimal value of the double integral (12). This will be realized if i q T l ( x ) = -dp.,(x)/dx = -pi ( i = 1,2,. . . , N, L) (17) where p l ( x ) is any position function. p : is the geodesic slop: with respect to position. Substituting dpu, for vu, in eqn (16) we obtain the extremal condition &[dL,t],,=q,z = -dpI ( i = 1,2,.. . , N, L). (18) The N + 1 position functions pt must be determined later with the help of physical conditions. Applying Euler’s theorem of homogeneous functions to dL on the right-hand side of eqn (1 5), and taking into account eqn (16) and (1 7), we obtain the function of state d G in the strip dx i = I i = 1 The second term in the integrand represents a total differential. As the addition of any total differential does not change the variation, we can omit this ferm.l4 Going over to the double integral and integrating eqn (19) with respect to position and time we obtain, taking into account eqn (14), the familiar equation of state: L To understand Hilbert’s theorem, eqn (15), we note that in the independent integral the three variables t, ni and ri must be taken as independent variables for a particle i. The slope j i , however, must be expressed as a function of qi, by solving eqn (16) for jk13 This connection between potentials and fluxes is fundamental to the theory of fields of extremals.In contrast, in the left-hand-side line integral a particle i is represented by two variables, t and n , and the slope dn,/dt. The following interpretation should provide a physical statement of the indepen- dent integral in eqn (15). In fig. 2 a field of extremals, consisting of potential lines and lines of slope, is represented. Let us consider the real path of a particle through this field, given by the curved line. According to Hilbert’s theorem, this curve represents an arbitrary path n i ( t ) in the field of extremals.Decomposing this path into components parallel to the lines of slope and potentials, we obtain the graph represented in fig. 2. Assuming an infinite number of particles and decomposing their paths in the same manner, we obtain lines covering the field of extremals. As energy must only be expended in the direction of the slope and not along the potential lines, it can be obtained from the state of energy of the field of extremals [eqn (20)]. However, the picture of the field of extremals is imaginary, and therefore the geodesic slopes ji and pi are not physical realities which can be introduced a priori. Any theory which starts from fluxes and potentials should anticipate a result which follows a posteriori from the variational principle, eqn (12). This principle is based on the introduction of the cyclic variables rii and the canonical variables ri.However, the geodesic slopes ji and p : are the resulting extremals. The above-mentioned statement of Gyaramati’ concerning the integral principles of162 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT potential lines, p, . - ? a - fn 0 fn a 0) wl .d Fig. 2. The independent integral. The curve represents an arbitrary path of a single particle in the field of extremals, given by the geodesic slope j , and the equipotential lines p,. Resolving the motion into components parallel to these lines, and regarding that energy must be expanded only in the direction of j,, the independence of the path results. thermodynamics represents a sharp-witted and correct analysis, stating that Hamil- ton's principle involving a definite time integral must be excluded if the geodesic slopes j , are introduced a priori.In this case the rigorous causal connection between j , and pi arising from the theory of extremals will be missed. 3. BOUNDARY CONDITIONS IN THE THEORY OF FIELDS OF EXTREMALS Emphasizing that it is our task to take into account open systems, let us start from a strip dx bordering different media. An example is a permeable membrane separating two solutions. Assuming small concentration differences we apply the Erdmann-Weierstrass corner conditions' 1912,15 to the Lagrangian dL. We obtain [dL- rizdLfl,]I = [ d L - i , = 1 ri,dL,, (21) ! = I nt = 451 [dLf121kt=9/, =[dLfl,]fil=qJ, ( i = ' 9 2, * - ? L)* (22) d p ; =dprl and p:' = p:" ( i = 1,2,, .. , L). (23) Eqn (22) yields, considering eqn (18), Regarding Euler's theorem for homogeneous functions, eqn (2 1) yields, considering eqn (1 8) and (23), j ; =jy ( i = l , 2 , . . . , L). (24) By integrating eqn (23) from x = 0 to x = Ax and choosing p(xO)I = p(xO)I1, we obtain at any arbitrary position Ax p:=p:I ( i = 1,2,. . . , L ) . (25) These conditions, well known from thermodynamics, must be used in the case of a single phase boundary 1/11. Going over from an open system to a closed one, all fluxes vanish and the potential conditions given by eqn (25) remain. It therefore follows that in bothG. DICKEL 163 closed and open systems the boundary conditions are determined by the same potentials. In addition, in an open system the conditions concerning the geodesic slope, ji, given by eqn (24) apply.Because the values of these fluxes are unknown, we speak of free boundary conditions in open systems. The following example should illustrate the problem of free boundary conditions. Fixing a chain at two points A and B we obtain a catenary. This function results from a variational problem by postulating the minimum value of the potential energy of the free hanging chain and will be given by a function C(x, y, A, B). Fixing point A and varying B(x, y) we obtain a family of catenaries with B(x, y) as a parameter. Free boundary conditions can be obtained by providing the B-end of the chain with a roller, moving freely on a rail, whose slope is given by y’ = dy/dx.In this case all points B under consideration lie on a curve of slope y’. In this case the catenary is given by C = d[x, y, A, B(y’, x,)], which represents a one-parameter family of curves (catenaries). This leads to the problem of determining x,, lying on the rail, in such a way that the minimal value of the potential energy is furnished. These considerations show that in our case the fluxes ji in the boundary conditions (21) and (22) must be taken as parameters whose values must be determined in such a way that the minimum value of eqn (13) is furnished. It is convenient to differentiate dL with respect to li, whilst taking all other fluxes as constant (partial differentiation). This, however, would be unrealistic, as in thermodynamics boundary conditions are given by potentials.These potentials can be taken as constant immediately and the fluxes only indirectly. Therefore the variation must be performed in such a way that all potentials are fixed, with the exception of the potential connected with the parameter being varied. This method was developed by Routh.I6 To go over from the Lagrangian to the Routhian we apply Euler’s theorem of homogeneous functions to the Lagrangian and obtain L d L = $ C rii dL,,. i = 1 Introducing the canonical variables of eqn (18) we obtain the Hamiltonian: In order to perform the variation of the flux of the solvent we go over to the Routhian: by restricting the introduction of the canonical variables to i = 1,2, . . . , N. This Routhian represents a Lagrangian with respect to the solvent and a Hamiltonian with respect to the solute, or generally the sum of Hamiltonian potentials and a ‘kinetic potential’.According to this transformation we consider instead of the Lagrangian problem (1 3) the Routhian problem We conceive immediately that the Routhian fulfils the above-mentioned condition that the variation of the flux rii must be performed by fixing the values of the potentials of the dissolved particles.164 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT In the same manner we get the Routhians Rk(pI, p 2 9 * - - 7 p k - 1 , p k + l , - 7 p L , nk)= c - n i dpi + A i r i k r i k dLri, i = 1 ( k = 1,2,. . . , N ) . (30) The canonical variables of the Routhians (28) and (30) are given analogously to eqn (16) by (31) [(dRi)ri,ri,]ri,=qj, = r i q dx ( i = 1,2,.. . , N, L). To obtain the connection between eqn (16) and (3 1) the following method, demon- strated with R,, will be Differentiating eqn (26) Solving eqn (33) for riL obtain successful. Introducing eqn (28) into eqn (31), we obtain $[dLri,, + ri, dLriLALIriLZqjL = r L q dx. dLriL = riL dLhLriL + C rii dLri,hL. (32) with respect to ri, we get N (33) i = 1 dLriLriL and introducing this expression. into eqn (32) we or considering eqn (1 7) The application of the same method to Ri yields [$ dLri, - i r i L dL,irik]ri,=q,, = - dpk (3 5 ) (36) PHYSICAL CONDITIONS Whilst the Lagrangian dL involves a concrete physical statement, given by the right-hand side of eqn (1 l), the potentials resulting from a spatial variation of the formally introduced canonical variables represent undetermined physical quantities.Bearing in mind that the system of fluxes resulting from eqn (35) and (36) by the fntroduction of eqn (1 l), must satisfy general physical conditions, we have to find properties which must be fulfilled by these potentials. Two conditions should be taken into account. ( a ) THE INERTIAL SYSTEM. Regarding a stationary state of fluxes through a strip dx, for example a membrane in any medium, the strip dx (membrane) must be at rest in the absence of a pressure difference. From this it follows that the sum of all forces K , in the strip vanishes: c Ki = 0. (37) ( b ) THE FRAME OF REFERENCE. If any particle k of a number of N + 1 particles is taken as the frame of reference we postulate thatj, can assume any arbitrary constantG. DICKEL 165 value: j , = constant.(38) Regarding a closed system, e.g. a solution in a bottle, any variation in the fluxes at the boundaries must be excluded and we obtain In this case eqn (35) and (36) go over into eqn (18). By introducing eqn (1 1) into eqn (1 8) and eliminating the constant flux jL postulated by condition ( b ) we obtain the system of fluxes where L;k = Lkl = f f k , if i Z Ic, and K , is a function of the potentials pi and pL. side of eqn (18) by c;. From eqn (37) we obtain In order to apply condition ( a ) we go over to specific forces by multiplying each L L C ci dLh, = C, d p i = 0. i = l ;= 1 The zero on the right-hand side results from the fact that C ci dL,, is a function of zero degree in ci. As eqn (41) represents the Gibbs-Duhem equation we see, considering eqn (25), that the potentials resulting from the canonical variable are in agreement with the Gibbs potentials.We may therefore write dp; instead of dpi. A system of fluxes and forces of the form of eqn (40) cannot be applied to an open system, e.g. to transport through a membrane. In the latter case eqn (35) and (36) must be applied, and the force relation (37) yields where ri, = qji must be considered. An application of this relation, however, requires a knowledge of the constraints resulting from the membrane itself. Therefore we will illustrate the application of this theory with a concrete example. 4. ISOTONIC OSMOSIS14717 In a cation-exchange membrane, as used in the following investigations, the matrix of the membrane contains fixed ions consisting of phenylsulphonic acid molecules, whose hydrated ions can be exchanged by other cations, called counter- ions.Beneath these, in equilibrium with an electrolytic solution, anions are present as a consequence of the Donnan equilibrium. Whilst the fixed ions in the matrix itself represent the frame of reference for the counterions, the frame of reference for the Donnan ions, D, is the solvent. Therefore the variation dLhDhL, vanishes and the second and third terms in eqn (42) involve counterions C only. Forces resulting from the potential differences and the frictional forces are acting on all particles, including the fixed ions F. In order to restrain a flux j , of the fixed ions, a counterforce arising from the matrix of the membrane must be taken into account in the sum of forces 2 ci d p i in eqn (42).Assuming cL d p L = cL dp; +dp and cF dpF = cF (dpg + F d$), eqn (42) yields, setting dp; = 0, and regarding eqn166 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT 1 I 1 I I 1 I N I 5 16 - 9 I 2 m a -------• \ 1 1 1 I I " 0 1 2 3 4 5 6 I I I I 1 I 1 I t 0.963 0.918 0.864 0.804 0.671 inner scale: c,,,/mvaI cmP3 outer scale: a, Fig. 3. Isotonic osmosis of the system HCl/HCl+ LiCl. Top: The osmotic cell fluxes. Bottom: ( a ) Flux of water, jL, as a function of the mole fraction Li/Li +HC1; ( b ) fluxes of the ions, j,: X, H+; +, C1- and 0, Li'; ( c ) electric potential. The abscissa shows the concentration and water activity of the solution. [Reproduced with permission from ref.(18).] (1 1) and C cj dL,, = 0 the electromechanical equilibrium3 N N $ C fJi dx +; 1 J(cj/cL)jL dx + c,@ dl(, + dp = 0. i = I I = I Here cF is the concentration of fixed ions. (43)G. DICKEL 167 Eqn (43) should be applied in the following to an isotonic solution of N - 2 univalent counterions, one coion D and a fixed ion. From eqn (11) and (36) it follows in the case of a compensated flux of solvent that The Gibbs-Duhem equation has been taken into account. Finally eqn (43) and (44) yield, assuming j , = 0 and dpD = 0, dp = -$(c,- cD)@ d+. (45) C The relation C ci = cF+ cD has been taken into account. Investigations using the isotonic system HCI/(HCl +LEI) are represented in fig. 3.” Since in a solution of HCI + LiCl at any arbitrary concentration a hydrogen ion can be exchanged by a lithium ion without any change in the activity coefficient,” dpD = 0 can be taken as true.By using different HCI + LiCl mixtures the driving force between the boundaries of the membrane can be varied. Experiments involving measurements of the electric potentials have confirmed the validity of eqn (45). This represents a linear relation between the electro-osmotic pressure p and the electric potential +. The strong variation of the flux of water results from the variation of the coefficient $(cF- c,) with the concentration of Donnan ions. If cD= cF, an inversion of the flux of water takes place, whilst the electric potential shows normal behaviour. Finally, the linearity between fluxes and forces follows immediately from which results from eqn (43), taking into account eqn (44) and (45). Eqn (45) and (46), valid for isotonic solutions involving an arbitrary number N of solvated particles, must also be valid for a single electrolyte.In this case, instead of the diffusion potential occurring in binary isotonic osmosis, an electric field must be applied and so we go over to electro-osmosis. The only difference which was found between isotonic osmosis and electro-osmosis2’ was that in the latter case the flux of water vanishing in the point cF= cD does not change sign and we have jL = 0, if cD 3 cF. Taking into account that a potential assumes its minimum and maximum values at the boundaries, the following is true. Applying in the range of lower concentrations a fixed potential difference AEb to the boundaries, a flux of water arises, generating a streaming potential AEs opposite to A&.An inversion in the range of higher concentrations would mean an inversion of the streaming potential. In this case, in the membrane a potential difference AEi = AEb + AE, 3 AEb would result, in contrast to the above-mentioned theorem. In isotonic osmosis, however, an electrochemical ratherthan an electric potential, involving the streaming potential, is applied to the boundaries. 5. DISCUSSION A characteristic feature of the theory of fields of extremals is the rigorous connection between the potential gradient and the coordinated geodesic slope. This leads to two methods of obtaining ‘the complete figures of the variational problem’.” We can start from the Euler-Lagrange equation as in our first paper,14 or from168 VARIATIONAL PRINCIPLES IN MEMBRANE TRANSPORT Hamilton's canonical variable, as presented here.Comparing the latter representa- tion with the eiconal, the following difference is seen. Whilst in eiconal the velocities of the light are given, and the air-lens interface must be varied in order to satisfy Fermat's principle, in thermodynamics the interface is given and the fluxes must be varied in order to satisfy Onsager's principle. It must be emphasized that the boundary conditions jr = j f ' [eqn (24)] are not trivial. The volume flux as used in membrane theories does not satisfy this condition! Moreover, gradients of electrical and chemical potentials are frequently taken as independent forces in place of the correct electrochemical potentials.Only the latter satisfy the boundary condition Having chosen fluxes and forces arbitrarily, relations of the form j , =: -(p' + R ) must generally be taken into account, where R is the remainder of a Taylor series. This results from Weierstrass's theorem as follows. Assuming that we have found the unique slopes p : and j , of the field of extremals, R vanishes according to Hilbert's theorem. Taking n f ( ( t ) , however, along an arbitrary path where rif = qjf # qj,, the line integral on the left-hand side of eqn (1 5) does not assume its minimum value and the remainder R must be taken into account. This means that fluxes and forces in linear thermodynamics cannot be chosen arbitrarily. With regard to the results found with arbitrary arrangements of irreversible thermodynamics,21 for many transport phenomena the range of approximate linearity extends far beyond equilibrium, whilst for most chemical reactions the linear approximation holds only very close to chemical equilibrium.This result underlines the importance of extending Hamilton's principle to Onsager's theorem of least dissipation of energy, in order to obtain fluxes and forces which furnish linear thermodynamics. p! = ip. I 1. Onsager, Phys. Rev., 1931,37, 405. ' Lord Rayleigh, Proc. Math. SOC. London, 1873, 363, 357. I. Prigogine, Etude thermodynamique des phe'nomines irreversibles ( Thksis) (Dunod, Paris and Desoer, Likge, 1947). S. Ono, Adv. Chem. Phys., 1961, 3, 267. I. Gyarmati, 2. Phys. Chem. (Leipzig), 1967, 234, 371. W. R. Hamilton, Theory of Systems of Rays (Irish Transactions, 1828-1 830, 15-17). H. V. Helmholtz, Crelles Journal fur Mathematik, 1884, 97, 1 1 1 . D. Hilbert, Math. Ann., 1906, 62, 351. ' I. Gyarmati, Non-equilibrium Thermodynamics (Springer-Verlag, Berlin 1970). l o D. Hilbert, Arch. Math. Phys., 1901, 3, Reihe, Bd. 1 , 44. ' I 0. Bolza, Lectures on the Calculus of Variations (Chelsea Publishing Co., New York, 1973). l 3 C. Carathedory, Variationsrechnung, in Frank-Mises Diflerential-gleichungen der Physik I (Frie- l 4 G. Dickel und G. Backhaus, J. Chem. SOC., Faraday Trans. 2, 1978, 74, 115; 124. l 5 P. Funk, Variationsrechnung und ihre Anwendung in Physik und Technik (Springer-Verlag, Berlin 1970). E. J. Routh, On the Stability o f a Given State of Motion (Macmillan, London, 5th edn, 1891-92). G. Dickel and H. Honig, 2. Phys. Chem., (N.F.), 1974, 90, 198. J. C. Clegg, Calculus of Variations (Oliver and Boyd, Edinburgh, 1968). drich Vieweg und Sohn, Braunschweig, 1930), chap. V, pp. 227-279. I2 16 l 8 R. Kretner, H. Honig and G. Dickel, Z. Phys. Chem. (frankfurt am Main), 1977, 106, 30. l9 H. S. Harned and B. B. Owen, Physical Chemical of Electrolytic Solutions (Reinhold, New York, 1950). G . Dickel and R. Kretner, J. Chem. Soc., Faraday Trans. 2, 1978, 74, 2225. P. Chartier, M. Gross and K. S. Spiegler, Applications de la thermodynamique du non-kquilibre (Herman, Paris, 1975).

ISSN:0301-7249    

DOI:10.1039/DC9847700157

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 169-179 Motion Induced by Surface-chemical and Electrochemical Kinetics BY A. SANFELD" AND A. STEINCHEN Chimie Physique 11, Universitk Libre de Bruxelles, Campus Plaine, CP 231, Bd. du Triomphe, 1050 Bruxelles, Belgium Received 30th November, 1983 It is well known that motion at a liquid-liquid interface may be generated by the transfer of matter. The constraint is the difference in concentration profiles between both bulk phases. In the same way, surface-chemical, sorption or electrochemical reactions may also induce convection. The constraint in this case is related to the non-equilibrium kinetic steps. A general theory based on a linear analysis of stability shows the role of mechanical (density, viscosity, interfacial tension, surface elasticity), chemical (kinetic constants, composition) or electrochemical (electrical field, dielectric constant) parameters in the onset of interfacial deformations and movements.The stresses acting on the system are mainly due to Laplace- Kelvin and Marangoni effects. Experimental evidence observed for solvent-extraction reagents are analysed within the framework of our theory. Interfacial hydrodynamic instabilities leading to deformation and to surface motion have been observed in many fluid-fluid They also induce ordered behaviour with spatial and temporal patterns.24 These phenomena occur in non-equilibrium conditions owing to chemical and physical constraints: diffusional, thermal, mechanical, electrical and chemical effects. The non-linear character of the phenomena responsible for mechanical instability is directly related to the coupling between mechanical, electrical, chemical or thermal processes through the physico-chemical local properties of the interface (boundary co ndi t i o ns) .536 From a fundamental approach, these processes may be reviewed as an example of the concept of dissipative structures developed by the Prigogine-Glansdorff- Nicolis group7,* and extended to electromagnetic fields and to interfaces by Steinchen and Sanfeld.' Our purpose is to determine the constraints and the conditions responsible for the onset of surface-mechanical instabilities and their influence on the adjacent phases for single interfaces. Experimental evidence observed in solvent extraction and in spontaneous emulsification is analysed within the framework of our theory.In order to obtain analytical predictions, we restrict our study to a linear stability analysis of a reference steady state at mechanical rest, at a constant and uniform temperature and under a pure electrostatic approximation. BASIC RELATIONS The non-autonomous character of the interface is responsible for propagation in the adjacent bulk phases of the dynamical instability generated in the surface. The interface between two immiscible fluids is a transition region in which the chemical composition and the related physical properties change abruptly. It is 169170 INTERFACIAL KINETICS usually described by a geometrical surface model with singular surface properties: surface mass density, surface tension, surface charge, surface viscosities and surface diffusion.Out of mechanical equilibrium, the dynamical properties may also be described in terms of singular surface quantities” balancing the discontinuity of momentum fluxes from the neighbouring bulb phases. Motion at a single fluid interface can be modelled by considering the transverse ( T ) and longitudinal ( L ) waves coupled by a coupling term C. The stability in then ruled by a general dispersion equation L x T - c = 0. (1) The contribution of the transverse (longitudinal) displacement to C, together with the longitudinal mode L (transverse T ) is the tangential (normal) stress. Tangential stress leads to Marangoni effects while normal stress is the Laplace- Kelvin generalized They are the main boundary condition acting on the interfacial layer.Other boundary conditions are the surface mass and charge balances and electrical continuity or discontinuity conditions. Finally, a surface-state equation is required for the closure of the system of e q u a t i o n ~ . ~ ’ I ” ~ ~ In the incompressible volume phases (V u = 0) we write the following. (1) Momentum balance: pu +v P = F with the pressure tensor (P)j=p6j - p ( d j +<;) and the body forces F F = p g + V - T with the Maxwell stress tensor T defined by In this description p is the Kelvin pressure. (2) Maxwell’s equation: where pz is the charge density. ( 3 ) Mass balance: atpr=-V -(P,v)-V - JY+RY (7) where Jy are the diffusion-migration fluxes and R, the chemical sources. concentrations, In the absence of chemical reactions the Fick-Nernst laws read, for molar RT To describe the dynamics of moving charged and polarized interfaces we have to take into account an electrical double layer composed of (i) a thin region of molecular dimensions (compact layer) containing adsorbed ions and (ii) an external continuous region (diffuse layer) in which adsorption forces are negligible.A.SANFELD AND A. STEINCHEN 171 The boundary conditions are as follows. (1) Gauss’ equation: The surface charge density zT is related to the surface concentrations of the ions adsorbed in the compact layer ry: z r = c qr. Y (2) Jump in electrical potential, $: where the surface dipole density dipole moments of the adsorbed the compact layer. (3) Continuity of velocities in As$ = Ps n (1 1) Ps includes both the contribution from oriented molecules and from the potential drop through each phase p ( p = I, 11): uBls = us.(12) (4) Surface momentum balance Tti’ = V, ‘TT + F” + As(-P +T) - n (13) where r is the total surface mass density, ‘TT is the intrinsic surface stress tensor and Fs is the total surface intrinsic body force. In the horizontal plane eqn (13) is the Marangoni condition while along the normal coordinates z the same relation is the generalized Laplace-Kelvin condition. Along the horizontal coordinates x, y we assume for a two-dimensional Newtonian system : 3-1 where the phenomenological coefficients qdil and q s h are the intrinsic surface dilational and shear viscosities and u is the interfacial tension. An analogous equation may be written in the curvilinear coordinates.Assuming the superposition of all contributions to the total force, we get F“=I’g+FL +Fh where T g is the surface weight, Fh is the excess chemical force due to very short-range interactionsi6 and FL is the electrical force.” The surface tension, u, is thermodynamically defined by a mechanical contribu- tion uM due to the surface composition and an electrical contribution uE due to the influence of the double layer:” where u E = - &E2( “Jg*),lsx’ 4T ‘ I with g* the determinant of the matrix of the space fundamental tensor and 1 the coordinate curve of the field lines in the general curvilinear orthogonal coordinates.172 INTERFACIAL KINETICS ( 5 ) Surface mass balance: I;, = -T,(V us +a*) -V, * JSy - A,{Jc } - n +RSy (18) where V, us is the surface divergence of the surface velocity us, a* is the change of the surface metric, RSy is the source of surface chemical reactions, A,Jc n accounts for the interchange of mass between the adjacent bulk phases and the surface, JSy is the singular diffusion-migration flux on the surface V, - JSy = DSy(V,T, +z,T,V,$) with DSy the surface diffusion coefficient and T, the surface concentrations of the adsorbed ions.The sorption fluxes Jc are related to the difference in electrochemical potentials between the surface and the sublayers. (4) Change of interfacial tension: (20) svs, z 6VS 6a= --~i(o, k ) - + k!P(w, k ) L = - C a J T , where F: is the dynamical surface elasticity, 11,12 related to the longitudinal displace- ment Dvt, !P is a phenomenological dynamical quantitity related to the normal displacement, and o and k are the frequency and wavenumber of the perturbations. The longitudinal displacement is connected to the local variations of surface area A w W Y 1 -- 6V“J - -6 In A =- Dvz.0 0 The phenomenological coefficients E: and !P are related to all the relaxation processes due to mass exchanges, chemical reactions and electrical effects. The coefficients a, are directly connected to the surface state equation.18 For a surface perfect gas, a, = RT. Restricting our analysis to plane and spherical interfaces, we solved eqn (2)-(5) in terms of velocities along the normal or radial coordinates. Taking into account the boundary conditions [eqn (6)-(20)], we obtai-, the general characteristic equations eqn (1).Let us now analyse various situations related to the different constraints imposed on the reference state. RESULTS As we are mainly interested in surface chemical or electrochemical reactions for single interfaces, we now briefly summarize the results obtained for pure Fickian diffusion and sorption.6” 1,19,20 PURE DIFFUSION Let us first consider plane interfaces. A necessary and sufficient condition for the onset of surface monotonous motion is that diffusion of only one species between phase I and phase I1 occurs from the liquid with the smallest value of D to the fluid with the largest value of 0.’’ Surface viscosity has a damping effect and the critical constraint of diffusion increases with viscosity, with surface elasticity and with the diffusion coefficient.Unstable periodic states are reached when --<-,with v = p / p . D’ v DII y I lA. SANFELD AND A. STEINCHEN 173 Moreover, the critical time for the onset of convective cells at the marginal state may be calculated easily from the diffusion coefficient, the composition and the surface viscosity. Our results are in good agreement with the e ~ p e r i m e n t . ~ , ~ * ~ ~ ' For spherical interfaces the results are also analysed in terms of a critical value of the ratio of the diffusion coefficients. New possibilities of oscillatory instabilities appear for the motion in toto of d sphere and for a pendant drop. (Interesting predictions are obtained for two diffusion species.22) SORPTION KINETICS AND DIFFUSION Pure diffusion kinetics in the bulk phase does not always account for the onset of motion in the interface, and relaxation mechanisms have to be considered.For example, non-equilibrium sorption processes may occur between sublayers and surface owing to orientation of polar head groups. 17923-26 We only consider that no matter is accumulated in the sublayers in the reference state as well as in the perturbed state while no matter is accumulated in the surface in the reference state. Transfer I -+ I1 by diffusion-sorption leads to unstable aperiodic regimes for D' < DII; I1 -+ I reveals new possibilities of instabilities.26 On the other hand, it is predicted that the potential barrier due to controlled sorption kinetics has a stabilizing effect in the oscillating regime.24 SURFACE-CHEMICAL REACTIONS AND SORPTION From eqn (18) we may define the kinetic matrix element Cyp (surface-chemical reactions and sorption steps): The linear stability analysis leads to a general dispersion relati~n:~" 1*28-30 H(w, v, k ) + kR(w, v, k): = 0 (23) 0 where H and R are functions of w, v and k.The quantity E / O is derived from the basic equation^^"^^ N 1 a, det L(') E y = l 0 det L _ - - where the matrices L and L(y) are, respectively, defined by L,, = - C,,p + 6; (w + k2Db) L$) = L,, + 6; (r; - L~,). The matrix L is only associated with non-convective surface kinetic processes while the matrix L(") is closely related to the coupling between the convective and the chemical processes. The general conditions for mechanochemical surface instabilities may summar- ized as follows. (1) Equilibrium surface-chemical reactions never induce mechanical instability. The only possibility of surface motion is then a drastic decrease in the interfacial tension, reaching transition zero or negative values due to very active174 INTERFACIAL KINETICS surfactants.(2) For only one fluctuating species the chemical reaction in itself has to be unstable to obtain the onset of surface movements. This is the case for autocatalytic or cross-catalytic mechanism^.^^' 1,31 (3) For two (or more) fluctuating species, the conditions are not so drastic. An intrinsically stable chemical reaction coupled with the hydrodynamic process may induce mechanical instability.5327731 (4) A stable chemical reaction may be destabilized by mechanical constraints (for example a difference of den~ities).~' (5) At spherical interfaces the onset of motion may lead to local deformations and to translation in t o t ~ ., ~ It is interesting to analyse the necessary conditions for the mechanochemical instability when: (i) the viscosities are negligible and (ii) the viscosities are taken into account. (i) This situation means that we are now looking for the unstable condition E / w < 0. Dalle-Vedove and Sanfeld28-30 obtained simple analytical necessary condi- tions for two fluctuating species (1,2). ( a ) Non-auto- or non-cross-catalytic chemical steps (C, I < 0; C,, < 0; C, , C22 - C,,C,, > 0). The monotonous convective regime starts when where C$ = Clj - k2Dt. The time-oscillating regime starts when ma2c21 -~,c2*22)+r~(~,c12-~2c;i; ) > O (28) 'rKa2C21 -a,C2*2)++r20(~1CC12-~2C;k,) (29) 4[r7@2c,, +a,CT,) +r20("1c12 +a2C2*2)1 with 4 > 1.( b ) Auto- or cross-catalytic chemical steps. An intrinsically unstable aperiodic (periodic) scheme may lead to monotonous (periodic) surface convection. However, oscillatory (aperiodic) solutions are also possible. For stable kinetics ( C, I + C2, < 0; C, , C,, - C12C21 > 0) the situation is comparable to the non-auto- or cross-catalytic kinetics. For example, oscillatory movements can be induced when conditions (28) and (29) are fullfilled. (ii) The viscosities have a damping effect when the kinetics is intrinsically stable. They have a damping effect on the oscillatory (aperiodic) mechanochemical regime when the kinetics is monotonously (periodically) unstable. For large viscosities in the bulk phases, the influence of the chemical mechanism is dominant when the periodic (aperiodic) instability is due to chemical unstable periodic (aperiodic) schemes.For small viscosities in the bulk phase it seems possible to stabilize the aperiodic (periodic) mechanochemical regime when the kinetics is aperiodically (periodically) unstable by itself. Several examples have been discussed in previous paper^.^*-^^ EXAMPLE OF INSTABILITY IN SOLVENT-EXTRACTION REAGENTS We now focus attention on experimental observations in solvent-extraction reagents within the framework of our theory. During the experiments interfacial movements, kicking of drops and spontaneous emulsification are observed.' In the liquid-liquid extraction of nickel from acid sulphate aqueous solutions using various mixtures of D2EHPAH and D2EHPANa in toluene, Durrani et observed wakes.They suppose that this effect is due to emulsification by the sodium salt. In the liquid-liquid extraction of copper from acid sulphate solutions using this time various mixtures of D2EHPAH and D2EHPANa in xylene, Dupeyrat andA. SANFELD AND A. STEINCHEN 175 N a k a ~ h e ~ ~ observed pendant drops, surface motion, organized cells and emulsifi- cation. In order to analyse such complicated situations we need knowledge of the various steps in the extraction mechanism. This means not only the value of the kinetic constants but also those of the physico-chemical parameters: composition, densities, interfacial tension, viscosities and diffusion coefficients. An interesting speculative discussion on the extraction mechanism reveals’the following possible rate-deter- mining steps in the extraction of metals by organic extract ant^.^^ (1) Diffusion of solvated metal ions and organic solvated extractant (monomers and aggregates) from the bulk phase to the interface, (2) sorption kinetics between sublayers and surface, (3) orientations of the extractant with polar groups towards aqueous phase, (4) solvation-desolvation kinetics at the interface, ( 5 ) formation of acid-metal complexes (monomers and aggregate), (6) ionization processes in the interfacial region, (7) expulsion of cations in the aqueous phase, (8) hydration of cations, (9) reorientation of the metal complexes to carry the metal to the organic side of the interface, (10) desorption of the metal complexes or exchange of ligands and (1 1) diffusion of the metal complexes to the bulk organic phase.” As an example we analyse a very simple model in the liquid extraction of copper from sulphate solutions of alkyl phosphoric acid (R are reservoirs).k5 U+Y a I + X k-5 k6 I?+Y F== M+X k-6 K6 I + Z e M k , M __+ R5 K 8 2R5 R,j k9 x - xa (adsorption of copper from a reservoir R,) (dimerization equilibrium of the extractant) (adsorption and Volmer desorption of the extractant) (dissociation of the extractant) (first complexation) (second complexation) (i o ni zat i o n equilibrium) (Volmer desorption of the complex) (dimerization of the complex) (desorption of the proton) * Within this domain many important contributions have recently been published by various groups, particularly in the Proceedings of the International Solvent Extractions Conferences ‘ISEC’ (London 1974, Toronto 1977, Montreal 1979, Liege 1980, Denver 1983); in particular see the papers of Hughes, Hanson, Bauer, Danesi, Yagodin, Cox, Flett etc.and their coworkers.176 INTERFACIAL KINETICS As observed by several a ~ t h o r s ~ ~ , ~ ~ the diffusion step seems not to be always the determining step. We will then assume that only competitions between sorption and chemical reactions may induce convective motion. The steady state is characterized by conservation of fluxes: Ms M k l R l = k 7 M - M, - M (G) y s k3R4 = k-3 Y- Y,- Y where M, and Y, are the saturation concentrations of the complex and of the extractant, respectively.The right-hand side of the two steps is a Volmer desorption step. We further suppose that the time evolution of the fluctuations of X and Y may be considered as quasi-stationary. The calculation of conditions (27)-(29) shows that the second complexation is responsible for the onset of mechanical instability, although the kinetics is always stable per se. For k,> k-6 an aperiodic convective regime may be predicted. For k, < k-, a periodic convective regime is possible. Explicit competitions between step (6) and the desorption (k,, kP3, b), as well as the fluxes k,R, and k , R 1 , may be important. Moreover, the role the parameters a,, [eqn (20)] is discussed in connection with the surfactant character of the extractant and of the complex.A much more realistic model would be the competition of the monomers Y and M with the dimers D [(RO)2POOH], interface and For example, we may analyse the previous model using the following additional steps: R3 D (sorption of the extractant) D + U e M +2X M + D e A +2X A + U UA (formation of the aggregate complex) UA --* & (complexation of the dimer with copper) (complexation of the dimer with the monomer) (desorption of the complex dimer). The appropriate calculations have not yet been carried out. which play an important role on the mechanism of Finally, we shall study the influence of the interfacial activity and of the viscosities ELECTRICAL AND ELECTROCHEMICAL CONSTRAINTS All the results have been published in a general (i) CONTINUOUS MODEL (DILUTE SYSTEMS) The system considered consists of a charged plane interface, including a compact layer between two immiscible ionic solutions with dielectric constants E' and E".The surface charge density is compensated by the integral charges of two electrical diffuse layers of thickness K - ' = ( ~ R T / 8 , r r z ~ C , ) " ~ (with C, the concentration inA. SANFELD AND A. STEINCHEN 177 the bulk phase, E = 0) extending into the neighbouring phases. The interfacial tension of such systems involves a mechanical term due to the free energy of the electrical double layers" (3 0 ) (T = a M -UE with Let us consider two situations. (1) Restored Boltzmann macroscopic distribution in the diffuse layers. The constraint is the jump in the electrochemical potential between both phases, which remains uniform in each phase. From an analysis of the characteristic equation it is shown that only the negative contribution, aE, to the total surface tension, a, may be responsible for the onset of surface motion.The marginal stability condition is then a = o or IaMl = I a E l . (3 2) Moreover, the viscosity increases the wavelength of the fastest rate of growth and reduces the fastest rate of growth; it thus has a stabilizing contribution. (2) Non-restored Boltzmann distribution in the diffuse layers. In this case the relaxation of diffuse layers (KD/A) is of the order of magnitude of the characteristic time of the perturbation ( w - ' ) . The constraint is also the discontinuity of the electrochemical potential, but in the perturbed state this quantity does not remain uniform in each phase.We have restricted our analysis to ideally polarized systems (no net fluxes through the interface) and to uni-univalent electrolytes. Instabilities are obtained even for a non-vanishing total surface tension 0. For low surface charge the general rules for the stability are Criterion (33) is in agreement with the experiments of Watanabe et aZ.44 on electrical emulsification of the system H20 + KCl in contact with a solution of sodium dodecyl- sulphate in methylisobutylketone. For a small potential drop or large surface charge the general rules are $Is - $& > +lls - $!* (stable) +Is - +k < +'Is - +Fa (unstable). (34) The system thus becomes unstable if the phase where the potential drop is largest is also the phase with the smallest pp.These effects could also partially explain the mechanical instabilities observed by Nakache and Dupeyrat.' (ii) DISCRETE ELECTRICAL AND CHEMICAL INTERACTIONS For large surface charges [e.g. for ionized monolayers spread at an oil (o)/water (w) interface] discreteness-of-charge effects have to be considered. The counterions are then located in an outer Helmholtz plane near the plane of primary charges (the inner Helmholtz plane). These two planes are separated by a layer of strongly oriented water molecules. The constraint is due to the absence of exchange between the inner Helmholtz plane and the solution. When dipoles are spread at an interface,178 INTERFACIAL KINETICS discrete interactions also exist between them. The surface tension for these two types of discrete systems (charged or dipolar layers) also consists of a mechanical part uM and an electrical part uE due to the electrical interactions between charges or dipoles.Mechanical instabilities are predicted in such systems even for (uEl < loM(. The general rules are pwpw > pop0 (stable) pwpw = popo (marginally stable) pwpw < pop0 (unstable). (3 5 ) The theoretical background of the influence of density, viscosity and dielectric constant on the onset of surface motion is disc~ssed.~’ Excellent agreement with criteria [eqn (35)] is obtained for experiments performed on medicinal paraffin + water systems with cholesterol and sodium dodecylsulphate. The inequalities in relation (35) are also the conditions for emulsification and de-emulsification.We thank Drs Dupeyrat, Nakache, Saumagne, Gentric, Bauer, Cote, Dalle Vedove and Adler for stimulating discussions. We also thank the C.E.E. (Actions de stimulation), the Belgian Government (National Education Ministery) and the F.N.R.S. Belgium for financial .support. J. T. Davies, Turbulence Phenomena (Academic Press, New York, 1972). H. Linde, P. Schwartz and H. Wilke, in Lecture Notes in Physics, ed. T. S. S~lrensen (Springer-Verlag, Berlin, 1979), vol. 105, p. 75. A. Orell and J. W. Westwater, AlChE J., 1962, 8, 350. A. Sanfeld, A. Steinchen, M. Heunenberg, P. M. Bisch, D. Gallez and W. Dalle Vedove, in Lecture Notes in Physics, ed. T. S. Sgrensen (Springer-Verlag, Berlin, 1979), vol.105, p. 168. T. S. S~rensen, in Lecture Notes in Physics, ed. T. S. Sfirensen (Springer-Verlag, berlin, 1979), 105, p. 1 . ’ P. Glansdorff and I. Prigogine, Thermodynamics of Structure, Stability and Fluctuations (Wiley- Interscience, London, 1971). G. Nicolis and I. Prigogine, Selforganization in Non-equilibrium Sysfems (Wiley Interscience, New York, 1977). ’ A. Steinchen and A. Sanfeld, in Modern Capillarity, ed. F. C. Goodrich and A. I. Rusanov (Akad-Verlag, Berlin, 1980). l o L. G. Napolitano, Acta Astronautica, 1982, 9, 1999. I ’ M. Hennenberg, Thesis (UniversitC Libre de Bruxelles, 1980). l 2 P. M. Bisch, Thesis (UniversitC Libre de Bruxelles, 1980). l 3 R. Ark, Vectors, Tensors and the Basic Equations of Fluid Mechanics (Prentice Hall, N.J., 1962). I4 V.Mohan and D. T. Wasan, in Colloid and Interface Science, ed. M. Kerker (Academic Press, New York, 1976), vol. 4, p. 430. l 5 D. T. Wasan, N. F. Djabbarah, M. K. Vora and S. T. Shah, in Lecture Notes in Physics, ed. T. S. S@rensen (Springer-Verlag, Berlin, 1979), vol. 105, p. 205. ’‘ A. Steinchen, Thesis (UniversitC Libre de Bruxelles), 1970. l7 A. Sanfeld, Introduction to the Thermodynamics. of Charged and Polarized Layers (Wiley Inter- science, London, 1968). R. Defay, I . Prigogine, A. Bellemans and D. H. Everett, Sur$ace Tension an Adsorption (Longmans- Green, London, 1966). ’ E. Nakache, M. Dupeyrat and M. Vignes-Adler, J. Colloid Interface Sci., in press. l 9 M. Hennenberg, T. S. Smensen, and A. Sanfeld, J. Chem. Soc., Faraday Trans. 2, 1977, 73, 48. ‘O T. S.Smensen and M. Hennenberg, in Lecture Notes in Physics, ed. T. S. Sarensen (Springer-Verlag, 2‘ C. V. Sternling and E. K. Scriven, AlChE J., 1959, 5, 514. 22 A. Marquez, A. Sanfeld and W. Dalle-Vedove, in Stability of Emulsion and Microemulsion (Special Report Belgian Government, Brussels Region, 1980). 23 P. Joos, G. Bleys and G. PetrC, J. Chim. Phys., 1982, 387. Berlin, 1979), vol. 105, p. 276.A. SANFELD AND A. STEINCHEN 179 2 4 I. Panaiotov, A. Sanfeld, A. Bois and J . F. Baret, J. Colloid Interface Sci., in press. 25 M. Hennenberg, P. M. Bisch, M. Adler and A. Sanfeld, J. Colloid Interface Sci., 1979, 69, 128; 26 M. Hennenberg, A. Sanfeld and P. M. Bisch, AIChE J., 1981, 27, 1002. 27 T. S. S~rensen, M. Hennenberg, A. Steinchen, A. Sanfeld, J. Colloid Interface Sci., 1976, 56, 191. I9 W. Dalle-Vedove, Thesis (UniversitC Libre de Bruxelles), 1984. ' O W. Dalle-Vedove and A. Sanfeld, personal communication, 1983. 1980, 74, 495. W. Dalle-Vedove and A. Sanfeld, J. Colloid Interface Sci., 1981, 84, 318; 328; 1983, 95, 299. 28 A. Steinchen and A. Sanfeld, Chem. Phys., 1973, 1, 156; Biophys. Chem., 1975, 3, 99. A. R. Marquez, W. Dalle-Vedove and A. Sanfeld, J. Chem. Soc., Faraday Trans. 2, 1981,77,2303. 31 3 2 3 3 J. L. Ibanez and M. G. Velarde, J. Math. Phys., 1977, 38, 1479. 34 T. S. S~rensen and J. L. Castillo, J. Colloid Interface Sci., 1980, 76, 399. 3 5 K. Durrani, C. Hanson and M. A. Hughes, Metall. Trans. B, 1977, 8B, 169. M. Dupeyrat and E. Nakache, personal communication, 1983. 77 N. M. Rice and M. Nedved, Hydrometallurgy, 197611977? 2, 361. 3H G. A. Yagodin, I . S. Yu and V. V. Tarasov, in ISEC Con$ (Liege, 1980), p. 1. '' P. R. Danesi, in ISEC Con$ (Denver, t983), p. I . C. Hanson, in ISEC Conf: (Liege, 1980), plenary lecture, p. 1. 4 ' M. Cox and D. S. 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ISSN:0301-7249    

DOI:10.1039/DC9847700169

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chern. SOC., 1984, 77, 18 1 - 188 Time-dependent Behaviour and Regularity of Dissipative Structures of Interfacial Dynamic Instabilities BY HARTMUT LINDE Akademie der Wissenschaften der DDR, Zentralinstitut fur physikalische Chemie, Rudower Chaussee 5, 1199 Berlin, German Democratic Republic Received 5 th December, 1983 Interfacial dynamic instabilities with self-amplifying and self-organizing convections driven by interfacial tension in a non-equilibrium two-phase fluid system show a surprising variety of dissipative structures. A complete investigation and description of them has to take into consideration at least four aspects. (1) First are the kinetic features of the convection behaviour and the deformation of the interface concerning stationary basic units of flow systems (b.u.f.) with the related deformations of the interface and different time-dependent behaviour (travelling quasi-stationary b.u.f. driven by long-range driving forces, relaxing oscillations with related autowave behaviour and classical mechanical waves).(2) The topological features include different spatial patterns, e.g. parallel, concentrically circular or spiral stripes, polygonal networks and hierarchically ordered structures. (3) The order- disorder features concern the size, shape and packing of the b.u.f. with respect to spatial regularity or spatial chaos. The time-dependent behaviour can be distinguished for harmonic, anharmonic and chaotic oscillations. (4) The driving faces (d.f.) and conditions for Marangoni instability I are heat-and/or mass-transfer and/or chemical reaction at the fluid interface.The resulting b.u.f., an interface-renewing flow, can behave ( a ) as stationary or quasistationary in travelling substructures, ( b ) as relaxing oscillations, e.g. travelling or spiral-shaped autowaves and ( c ) as classical longitudinal capillary waves. Marangoni instability 11, with the same d.f. as instability I, induces in thin-layer amplification of the differences in the thickness of the layer. Marangoni instability 111, with shear stress as the d.f. at a tenside- covered fluid interface, shows stationary or oscillatory hair needle-like or elliptical eddies jn the plane of the interface itself. Meniscus instability, resulting from the viscous pressure as the d.f. at a travelling meniscus, is an excellent example of amplification as well as of stationary spatial deformations of the meniscus-shaped interface in a determinate way and travelling spatial deformations of substructures, which are caused by a repeated stochastic process.~~ One of the most manyfold spectra of dissipative structures (d.~.)'-~ is caused by interfacial dynamic instabilities for the driving forces of heat- and/or mass-transfer and/or chemical reaction and/or shear stress in two-phase systems with fluid interfaces, if the systems have an internal feedback mechanism and exceed critical conditions. Stability theories use the Navier-Stokes equations, the laws governing the transport of matter and heat and some additional boundary conditions with respect to the usual hydrodynamics.The Gibbs-Marangoni effect is expressed by the stress balance at the interface where ( d u l a x ) , , is the derivative of tangential velocity in a direction normal to the interface in phase a or 6 (x = 0), pa& is the dynamic viscosity in phase a or 6, cr is the interfacial tension and x, y are the Cartesian coordinates perpendicular and 181182 DISSIPATIVE STRUCTURES OF MARANGONI INSTABILITIES tangential to the flat interface. Eqn (1) shows that a fluid interface responds to the difference in the interfacial tension, which is due to local adsorption of surface active agents (tensides) or to local heating, by interfacial convection from areas of lower tension to areas of higher tension, inducing the related shear stress p(du/dx) in both phases.The inversion of action and reaction can be observed in a system with shear stress, which leads to a difference in the interfacial tension at a tenside- covered interface. Secondly, we have to take into consideration the reaction of the interface to a space-dependent viscous pressure difference in both phases at the interface. For an originally flat interface the normal stress (pressure) balance at the interface is for x=O, where Pa& is the hydrostatic pressure at the interface in phase a or b, (du/dX),b is the derivative of the velocity in a direction normal to the interface in phase a or b (x = 0) and r l , r2 are the principal curvatures of the slightly deformed interface. The viscous pressure causes a deformation ( r , and r2 have finite values) even if the interfacial tension i s not space dependent [contrary to the Gibbs- Marangoni effect, eqn (l)].At least four different features play an important role in the investigations and therefore also in the description of the d.s. of interfacial dynamics: ( a ) kinetics, ( b ) topology, (c) order-disorder transitions and f d ) driving forces. KINETIC FEATURES OF THE CONVECTION AND DEFORMATION BEHAVIOUR The stationary state of the basic unit of flow (b.u.f.), shown in fig. 1, is due to interfacial convection enclosing circulating flows in both phases. Periodic reamplifi- cation and breakdown of the b.u.f. of interfacial convection (relaxation oscillation of the intensity) occurs. Travelling b.u.f. convection systems originate at a leading line or centre4 and behave as autowaves (no reflection at a wall, no interference but annihilation of colliding wavefronts).The periodic tangential or normal deforma- tions of the interface (with related convections of the adherent fluid layers) behave as classical travelling or standing waves with reflection and interference. Deforma- tions occur in the shape of the interface, which can be stationary or autowave-like travelling along the interface. To distinguish classical waves and autowaves, note that classical elastic waves of small amplitude can be described by Helmholz’s wave equation (a hyperbolic differential equation, invariant with time inversion): aLx a t 2 -= c2 AX where A is the Laplace operator and c is the velocity of the waves. For longitudinal waves, x is the characteristic parameter of the scalar field, e.g.density in sound waves or the concentration of surface-active agents, c,.,,,., at the interface in longi- tudinal (capillary) waves. Autowaves can be described by a system of parabolic differential equations (variant with time inversion) i = l , ..., n in which non-linear functions Fi(xi) are necessary, and where, in chemical systems, xi are the volume concentrations of autocatalysing or inhibiting chemical species,H. LINDE 183 Fig. 1. Basic unit of flow. Dj are the diffusion coefficients of the chemical species. xi, in interfacial dynamic systems, are the concentrations of surface-active agents, c ~ , ~ , ~ , , at the interface. Note that in the same interfacial system both classical elastic (capillary) waves and autowaves are possible, with variation of the direction of mass- or heat-transfer, respectively, of d a d a or - d Cs.a.a.d T' TOPOLOGICAL FEATURES OF TWO-DIMENSIONAL IMAGES OF BASIC UNITS OF FLOW OR OF INTERFACIAL DEFORMATION Straightly parallel stripes are sometimes interrupted by splitting or by unification of stripes [fig. 2( a ) ] or by the free ends of newly formed stripes [fig. 2( b ) ] . Concentri- cally circular [fig. 2(c)] or irregular parallel curvaceous stripes can be stationary or travelling. Spirals may exist with one [fig. 2 ( d ) ] or more arms [fig. 2(e)] moving radially whilst the centre is rotating. Polygonal networks of stationary or travelling roll cells also occur [fig. 2 ( f ) ] , Structures of higher order (structure hierarchy by substructuration) occur if two or more of the basic structures expanding from different leading centres col!ide.The collision areas form new structural elements of higher order [fig. 2(g)]. Finally, there may be circular, elliptical [fig. 2(h)] or hair needle-like [fig. 2(i)] eddies in the plane of the interface itself, i.e. another convection system rather than the above-mentioned b.u.f. ORDER-DISORDER FEATURES Order-disorder features consist of ( a ) spatial structures characterized by one or more wavelengths, which can be highly ordered with single- or multi-peak184 DISSIPATIVE STRUCTURES OF MARANGONI INSTABILITIES Fig. 2. ( a ) Splitting and unification of stripes; ( b ) free ends of newly formed stripes; ( c ) concentrically circular stripes; ( d ) spiral stripes with one arm; ( e ) spiral stripes with two arms ; (j) polygonal networks (of roll cells); (8) structure hierarchy by substructuration; ( h ) elliptical eddies in the plane of the interface; (i) hair needle-like eddies in the plane of the interface.H.LINDE 185 wavelengths distributions or disordered with wide distributions of wavelengths or sizes, ( b ) spatial structures characterized by the shapes of the topological features, ( c ) high-order systems with polygonal networks of regularly shaped and regularly packed stripes or polygons or disordered structures with irregularly shaped polygons and therefore also with irregularities in their packing, ( d ) time-dependent behaviour of oscillations: harmonic oscillations, or anharmonic oscillations, e.g. sawtooth oscillations or chaotic oscillations.DRIVING FORCES, CONDITIONS AND ESSENTIAL BEHAVIOUR DISSIPATIVE STRUCTURES OF MARANGONI INSTABILITY I Heat- and/ or mass-transfer of surface-active agents leads to Marangoni instability I and spontaneous interfacial convection. Both the stationary regime and classical wave-like oscillation (longitudinal capillary waves) are predicted from linear stability theory’ and observed in real physical systems.”* From an analysis including the thickness of the adjoining fluid layers6 conditions for the critical Marangoni numbers of both basic regimes are predicted; the influence of additional exchange of latent heat on the Marangoni numbers and on the kind of regime has also been analysed recently.’ In reality the ‘stationary’ regime is more complicated than its theoretical descrip- tion: i.e.the ‘stationary’ regime is expected to be time-independent like fig. 1 or fig. 2 ( f ) and to exhibit order-disorder features with a sharp single peak. At the lowest level of instability, roll cylinders or roll cells of the theoretically predicted smallest size show relaxation oscillation, which is the reason for the recently recognized autowaves with travelling parallel stripes, concentrically circular waves and even spiral leading centres. These autowaves, like autowaves in autocatalytic reaction4 systems, are expected to be propagated by a local driving force along the interface. Whether these travelling autowaves can form a stationary stable structure of higher order because of the structure of the collision area is, even in the case of travelling autowaves of the Belousov-Zhabotinski r e a ~ t i o n , ~ unknown.The next highest level of instability allows roll cylinders or polygonal cells as a network in stationary convection systems, which remain in place, especially in thin liquid layers. With a further increase in roll cell instability, characterized by an increase in the Marangoni number, convection systems again show travelling waves but with higher velocity than the above-mentioned pure autowaves. From the point of view of origination at a leading area’ and annihilation at a wall or at a collision area, they behave like autowaves; but their greater velocity is caused by a long-range interfacial tension gradient from a second-order convection system.Roll cells of first, second and higher order are observed to form a hierarchical system. An approach using non-linear terms’ was able to show the existence of second-order roll cells. From this behaviour we find selection of different kinetic regimes with different topological features: e.g. hexagonal patterns are preferred for stationary structures and tetragons ; ladder structures with different diameters between rungs and beams are preferred for travelling systems, if the movement is caused by hydrodynamic (or interfacial dynamic) shear stress. High velocity and high shear stress can cause chevron (herring-bone) patterns to be formed by deformation of the ladder structure. With increasing driving force the irregularities increase and lead to chaotic distributions of sizes and roll cells of irregular shapes: i.e.the first transition to chaotic behaviour in Marangoni instability.186 DISSIPATIVE STRUCTURES OF MARANGONI INSTABILITIES Roll cells of second and higher order can degenerate by relaxation oscillation, giving a wide range of diameters of chaoticaly spreading and oscillating cells (diameters decreasing and frequencies increasing with increasing driving force). Autowaves of roll cells of higher order have also been observed. The chaotic interaction of an ensemble of these stationary roll cells is characterized by a fast annihilation of every roll cell after or during the first period of oscillation by the consecutively very often nucleating adjoining cells. The chaotic features of spatial and time-dependent behaviour may be due to the stochastic behaviour of nucleation resulting in irregular anharmonic oscillations, which are not synchronized.There is a strong contrast between the three kinetic features of the 'stationary' regime (real stationary roll cells, structure hierarchy by travelling substructures and relaxation oscillations, which lead on the one hand to autowave behaviour and on the other to chaotic oscillations) and the classical oscillatory regime of the Marangoni instability. The latter is identical to undamped longitudinal capillary waves and can occur for travelling or standing classical waves with reflection at a wall and with interference. For lower supercritical driving forces, the regularity is very high and the topological features correspond to fig.2(a) or ( b ) . We observe with increasing driving force a transition from travelling straight waves (stripes) to standing waves (with mutually penetrating stripes) and from these one-modal waves to two-modal and even three-modal waves [with angles between the corresponding parallel stripes of 90" (two modal) or 60" (three modal)]. For very high driving forces the irregularities increase again and lead to chaotic behaviour. The experimental results are in good agreement with the predictions of stability and with the more detailed description obtained by computer simulation.'' The classical wave can be amplified as mentioned before by the driving forces caused by heat- and/ or mass-transfer and/ or chemical reaction at the interface: i.e. autowaves and classical waves are distinguished theoretically by the above- mentioned differential equations and the related kinetic behaviour concerning reflec- tion and interference and not by the kind of energy supplied by local sources at the interface or by the entire interface itself.MARANGONI INSTABILITY I1 ' Marangoni instability I1 results from the same driving forces as Marangoni instability I, but is connected with increases in the thickness differences in thin layers, i.e. increases in deformations normal to the interface. Thin layers, jets and droplets can be destabilized and broken into smaller compartments. MARANGONI INSTABILITY I I I ~ * - ' ~ Marangoni instability 111 results from shear stress in the liquid and/or the gas phase at a tenside-covered liquid/gas interface and is characterized by stationary (with small driving force, e.g.in systems where flow in the gas phase is the only cause of this dissipative structure) or oscillatory (with higher driving force) hair needle-like [fig. 2 ( i ) ] or elliptical eddiesi4 [fig. 2(h)] in the plane of the interface itself. This means that there is no surface renewal convection in this pattern of shear flow on the surface (which is, of course, accomplished by related convection in both boundary layers). As with the other dissipative structures, this instability occurs only if we exceed critical conditions, which are lower than the values of the critical conditions for transition from laminar to turbulent flow at a solid wall.direction - of f l o w Plate 1. ( a ) Moving meniscus between two plates; ( h ) first-order deformation of a moving meniscus; ( c ) second-order deformation of a moving meniscus; ( d ) fixed consecutive structure of first-order, X, and second-order, 0, meniscus deformations.[To face page 187H. LINDE 187 MEN I SC U S I NSTA B I LITY ’ This last example of surface instabilities results from the viscous pressure being the driving force, which operates at a travelling meniscus [plate l(a)] and is separate from the above-mentioned Marangoni instabilities. This condition obtains if a Newtonian or non-Newtonian liquid in the gap between the two plates is displaced by the penetration of air, forming a moving half-cylinder-shaped meniscus. The first regime of meniscus instability is characterized by a stationary deforma- tion of the meniscus in the shape of a waveline in the z direction [plate l(b)].The fixed consecutive structure is a system of equidistant stripes of smaller and larger thickness in both layers, remaining at the surface of both plates [fig. 2(a) and (b)], and whilst the ‘air fingers’ produce thin stripe-like layers the ‘liquid fingers’ produce thick layers stripe-like layers [plate l(b)]. The distance between these stripes (to avoid the expression wavelength, because we have to distinguish between classical waves and a variety of other wave-like phenomena) depends strictly on the viscosity, the velocity of the moving meniscus and the distance between the two plates (the radius of meniscus), so we observe regular parallel stripes (at small driving force) and a transition to a stripe system with smaller or larger distances if we change the plate distance during the experiment.16 The transition to narrower stripes is caused by origination of new stripes of fig.2(b), and the opposite transition is caused by the unification of stripes, fig. 2(a), i.e. in the first case there are new liquid fingers and in the second case there is unification of two liquid fingers [plate l(c)]. This instability is a good example of a chance process, if with increasing driving force by a second bifurcation additional deformations (of second order) [plate l(c) and ( d ) ] with smaller characteristic length than the first-order deformation of the meniscus occur. The second-order deformations originate at the top of the air fingers as small liquid fingers, and they travel to the base of the air finger and then disappear.The nucleation of this second-order deformation is the cause of its chance mechan- ism: from both its timing and its direction of travel the process has an event distribution of probability. Thus we can recognize another basic mechanism causing chaotic behaviour, which follows the condition ‘sensitive to initial conditions’.’’ The resulting fixed consecutive structure shows relatively regular first-order stripes and the irregular branches of the second-order stripes [plate l(d)]. ‘ H. Linde, Marangoni Instabilities, in Dynamics and Instability of Fluid interfaces, Lecture Notes in Physics no. I US, ed. T. S. Sorensen (Springer-Verlag, Berlin, 1979). * H. Linde, in Conuective Transport and Instability Phenomena, ed. J. Zierep and H. Oertel Jr (G. Braun-Verlag, Karlsruhe, 1982). H. Linde, Dissipative Strukturen der Grenzflachendynamik, in Fortschritte der experimentellen und theoretischen Biophysik Bd. 21, ed. E. Kahrig and H. Beaerdich (VEB Georg Thieme-Verlag, Leipzig, 1977). A. M. Zhabotinsky and A. N. Zaikin, J. Theor. Biol., 1973, 40, 45. L. E. Scriven and C . V. Sternling, AIChE J., 1959, 5, 514. H. Linde and J. Reichenbach, J. Colloid Interface Sci., 1981, 84, 433. G. Frenzel and H. Linde, Teor. Om. Khim. Tekhnol., 1983/84, in press. A. N. Zaikin and A. M. Zhabotinsky, Nature (London), 1970, 225, 535; A. N. Zaikin and A. L. Kawczynski, J. Non-equilib. Thermodyn., 1977, 2, 39. H. Wilke, Chem. Tech. (Leipzig), 1974, 26, 456; 1977, deposition system: Z. Angew. Math. Mech. (ZAMM), 1980, 9, 437. ‘ I C . Arcuri and D. W. De Bruijne, Roc. Vth Int. Congr. Surface Active Substances, Barcelona, 1968. ’ H. Linde and P. Schwartz, Chem. Tech. (Leipzig), 1974, 26, 455; 1977, deposition system. 10188 DISSIPATIVE STRUCTURES OF MARANGONI INSTABILITIES H. Linde and P. Friese, 2. Phys. Chem. (Leipzig), 1971, 247, 225. l 3 H. Linde and N. Shulewa, Mber. Dtsch. Akad. Wiss. Berlin, 1970, 12, 883. l4 H. Linde and P. Schwartz, Teor. Osn. Khim. TekhnoL, 1971,401. I’ L. Weh, Dissertation (Humboldt-Universitat, Berlin, 1972). H. Linde, Nova Acta Leopold., 1984, in press. J. A. Yorke and E. D. Yorke, in Hydrodynamic Instabilities and rhe Transition to Turbulence (Springer-Verlag, Berlin, 198 1).

ISSN:0301-7249    

DOI:10.1039/DC9847700181

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 189-196 The Contribution of Chemistry to New Marangoni Mass-transfer Instabilities at the Oil/ Water Interface BY EVELYNE NAKACHE” AND MONIQUE DUPEYRAT Laboratoire de Chimie Physique de l’Universit6 Pierre et Marie Curie, 1 1 Rue Pierre et Marie Curie, 75231 Paris Cedex 05, France AND MICHELE VIGNES-ADLER Laboratoire d’A6rothermique du C.N.R.S., 4 ter Route des Gardes, 92 130 Meudon, France Received 29 th December, 1983 Spontaneous interfacial motions a?pear at an interface between two immiscible phases in a state far from equilibrium, e.g. an aqueous phase of an organic acid or a complex ion and an organic phase of a long-chain surfactant molecule. The instabilities observed are related to variations in the interfacial tension. It is shown that they resemble the well known Marangoni effect by considering interfacial convection and the coupling between diffusion and convection fluxes, but they differ by the presence of chemical reactions.The notion of assisted desorption is defined in order to interpret the experiments. The analysis of this phenomenon could be useful in determining the optimal conditions for obtaining convective interfacial transfer to enhance liquid-liquid extraction processes. Mass transfer accompanying chemical reactions is involved in many industrial and biological processes. Under certain conditions it is associated with interfacial turbulence. Many authors’4 have shown the important role of the interface and the influence of surfactant molecules on the rate of liquid extraction.’ Some of them, e.g.Dobson and Van der Zeeuw,6 studying the extraction of copper by hydroxyoximes, observed that the rate is greater when using Shell SME 529 extractant than when 2-octyl-5-hydroxyheptophenone oxime is used, although the interfacial density of the latter is higher. We discuss here the role of the surfactant and show that interfacial convection, which may enhance the extraction rate, can be attributed to the Marangoni the interfacial flow can be governed by gradients in the interfacial tension driven by local concentration variations resulting from mass transfer. As an example of interfacial convection, this paper reports observations of large-scale, chemically driven interfacial motion, first observed in our laboratory. l o It appears at an interface between two immiscible phases, kept at constant tem- perature, and seems to be due to the simultaneous transfer in opposite directions of two solutes, one of them surface active.For example, if an aqueous solution of a long-chain hydrophobic molecule is poured over a solution of various organic acids or complex ions in nitrobenzene, two different spontaneous motions can be observed provided that the concentrations of the two compounds are suitable. If the wall of the container is made of polyethylene, local contractions and expansions of the interface are seen owing‘to the appearance of an emulsion some time after both phases are put in contact. We confirmed that this emulsion was not necessary for the onset of the movement and that no noticeable perpendicular deformation 189190 INSTABILITY AT THE OIL/WATER INTERFACE 30 25 20 15 10 5 0 3 2.30 2 1.30 1 0 t/min Fig.1. Variation of y with time: ( a ) interface (nitroethane) 3.5 x lop4 mol dm-3 HPi/(water) 5 x lov3 mol dmP3 CI2Br; ( b and c ) interface (nitrobenzene) 3.5 x lop4 mol dmW3 HPi/(water) C,6Cl [ ( b ) 4 ~ 1 0 ~ ~ and ( c ) 2 ~ 1 O - ~ m o l d m - ~ ] . occurred. In a glass container the instability turns into a strong deformation of the interface resulting in a wave of 1 cm in amplitude, propagating along the wall, followed by a total disturbance of the interface. We have checked that the available models,8393' I improved by adaptation to particular experimental conditions, could not account for the instabilities observed. The purpose of this work is to understand, from experimental data, the mechanism of the motion, in particular the influence of the interface on the hydrodynamical and physicochemical effects.EXPERIMENTAL We chose to study first movement in the plane of the interface, because the wall introduced wettability conditions which made the problem more complicated. A solution of a classical surfactant, cetyltrimethylammonium chloride (C ,6Cl, gift from a private laboratory), purified three times by crystallisation in methanol, was poured over a solution of picric acid (HPi, Merck), in nitrobenzene (chromatographic grade, UCB) or nitroethane (Carlo Erba). The solvents were previously saturated by each other. We chose to follow the interfacial convection by measuring the variation in interfacial tension, which is correlated to the longitudinal deformation of the interface.The detachment method, using a stirrup instead of a ring, was used. The curves of fig. 1 show several pseudoperiodic oscillations of y as a function of time for various solute concentrations. In curve ( a ) , where the pseudoperiod is very large, oneE. NAKACHE, M. DUPEYRAT AND M. VIGNES-ADLER 191 d b Fig. 2. Hydrodynamical effects related to the density of the adsorbed layer. can see y increasing progressively and then decreasing abruptly while an expansion of the interface, i.e. the arrival of surfactant molecules, is observed. DISCUSSION The transfer of these solutes from one phase to another may result in (i) hydrodynamical effects which depend on the transfer processes (diffusion, con- vection, adsorption-desorption) and on interfacial tension gradients and (ii) physicochemical effects, eventually involving chemical reactions.HYDRODYNAMICAL EFFECTS Our analysis will be made easier if we first try to interpret a well known instable extraction phenomenon studied by Davies and Haydon,” termed the ‘kicking drop’ by these authors: a stable pendant drop of water in toluene undergoes violent erratic movements or ‘kicks’, more or less rapidly damped by viscous drag when acetone is added to the toluene. Owing to the local convective currents a local increase of surfactant molecules near the interface produces at some point an increase in the surface pressure, AT. The monolayer tends to spread further over the surface, dragging some adjacent liquid with it.If appropriate conditions of viscosity, diff usiv- ity and concentration are fulfilled, according to Sternling and Scriven for example, an eddy of fresh solution would occur at this point, amplifying the movement which appears as an ‘expansion’, as shown in fig. 2(a). Then, owing to momentum transfer, eddies should also occur on the other side of the interface. If the density of surface-active material becomes such that the adsorbed layer is sufficiently con- densed, AT tends to zero and the surface pressure of this monolayer resists the eddy [fig. 2(6)]. The interfacial convection is further inhibited by highly viscous dissipation. Transfer then becomes purely diffusive and of course slower. As acetone is not very surface active it can easily desorb, inducing a ‘contraction’ of the interface,192 INSTABILITY AT THE OIL/WATER INTERFACE and the latter step is not reached [fig.2(c)]. If dodecyltrimethylammonium chloride (CI2C1) is added, the movement is inhibited. Indeed, this very surface-active com- pound cannot desorb, so that the interfacial convection is inhibited by viscous dissipation. We have observed that no motion occurs if our system consists of an aqueous solution of cl6c1 in contact with pure nitrobenzene. The question then arises: how can the presence of HPi, a non-surface-active compound,- bring about instability? The answer to this question requires further physicochemical information concern- ing transfer of the solutes. PHYSICOCHEMICAL EFFECTS In a recent paperI3 we have analysed the importance of the transfer of each species from the equilibrium concentrations computed from electroneutrality, parti- tion coefficients and the dissociation equilibrium constant of HPi in nitrobenzene.At equilibrium this results in the complete dissociation of HPi and almost total exchange of H+ with ct6 as the counter-ion of Pi-. This means that, although the driving force comes from the fluxes of CI6Cl and HPi in opposite directions, only ct6 and H+ pass through the interface, CI- and Pi- remaining in their respective phases. Indeed the structure of Pi- is very similar to that of the nitrobenzene molecule, while Hf is very polar, like water. Thus the very different affinities for the two phases of the species concerned permit a flux of CT6 by means of two opposite cation fluxes (H+ and cT6).This interfacial transfer can be symbolized by the following equation, possible in one direction only: The transfer thus results in a decrease in CI6Cl concentration and in the formation of &Pi. Now, because of the very different structures of C1- and Pi-, the partition coefficient between water and nitrobenzene ( Pwater/nitrobenzene) is much larger for Cl6C1 than for C16Pi. Thus for the same initial concentration of C16X (X = C1- or Pi-) the concentration of c7'6 in the aqueous phase is higher with the counter-ion Cl-. The interfacial density of cT6 ions, which governs the interfacial tension, depends on the aqueous concentration of Ct4. Therefore, if C1- ions are replaced by Pi- ions in the bulk phases, the CT4 interfacial density decreases and the interfacial tension increases.The question is now to examine how the concentration of C1- and Pi- can vary. Obviously this depends on the transfer processes. If we take into account that at this type of interface several author^'^,'^ have shown that the adsorption-desorption phenomenon is fast compared with the diffusive-convec- tive one, we can assume that the adsorbed monolayer is always in equilibrium with two small zones adjacent to the interface, so that the diffusion-convection process is the limiting step of the transfer. Therefore the concentration variation in these bulk zones rules the concentration variation at the interface. We can deduce that, if Cl- ions are replaced by Pi- ions in these adjacent layers, CT6 ions will immediately desorb towards the organic phase, clearing the interface and increasing the interfacial tension.COUPLING BETWEEN THESE TWO EFFECTS The mechanism of the observed phenomenon will be a coupling between the two effects.4 diffusive I flux I I E. NAKACHE, M. DUPEYRAT AND M. VIGNES-ADLER 4 convective I 193 - 1 - PiH *llrH' +Pi- 1 II !IH' Pi- H Pi t u Fig. 3. Coupling between hydrodynamical and physicochemical effects. The value of y at the beginning of the phenomenon [fig. l ( a ) ] means that C16C1 is rapidly and massively adsorbed at the interface. The condensed layer thus formed tends to oppose the enhancement of convection, as shown before in fig. 2(b). At the same time C16C1 brought to the interface is progressively transformed by 'cation fluxes' in CI6Pi, increasing the interfacial tension.As convection is inhibited by the density of the adsorbed layer, the cation flux is diffusive. Owing to the very weak dissociation of HPi in nitrobenzene (Kd= the Hf flux should be stopped194 INSTABILITY AT THE OIL/WATER INTERFACE 0.8 0.6 - I E z E 2 0.4 0.2 0 + x X I 1 1 l 1 1 1 1 1 1 1 1 1 1 1 + 12 24 36 48 60 72 (/5 Fig. 4. Variation of y with time and with square root of time. Interface (nitroethane) HPi 3.5 x mol dm-3/(water) C,zBr 5 x mol dm-3. rapidIy; however, it is sustained by the very fast dissociation of HPi according to the dissociation reaction in the forward direction: HPi S H’+Pi-. During the time the Pi- concentration in the organic sublayer increases, more and more C,6Pi is formed, which in turn promotes the desorption of Ct6 molecules as shown above, This increases the interfacial tension in a diffusive way, but also enhances the compressibility of the interface until a threshold is reached where natural convection can be amplified. Indeed we observed this convective behaviour at the beginning of an oscillation (fig.4), where the increase of y is proportional to time for ca. 15 s. {As this interfacial convection becomes predominant the cation exchange is very rapid and depletes the sublayers in H+ and cT6, while C,6Cl and HPi are consumed [fig. 3 ( a ) ] . } At this stage the feeding of the sublayers in CI6Cl and HPi is ruled by diffusion from the bulk [fig. 3(6)], and the variation of the interfacial tension should be proportional to the square root of time.Fig. 4 shows, as expected, that in the second part of an oscillation y increases with t1’2. However, while diffusion is continuing for a relatively long time, CI6Pi is accumulating in the organic phase. Therefore enhancement of Pi- concentration relative to that of H+ favours the displacement of the dissociation reaction of HPi in the backward direction. The recombination of HPi consumes H’ ions. These are no longer available to pass through the interface and the ‘cation fluxes’ stop.E. NAKACHE, M. DUPEYRAT AND M. VIGNES-ADLER 195 c- 3 Fig. 5. Variation of y and AV with time. Lines on the t axis refers to a synchronisation between a decrease in y (increase in CT6Cl-) and a decrease in AV (increase in Cl-) near the interface. At this stage the system increases its entropy by means of the flux of C1- and Ct6 ions in the same direction, CI&l then becomes predominant in the aqueous sublayer just as the accumulation of CI6Pi in the organic sublayer induces a clearing of the interface, thus enhancing the compressibility of the interface until the critical threshold is reached where natural convection can be amplified.As the CI6Cl flux arriving at the interface is convective, a rapid decrease in y occurs, corresponding to the last part of the curve in fig. 3(c). This convection would restore the bulk concentration of the species on either side of the interface. Thus the cycle can start again. EVIDENCE FOR SUCH A COUPLING We report here only some evidence for the model. (i) If the proposed mechanism is correct, the dissociation of HPi is crucial for the explanation of oscillation.We have observed that if HPi is rephced by KPi, a compound very similar but fully dissociated in nitrobenzene, no motion occurs. (ii) During the descending part of the oscillation, an increase in the concentration of C16Cl should be correlated with a decrease in the interfacial tension. We have performed simultaneous measurements of C1- concentration (by means of a silver, silver chloride electrode) and of y (fig. 5). It can be seen that the expected correlation is verified. (iii) If the HPi concentration is kept constant while CI6C1 decreases (fig. l), the desorption is relatively more important for small values of CI6C1 [curve ( b ) ] . The convenient compressibility and the amplified interfacial convection appear more rapidly, and thus the period of oscillation is shorter and its frequency higher.CONCLUSION This system is only one particular case of the coupling which can occur at a liquid-liquid interface. We can now try to draw some more general conclusions196 INSTABILITY AT THE OILjWATER INTERFACE about such heterogeneous systems and define the contribution of chemistry to these instabilities. (1) A maximum in the interfacial tension as a function of time can be observed because there is possible competition between two paths for the transfer of material: fluxes of c;", and c1- in the same direction or cT6 and H' in opposite directions, governed by a chemical reaction, the dissociation of HPi. (2) Successive oscillations can be observed because under certain conditions the natural convection is amplified in the vicinity of the interface, resulting in the replacement of the usual diffusive interfacial transfer by a much faster convective one.This amplification is possible during a reasonable time only if a desorption process occurs allowing the adsorbed layer to reach critical compressibility. Desorp- tion can be spontaneous with a short-chain surfactant which is easily desorbed. In this case the same molecule will be both adsorbed and desorbed. When the surfactant is not or only slightly desorbable ( i e . if the chains are long) desorption cannot be spontaneous, but it may be 'assisted' by an interfacial reaction which transforms a very adsorbable species into an easily desorbable one: Aadsorbable +x Ddesorbable+Y- The kinetics of this 'assisted desorption', eventually taking into account solvatation or reorientation processes, has to be considered simultaneously with the kinetics of transfer in order to account for instability.I6 This model seems to be relevant for liquid-liquid extraction and can explain the contradictory experiments reported by Dobson and Van der Zeeuw.6 The specificity of interfacial transfer reported by many workers, but little studied up to now, could be approached fruitfully by this method.' R. J. Whewell, M. A. Hugues and C. Hanson, J. Inorg. Nucl. Chem., 1975, 37, 2303. * D. S. Flett, D. N . Okuhara and D. R. Spink, J. Inorg. Nucl. Chem., 1973, 35, 2471. R. Price and J. Tumelty, Ind. Chern. Eng. Symp. Ser., 1975, 42, 18.1. D. S. Flett, M. Cox and J. D. Heels, in Proc. Inf. Solvent Extraction Con$ (SOC. Chem. Ind., London, 1974), vol. 3, session 24, p. 2560. ' W. Nitsh and L. Navazio, in Roc. Znf. Solvent Extraction ConJ, 1980, vol. 80, p. 220. ' S. Dobson and A. J . Van der Zeeuw, Chem. Ind., 1976, 5 , 176. ' L. E. Scriven and C. V. Sternling, N a m e (London), 1960, 187, 186. * C. V. Sternling and L. E. Scriven, AICHE J., 1959, 5, 514. l o M. Dupeyrat and J. Michel, J. Exp. Suppl., 1971, 18, 269. I ' M. Hennenberg, P. M. Bisch, M. Vignes-Adler and A. Sanfeld, J. Colloid Interface Sci., 1980, 74, l 2 J. T. Davies and D. A. Haydon, Proc. R. SOC. London, Ser. A , 1958, 243, 492. l 3 E. Nakache, M. Vignes-Adler and M. Dupeyrat, J. Colloid Inferface Sci., 1983, 94, 187. l 4 J. T. Davies and E. K. Rideal, in Interfacial Phenomena (Academic Press, New York, 1963). I s L. Ter Minassian Saraga, J. Chim. Phys. Phys. Chim. Biol., 1955, 52, 181. H. Linde and M. Kunkel Waerme Stoflubertrag., 1969, 2, 60. M. Dupeyrat and E. Nakache, C. R. Acad. Sci., Ser. C, 1973, 277, 599. 495. M. Dupeyrat, E. Nakache and M. Vignes-Adler, in Chemical Instabilities, ed. G. Nicolis and F. Baras, NATO Advanced Science Institute, series C (D. Reidel, Dordrech, 1984), vol. 120. 16

ISSN:0301-7249    

DOI:10.1039/DC9847700189

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 197-208 Double Layers at Liquid/ Liquid Interfaces BY ZDENEK SAMEC,* VLADIM~R MARECEK AND DANIEL HOMOLKA J. Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Utoviren 254, 10200 Prague 10, Czechoslovakia Received 2 1 st November, 1983 The electrical double layer at the interface between two immiscible electrolyte solutions (ITIES) has been studied by the fast-galvanostatic-pulse method for the system consisting of aqueous NaBr and a solution of tetrabutylammonium tetraphenylborate in nitrobenzene. The double-layer capacity has been evaluated as a function of the potential difference across the interface. The modified Verwey-Niessen model, in which a layer of oriented solvent molecules (the inner layer) separates two space-charge regions (the diffuse double layer), seems to provide a reasonable framework to interpret the experimental data, assuming (i) that the approximations to the Poisson-Boltzmann equation by Gouy and Chapman are removed and (ii) that the boundary between the space-charge region and the inner layer is considered to be diffuse rather than sharp.The use of the tetrabutylammonium cation as the reference ion in voltammetric studies of the water/nitrobenzene interface is discussed. In many respects the development of models for the interface between two immiscible electrolyte solutions (ITIES) has paralleled that for metal/ electrolyte or semiconductor/ electrolyte interfaces. In the earliest model by Verwey and Niessen,’ the ITIES was represented by a diffuse double layer (i.e.one phase contains an excess of the positive space charge and the other phase an equal excess of the negative space charge) which can be treated by the theory of Gouy’ and Chapman’ (GC). By analogy with Stern’s modification4 of the GC theory, Gavach et aL5 introduced the concept of an ion-free layer of oriented solvent molecules which separates the two space-charge regions at the ITIES. On the other hand, Boguslavsky et al.677 neglected the diffuse double layer and assumed a? ionic bilayer at the ITIES formed by the specifically adsorbed ions on one side of the interface and by ions of the opposite charge on the other. A similar model based on ionic adsorption up to a monolayer thickness was adopted by Joos and Vanden BogaerL8 The structure of the electrical double layer at the n~n-polarized~,~-” as well as at the ideally p ~ l a r i z e d ’ ~ ’ ~ interfaces between two immiscible electrolyte solutions has been studied by measuring the surface t e n s i ~ n ~ ~ ~ - ’ ~ and impedan~e,’~’~’ mainly for the systems water/nitroben~ene~,~~’&’~ and water/ 1,2-di~hloroethane.’’.’~ The experimental data are consistent with the modified Verwey-Niessen (MVN) m0de1,~ although the contribution of the inner layer to the double-layer properties is much less pronounced than in the case of metal/electrolyte interfaces.Thus the potential drop across the inner layer at the water/nitrobenzene interface has been found practically to be independent of the surface charge density”’14 and equal to l,I4 O* 5 ’ * and 42 mV,I6 or its variation with the surface charge density was detected with the inner-layer potential drop being ca.20 mV at the potential of zero charge.” In the latter case, however, the corresponding inner-layer capacity is rather large, as confirmed by the capacity data, which were inferred from the impedance measure- ments.18 The evaluation of the surface excess of water at the water/nitrobenzene interfacei3 implied that the inner layer provides only a fraction of the monolayer198 DOUBLE LAYERS AT LIQUID/LIQUID INTERFACES of the solvent molecules. This led the authors of ref. (13) to the conclusion that the concept of an ion-free layer at the ITIES is doubtful, while the continuous change in the composition from one phase to the other is a more realistic picture.Neverthe- less, such an idea can be incorporated into the MVN model by considering the boundary between the space-charge region and the inner layer to be diffuse rather than sharp, by analogy with the treatment of the metal/electrolyte interface using the non-local electrostatic approach.'' In this paper we have tried to obtain insight into the structure of the interface between aqueous NaBr and a solution of tetrabutylammonium tetraphenylborate (TBATPB) in nitrobenzene on the basis of fast-galvanostatic-pulse measurements, which have recently been shown to provide reliable capacitance data for the ITIES.20 EXPERIMENTAL CELL A diagram of the four-electrode cell is shown in fig. 1. In contrast to the arrangement used in several l a b o r a t o r i e ~ , ~ ~ - ~ ~ the lower-density aqueous phase occupied the bottom of the cell, with the nitrobenzene phase above it.By means of a microsyringe connected to the cell, a flat and reproducible water/nitrobenzene interface with a geometric area of 22 mm2 was adjusted in the round hole cut in the glass barrier B (cJ fig. 1). A remarkable improvement in the cell's response to voltage or current pulses was achieved by placing an isolated metallic wire inside the Luggin capillary for the nitrobenzene phase, so that only the metallic disc was exposed to the solution at the tip of the capillary, with the other end of the wire connected to silver of the reference electrode RE2. Prior to the experiment the cell was carefully washed with acetone, then with doubly distilled water and finally dried in a dry-box.During the experiment the cell was immersed in a water bath, the temperature of which was maintained at 25.0 f 0.1 "C. The potential difference E of the galvanic cell (I) Ag/ AgBr 1 co( NaBr) (w) j/ c"(TBATPB) 1 c"(TBABr) AgBr/Ag' RE 1 (0) (w') I RE2 (1) was controlled or measured in the potentiostatic or galvanostatic experiments, respectively, with co = 0.01,0.05 or 0.10 mol dm-3. Since the potentials of the Ag/AgBr reference electrodes RE1 and RE2 practically cancel each other, the potential difference E can be written as where YTBA+(o) and Y~BA+(w') are the activity coefficients of the TBA+ ion in nitrobenzene and in the reference aqueous phase, respectively. Consequently, E is the Galvani potential difference across the tested interface, A T 4 = 4(w) - 4(0), and is related to the formal potential difference for TBA+ ion: The standard potential difference A:& for an ion X' of charge z can be calculated from the standard Gibbs energy of transfer of the ion from water to the organic-solvent phase, AGO,~W+O .25 tr,X - A,"& = AG:;,S-"/zF (3) e.g. for the TBA+ ion, Ar+;BA+ = -0.248 V.25Z .SAMEC, V. MARECEK AND D. HOMOLKA 199 Fig. 1. Diagram of the electrolytic cell: RE1 and RE2 are the Ag/AgBr reference electrodes dipped in aqueous solutions of NaBr and TBABr, respectively; CEl and CE2 are the platinum counter-electrodes dipped in an aqueous solution of NaBr; oil is the nitrobenzene solution of TBATPB; A is the connection to the microsyringe for the interface adjustment; B is the glass barrier in which a round hole has been cut (5.3 mm in diameter).ELECTROLYTES The aqueous electrolyte solutions were prepared from doubly distilled ,water and NaBr (p.a., Lachema) or tetrabutylammonium bromide (TBABr) (puriss, p.a., Fluka AG). NaBr was recrystallized from water prior to use. A fresh nitrobenzene solution of the electrolyte was prepared from nitrobenzene (p.a., Lachema) and tetrabutylammonium tetraphenylborate (TBATPB). Nitrobenzene was purified by fractional distillation under reduced pressure. TBATPB was prepared by the precipitation26 of tetrabutylammonium iodide (Schuchardt) and sodium tetraphenyiborate (puriss., p.a., Fluka AG). The product was purified by double recrystallization from acetone. The bromide contents of the aqueous solutions were checked by argentometric titration.APPARATUS Cyclic voltammetry was performed using a four-electrode potentiostat with ohmic potential-drop compensation based on positive feedba~k.~’ A block diagram of the potentio- stat, which can be adapted from a conventional three-electrode potentiostat,27 is shown in fig. 2. The potentiostat was controlled by a voltage-pulse generator and the current flowing through the cell was measured as the floating voltage drop across the measuring resistor R3 in fig. 2. The electronic circuit used in the galvanostatic-pulse measurements is shown schematically in fig. 3. A single-current pulse of amplitude I, = 25, 50 or 100 p A was generated in the feedback loop of the operational amplifier OAl by applying a square voltage pulse from a digital-to-analogue converter (12-bit DAC 12QZ, Analog Devices) across a 1 ki2 input resistor.The potential difference between the reference electrodes RE1 and RE2 was sampled by200 DOUBLE LAYERS AT LIQUID/LIQUID INTERFACES PG 0- R1 ..( R2 Fig. 2. Block diagram of the four-electrode potentiostat with positive feedback for the ohmic potential-drop compensation. -112 bit DAC MICROCOMWTER] Fig. 3. Block diagram of the electronic circuit for the galvanostatic-pulse measurements. means of a data-acquisition system (SDM 853, Burr Brown) every 100 ps for 5 ms before the current pulse was applied ( I = 0) and for the next 5 ms pulse duration. All 100 points of the sampled potential difference were stored in the memory of a microcomputer (Intel 8080 microprocessor) which was also used to operate the digital-to-analogue converter and the data-acquisition system.Throughout the paper the electric current connected with the transfer of the positive charge from the aqueous phase to the nitrobenzene phase will be considered as positive. RESULTS AND DISCUSSION CYCLIC VOLTAMMETRY In the voltammetric experiment the principal aim was to find the potential range to use in the galvanostatic-pulse measurements, i.e. the range within which the boundary behaves as an ideally polarized interface. Fig. 4 shows a cyclic voltam- mogram of 0.01 rnol dm-3 NaBr in water and 0.01 mol dm-3 TBATPB in nitroben- zene. Since Na+ ion transfer from water to nitrobenzene is more favourable energeti- cally (AG:;,;-;+O = 34.2 kJ mol-1)28 than the transfer of the TPB- ion in the opposite direction (AG:;,;Tt- = -35.9 kJ mo1-1),28 the increasing positive current at ca. 0.45 V probably corresponds to the former ion transfer.Analogously, the increasing nega- tive current at cu. 0.13 V is due to TBA+ ion transfer from nitrobenzene to water (AGG,;,TBA+ = -24.0 kJ mol-1)28 rather than to Br- ion transfer from water to nitroben- zene (AG;;,",'" = 28.4 kJ mol-1).28 In the potential range 0.13-0.45 V the current is controlled mainly by charging the interface, and hence in this range the system can be expected to possess the properties required. 0 w-0z. SAMEC, v. M A R E ~ E K AND D. HOMOLKA I I 1 4 I . 0.2 0.3 E I V 20 1 I 1 I 1 Fig. 4. Cyclic voltammogram of 0.01 mol dm-3 NaBr in water and 0.01 mol dmP3 TBATPB in nitrobenzene.Scan rate 0.1 V s-'. Ohmic potential-drop compensation adjusted to 1.35 kS1. Table 1. Comparison of the standard potential differences E g = A:+% - from voltammetric (CV) and extraction (EXT) measurements for several ions tetramethylammonium 0.3 2030 2.64 0.308 0.283 tetraethylammonium O.23O3O 2.03 0.22 1 0.189 cs+ 0.4 13" (4.4) 0.436 0.407 picrate 0.3 lo2' 1.87 0.3 18 0.295 tetrabutylammonium - 1.69 (0) (0) ~~ ~~ " Estimated as the ratio of the limiting ionic conductivities in water3' and nitr~benzene.~~ The limiting ionic conductivity of the Cs+ ion in nitrobenzene was assumed to be the same as for K+. Evaluated from the standard galvanic potential differences, which were calcu- lated25 from the extraction data.*' REFERENCE ION Standard Gibbs transfer energies or standard potential differences for the individual ions are not accessible to direct measurement, since they are always related to the corresponding quantity for another ion, cJ eqn (1).Using an extra- thermodynamic hypothesis, Rais28 evaluated standard Gibbs energies of transfer of an ion from water to nitrobenzene from extraction data. Standard potential diff eren- ces for ion transfer across the water/nitrobenzene interface were inferred from the voltammetric measurements using exclusively TBA' as the reference ion and have been compiled by together with values obtained from the extraction data. However, a closer inspection of the voltammetric data reported in the literature indicates that the value A:+&+ = -0.248 V25 on which the evaluations of the standard potential differences have been based should be corrected.Table 1 summar- izes the reversible half-wave potentials E ie/v2 which were determined for several ions202 DOUBLE LAYERS AT LIQUID/LIQUID INTERFACES 20 10 U 3 0 --. c, -10 1 I . + - 0.2 O.! Fig. 5. Cyclic voltammogram of the transfer of tetramethylammonium ions across the water/nitrobenzene interface at 10 mV s-'. Nitrobenzene phase: 0.01 mol dme3 TBATPB; aqueous phase: 0.01 mol dm-3 NaBr (1) or 0.01 mol dmd3 NaBr and 0.8 mmol dm-3 TMABr (2). by means of cyclic v ~ l t a m r n e t r y . ~ ' ~ ~ ' ~ ~ ~ The standard potential differences E g = Arqb: - Ar#&A+ for the tetramethylammonium, tetraethylammonium and picrate ions have been calculated from the equation E i z = E: +(RT/zF) In [Dx(w)/Dx(o)]'/2 +AE' (4) where z is the charge number of the transferred ion X'.The ratio of the diffusion coefficients in the aqueous and the nitrobenzene phases, D,(w)/ Dx(o), has been estimated as the ratio of the limiting ionic conductivities in water3' and nitroben- ~ e n e ~ ~ (cJ: table 1). The activity-coefficient term AE' has been neglected, since its estimate from the extended Debye-Huckel equation amounts to AE'e 5 mV. With respect to the appreciable association between the Cs' and TPB- ions in nitroben- zene, the standard potential difference for the Cs' ion must be evaluated from the equation33 Ere" - 1/2 - K S + +(RT/F) In [ ~ c s + ( w ) / ~ c s + ( o ) l ' ~ 2 - ( R T / F ) { 1 + K,c';~B-(o)[oC~TPB(o)/ DCs+(o)]'/2> ( 5 ) where c % ~ ~ - ( o ) is the bulk concentration of TPB- ion in nitrobenzene, the association constant K , = 180 dm3 mol-' at 20 "C and DCsTpB(0)/ DCs+(o) =: 0.22.33 The standard potential differences Eg which have been obtained in this way are more positive by ca.30 mV than those evaluated from the extraction measure- ments ( c j table l), the mean being 27 * 4 mV. Consequently, the reasonable agree- ment between the two sets of the data is reached by taking Azqb&jA+ = -0.275 V. In this study we'have used the tetramethylammonium cation as the reference ion in situ, i.e. after the galvanostatic experiment was complete, TMA+ was dissolved in nitrobenzene or the aqueous phase and the cyclic voltammogram measured. A typical curve is shown in fig.5. The conversion of the potential E into the Galvani potential difference A:+ has been made using the standard potential which has been inferred from the cyclic voltammogram, and A~c$%MA+ = 0.035 V.250.20 > 10.15 Q 0.10 Z . SAMEC, V. MARECEK AND D. HOMOLKA I 1 I I I 1 I I I I I I 1 1 I I 1 1 I I 1 L 0 2 4 6 8 10 t/ms 203 Fig. 6. Galvanostatic transient ( I o = -50 PA) at the water/nitrobenzene interface. Aqueous phase: 0.01 mol dmV3 NaBr; nitrobenzene phase: 0.01 mol dm-3 TBATPB. C Fig. 7. Equivalent circuit for the water/nitrobenzene interface: C is the capacitance of the interface, 2, is the faradaic impedance and R, is the solution resistance between the tips of the Luggin capillaries. GALVANOSTATIC-PULSE MEASUREMENTS An example of a galvanostatic transient for-the water/nitrobenzene interface is shown in fig.6 . In general, the current I. is the sum of the double-layer charging current 1, and the faradaic current (cJ: the equivalent circuit in fig. 7) Io= I , + I f = C(dE/dt) + I f (6) where C is the capacity of the double layer. When a current step 61 = I. is initialized at t = to = 5 ms, the charging current I, decreases with time while the faradaic current If increases. In the present case the faradaic current is due to the transfer of Na+ or TBA+ ions across the water/ nitrobenzene interface. Since these processes are fast,27 the quasiiequilibrium Nernst potential difference E, should be established when the current flowing through the interface is zero, i.e. E,= E';> +(RT/zF) In [Dg2(o)c$(o)/D2 (w)c$(w)] (7)204 DOUBLE LAYERS AT LIQUID/LIQUID INTERFACES where the reversible half-wave potential E ; z is given by eqn (4) and &(o) or c$(w) are the concentrations of the transferred ion at the interface on the nitrobenzene or aqueous side, respectively.For a small variation SE << RT/zF of the potential difference E from E,, I , decreases with time according to2' where A t is time-elapsed from t = to. Obviously, at very short times ( I c / Io) ---+ 1 and I0 = C(dE/dt),,-+o. (9) Consequently, the interface behaves as a resistor R, and capacitor C in series, cJ: fig. 7. Under these conditions the ohmic potential drop 6Eo= IoR, appears as a step on the galvanostatic transient at t = to, while the slope of this transient at t > to is controlled exclusively by the capacity C, eqn (9).The potential range over which eqn (9) holds with sufficient accuracy (I,/ Io> 0.99) in the course of a pulse duration A r = 5 ms can be estimated from eqn (7) and (8). This estimate shows2' that eqn (9) is applicable when E, ( ZIS TBA+) falls between ca. 150 and 450 mV or for the galvanic potential difference A,W4 between CQ. -150 and 150 mV. The capacitance C of the water/nitrobenzene interface has been evaluated using eqn (9) from the slopes of the galvanostatic transient at t = to = 5 ms and at t = 10 ms. In fig. 8 C is plotted as a function of the potential difference A,W+ which was evaluated from the potential difference Er as described in the previous section. E, was estimated as the limit of E ( t ) for t ---+ to-.We shall now examine the compatibility between the capacitance data obtained and the MVN model. ZERO-CHARGE POTENTIAL DIFFERENCE For the MVN model the galvanic potential difference A:@ can be written as the sum of three contributions: A r 4 = nZ4i + 42(w) (10) where A:& is the potential difference across the inner layer and 42(0) or @2(w) are the potential differences across the diffuse layers in the organic solvent and the aqueous phase, respectively. In the absence of specific adsorption in the inner layer, the double-layer capacitance, C, can be represented as a series combination of the inner-layer capacitance Ci and the diffuse-layer capacitances C2,0 and C2,w: l 6 where q(w) is the surface charge density on the aqueous side of the interface, Ci = dq(w)/dAr#i, C2,0 = dq(w)/d#,(o) and C2,w = -dq(w)/d+,(w).By solving the Poisson-Boltzmann equation of Gouy and Chapman2-' for 1 : 1 electrolyte^"^ the capacitance of the diffuse double layer, C,, can be expressed asI6 A O ( W ) - - [ 2 R TE O(W) CO]' where E O ( ~ ) is the dielectric constant and co the bulk electrolyte concentration.0.5 0.4 N I 0.3 14 2- 0.2 0.1 2. SAMEC. V. MARECEK AND D. HOMOLKA 205 0 0 '\ \ \o 0 rn / / / I I 1 1 I I I -0.1 0 0.1 A,"+/ v Fig. 8. Plot of the capacitance C of the water/nitrobenzene interface as a function of the potential difference art#^ for two concentrations of NaBr in water and of TBATPB in nitrobenzene: (A) 0.01 and (B) 0.1 mol dm-3. Capacitance data evaluated from the slope of the galvanostatic transient at t = 5 ms (0) and t = 10 ms (0).Dashed lines show the capacit- ance of the diffuse double layer, C,, calculated using Gouy-Chapman theory for A14i= constant = 0 and relative permitivities E~ = 78.54, EO = 34.82. The zero-charge potential difference A,"&zc [ q( w) = q(o) = 01 has been found from the potential difference corresponding to the minimum experimental capacit- ance at low electrolyte concentrations assuming that close to this potential difference Ci >> C, and hence C = C,. Since the minimum capacitance at c' = 0.01 mol dm-3 is found at A:+ = 0 (cJ fig. 8), we conclude that the zero-charge potential difference for the system under the investigation is AOWq5pzc = 0. This result is in a good agreement with the literature data,15316 provided that the corrected value A:@&+ = -0.275 V is used for the standard potential difference of TBA+ ion transfer.In such a case the zero-charge potential difference reported for the system comprising LiCl in water and TBATPB in nitrobenzene by Kakiuchi and Senda15 should read A,"4pzc= -0.007 V instead of 0.020,15 while the value we have reportedI6 should read A,"+,,,, = 0.015 V instead of 0.042 V.I6206 DOUBLE LAYERS AT LIQUID/LiQUID INTERFACES The dashed lines in fig. 8 show the capacitance of the diffuse double layer Cd calculated from eqn (1 2) for A r 4 i = constant = 0. At low electrolyte concentrations the experimental capacitance practically coincides with the calculated value, which justifies the use of our assumption leading to the evaluation of the zero-charge potential difference. As the surface charge density increases, the experimental capacitance tends to rise above the theoretical value, particularly at higher electrolyte concentrations.Qualitatively this effect is in line with theories of the electrical double layer34 in which the approximations involved in the Poisson-Boltzmann equation of Gouy and Chapman2s3 have been removed. CAPACITY OF THE INNER LAYER Another trend which is apparent from fig. 8 is the drop in the experimental capacitance from the Gouy-Chapman value at low surface charge densities and high electrolyte concentrations. This effect can be ascribed to the formation of an inner layer at the water/nitrobenzene interface with a finite capacitance Ci, cf eqn (1 1). In this case C, must be evaluated from the surface charge density q obtained by integrating the plot of capacitance against potential difference.This has been done for the electrolyte concentrations co = 0.05 and 0.10 mol Fig. 9 shows plots of the inner-layer capacitance Ci against the surface charge density q(w); these are similar in shape and coincide to some extent. The capacitance of the inner layer is rather large and the corresponding variation of the potential difference across the inner layer AOW4i rather small, although observable (cf: fig. 10). The evaluation of the capacitance of the diffuse double layer, C,, using the modified Poisson- Boltzmann equation34 would probably lead to a lower estimate of the inner-layer capacitance, Ci, and to a closer coincidence for different electrolyte concentrations, but it should hardly produce a significant change in the picture emerging from fig.9 and 10. Note that the model in which the two space-charge regions are separated by a monolayer of solvent molecules is physically realistic, at least as the limiting case. The capacitance of such a monolayer can be approximated by the equation for a plate capacitor, i.e. ci = E E o d - I where E is the relative permitivity, cO=8.85 ~ 1 0 - I ~ Fm-’ is the permitivity of a vacuum and d is the monolayer thickness. By taking d = 0.3 1 nm (the diameter of a water molecule) the minimum Ci = 1 F m-* corresponds to E == 35, which is roughly the value for monomeric water molecules ( E == 25) with random orientations in the absence of an electric field. However, on increasing the charge density, Ci should decrease owing to dielectric saturation.Since the contrary is observed (cffig. 9), the electrolyte ions probably gradually penetrate the solvent layer over some distance. Through the shielding of the electric field by ions, the high dielectric permitivity in the solvent layer can be preserved. Moreover, replacement of the solvent molecules by ions could make the solvent layer effectively thinner. In summary, the MVN model represents a reasonable framework for interpreting double-layer data for liquid/liquid interfaces in the presence of spherical ions. However, its improvement along two lines is needed. First, a more elaborate treatment of the diffuse double layer seems to be desirable, such as that based on the modified Poisson-Boltzmann e q ~ a t i o n .” ~ Secondly, a diffuse rather than sharp boundary between the space-charge region and the solvent layer should be con- sidered. The picture resembles the spillover of metal electrons into the inner solvent layer which has been envisaged by Kornyshev et all9 for a metal/electrolyte interface.2. SAMEC, V. MARECEK AND D. HOMOLKA 207 1 -10 0 10 20 30 40 q(w)/mC m-' Fig. 9. Capacitance of the inner layer, Ci, at the water/nitrobenzene interface plotted against the surface charge density q(w) on the aqueous side of the interface for two concentrations of NaBr in water and TBATPB in nitrobenzene: 0, 0.05 and 0 0.1 mol dm-'. 10 20 30 UO q(w)/mC m-2 -20 -10. o* 0. Q .O Fig. 10. Potential difference across the inner layer A ~ C $ ~ at the water/nitrobenzene interface plotted against the surface charge density q(w) on the aqueous side of the interface for two concentrations of NaBr in water and TBATPB in nitrobenzene: a, 0.05 and 0 , O .1 mol dm-3. ' E. J. W. Verwey and K. F. Niessen, Philos. Mag., 1939, 28, 435. ' G. Gouy, C. R. Acad. Sci., 1910, 149, 654. D. L. Chapman, Philos. Mag., 1913, 25, 457. 0. Stern, 2. Elektrochem., 1924, 30, 508. C. Gavach, P. Seta and B. d'Epenoux, J. Electroanal. Chem., 1977, 83, 225. V. S. Krylov, V. A. Myamlin, L. I. Boguslavsky and M. A. Manvelyan, Elektrokhimiya, 1977, 13, 834. M. I. Gugeshashvili, M. A. Manvelyan and L. I. Boguslavsky, Elektrokhimiya, 1974, 10, 819. P. Joos and R. Vanden Bogaert, J. Colloid Interface Sci., 1976, 56, 206. M. Kahleweit and H.Strehlow, Z. Elektrochem., 1954, 58, 658. l o L. I. Boguslavsky, A. N. Frumkin and M. I. Gugeshashvili, Elektrokhimiya, 1976, 12, 858. " P. Seta, B. d'Epenoux and C. Gavach, J. Electroanal. Chem., 1979, 95, 191. I* J. D. Reid, 0. R. Melroy and R. P. Buck, J. Electroanal. Chem., 1983, 147, 71. '' H. H. Girault and D. J. Schiffrin, J. Electroanal. Chem., 1983, 150, 43. l 4 M. Gros, S. Gromb and C. Gavach, J. Electroanal. Chem., 1978, 89, 29. I s T. Kakiuchi and M. Senda, Bull. Chem. SOC. Jpn, 1983, 56, 1753. Z. Samec, V. MareEek and D. Homolka, J. Elecrroanal. Chem., 1981, 126, 121. P. Hijkovi, D. Homolka, V. MareEek and Z. Samec, J. Electroanal. Chem., 1983, 151, 277. 16 17208 DOUBLE LAYERS AT LIQUID/LIQUID INTERFACES D. Homolka, P. Hajkova, V. MareEek and Z. Samec, J. Electroanal. Chem., 1983, 159, 233. 18 l 9 A. A. Kornyshev, W. Schmickler and M. A. Vorotynsev, Phys. Rev. B, 1982, 25, 5244. 2o V. MareEek and Z. Samec, J. Electroanal. Chem., 1983, 149, 185. *' D. Homolka and V. MareEek, J. Electroanal. Chem., 1980, 112, 91. T. Kakutani, T. Osaki and M. Senda, Bull. Chem. Soc. Jpn, 1983, 56, 991. 23 0. R. Melroy, W. E. Bronner and R. P. Buck, J. Electrochem. Soc., 1983, 130, 373. Z. Koczorowski and G. Geblewicz, J. Electroanal. Chem., 1982, 139, 177. 25 J. Koryta, P. Vanisek and M. Biezina, J. Electroanal. Chem., 1977, 75, 21 1. C. Gavach and F. Henry, J. Electroanal. Chem., 1974, 54, 361. Z. Samec, V. MareEek and J. Weber, J. Elecrroanal. Chem., 1979, 100, 841. 22 24 26 27 28 J. Rais, Collect. Czech. Chem. Commun., 1971, 36, 3253. 29 Le Q. Hung, J. Electroanal. Chem.. 1980, 115, 159. 30 T. Osakai, T. Kakutani, Y. Nishiwaki and M. Senda, Bunseki Kagaku, 1983, 32, E81. 3' D. Dobos, Electrochemical Data (AkadCmiai Kiad6, Budapest, 1975), p. 76. 32 J. F. Coetzee and C. P. Cunningham, J. Am. Chem. Soc., 1965,87, 2529. Le Q. Hung, Ph. D. n e s i s (J. Heyrovski Institute of Physical Chemistry and Electrochemistry, Prague, 1980). C. W. Outhwaite, L. B. Bhuiyan and S. Levine, J. Chem. Soc., Furaduy Trans. 2, 1980, 76, 1388. 35 R. Parsons, in Advances in Electrochemistry and Electrochemical Engineering, ed. P. Delahay (Wiley-Interscience, New York, 1970), vol. 7, p. 177. 33 34

ISSN:0301-7249    

DOI:10.1039/DC9847700197

出版商:RSC    

年代:1984

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1984, 77, 209-2 16 Transfer of Alkali-metal and Hydrogen Ions across Liquid/ Liquid Interfaces Mediated by Monensin A Voltammetric Study at the Interface of Two Immiscible Electrolyte Solutions BY JrRi KORYTA," Guo Du,? WOLFGANG RUTH§ AND PETR VANYSEK J. Heyrovsk9 Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Opletalova 25, 1 1000 Prague 1, Czechoslovakia Received 2 1 st November, 1983 Under certain conditions the interface between an aqueous phase and an organic phase (ITIES, interface of two immiscible electrolyte solutions) has certain properties analogous to a metal/electrolyte-solution interface. By polarization of the ITIES using potential-sweep voltammetry reproducible voltammograms corresponding to ion transfer across the ITIES are obtained.In the presence of cation-complexing ionophores in the organic phase cation transfer is facilitated. The acidic form HX of carboxylic ionophores, monensin A and B, acts in the nitrobenzene/water system as a sodium carrier while the complex of its anion with sodium or lithium cation (M+) is a proton carrier. The equilibrium constants of the reactions M+ + HX MHX+ and MX + H' E MHX+ have been determined from the voltammograms. The stabilities of the complexes correspond to the series Li+ > Naf >> K+. The substitution of methyl (monensin B) for ethyl (monensin A) on ring C increases the stability of the sodium complex by ca. 1 kJ mol-' and has no effect on the acidity of the carboxy group. Interest in electrochemical processes taking place at liquid/ membrane surfaces has led to the development of a new method, voltammetry at the interface of two immiscible electrolyte solutions' (VITIES), which has various applications in mechanistic investigations as well as in analysis [for reviews see ref.(2)-(5)]. In this method, the interface between an aqueous phase and an organic phase is polarized by a triangular voltage pulse using a four-electrode potentiostat with positive f e e d b a ~ k ' . ~ in order to control the interfacial potential difference under electric current flow. Given a proper composition of both the phases, the interface (ITIES, interface between two immiscible electrolyte solutions) behaves similarly to a metal- electrode/electrolyte-solution When the organic phase contains a strongly hydrophobic indifferent ('base') electrolyte and the aqueous phase a strongly hydrophilic base electrolyte then, under polarization, a potential window is formed in the current-potential curve where the main contribution to the current is due to charging of the interface (a non-faradaic current), see fig.1 ( a ) . Consider that an ion whose concentration is considerably lower than that of the base electrolytes and which has a suitable value of the standard Gibbs energy of transfer between both the phases' is present in one of the phases. Under polarization in a triangular potential-pulse mode both positive and negative current peaks are observed on the polarization curves [fig. 1 ( b ) ] . The rates of ion transfer are rapid so for low polarization rates the concentration of the ion concerned, close to the ITIES, follows the Nernst potential equation.In this 'reversible' case the current-potential depen- dence is exactly described by the Randles-SevEik equation,9310 which was originally deduced for a mercury-electrode/electrolyte-solution interface. T Present address: Institute of Applied Chemistry, Changchun, Jilin, China. 0 Present address: Section Chemie, Universitat Rostock, Rostock, German Democratic Republic. 209210 VOLTAMMETRY AT LIQUID/LIQUID INTERFACES Fig. 1. Triangular-sweep voltammogram for the water/nitrobenzene interface polarized from E = +0.21 to 0.51 V and back; polarization rate dE/dt = 0.005 V s-'; base electrolytes: 0.05 mol dm-3 LiCl in water, 0.05 mol dmP3 tetrabutylammonium tetraphenylborate in nitrobenzene.( a ) Base electrolyte voltammogram, ( b ) 0.001 mol dm-3 Cs+ in the aqueous phase. According to ref. (6). The ITIES charge-transfer kinetics is closely connected with the structure of the electric double layer at the ITIES. According to the Verwey-Niessen model," which correctly describes the situation at the ITIES in the absence of ion adsorption,I2 it consists of two diffuse double layers, the compact layer being absent. Under these conditions the influence of the electric potential difference across the ITIES is displayed as the change in the interfacial concentration of the transferred ion.I3-l6 A number of metabolites act as mobile sites (ionophores) for transport of alkali-metal or alkaline-earth-metal ions across biological membranes. These sub- stances alone or, at least, when bound in a complex have a cyclic structure with polar groups stretching into the internal cavity and with a lipophilic outer envelope which helps to solubilize the complex in non-polar media [for a review see ref.(17)]. The action of these substances has also been modelled by VITIES.2-5~'8-20 In these experiments the aqueous phase usually contains a solution of the chloride of the cation concerned while the non-aqueous phase is a solution of the base electrolyte containing the ionophore at considerably lower concentration than the cation in the aqueous phase. Under these conditions the transfer of the cation can be observed at considerably lower potentials than in the absence of the ionophore, the potential shift being a function of the stability of the complex.The current-generating process is entirely controlled by diffusion of the ionophore to the ITIES and the diffusion of the complex formed from the ITIES into the bulk of the organic phase. The shape of the voltammogram usually corresponds to that of a fully 'reversible' process. This kind of ion transfer is termed 'facilitated' [cJ: ref. (21)]. Monensin is a carboxylic i ~ n o p h o r e , ~ ~ , ~ ~ three homologues of which are produced by Streptomyces cinn~rnonensis~~ (fig. 2). Although it is an acyclic acid it enters theJ. KORYTA, GUO DU, W. RUTH AND P. VANYSEK A B C D 21 1 E Fig. 2. Structures of monensins A, B and C [according to J. W. Westley in Antibiotics, ed. J. W. Corcoran (Springer-Verlag, Berlin, 1981), vol.4, pp. 41-73] R* R2 A CH2(Me)C02H Et B CH2(Me)C02H Me c (CH2)3C02H Me. complexes in a cyclic form, the terminal groups closing the cycle with a hydrogen bond.25 Among the alkali-metal cations it predominantly complexes odium.^^^^ Because of its acidic properties monensin mediates the diffusion of sodium and hydrogen ions across biological membranes as well as bilayer lipid membranes, the transported species being the undissociated acid and the sodium complex of the monensin However, a sodium complex with the undissociated acid has also been found in the solid state.30 The mechanism of the transfer of an alkali-metal ion across the nitroben- zene/water interface and the determination of the equilibrium constant characteriz- ing this process are the subjects of the present paper. EXPERIMENTAL The electrolytic cell is shown in fig.3. The four-electrode potentiostat with positive feedback was the same as described in earlier communications.'96 The organic phase contained 10 mmol dm-3 tetrabutylammonium tetraphenylborate as base electrolyte. The aqueous phase contained either alkali-metal nitrate together with dilute nitric acid or acetate, phosphate or borate buffer prepared from the salts of the alkali metals under investigation. The aqueous solution always contained 1 mmol dm-3 C1-. Before each measurement both the aqueous and the organic phase were brought into contact and equili- brated by shaking. Monensins A aild B (sodium salts) were the gift of Dr W. R. Fields, Lilly Research Laboratories, Indianapolis, Indiana, U.S.A.The mixture of monensins A and B (sodium salts) was the gift of Dr 2. Vangk, Institute of Microbiology, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. Nitrobenzene was a reagent grade product of Lachema, Brno, Czechoslovakia. RESULTS The voltammograms of the monensins recorded under the conditions described above (fig. 4) have the following characteristics: (i) the peak voltammograms appear212 VOLTAMMETRY AT 71 I 2 LIQUID/ LIQUID INTERFACES m m Fig. 3. Electrolytic cell. 1,l’: Auxilliary platinum electrodes ; 2,2’: reference electrodes attached as close as possible to the ITIES by means of Luggin capillaries; 3: the ITIES; 3‘: the interface between the aqueous electrolyte of the reference electrode 2’ and the organic electrolyte; 4,4’: sintered glass diaphragms ; 5: 4-electrode potentiostat and pulse generator; 6: recorder.The potential difference at 3’ is kept constant as the organic electrolyte and the aqueous electrolyte of the reference electrode 2’ have a common ion. in aqueous solutions containing sodium or lithium as cations while potassium has no effect (the pH of the aqueous solutions must be <8); (ii) both the positive and the negative peak currents are proportional to the concentration of the monensin species; (iii) the difference in the potential of the positive and negative current peak, E ; and Ep, is 60*4mV; (iv) the difference in the peak potential and half-peak potential, E,- Epi2, is 60 mV; (v) the peak potentials do not depend on monensin concentration; (vi) the peak current is directly proportional to the square root of the sweep rate, v = d E / d t ; (vii) fig.5 shows the dependence of the half-wave potential of the voltammogram, E l / * = 1/2 ( E ; + E p ) , on pH (obviously, at low pH values the half-wave potential is independent of pH while at higher pH it increases linearly with slope aE,,,/dpH = 59 mV); (viii) in acidic media the half-wave potential shows a linear dependence on the logarit5m of the concentration of the alkali-metal ion cM+ with slope dE,,,/d log cM+ = 59 mV (at pH > 6 the half-wave potential is indepen- dent of the concentration of the alkali-metal ion). From these findings we reach the following conclusions: Ci) the voltammograms correspond to a reversible one-electron process of charge transfer’,’’ [for an instruc- tive survey of the necessary criteria see ref.(31)]; (ii) while sodium and lithium show appreciable complex formation, the complexation of potassium is negligible ;J . KORYTA, GUO DU, w. RUTH AND P. VANYSEK 213 - 150- 100 - 4 i 2 50- 0 - - 50- -50 0 50 100 150 200 EImV Fig. 4. Triangular sweep voltammograms of monensin. Aqueous electrolyte: 0.1 mol dm-3 sodium acetate, 3.2 rnol dmP3 acetic acid, 0.01 rnol dmP3 NaCl; nitrobenzene electrolyte: 0.01 mol dm-3 tetrabutylammonium tetraphenylborate, 0.001 rnol dm-3 monensin. Polariz- ation rates dE/dt: ( a ) 0.005, ( b ) 0.01, ( c ) 0.025, ( d ) 0.05 and ( e ) 0.1 V s-'. The peak current is directly proportional to the square root of the polarizaion rate while the peak potential is constant.(iii) the dependence of the half-wave potential on the concentrations of both the hydrogen and metal ions is described by the equation = ( R T / F ) In where cH+(w) is the concentration of the hydronium ion in water. DISCUSSION The finding that the charge-transfer process is reversible, that the current is proportional to the concentration of the monensin species and that the half-wave potential depends in a characteristic way on the concentration of either the alkali- metal or the hydrogen ion is in agreement with the characteristics of ionophore- facilitated ion transfer across the ITIES.2y435 At low pH values the monensin species facilitates alkali-metal-ion transfer across the ITIES, while at higher pH it mediates hydrogen-ion transfef.Thus, we assume that the monensin species at lower pH is the undissociated acid HX while at higher pH it is converted during equilibration into the complex MX, which then acts as an ionophore for the hydrogen ion. This transformation occurs in an electroneutral exchange reaction M'(w) + HX(o) MX(o) + H+(w). (2)214 150 140 130- > 120- E \ w: 110- 100 90 80 70 60 VOLTAM METRY AT LIQUID/ LIQUID INTERFACES - - - - - - - 1601 0 A 1 I I I I I I I PH Fig. 5. Dependence of half-wave potential El,* of ( a ) monensin A and ( b ) monensin B at cNa+ = 0.1 mol dm-3 on pH. Because of overlapping of the facilitated transfer of Na+ with the transfer of the base electrolyte ions the determination of E,,2 at pH 7.1 is inaccurate. 1 2 3 4 5 6 7 Both the alkali-metal and hydrogen ions are transferred through the species MHX+, whose existence in the solid state has been shown by X-ray ~rystallography.~' At low pH the potential difference across the ITIES is determined by the activities of the alkali-metal ion in the aqueous and organic phases, according to the Nernst equation A:+ = A:t$,"+(RT/F) In cM+(o)/CM+(W) (3) where cM+(0) and c,+(w) are the concentrations of M' in the organic phase and in the aqueous phase, respectively, the activity coefficient being included in the standard potential term, and A:+&+ is the standard potential difference of transfer of M+ from the organic phase to the aqueous phase related to the Gibbs standard energy of transfer of M+ from the organic to the aqueous phase,' AG:;,Tw, by the equation The equilibrium in the organic phase is characterized by the equation KI = CMMHX+(O)/ cM+(O)CE!tx(O)- ( 5 )J. KORYTA, GUO DU, w.RUTH AND P. VANYSEK 215 Table 1. Equilibrium constants K1, K2 and Kexch for monensin A and B (at 22°C) based on the values of A,"&,+ = 0.354 V, AE4Ei+ = 0.395 V and ATc$&+ = 0.337 V Na+ monensin A 5.9 10.4 -4.8 Na+ monensin B 6.05 10.4 -4.65 Li + monensin A + B mixture 6.4 13.3 -5.16 After insertion of eqn (3) into eqn (5) we have A:+ = Ar4&+ + ( R T / F ) In cMMNX~(O)/CHX(O)KICM+(W). (6) The condition for the half-wave potential ( A r 4 = tions of the diffusing species, HX' and MHX', at the ITIES, that prescribes for the concentra- (7) DMHX+CMHX+(O) = DGCHAO) where DMHX+ and DHX are the diffusion coefficients of MHX+ and HX, respectively, in the organic phase.Because of the similar cyclic structure of both molecules~0~32 DMHX+== DHX. Thus, we obtain from eqn (6) and (7) 1/2 E1/'=A:4;+ -(RT/F)ln K,c,+(w). (8) The excess concentration of M+ in the aqueous phase, cM+(w), is not affected by the charge-transfer process. In a similar way we obtain for higher pH Eli2 = AI4;+ - ( R T / F ) In K2CH+(W) (9) K2 = cMHx+(o)/ cH+(o)cwc(o>- (10) where K2 is given by The significance of the constants kl and k, appearing in eqn (1) is given by k , =exp(FA:+R+/RT)K;' k2 = exp (FAz#L+/RVK;'. A more detailed analysis of the transport process has been published elsewhere.33 Finally the equilibrium constant of the exchange reaction (2) is given by Kexch = ~M~(o)cH+(w)/cM+(w)cHx(o) = K2/K1* (12) In table 1 the values of K,, K2 and Kexch are listed for sodium and hydrogen ion interactions with monensins A and B and for lithium and hydrogen ion interac- tions with the mixture of monensins A and B.Tt is remarkable that the stability constants of complexes with HX, K , , are in the order Li+ > Na+ >> K+, which differs considerably from the order of membrane selectivities, Na' > K+ > Li', found with decan- 1 -01-based liquid membranes.32 The transfer of MHX' across the ITIES as a current-generating process obviously has no analogy with processes at bilayer lipid membranes or biological membranes. This may be ascribed to the fact thqt in the present process MHXt is stable in a medium of high permittivity (relative permittivity of nitrobenzene saturated with water is cu.35 at 25 "C) while in a bilayer lipid membrane it can hardly exist in the non-polar interior of the membrane. This is the cause of the negligible change in the conductivity of a bilayer lipid membrane in the presence of m ~ n e n s i n . ~ ~216 VOLTAMMETRY AT LIQUID/ LIQUID INTERFACES The substitution of methyl (monensin B) for ethyl (monensin A) on ring C increases the stability of the sodium complex by ca. 1 kJ mol-' while it has no effect on the acidity of the carboxy group. ' Z. Samec, V. MareEek, J. Koryta and W. Khalil, J. Electroanal. Chem. Interfacial Electrochem., 1977, 83, 393. J. Koryta, Electrochim. Acta, 1979, 24, 293. J. Koryta, Electrochim. Acta, 1984, 29, in press. J. Koryta and P. Vanysek, in Advances in Electrochemistry and Electrochemical Engineering, ed.H. Gerischer and C. W. Tobias (Wiley-Interscience, New York, 1981), vol. 12, pp. 113- 176. J. Koryta, Ion-selective Electrode Rev., 1983, 5, 13 1 . Z. Samec, V. MareEek and J. Weber, J. Electroanal. Chem. Interfacial Electrochem., 1979,135,265. J . Koryta, P. Vanysek and M. Biezina, J. Electroanal. Chem. Interfacial Electrochem., 1977,75,211. A. J. Parker, Electrochim. Acta, 1976, 21, 671. J. E. B. Randles, Trans. Faraday SOC., 1948, 44, 327. E. J. W. Verwey and K. F. Niessen, Philos. Mag., 1939, 28, 435. l o A. SevEik, Collect. Czech. Chem. Commun., 1948, 13, 349. l 2 M. Gros, S. Grornb and C. Gavach, J. Electroanal. Chem. Interfacial Electrochem., 1978, 89, 29. l 3 E. D'Epenoux, P. Seta, G. Amblard and C. Gavach, J.Electroanal. Chem. Interfacial Electrochem., '4 J . Koryta, Anal. Chim. Acta, 1982, 139, 1. I s 1. Koryta and K. Stulik, Ion-selective Electrodes (Cambridge University Press, Cambridge, 2nd 1979, 94, 77. edn, 1983), p. 18. Z. Samec, V. MareEek and D. Homolka, Faraday Discuss. Chem. SOC., 1984, 77,197. Yu. A. Ovchinnikov, V. I. Ivanov and M. M. Shkrob, Membrane Active Complexones (Elsevier, Amsterdam, 1974). A. Hofmanova, Le Q. Hung and M. W. Khalil, J. Electroanal. Chem. Interfacial Electrochem., 1982, 135, 257. l 9 D. Homolka, V. MareEek, Z. Samec, 0. Ryba and J. Petranek, J. Electroanal. Chem. Interfacial Electrochem., 198 1, 125, 243. 2o P. Vanysek, W. Ruth and J. Koryta, J. Electroanal. Chem. Interfacial Electrochem., 1983,148,117. 21 W. J. Ward, AIChE J., 1970, 19, 736. M. E. Haney and M. M. Hoehn, Antimicrob. Agents Chemother., 1967, 349. 23 A. Agtarap and J. W. Charnberlin, Antimicrob. Agents Chemother.. 1967, 359. 24 M. Gorman, J. W. Chamberlin and R. L. Hamill, Antimicrob. Agents Chemother., 1968, 363. 25 M. Pinkerton and L. K. Steinrauf, J. Mol. B i d , 1970, 49, 533. 26 B. C. Pressman, Fed. Proc., Fed. Am. SOC. Exp. Biol., 1968, 27, 1283. 27 P. J. F. Henderson, J. D. McGivan and J. B. Chappel, Biochem. J., 1969, 111, 521. 28 R. Ashton and L. K. Steinrauf, J. Mol. Biol., 1970, 49, 547. 29 R. Sandeux, J. Sandeux, C. Gavach and B. Brun, Biochim. Biophys. Acta, 1982,684, 127. 30 D. L. Ward, K-T. Wei, J. C. Hoogherheide and A. Popov, Acta Crystallogr., Sect. B, 1978,34, 110. 3 1 A. J. Bard and L. R. Faulkner, Electrochemical Methods, Fundamentals and Applications (Wiley, 32 W. K. Lutz, H-K. Wipf and W. Simon, Helv. Chim. Acta, 1970, 53, 1741. 33 Guo Du, J. Koryta, W. Ruth and P. Vanjkek, J. Electroanal. Chem. Interfacial Electrochem., 1983, 34 R. Sandeux, P. Seta, G. Jeminet, M. Alleaurne and C. Gavach, Biochim. Biophys. Acta, 1978,511, 16 22 New York, 1980). 159, 413. 499.

ISSN:0301-7249    

DOI:10.1039/DC9847700209

出版商:RSC    

年代:1984

数据来源: RSC