24 COMBINATION OF ACIDS THE COMBINATION OF ACIDS AND COLOUR ACIDS WITH KERATIN BY L. PETERS AND G. H. LISTER* Textile Chemistry Laboratories, Dept. of Textile Industries, The University, Leeds 2 Received 10th July, 1953 A study has been made of the equilibrium with, and rate of diffusion into, wool keratin fibres of (i) hydrochloric acid and (ii) the free acid of Orange I1 @-naphthol-azo-p-benzene sulphonic acid). The effect of temperatures and concentration has been examined and the results analyzed from a thermodynamic viewpoint. The entropy term TAS was found to provide the major contribution both to the equilibrium free energy AG" of desorption and to the activation free energy AG* of diffusion at the temperatures (60"- 100" C ) which are usual for the acid dyeing of wool, These phenomena can be attributed to the effect of the solvent (water) whose negative affinity for the dye accounts for the fibre having a large positive affinity, and whose hydration of the polar groups adds to the barrier to diffusion.I. EQUILIBRIUM The combination of keratin with acid dyes is very similar to that with simpler acids, and data on a wide range of compounds at different temperatures have been accumulated, mainly by the careful work of Speakman et d , 1 by Steinhardt, Fugitt and Harris 2 and by Lemin and Vickerstaff.3 The nature of the reaction has been analyzed from several points of view. Steinhardt et al. studied the rc- action as an equilibrium between the ions in solution and four species of reacting groups : iso-ionic keratin, keratin-anion, keratin-proton and keratin-acid com- pounds.Gilbert and Rideal4 extended the Langmuir adsorption equation to cover separate anion and cation adsorption at fixed sites in the protein structure, and Peters and Speakman 5 treated the equilibrium of strong mineral acids with wool keratin as a Donnan membrane effect. Controversy over the applicability of each of these theories is still raging6,7 and this Discussion may provide an opportunity to clarify ideas and attempt a reconciliation of the different view- points; but this can be done only if there exists an agreed body of consistent data on which to base a satisfactory decision. Despite all the above-mentioned extensive research, the published experimental data are somewhat inconsistent even for hydrochloric acid and the simple dye Orange I1 (p-sulphonate of benzene-azo-/l-naphthol).For instance, many different values for the pH at which the keratin is 50 % saturated (i.e. pK values) are re- ported in the literature. There are, thus, no definitive values and the discrepancies, although apparently small, prevent adequate interpretation of the mechanism of combination. For * present address : Messrs. Sandoz Products, Ltd., Bradford.L . PETERS AND G . H . LISTER 25 this reason a more intensive experimental study of the reaction of these two acids with keratin has had to be undertaken. Variability in the properties of the material due to the biological origin of the fibres or to diffcrenccs in initial processes of purification may account for some of the inconsistencies.The major source of error in the past, however, must have been due to hydrolysis of amide groups at high temperatures and low pH values, especially in the presence of dyc anions or high salt concentrations. The particular way in which the reaction R . CONH;? + H20 -- RCOO- + NH4+ has been formulated emphasizes that there is an increase in the number of sites for hydrion adsorption as a result of the hydrolysis. The usual procedure of attempting to correct for this effect by subtracting the amount of ammonia found in solution from the apparent acid combined is, therefore, not strictly accurate. At high pH values only a few of the carboxyl groups thus produced will be in the form of -COOH but at low pH values they will all tend to be so and the apparent value for combined H+ is then the true value.The degree 8, of saturation by H+ must thcn be calculated by expressing the amount combined as a fraction of the increased number of sites. When some hydrolysis has occurred, &, the degree of saturation by anions, will not necessarily equal 8, since the fibre can then be electrically neutral without this condition. Close inspection of the isoelectric region of the HCI/KOH titration curves of keratin given by Steinhardt et al. reveals that some hydrolysis of amide groups probably occurred, in the wool thcy uscd, during the scouring processes prior to their experiments, for there seems to be an e x e s of -COOH groups over -NH2 groups not found in solvent- scoured virgin wool. The most important effect of hydrolysis in situ, however, is on the relative con- centration of H+ and NH4+ in solution.Evcn when the amount of ammonia in solution is negligible as a corrcction factor to the acid-combining capacity, i.e. at high pH values, ammonium ions may nevertheless constitute a high pro- portion of the cations present and render pH no longer equal to - log [X-], where X- is the anion concentration in solution. For HC1 this effect is always practically negligible but for Orange I1 the discrepancy leads to quite large errors. The NH4+ concentration, at times, is even greater than the H+ concentration, so that the reaction becomes that of the ammonium salt in the presence of a small amount of acid rather than that of the free acid alone. A further obstacle to precise calculation of affinities is brought out by the data of Meggy 8 on the activity coefficients of Orange IT.These show that the anion concentrations of Orange IT may have to be multiplied by factors up to 100 to convert them into activitics in aqueous solution and this can lead to crrors in estimating the free energy of adsorption of as much as 2.7 kcal/mole (i.e. 2.3 RTloglo 100). But until precise values of the activity coefficients at the appro- priate concentrations and temperatures are obtained, the use of concentrations instead of activities will have to continue, with the consolation that at high tem- peratures such corrections are likely to be smaller than the above limit. From all that has been said above it is clear that to estimate the affinity of dycs for keratin it is necessary to determine, at one and the same time, not only the pH of the solution, but also the ammonium and anion concentrations in solution and the separate amounts of hydrion and anion combined-data which are not provided in any previously published paper.EXPEKIMENTAL MATERTALS.-Wod.--ThC wool keratin was that of thc root ends of fibres taken from the shoulder and back of a New Zealand Romney fleece. It was purified by soxhlet extraction with alcohol and then ether for 24 h each. The wool was then thoroughly washed in distilled water to remove soluble salts and combed to shake out grit. After26 COMBINATION OF A C I D S soaking in N/1000 hydrochloric acid for 24 h, the fibres were immersed in successive baths of distilled water until an equilibrium pH of 4-8 was obtained.The wool was then centrifuged, pressed between filter paper, and allowed to condition at 22.2" C and 65 % relative humidity. The conditioned material was found to have a 15.20 % moisture and 0.06 "/, ash content. Orange I I free acid.--Commercial Naphthalene Orange was re-crystallized from dis- tilled water, precipitated as the barium salt, washed thoroughly to remove sodium salts, and the free acid prepared from the residue by the addition of the theoretical amount of A.R. sulphuric acid. Repeated precipitation with A.R. hydrochloric ensured the complete removal of any remaining sulphuric acid and evaporation to dryness removed all traces of hydrochloric acid. DETERMINATION OF TITRATION cuRvEs.-The titration curve of the wool with hydro- chloric acid was determined at 22.2" C and 60.0 f 02" C and that with the free acid of Orange I1 at 40.0 f 0.1" C, 50.0 0.1" C, 60.0 f 0.2" C and 80.0 :II 0.5" C.Samples of the conditioned wool (2.2000 g) were immersed in measured amounts of acid solutions (approximatcly 270 ml) in flasks having ground-glass stoppers. To prevent concentra- tion errors by evaporation or condensation on the cooler parts of the flasks they were always completely filled and the stoppers sealed with paraffin wax. Two days were allowed for the wool to reach equilibriuni with hydrochloric acid and the times allowed for the free acid of Orange I1 were determined by control experiments. FIG. l.-Titration curve of HCl + keratin at 22.2" C and 60.0" C and of Orange I1 free acid at 80" C ; (a), (6) H+ combined against pH; (c) X- combined against - loglo X. Each solution was rapidly decanted from the wool through a filter pad of glass fibres and, after cooling to 18.0" C, the pH values and the concentration of acid and ammonia in solution was detcrrnined.Determination of hydrogen ion concentration.-When the pH value of the originaI or final solution was less than 2.5, the hydrogen ion concentration was estimated by potentiometric titration. For solutions of higher pH values the concentration was obtained from the pH value by means of a calibration curve. Determination of ammonia in solution.-Aliquots of the solution were made alkaline with M/20 sodium borate and distilled from a Kjeldahl flask into ammonia-free distilled water. The ammonia was estimated in the distillate by colorimetric comparison with standard solutions of ammonium chloride after treatment with Nessler reagent.Determination of anion concentratioa-For the hydrochloric acid titration curve the chloride ion concentration was determined by titrating with silver nitrate, using potassium chromate as indicator. In the experiments with the free acid of Orange TI, the chromo- phore concentration in solution was determined colorimetrically on a Spekker absorptio- meter. The amounts of acid or anion combined were estimated from the changcs in concentra- tion, assuming that the whole of the moisture content in the conditioned wool was water capable of diluting the acid. The results for Orange TI are shown in table 1, and for HC1 in fig. 1.t t TABLE COMBINATION OF KERATIN WITH ORANGE rI FREE ACID 27 final PH 2.08 2.66 3.03 3.49 3.72 3.88 4.20 4.65 4.94 2-05 2.35 2.63 2.8 1 2.94 3.00 3.32 3.60 3.88 4.23 4-61 2.48 3-03 3.18 3-49 3.74 3.83 4.07 4.26 4.34 4.40 4-80 2.40 2.68 3-1 8 3.45 3.68 3.87 3.98 4-14 4.26 4.49 4-65 -log x 2.05 2.47 2.92 3-39 3.58 3.69 3-98 4.43 4.7 1 2.02 2.30 2-57 2.62 2.85 2.90 3.09 3.41 3.60 3.96 4.40 2.42 2.88 3.00 3.23 3.43 3-50 3.69 3.88 4.00 4.05 4-29 2.3 1 2.54 2-91 3.12 3.32 3.49 3.60 3.75 3.84 4.1 1 4.28 ammonia amount combined in solution hydrions anions ( C N ~ (%I) (UX) (mmolcj100 g dry wool) ___ .- ~ _ _ _ _- 9% 7-2 3-8 1.2 1.0 1.0 0.6 0.2 0.1 10.3 7.4 5.1 4.0 3.6 3.6 2-4 2.0 1-7 0.6 0.2 7.4 5.7 5-0 3.8 2-8 2.4 1.7 1.1 0.8 0.7 0.5 13.1 11.5 8.5 5.9 4.0 2 7 2.1 1.5 1.3 0.6 0.4 98.1 90.0 83.3 68.8 53.6 43.4 27.6 12.1 4.8 98.8 93.4 86.8 83.2 79.3 77.5 69-1 56.1 41.7 24.0 11.9 98.3 89.7 85-5 74.2 58.7 47.6 37.2 26.6 21.2 18.7 6.1 11 1.1 106.7 93.0 77.1 62.7 48.4 40.2 29-5 25.1 14.3 8.8 86.2 80- 1 78.2 66-2 51.4 41.4 26-5 11.8 4.9 87.1 84.0 80.2 78.5 74.9 721 65.0 53.2 39.2 23.1 11-5 88.1 81.7 79.0 68.7 54.7 43.8 34.9 25.2 20.1 17-7 6.0 94.1 92.6 83.1 70.1 58.2 46.1 38.4 27.5 23.7 13.8 8.3 DEFINITION OF AFnNIm.-There are several difficulties in attempting to estimate the affinity of an acid for keratin from data such as those given above.Tn the titration of a soluble amino-acid with hydrochloric acid, for instance, the pH of the solution in which the -COOH group is 50 % dissociated (the pK value) is a good measure of the free energy of ionization of that group because it is un- complicated by significant association between the chloride ion and the charged amino group -NH3+.When an insoluble protein is titrated, however, the adsorption of hydrions must be accompanied by adsorption of anions and the free energy of this process will, of course, affect the equilibrium value. Gilbert and Rideal overcome this difficulty by defining the standard state of the acid on the protein as that in which half the available sites are occupied (8 = 4). They then take as a measure of the affinity of the acid, the total free energy AG28 COMBINATION OF ACIDS of its ions, i.e. 2*3RTIog1o[Hl[X], where [HI and [XI are the concentrations (assuming unit activity coefficients) of the hydrions and anions under the above conditions.This implies that the zero free energy of desorption is taken as that of a thcorctical acid which can only half-saturate keratin when its concentration is 1 N. For hydrochloric acid, their viewpoint is, fortunately, easy to reconcile with thc Donnan treatment. According to this theory thc product of thc equilibrium activitics of the ions in the external solution must be equal to that in the internal solution, while at the midpoint the internal anion concentration can be assumed to be of the order of 1 3 N because of the low affinity of C1-. This is not far from unit activity, so that - loglo [H][Cl] is not appreciably different from the internal pN. The internal pH value at the midpoint is a measure of the affinity of the -COO- groups for H+ (AG == 2.3 RTpK) which is thus almost identical with the above Gilbert-Rideal definition of the affinity of kcratin for both ions, The effect of the internal anion concentration a&, where a, is the amount of uncombined internal anion and v is the volume of the internal phase, is too large to be neglectcd for collagen9 because of the large volume swelling; it can be neglectcd for keratin because its volume swelling is small but even then only when the amount of anion combiiied (in rnmolelg) is of the same order as the internal volume (in ml/g).At very low degrees of combination this correction factor becomes significant .7 The free energy AC of desorption when 6 differs from & is assumed by Gilbcrt and Rideal to be given by the equation Unfortunately, when AG is calculated from this equation the value found is not constant but depends on the degree of saturation.This could be explained as due to some sites having different affinities for the ions, or what axnounis to the same thing, each site may be influenced by the state of combination of its neighbours. It is also not cerlain that the number of sites for anions is fixed and definite in the same way as for hydrions. The attraction between anions and the charged -NH3-l- groups is a long-range coulombic effect and need not be one- to-one as in covalent bond formation. The non-anionic moiety of the dyc molecule, too, is often hydrophobic and this could cause the dye to accumulate in the solid- liquid interface as a mobile monolayer-a form of adsorption different from that implied by thc Gilbert-Rideal theory. Because the value of AG caIculated from eqn.(1) is not constant but depends on 8, it is not correct to take the mean of several values, because the result thus obtained is determined by the pH at which the experiments were performed. This is also true of the speciously elegant desorption method devised by Gilbert 10 and used by Lemin and Vickerstaff.3 A more rigorous approach would be to take the total area under the titration curve since this would include small pro- portions of groups of different affinities and thus give a truer estimate of the total free energy associated with complete saturation. The titration curves, howcver, are very symmetrical, and because of this, it has been found that the following simpler method gives almost the same results.The ammonia correction cNH3 and the amount aH of H+ combined were used to cstimatc the degree to which the carboxyl groups are saturated by assuming thc maximum at any time to be (90 + cNHJ mmole/l00 g dry wool. The amount ax of anion combined was assumed to have a constant Iiinit of 90 mmole/l00 g, i.e. pcptide hydrolysis was neglected. The data of table 1 were then uscd to find by graphical interpolation the value of pH - loglo X at which was zero. The resuIts obtained are plotted in fig. 2.L. PETERS AND G . H. LISTER 29 These interpolated values represent mean activities of the acid in solution which is in equilibrium with acid on the protein in a standard state. From them, thcreforc, an estimate of the free energy of desorption may be calculated.In what follows, the symbol AGO will refer only to this definition. It is a true measure of affinity in that large positive values refer to high affinities and it is to be preferred to the usual convention which involves the uOe of negative values. thc heat AH" and entropy AS" of ionization of weak acids (including amino-acids) are not indepcndent of temperature, a parabolic curve being found when pH is VARIATlON OF HEAT AND ENTROPY WITH TEMpERATURE.-It iS Well known that FIG. 2.-Temperature variation of pH at midpoint of HCl + keratin titration curve and of pH -log10 X for Orange I1 + keratin. 0 experimental - theory. plotted against T. Harned and Robinson11 have shown that the parabolic curve can also be closely fitted by an equation of the form (2) where A, B and C are constants such that pK == (A/T) + BT - C, and AH" == 2.3 R(A - BTZ), ASo = 2.3 R(C - BT).(3) (4) To apply this equation, at least three points are needed and the data for HCl/keratin in table 1 have been fitted to (2) with the help of the experimentally-determined value of AH& = 3650 cal/mole 12 and eqn. (3). The equation thus obtaincd is ( 5 ) For Orange II/keratin the equation fitting all four points is (6) The graphs of these equations are shown in fig. 2. From the numerical values of the constants, estimates of AGO, AH" and AS" have been calculated for different temperatures and the results are illustrated in fig. 3. No great reliance, of course, is to be placed on the exact numericaI values because of the paucity of data from which they were derived but the following conclusions are qualitatively indubitable.At the temperatures at which dyeing is usually carried out (60" to 100" C) the heats of reaction of both HCI and Orange I1 are equally small (AH" less than 0.8 kcal/mole). On the other hand there is a considerable free energy of dc- sorption, that of Orange I1 (AGO = 1 1 to 12J kcal/mole) being larger than that pKHcl = (1912*3/T) + 0.014956T - 6.3969. pKo,, = (5353*2/T) + 0.043957 - 23.409.30 COMBINATION OF ACIDS of HCL (AGO = 64 to 7 kcal/mole) in agreement with its greater affinity. But the small values of AH" imply that the major contribution to the free energy of desorption is the entropy change ; for HCl in this temperature range AS" is - 16 to - 22 caI/deg. mole and for Orange 11 AS" is - 27 to - 43 cal/deg.mole; i.e. the system loses degrees of freedom when desorption occurs. magnitude of the entropy change contradicts any idea of the anion being adsorbed on specific sites because desorption leads to a more ordered state. However, when it is remembered that these thermodynamic quantities refer to the system as a whole, including the aqueous solvent, the paradox can easily be resolved. Desorption of hydrogen atoms from uncharged carboxyl groups leads to oricnta- tion of water molecules around the ions thus created and it is to this entropy change that much of the above effects can be attributed. The entropy of formation INTERPRETATION OF THERMODYNAMIC VALUES.-At first sight the Sign and large FIG. 3.-Calculated values for the free energy AGO, heat AHo and entropy ASo of &sorption of Orange I1 from keratin at different temperatures.of ice (corresponding to complete orientation of the molecules) is about - 5 cal/mole deg. and it would only need about two water molecules to be oriented around each charge to give an entropy change of the right order for HCI. The higher value for Orange I1 shows that its larger molecule may be displacing a greater number of water molecules (another 4). Such an interpretation leaves very little scope for theorics based on adsorption at specific anion sites, but it is quite in harmony with the conception of surface adsorption at a vast 9 internal micellar surface (106 cm2/g) in a mobile monolayer which inhibits water adsorption-and this could be the source of the affinity.On this view, the larger the surface area of a dye molecule the greater would be its affinity- view put forward by Meggy13 who has attempted to calculate affinities on this basis. Further work is in progress on the adsorption by keratin of weak acids having small organic anions. 11. RATE OF DIFFUSION The histological complexity of wool fibres and the amide hydrolysis which occurs at high temperatures make exact interpretation of diffusion studies difficult, but the approximate treatment given below is probably sufficient for the present.L . PETERS A N D G . H . LISTER 31 EXPERIMENTAL The rates with which wool fibres take up acid from solutions maintaincd at constant concentration were studied by means of a specially built apparatus described elsewhere.14 Measurements were made of the absorption by keratin of Orange I1 free acid from solutions whose pH values ranged from 2.60 to 4-60.The rates were measured at 40", 45", 50", 60" and 80" C over periods of 180 n i n at the high temperatures and 300 min at the lower temper- atures. The general form of all the results ob- tained is illustrated by fig. 4, which gives as an example the data obtained with Orange I1 acid at 80" C . The slope of the graphs of the amount u taken up at different values of t ) increases in all cases during the first 4 min but remains constant afterwards until ultimately the curve flattens as equilibrium is approached. Thc slope (s=- da/pt)) of this linear region was measured in each case, and its reciprocal l/s plotted against that of the hydrion concentration (l/[H '1 = antilog pH).These are straight lines, except at low pH values, and the results of all the experinients at different temperatures with Orange I1 are given in this graphical form in fig. 5 . For comparison, the rate of absorption of hydrochloric acid by a sample of wool was measured at pH 3.73 and continued until equilibrium was almost complete. The wool was then removed and thoroughly pressedibctween sheets of filter paper. Sufficient hydrochloric acid was added to the residual solu- tion! to:bbring!gthe'[pH value to 3.43 and the damp wool re-immersed in the stronger solution. Measurement of the rate of the further uptakc FIG. 4.-Rate of absorption at 80" C of Orange I1 free acid at different pH values.was also prolonged until the characteristic approach to cquilibrium appcared. Both sets of data are presented in fig. 6. FIG. 5.-Variation of the reciprocal of the slope (11s) for Orange I1 free acid with reciprocal of concentration of ( l / [ H i ] ) at different temperatures.32 COMBINATION OF ACIDS DIFFUSION INTO A cuLINDm.-Crank 15 has shown that diffusion into a cylinder of radius Y from a solution having a constant conccntration, should obey the equation (7) a/A = 4(at)h - m t - 7~(Xt)%/3 f . . ., (Z - 0 0 0 \800c lI " 060°C 50 "C o o %P 0 0 0 - /2 0 0 0 0 " O * " 40 "C 3 P H 4 5 - ,I3 FIG. 6.-Rate of absorption of HCI at 40" C . (a) at pH 3.73, followed by a further adsorption ; (b) from pH 3.43.L. PETERS AND G . H. LISTER 33 calculated from (9) and the data in fig.5. The values thus obtained are shown in fig. 7. The smallness of the values for Orange I1 in keratin (10-11 to 10-12 cm2/sec) is in contrast to the magnitude of the values found for direct dyes in cellulose which are of the order of 10-8 to 10-11 cm2/sec (see Vickerstaff, ref. (6), p. 235). Tho value for HCl at 40" C from fig. 6 is also very small (D = 1.2 X 10-10 cm2/sec). Crank assumes that D = K(P + l), where K is the true diffusion coefficient and P is the partition ratio in which the diffusing substance distributes itself between the material of the cylinder and the exterior solution. In the derivation of (7), P is taken as constant, which seems unlikely to be true for keratin. From fig. 7, however, it appears that D is not very pH dependent (except at 80" C) SO there is some justification for assuming P to be constant.It is difficult to decide what value to assign to P. For HCl it would be of the order of 3000 if all the acid combined could be assumed to be dissolved in the wool fibre. This would give K the value of 3.6 x 10-7 cm2/sec. Similar calculations with the data on Orange 11 are possible but the signficance and validity of such "correction" is hard to assess. In the subsequent analysis, therefore, D will be preferred as a measure of the rate of diffusion. FIG. 8.Variation of activation heat AH*, entropy AS* and free energy AG* of diffusion of Orange I1 in wool keratin. Treating the diffusion of acid into keratin as an activated process, the diffusion coefficient D may be assumed to have the form 16 D == h2(kT/h) exp (- AG*/RT) = X2(kT/h) exp (AS*/R) exp (- AH*/RT>, (10) where h is the distance moved by each molecule of acid in overcoming the activ- ation energy barrier (AG*).The plot of log (D/T) against 1/T, however, is not linear so that the heat of activation (AH*, the Arrhenius activation energy E ) varies with temperature just as does the equilibrium heat of desorption (AH"). Estimates of AH* at the mean of the temperature intervals have been calculated and these are shown in fig. 8. The activation entropy AS* cannot be unambiguoudy determined since h is unknown. If it is assumed that the sum of the equilibrium free energy AGO and the activation free encrgy AG* is approximately constant and if h is constant, the values of D given in fig.7 and those of AGO in fig. 3 lead to the estimate that AG* - 13.5 kcal/mole and h = 2.8 A. On the basis of this assumption, estimates of AS* have been derived and the values are given in fig. 8 together with those of AG*. If the above assumption is not valid, however, the graph of AS* will only be displaced vertically. Consequently it seems incontrovertible that, at high temperatures, the major contribution to the activation free energy barrier is that of the entropy term. B34 DIFFUSION OF SORBED SUBSTANCES The authors are grateful to Prof. J. B. Speakman for encouragement and guidance, and to Messrs. Sandoz Products Etd. for a grant to one of them (G. H. E.)-which enabled this work to be carried out. ISpeakman and Hirst, Trans. Faraday SOC., 1933, 29, 148. Speakman and Stott, Trans. Furuduy Soc., 1934, 30, 359 ; 1935, 31, 1428. Speakman and Elliott, Symp. Fibrous Proteins, J . Soc. Dyers Col., 1946, p. 116. ZSteinhardt and Harris, J . Res. Nat. Bur. Starid., 1940, 24, 335. Steinhardt, Fugitt and Harris, J. Rcs, Nat. Bur. Stand., 1940, 25, 519 ; 1941, 26, 293 ; 1942, 28, 201. 3 Lemin and Vickerstaff, Symp. Fibrous Proteins, J. Sue. Dyers Col., 1946, p. 129 ; Symp. on Dyeing, J. Soc. Dyers Col., 1947, p. 41. 4 Gilbert and Rideal, Proc. Roy. SOC. A , 1944, 182, 335. 5 Peters and Speakman, J. Soc. Dyers Col., 1949, 65, 63. 6Kitchencr and Alexaiidcr, J . SOC. Dyers Cul., 1949, 65, 284; Text. Res. J., 1950, 20, 203. Olofsson, J. Sue. Dyers Col., 1951, 67, 57 ; i952, 48, 506. Vickerstaff, Physical Chemistry of I>yeii.rg (Oliver and Boyd, 1950), pp. 289-96. 7 Peters and Speakman, J . Soc. Dyers Col., 1949,65,287 ; J. Soc. Dyers Col. (in press). 8 Meggy, this Discussion. 9 Speakman, Proc. Roy. SOC. A, 1931, 132, 167. 1" Gilbert, Proc. Roy. SOC. A , 1944, 1183, 167. 11 Harned and Robinson, Trans. Faraday Soc., 1940, 36, 973. 12 Speakman and Stott, Trans. Furuduy Soc., 1938, 34, 1203. 13 Meggy, J. SOC. Dyers Col., 1950, 66, 510. 14 Chamberlain and Lister, .?. Soc. Dyers Col., 1951, 67, 176. 15 Crank, Phil. Mag., 1948, 39, 362. 16 Glasstone, Laidler and Eyring, TCteory of Rate Processes (McGraw-Hill, 1911), p. 524.