THE KINETICS OF ACID ABSORPTION ON WOOL FIBRES BY R. F. HUDSON Queen Mary College, Mile End Road, E.1 Received 6th July, 1953 The kinetics of the adsorption of acids on wool initially in the isoelectric condition have been studied, varying the concentration of acid in solution, temperature, degrec of agitation, and the nature of the anion. The variation in rate with time is interpretcd quantitatively by assuniing the diffusion of acid through the fibre, accompanied by adsorption on specific sites (carboxyl groups) to be rate determining. The rnagnitudc of the apparent diffusion coefficients, calculated on the assumption of a linear relation between the concentration of acid in solution and sorbed on the fibres, indicates that the diffusion is controlled by a small concentration of H t.ion in the aqueous phase within the fibres, which may be estimated from the Donnan membrane theory. The activation energy of this process is found to be similar to the value for diffusion in aqueous solution and for the diffusion of water through the swollen fibre. In ion exchange and dyeing, however, where the rate is controlled by the coupled diffusion of two ions in opposite directions, high activation energies, which have bccn attributed to the deformation of polymer chains are observed. In acid sorption, the mechanical restraint is removed by the simultaneous swelling, so that less energy is required for migration through the fibrc. In acid solution, the carboxyl groups of the wool macromolecule are neutralized leaving frec charged amino groups which attract negative gegen ions thus main- taining electrical neutrality within the fibre.These anions are probably mobile within a Gouy double layer surrounding the wool micelles as they rapidly exchange with other anions in an external solution until equilibrium is reached.1 This process is largely responsible for acid dyeing2 although the simple exchange is modified by the high affinity of the dye anion which may enable it to cnter the fibre as the potential-determining ion? For this reason, the rate of exchange of simple ions has been studied and shown to be controlled by a coupled diffusion of the ions within the fibre.4 The diffusion process involves the simultaneous migration of the ion of two kinds in opposite directions which is observed to require considerable energy of activation.This has been attributed to the energy required to deform the polypeptide chains ; this may in turn be causcd by electro- static repulsion between the migrating ions which becomes significant in a gel of low water content comparcd with more highly swolIen cationic resins. Exchange in the latter is usually accompanied by low activation energies similar to the values observed for diffusion in water. Acid absorption on the other hand involves the simultaneous diffusion of hydrogen ions and anions into the fibre and in this sense is unidirectional. The hydrogen ions form covalent bonds with carboxyl groups, a process which may be assumed to be instantaneous, and the anions accompany the protons merely to maintain electrical neutrality.This process continues until the chemical potential of sorbed ions is equal to the chemical potential of the ions in the external solution. This equilibrium may be expressed quantitatively in two alternative ways, either by considering both ions to be localized on specific absorption sites according to a Langmuir type of adsorption, or by considering the proton to 14R . F. HUDSON 15 combine chemically with carboxyl groups as determined by the dissociation con- stant, and applying the Donnan membrane concept to the resulting system of fixed amino-ions, and mobile anions.6 The former developed by Gilbert and Rideal5 is highly successful in providing a quantitative measure of specific anion affinity, and the latter provides a more realistic approach but is far more difficult to apply rigorously.In equilibria involving simple acids, the anions of which exert no specific affinity, the two treatments are equally satisfactory owing t o their common thermodynamic basis. Both theories are necessarily equally correct, and whereas the Gilbert and Rideal theory provides some information on the interaction between anion and absorption site, the Donnan theory can provide a quantitative estimation of the concentration of free protons within the fibre. Although the free acid within the fibre makes a negIigible contribution t o the chemical potential of acid in this phase, it provides the driving force for diffusion through the fibre, and therefore studies of kinetics of acid absorption should provide data for further examination of the Donnan theory.EXPERIMENTAL Fine botany wool in the form of loosely knitted fabric was employed in this work and all the samples were taken from the same bale. 2 g samples, purified by Soxhlet extraction in ether and alcohol, were wetted for 12-15 h in distilled water. This treatment was repeated until no change in pH of the distilled water was observed. In the early experiments? each sample was fitted to a cylindrical glass frame attached to an electric motor. This rotating frame stirrer was lowered into a known volume of acid in a beaker to initiate the sorption? and 5-ml samples withdrawn at known times and titrated with standard alkali. With sulphurous acid, the closed vessel used previously 7 was used, and the samples estimated iodometrically. When a relatively small volume of liquid was used (e.g 50 ml/g wool), not more than 3 samples were withdrawn in any particular experiment so that the volume of the solution was not affected seriously. In most of the experiments? mechanical shaking was used instead of frame stirring, as this mode of agitation was found to be the more efficient.Each sample of wool was attached to a piece of strong thread and suspended in the neck of a flask above the acid. The two phases could be mixed simply by a sharp movement of the flask, and a stopwatch started at the same time. At the end of a pre-determined time, the wool was rapidly removed by means of the thread attached to the stopper of the flask, and a given volume of the acid titrated. By this procedure the timing could be made more accurate? and a larger volume of acid titrated each time, but each measurement involved a different sample of wool and solution.This is an advantage in that any experimental inaccuracies will be minimized by making a considerable number of these determinations in each case, and in spite of the extreme simplicity, the results were found to be highly reproducible. The total sorption was obtained by allowing several samples to remain in contact with the appropriate volumes of acid for at least 2 days. RESULTS THE RATE-DETERMINING MECHANISM.-PreViOUS studies Of the kinetics Of ion exchange,4 dyeing 8 and chemical oxidation 9 have shown that the rate is controlled either by diffusion of reactant to the fibre surface (liquid diffusion), or by diffusion through the fibres (fibre diffusion) provided that the absorption on or reaction at specific sites is rapid compared with the diffusion rate.As the ionization and neutralization of acids are instantaneous processes this condition is satisfied in the present case and consequently it is necessary to differentiate between liquid and fibre diffusion. Either mechanism may become rate- determining depending on the conditions of the experiment given by the following variables (a) agitation of the liquid, (b) temperature? (c) particle size, (4 fibre and liquid diffusion coefficients, (e) the distribution coefficient of solute between the two phases, (f) solution concentration. In the present case all the factors may be varied with the exception of particle size and the results will now be discussed in an attempt to elucidate the rate- determining mechanism.(a) THE INFLUENCE OF AcrrA-rroN.-In general the rate will be sensitive to agitation if the process is controlled by liquid diffusion? and the results shown in fig. 1 where the calculated diffusion coefficient is plotted against rate of frame stirring, show that the rate16 KINETICS OF ACID ABSORPTION reaches a maximum value at ca. 350 rev/min, using 0.1 N HCl. This may be due to a change in mechanism as in previous cases where a sharp change in activation energy is observed.79 9 Alternativcly the rate may reach a maximum because the stirrer reaches a limiting hydrodynamic eficiency. In any case, increasing the rate of the stirrer reduces the width of the liquid diffusion layer at the surface asymptotically so that it is usually P Stirring rate 300 400 500 , FIG.1.-The influence of agitation on the rate of sorption represented by the diffusion coefficient Of. 0 frame stirring ; A hand shaking ; x mechanical shaking. difficult to differentiate bctween the effect of stirring in reducing the diffusion layer, and a change of mechanism. For this reason mechanical shaking was employed in some experiments as an alternative form of agitation. The results also given in fig. 1 show that this form of agitation is more efficient than frame stirring and that the rate of absorption is almost equal to the limiting rate using frame stirring. These observations, TABLE 1 .-DIFFUSION COEFFICIENTS CALCULATED FROM EQN. (3) AND (4) AND ARRHENIUS ACTIVATION ENERGIES FOR SEVERAL ACIDS acid DI in ' t z p .solution at '5 15" C sec K CC HCI 5 19.0 35.0 HNO3 19.0 C~HSSO~H 19.0 36.0 picric 20.5 naphthalene 19.0 H2S03 - 236 55 0.90 2.4 138 55 0.90 - 84 55 0.90 2.4 105 63 0.78 1.25 258 63 0-78 - - 63 0-78 0.69 335 75 0.67 - 390 1-00 - - - - - 1OSD E cni2/sec caljmole 0.508 - 0.825 5.7 1.375 - 0.843 - 0.350 - 0.640 6.3 0.2 10 I - - I - 2 g fibres in 100 ml solution ; 0.01 N initial concentration. although inconclusive, indicate that at high stirring rates, the sorption is controlled by diffusion through the fibre. were differentiated readily by the considerable difference in temperature coefficient. The liquid diffusion mechanisni is normally accompanied by an activation cnergy equal to that for diffusion in aqueous solution, whercas the fibre diffusion niechanisni has an activation energy of 10-12 kcal/molc.(b) THE EFFECT OF TEMPERATURE.-In the processes SO far studied the two mechanismsR. F. HUDSON 17 The data given for several acids in table 1 show that the sorption proceeds with a low activation energy only slightly greater than the corresponding values in aqucous solution. Krcssman and Kitchener 10 have shown, however, that high activation energies are not nccessary for diffusion in porous solids, and for rigid solids containing molecular pores, the activation energy is frequently about the same as the value for aqueous diffusion although the size of the molecular pores may only be slightly greater than the size of the solutc molecules. The rate processes so far studied with swollen wool fibres which are characterized by high activation energies involve coupled diffusion of anion or reactants and products, and consequently the energetic and steric requirements may be entirely different from those involved in the unidirectional diffusion which accompanies sorption.Thus King 11 has found that the activation energy for the sorption of water in keratin is approximately 7-5 kcallmole at low regains, but decreases to 4.5 kcaljmole as saturation is approached. Thus although the low values of the activation energy of acid absorption do not support the fibre diffusion mechanism, the interpretation is not unambiguous in this case and the rate process must be examined further before a decision may be made. (c) THE FORM OF THE KINmcs.-(i) Difiusion across a liquidfiZrn.-The kinetics may be investigated further by analysis of the form of the sorption curve which will differ considerably for the two mechanisms. The first possibility will be considered by supposing that the diffusion of acid through the fibre is the more rapid process.If Dr is the diffusion Coefficient of HC1 in water, A the surface area of the fibres in contact with Y ml of solution, and S the thickness of the hypothetical diffusion layer at the surface, the rate of transport, d(x V)/dt is given by d(xV)/dt = (DiA/S) (a - x - CI), where Cr is the concentration of acid in a small volume element of solution adjacent to the fibre surface, a the initial concentration in solution and a - x the concentration at time t . The acid in the volume element is supposed to be in equilibrium with the sorbed acid within the fibre, given by the equation of the Gilbert and Rideal theory.5 [H-k]i[CI-lr = K[H+]f[Cl-b.For the absorption of pure acid [H+] = [Cl-] in both phases, and the activity within the fibre is given by the activity of a Langmuir absorbate 12 oJ(l - oi), where Bi is the fraction of the total number of sites available occupied by ions of species i. Thus The rate of transport is then given by whcre Xis the maximum total acidcombining capacity of a quantity of wool with surface area A . On dividing through by a and putting x/a = F. whcre F, is the value of F corresponding to maximum acid combining capacity. When K*F, dF/dt = 0, F = F, SO that Fm=Fw 4- . F, is given alternatively by 088 W/aV, a(l-F,) where W is thc weight of wool of area A in volume Vml of solution, so that a check is available on the maximum value of the absorption in a given experiment.The expected rate of sorption can be calculated from this expression for any value of F, as the value of Di for HC1 in water is known, and a value of 6 may be obtained from independent experiments. Thus in previous work with dilute chlorine solutions, using the identical apparatus and a stirring rate of 450 revlmin, 6 is ca. 0.3 x 10-2 cm.7 The value of S is slightly dependent on the diffusion coefficient and for a given medium and stirring condition S tc Db. Values of b are not known with certainty and values between 0.5 and 0.2 have been reported as a result of experimental and theoretical studies.If the higher and more likely value is taken, a value of 0.75 x 10-2 is obtained for S for hydrochloric acid. Using this value, calculated rates may be obtained under any given conditions at this stirring speed. The results given in tables 2 and 3 show that the observed rates ate 10-100 times smaller than the calculated rates, so that the diffusion of acid to the surface is greater than the rate of diffusion through the fibres.18 KINETICS OF ACID ABSORPTION TABLE 2 TABLE 3 0.092 N HCl dF/dt (sec-1) 0.01 N HCl dF/dt (sec-1) F Oh. calc. F obs. calc. 008 0.0035 0.070 0-1 00070 0.0653 0.09 0.00225 0.069 0.2 0.0026 0.0590 0.10 0.001 66 0.0665 0.3 0.001 14 0.0457 0.1 3 04009 0.060 0.4 0.000855 0-0365 0.18 0.0 c 0.7 1 0.0 - Observed rates of sorption, dF/dr, compared with theoretical values ; A = 103 cmz/g ; V = 50 ml; W = 1 g; K+ = 1/160; D1 at 18" C = 3 X 10-5 cm2/sec.FIG. 2.-Theoretical test of the rate-deter- mining mechanism governed by film diffusion for 0.01 N HCl at 19" C. The results in table 2 and 3 also shows that the observed rate curve is entirely different in form from the theoretically predicted curve. This is shown more clearly in fig. 2 where observed values of dF/dt are plotted against [l - F - K+{F/(Fm - ~ ) } / a ] . The calculated values of the rate rapidly approach the observed values as the ex- tent of sorption decreases, so that the rate must be governed by liquid diffusion in the very early stages of the process. Owing to the entirely different kinetic form of the steady-state diffusion and non-steady-state diffusion, it may be concluded that fibre diffusion controls most of the sorption.(ii) DIFFUSION THROUGH THE FIBRE. -The values given in table 2 show that only 18 % of the acid is removed from solution during the diffusion corre- sponding to a pH change of 0.09 units, so that the fibre surface remains almost saturated during the sorption. The quantity of acid Qt diffused from a con- stant surface concentration Qs into a semi-infinite solid in time t accompanied by adsorption assumed to be linear with an adsorption coefficient K is given by 13 Qt = 2QSA(Dt/Kn)*. (1) It is found that QJQ, is proportional to t* for approximately 60 % of the reaction (fig. 3) giving the diffusion coefficient recorded in table 5. When more dilute solutions of acid are employed, however, the change in solution concentration is considerable, and the diffusion within the fibre proceeds from a variable surface concentration.Mathematical solutions for this condition have only recently been realized, and a formal solution of the general case cannot be obtained.14 A solution is available, however, for a linear absorption isotherm 15 based on the general diffusion equation, For diffusion into a cylinder this equation is transformed into polar co-ordinates using the relation The cylindrical fibre of radius a and infinite length is imagined to be surrounded by a cylinder of liquid of cross-section A excluding the space occupied by the fibre. AssumingR. F. HUDSON 19 the absorption to be rapid compared with the diffusion, Wilson 15 obtained a solution in the following form.where qn is the nth positive root of the Bessel function equation : and the constants a and fl are given by wnJo(qn) + Wl(qn) = 0, 0: = A/.rra*(K -1- 1) ; /3 = D/a2(K -1- 1). This solution is only convenient for moderate values of cc and f ; for small values of t and moderate values of a, Crank has transformed the above equation into the form 16 /2 % J 8 4 / 4D FIG. 3.-Rclation between the quantity of acid sorbed and the square root of time for 0.1 N HCl at 16" C with the following rates of frame stirring in rev/min : @ 200 ; x 300 ; 0 450; 0 550. In the present case the absorption is of the Langmuir type, but may be taken to be approximately linear under some conditions for a limited concentration range. This procedure is rendered possible as the form of the theoretical curves given by (3) and (4), is not highly dependent on the value of 01.The variations in cc over the various absorption ranges is illustrated by the data in table 4. TABLE 4 The eITect of acid conccntration on the value of a. 0.01 N 0.02 N 0405N 8% 0.005 0.004 0.003 0.002 0.0 1 71 0.08 0.07 0.04 0-02 0.0 1 51 % 0.015 [acidlj 20 0.45 0 -39 0.37 0.285 0.55 0.50 0.48 0.39 0.67 0.62 0.55 a 0.555 0 5 1 0.40 0.35 0.90 0.80 0.73 0-51 1-47 1-25 0.920 KINETICS OF ACID ABSORPTION A theoretical rate curve for HCI calculated from eqn. (4) is comparcd with the experi- mental data in fig. 4 ; the agreement is observed to be very close. The form of the sorption curve is in agreement with the rate-determining fibre diffusion mechanism, but is completely different from the curve predicted for a liquid diffusion pro- cess.To illustrate the operation of this mechanism further, a sample of fabric was rc- moved in the course of a typical run and after passing rapidly through a small mangle to remove adhering liquid, was allowed to remain out of contact with the solution for several minutes to allow the diffusion gradient within the fibres to decrease. On rc- immersion, the rate of sorption is found to be considerably greater than in an identical experiment without interruption (fig. 4). This supports the conclusion that the rate- controlling process is determined by the diffusion gradient within the fibre. CALCULATED DIFFUSION coEFFIcImm-The rates of absorption of several acids of initial concentration 0.01 N are given in fig.4 where QJQ is plotted against t . The approxirnatc values of D obtained from eqn. (3) and (4) and the values of a corre- sponding to the initial concentration are given in table 1. The calculated diffusion coefficients are seen to decrease with size of the anion and are in the same order as the diffusion coefficients in solution, as far as can bc ascertained. FIG. 4.-% sorption-time curves at 19" C for the following 0.01 N acid solutions : 0 HNO3; x HCI; 0 C6HsS03H; El C&b(N02)3. OH; A CioH7SO3H; @ interrupted curve ; - - - - theoretical curve. The high rate of sorption of nitric acid compared with hydrochloric acid is due to the greater distribution coefficient K, and the calculated diffusion coefficients are observed to be almost equal as in aqueous solution.The proportionality between the calculated diffusion coefficients in the fibre and in solution also indicates that diffusion proceeds through the aqueous phase within the fibre, in agreemcnt with the low activation energies. The order of magnitude of the diffusion coefficients is extremely low and inconsistent with these deductions. As the diffusion coefficients are calculatcd from the relation pt = D/a2(K + l ) t , the low values may be due either to the use of a low value of a or of K. In the present work the first possibility might follow from the USC of loosely knitted fabric, and if the value of a is identified with the radius of the yarn (ca. 0.25 mm), values of D of the order of 10-5 cni2/sec are obtained.Thc calculated values of ca. 10-8 cm2/sec are, however, in agreement with the values 0.5-5 X 10-8 cm2/scc, obtained by Lind- berg17 depending on the pre-treatment. He used chopped fibres, a large volume of liquid, and a different mode of agitation. This suggests strongly, therefore, that the low values of the diffusion coefficient given in table 1 arc not due to the USC of an incorrect value of a. If the values of K previously used arc too low, it follows that the concentration of free acid within the fibre is less than the conccntration in the external solution as these two concentrations were originally assumed to be equal. An approximate allowanccI<. F . HIJDSON 21 for a decreased internal concentration may be madc, if the internal concentration is given by kc, where c is the external concentration.The diffusion equation may then be written : W c ) D 32(kc) -~ __ -___ - -- Zit K/k -I- 1 3x2 ’ D wC --._ 3 C 3t K/k -1 13x2’ - _ Each fibre is imagined to be surrounded by a volume element of solution of cross-section A and concentration c. The corresponding hypothetical cross-sectional area of liquid of concentration kc would therefore equal A/k, so that the parameters of eqn. (2) and (4) now become and It follows, thcrcforc, that thc form of the thcorctical curvc, determined by a, is unaffected by this modification. The true diffusion coefficients derived from p are greater by the factor Ilk than the previous values. INFLUENCE OF THE DONNAN MEMBRANE-AS the hydrogen ions which enter the fibre combine extensively with the carboxyl groups, and the anions largely retain their mobility, the protein may be regarded as a highly ionized salt.According to the general principles established by Donnan, the concentration of free acid in the aqueous phase within the fibre cannot be equal to the concentration in the external solution. Difficulty is encountered in applying this theory owing to the definition of the aqueous phase within a swelling material such as a fibre. There is no doubt that small regions of water exist within the fibre, but the dimensions are not known with certainty. Estimation of the volume of free water within the fibre is also difficult, and the usual assumption that activities may be equated to concentrations renders the treatment necessarily approximate.From this treatment it follows that k = [H+[[I/[H’]~ is given by the ratio of the concentration of acid in the liquid phase to thc concentration of sorbed acid in the fibre, which is of the order of 10-2 in the pH 1-3 range. Using the values of Peters and Speakman 6 obtained by a more detailed treatment, the modified values of the diffusion coefficient Dj given in table 5 are obtaincd. TABLE 5 initial cone* t j (scc) ~ O S D (cin+x) ~ C I I ~ N 0.092 17 2.76 04030 0-02 110 0.88 0*00020 0.0 1 135 0.825 0.00 10 0.005 160 0.61 0.0035 106Df (cm2,kcc) 0.85 0.88 0-825 0.87 Thc effect of concentration on the diffusion coefficient D calculated from eqn. (3) and (4), and values Df allowing for the Donnan membrane. It is observed that the values of Dfare almost independent of acid concentration, and the magnitude of ca.10-6 cm2/sec is in harmony with the low activation energy. Several additional observations indicate the influence of the Donnan membrane in reducing the concentration of H-i- ions within the fibres. Thus it was observed that sulphurous acid is absorbed more rapidly than the acids given in table 1. Complete agreemcnt between all the observed and theoretical rate curves was observed for values TARLE 6 of Q,/Qco LIP to 0.85. tcmp 2 (SCC) 1OSD (crnZ/scc) 2 180 2.08 15 105 ’ 2.57 25 72 5.20 35 51 7.3522 KINETICS OF ACID AnSORPTION The rate of sorption of 0.01 N sulphurous acid at various temperatures ; 1 g wool in 150 ml solution ; stirring rate = 500 rev/min. The high diffusion coefficients are probably due to the undissociated SO:! within thc fibres, which diffuses together with the ions and is uninfluenced by the membrane.Lindberg 17 has similarly observed that H3P04 and HCQQH) are sorbed more rapidly than HCI and HNO3. Further, the addition of salt is found to increase the rate as well as the extent of sorption (fig. 3, in agreement with the increased conccntration of free acid within the fibre predicted by the Donnan equations. FIG. 5.-% sorption-time curves at 19" C for 0.01 N HCI in the presence and absence of salt; 0 no salt; x 0.2 N KCl. DISCUSSION The detailed discussion of the results has shown that the rate of acid sorption is controlled by a non-steady state diffusion, provided that sufficient agitation is employed. The kinetics alone may equally well be explained by diffusion into the yarn treated as a composite cylinder of closely held fibres as by diffusion through individual fibres.In the first case, values of the calculated diffusion coefficient of about 5 x 10-6 cm2/sec are obtained for HCI at 18" C in agreement with the low activation energy of ca. 5.5 kcal/mole. This possibility is dismissed, however, as the rate of sorption, given by the internal diffusion coefficient, is foilnd to be very similar for individual fibres and fabric, i.e. ca. 10-8 cm2/sec at 18" C. This low value suggests that the concentration of free acid which con- trols the diffusion through the fibre is much lower than the external concentration of acid in agreement with the predictions of the Donnan membrane concept. Estimations of the concentration of free acid supposed to be located in an aqueous phase within the fibre lead to true diffusion coefficient about 20 times smaller than the value for HCl in water.This reduced value is due to the small pro- portion of free water within the fibres accommodated in channels of molecular dimensions between the micelles. Owing to the anisotropic swelling of the fibres (1.8 % longitudinal and ca. 16 % transverse) a resultant increase of approximately 15 % in the surface area is produced, which gives the fraction of the surface covered by water molecules. If all this water is localized in micropores and is not chemically bound to specific groups in the wool macromolecules, the diffusion coefficient would be approximately seven times smaller than the corresponding \ralue in aqueous solution.The agreement between predicted and calculatedR. F . HUDSON 23 diffusion coefficients (i.e. within a factor of 2 or 3) must be considered satis- factory in view of the approximations and assumptions which had to be made. Tt has hitherto been observed that diffusion controlled reactions with swollen wool fibres were characterized by activation energies of about 10-12 kcal/mole.89 9 These high values were attributed to the energy of deformation of the protein chains to allow the solute molecules to migrate through the micropores. In exchange rcsins, the activation energy is determined largely by the pore size, and in most cases the values are of the same order as in aqueous solution.10 Increase in size of the ion has little effect until a critical size is reached when increasc in encrgy is observed.The exchange of anions on wool fibres requires activation energies of about 10-12 kcal/mole, and if the ions are assumed to be completcly mobile within the fibres, diffusion coefficients of the order of 10-9 cm2/sec are obtained for simple ions.4 This value is of a similar order of mag- nitude to the value of the self-diffusion coefficient of Br- ions in horn leratin,21 which relates to the B r - B r - exchange. It is interesting to observe that the temperature-independent parameters A of the Arrhenius equation are very similar (- loglo A = 1.5 and 2.0 respectively) for the exchange and sorption processes in spite of the considerable difference in activation energy. The low activation energies observed for the sorption of HCl, H2SO3 and C~HSSO~H, and by King11 for water, show that the macromolecular network offers no mechanical restraint to the penetrating solute.The diffusion in this case is accompanied by swelling to accommodate the molecules or solvated ions, and provided that the hydrated radii are less than the pore diameter the activation energy will be similar to that in aqueous solution. In ion exchange and dyeing (and electrical conduction 18), hydrated ions migrate simultaneously in opposite directions in the micropores. If the combined hydrated radii are greater than the mean pore radius diffusion can proceed only by deformation of the polypeptide chains or side chains which would protrude into the micropores. The increased energy cannot be due to electrostatic repulsion as diffusion controlled chemical reaction require similar activation energies.It is probably significant that the activation energy is not highly dependent on the size of the anion. Thus the value for the HSO~---CGH~S~~- exchange is almost equal to that observed for dyeing with Acid Orange 11. This supports the idea that the micropores are relatively large, about 30-40 8, as suggested by Speakman 19 but the diffusion is restricted by side chains, the deformation of which requires a constant energy almost independent of the size of the anions. The unidirectional diffusion of molccules or ion pairs below a critical size is not hindered by these side chains, and the diffusion therefore proceeds as in aqueous solution. I wish to thank Dr. P. Alexander and J. A. Kitchener and Mr. D. Reichcnberg for several helpful discussions. 1 Elod, Trans. Faraday SOC., 1933, 29, 327. 2 Steinhardt, Fugitt and Harris, J. Res. Nut. Bur. Stand., 1942, 29, 417. 3 Alexander and Kitchener, Textile Rw. J., 1950, 20, 203. 4 Hudson and Schmeidler, J. Physic. Chem., 1951, 55, 1120. 5 Gilbert and Rideal, Proc. Roy. SOC. A , 1944, 182, 335. 6 Peters and Speakman, J. Soc. Dyers Col., 1949, 65, 63. 7 Alcxander, Gough and Hudson, Trans. Faraday SOC., 1949, 45, 1058. 8 Speakman and Smith, J. SOC. Dyers Col., 1936, 52, 121. Alexander and Hudson, 9 Alexander and Hudson, J. Physic. Chem., 1949, 53, 733. Alexander, Gough and 10 Kressman and Kitchener, Faraday SOC. Discussions, 1949, 7,90. 11 King, Trans. Faraday SOC., 1945, 41,483. 12 Fowler and Guggenheim, Statistical Thermodynamics (Cambridge, 1939). 1 3 Hill, Proc. Roy. Soc. B, 1929, 104, 39. Textile Res. J., 1950, 20, 481. Hudson, Trans. Faraday Soc., 1949, 45, 1 109.24 COMBINATION OF ACIDS 14 Crank, Phil. Mag., 1948, 39, 140. 15 Wilson, Phil. Mag., 1948, 39, 48. 16 Crank, Phil. Mag., 1948, 39, 362. 17 Lindbcrg, Textile Res. J., 1950, 20, 381. 18 King and Medley, J . Colloid Sci., 1949, 4, 9. 19 Speakman, Proc. Roy. Sor. A, 1931, 132, 167. 20 Steinhardt and Harris, J. Res. Nut. Bur. Stand., 1940, 24, 335. 21 Wright, Trans. Faraday Soc., 1953, 49, 95.