58 SELF-DIFFUSION OF A DYE THE SELF-DILFFUSION OF A DYE IN A FOLAR POLYMER MEMBRANE BY M. L. WRIGHT Wool Industries Research Association, Torridon, Headingley, Leeds 6 Received 1st July, 1953 ’ Measurements are reported of the self-diffusion coefficient of the anion of the dye Orange 11 in a membrane of horn keratin. Estimates of the mobility of the hydrogen ion have been made, using this data in conjunction with membrane conductivity measure- ments ; the results have been qualitatively confirmed by means of membrane potential experiments. It has been found that the dye anion mobility is much smaller than that for the hydrogen ions and that it varies strongly with concentration. This work is concerned with the processes involved in the dyeing of wool and in particular with the kinetic aspects.Existing data on the diffusion of ions in wool fibres immersed in aqueous electrolyte solution are not numerous. There are several reasons for this, including those difficulties arising from the hetero- geneous nature of the fibres in a wool sample both along one fibre and from fibre to fibre, but in the main they are connected with the behaviour of the outermost layer or epicuticle of the wool fibre.l* 2, 3 I t is well established from visualM. L . WRIGHT 59 evidence that the dyc penetrates more readily through imperfections in the outer skin and that the diffusion rate inside the fibre is much greater than in this skin. In general the dye is constrained to pass through the narrow breaks in the outer surface which then act as line sources as the dye spreads out into the fibre interior.It is also known that this outer layer becomes damaged throughout the life of the sheep and in all stages of subsequent handling so that it is impossible to obtain a " standard " sample of wool with which to perform rate experiments. (Equili- brium sorption is little affected as the epicuticle forms only a small proportion of the total fibre weight.) Added to these are the complications arising from the concentration-dependence of the diffusion coefficient often found in such systems and also from the electrical diffusion potential ; these, however, may be eliminated by the measurement of self-diffusion using radioactive isotopes rather than " chemical " diffusion down a concentration gradient. Self-diffusion is the more fundamental property since a coeficient is obtained for each ion-species rather than a mean value depending on the properties of both anion and cation.The first two difficulties associated with the wool fibre still remain and therefore to simplify the problem a study has been made of membranes of fibrous protein and polymers which h v e properties related to those of the keratin found in the interior of wool fibres. The use of membranes confers two further advantages; firstly, their simple geometry enables an easier solution of the diffusion equation to be used than for fibres and secondly it is simpler when using a membrane rather than a bundle of fibres to ensure that diffusion in the polymer, and not some surface mechanism, is the rate controlling process.It must be emphasized that although the problems related to the surface properties have been temporarily side-stepped, this may well be the most important aspect of wool dyeing. Since there are no data yet available for the self-diffusion of large ions in an electrically charged network of polymer chains, it is felt that these data must first be obtained before proceeding to an investigation of the properties of the cuticle layers. The membrane data and methods described here will clearly be of direct interest in research dealing with synthetic fibres. This paper presents preliminary resuI ts for the self-diffusion in a membrane of cow-horn keratin, of the anion of the free acid of Orange I1 which was " labelled " with 35S, viz., OH Previous work has dealt with Ihe diffusion of a mineral acid 4 and a simple salt 5 in such a system; the original paper should be consulted for much of the detail.EXPERIMENTAL APPARATUS.-The diffusion apparatus is shown in fig. 1 ; it is designed to have a large cross-sectional area for diffusion and to operate using a small volume of solution. The membrane is held directly between the ground edges of the two glass cells which are pressed together by means of a metal clamp fitted with rubber inserts. The whole apparatus is rotated by an electric motor at 60 rev/min about a horizontal axis ; stirring in the solu- tion takes place as an air bubblc is left in each sidc when filling the cells with solution and a series of glass projections (only one of which is shown) also tend to break up the liquid flow.Either side may be filled as follows : after thc rotation has been stopped, a clutch allows the shaft to bc rotated by hand until the hinge axis is horizontal and then the apparatus itself may be swung into the horizontal position. After replacing the rubbcr stopper in the cell a piece of glass rod is used to close the narrow hole through the stopper ; this ensures that the cell contents are only slightly compressed. The apparatus together with the stock solutions and pippettes is kept inside an air thermostat which is controlled60 SELF-DIFFUSION OF A DYE to 0.1" C. The air in thc thermostat is kept saturatcd with water vapour to reduce cvapor- ation from the cdge of the membrane. MEMBRANE.-TO reduce equilibrium times, very thin membranes have been used ; some of these were about 25 p in thickness which is comparable to the diameter of an average wool fibre.The absence of small holes in thc membrane may bc tested by placing a dye solution at one side of the membrane and water at the other, both at room tcm- pcrature ; the dye has a negligible permeability through an intact membrane at low tempera- tures. Small areas of the membrane which are thinner than the rest may be detected by the difference in coloration after dyeing the membrane to a light shade. The thickness of the membrane was obtained by a micrometer and this was checked using density data after weighing the membrane at a known relative humidity. Before use, the mem- brane is eIectrodialyzed to remove any ionic impurities, using a platinum electrode placed at either side of the membrane in distilled water which is constantly renewed.To reduce degradation effects a new membrane is used for each concentration. Although it is possible to relate the permeability of one membrane to another by thickness measurements it is preferable to use conductivity measurements. THE DYE soLunoN.-The purified non-radioactive dye solution required for the experi- ment was prepared from /3-naphthol and sulphanilic acid using A.R. reagents. After recrystallizing once from aqueous solution the dye was redissolved and salted-out with 0.25 N NaCl. The salting-out procedure was repeated three times and thcn the dye was finally recrystallized from aqueous solution to remove the majority of the salt. (It is \ 1 rnerntmmz FIG.1 .-Diffusion cell. found that the precipitates obtained by salting-out with NaCl rather than with HCl are easier to filter.) The sodium dye, plus any salt remaining, were converted to the free acids by passing through a Zeo-Karb 225 ion exchange column in the hydrogen form. By using radioactive sodium ions in a trial experiment under the same conditions, it was found that the concentration of sodium ions was reduced lo00 times on each passage through the column. Following the method of Kressman 6 the solution which now contained the dye acid plus a small amount of HCl, was run down a column of Deacidite E which absorbed the mineral acid and allowed most of the dye solution to pass through. A sample of the dye solution was then dried in VCICUO to constant weight at 110" C and used to make a standard solution.The method of Durrurn,7 in which thc dye solution is flowed down a vertical paper sheet across which there is an electrical potential, was used to test for isomers or any other coloured matter having a diffusion coefficient different from that of the majority of the solution. In fact many of the methods developed for protein analysis can be used to test for dye purity ; the ionophoretic method of Tiselius 8 using a horizontal paper between two glass sheets is particularly usefuI. PREPARATION OF DYE CONTAINING 35S.-Apart from the normal necessity of thoroughly purifying colloidal substances before attempting to use them for physico-chemical measure- ments, it is also essential in this case to remove all traces of impurities containing radio- active sulphur remaining after the synthesis, such as Hzs*04 or NH2-*03H, since these smaller ions would diffuse much faster in the keratin than the dye anion.The dye containing radioactive sulphur was synthesized from sulphuric acid received fromM. L. WRIGHT 61 Harwell which contained 35s (half-life, 87 days). The sulphuric acid was fist converted to sulphanilic acid, which was purified by recrystallizing three times from hot water to remove all traces of HzS*04, and the filtrate tested using BaC12, since the barium salt of sulphanilic acid is soluble. The diazotized sulphanilic acid was then coupled to 15-naphthol. Any radioactive sulphanilic acid remaining was removed by salting-out twice with NaCl from a slightly alkaline solution in which the dye itself is very soluble.In a trial experi- ment using radioactive sulphanilic acid and non-radioactive dye, it was found that 97 % of the sulphanilic acid was removed on one salting-out, The solution was then acidified and the purification carried out as before. Paper electrophoresis was used to check that all the radioactivity was contained in the coloured spot after it had moved along the paper. RADIOACTIVITY MEAsurnMEN-rs-Since 35s is a weak beta emitter it is necessary to evaporate an aliquot of the solution to dryness before radioactive assay, taking precautions to obtain a layer of uniform thickness so that allowance can be made for the self-absorption occurring in the material itself. A gas-flow proportional counter in which the samples are placed inside the counter has been used.Although it is possible to count 355 using a thin end-window Geiger counter, the gas-flow counter method is more sensitive. PROCEDURE.-The membrane is brought to equilibrium at a particular temperature with non-radioactive dye solution. As the temperature coefficient of equilibrium sorption is not large it is possible to speed-up this operation by first increasing the temperature, renewing the solution at intervals and then returning the temperature to its correct value in the later stages. When chemical equilibrium is reached, the dye solution is drained from one side of the diffusion cell and this is refilled with dye of the same concentration but with some dye anions containing radioactive sulphur atoms.At intervals the contents of the other ccll are sampled, to measure the rate at which the radioactive ions are coming through the membrane. This is continued until the steady state has been established; the steady-state refers to the concentration gradient of the radioactive atoms. The extra- polation backwards of the steady-state slope gives an intercept on the time-axis known as the time-lag T from which the self-diffusion coefficient D* can be calculated using the Barrer 9 equation D = (Ax)2/6T, where Ax is the membrane thickness. The flow at the steady state gives a measure of the self-permeability coefficient P* and the solubility or partition coefficient S is given by the ratio P*/D*. The permeability coefficient is defined in terms of the gradient across the membrane as measured in the solution whereas that for the diffusion coefficient refers to the gradient as measured just inside the membrane.RESULTS Measurements have been made at 60" C for three concentrations of the dye acid, viz. at pH 3.5, 2.5 and 1.5, and the results for the self-diffusion coefficients arc shown in table 1. TABLE 1 pH D* (cmz secl) PH D* (cm2 SCC-I) PI* D* ( c d sec-1) 3.5 0.9 X 10-11 2.5 1-8 x 10-11 1.5 6.5 >: 10-11 DISCUSSION The diffusion of the ions of a simple salt in membranes of keratin,5 Cellophane 10 and Nylon 11 has been investigated in earlier work and it has been found that in general the diffusion coefficients of both ions are similar in magnitude and that there is only a slight variation with concentration. From these results and other published work it appears that the magnitude of the diffusion coefficient for simple salts follows a course parallel to the magnitude of the water absorption of the polymer a t saturation water vapour pressure, although it is to be emphasized that no suggestion is made that diffusion takes place in liquid water in the polymer except in the case of the most swollen ones.Approximate values of the diffusion coefficients for simple salts diffusing in some polar polymers are shown in table 2 ; the values are in terms of the diffusion coefficient of the electrolyte in aqueous solution.62 SELF-DIPFUSION OF A D Y E TABLE 2 CX, water %olymer/ rcf. sorption Ijwater gelatin 800 1 Lodge 12 sulphona ted pol y s tyrenc resin Celiophanc 100 10-1 Wright 10 horn keratin 33 10-3 Wright 4 66-Nylon 10 10-4 Wright 11 Teiy lene 1 veiy small Sunmer 14 (Dowex 50) (100) 2 X 10-1 Bauman and Eichhorn 13 The list ranges from the highly swollen gels of gelatin as instanced by the work of Sir Oliver Lodge in the classical experiments on ionic mobilities, to Terylene which is only slightly polar.For the highly swollen polymers the diffusing electro- lyte is little influenced by the polymer as there is only a small probability of the ion coming near an absorption site and so there is little difference in magnitude between diffusion in water and in the polymer for either a salt or an acid. (In several cases these results are somewhat arbitrary as they depend on how the polymer film has been prepared and in which direction the diffusion has been measured.) It is not suggested that the degree of water sorption is the only factor determining the value of the diffusion coefficient but it gives a general indication of what magnitude is to be expected.It is probable that the degree of cross- linking between the chains in the polymer whether by direct bonding or partial crystallization has a profound influence on the value of the diffusion coefficient; the magnitudc of the water sorption itself also indicates the degree of cross-linking. Ultk 15 has suggested that the epicuticle of the wool fibre is a protein similar to keratin but with a higher degree of cross-linking. This would account for the lower diffusion coefficient in the outer layers of the wool fibre than in the interior. For the ions of simple salts there is little modification of the magnitude of the diffusion coefficient due to absorption effects.If, however, there is strong inter- action between an ion species and adsorption sites in the polymer, then for those polymers which do not swell much the magnitude of the diffusion coefficient may be quite different from what might be expected on the basis of the water sorption analogy. The less the polymer swells the greater the distinction it makes between two ionic species having different absorption properties. This was demonstrated for the keratin -1- HBr system in previous work 4 when it was found that at low concentrations the self-diffusion coefficient of the hydrogen ion was much smaller than that of the bromide ions although the value for the bromide ions was itself 1000 times smaller than in aqueous solution.The hydrogen ion mobility varied strongly with concentration and when the keratin was saturated with acid, thc hydrogen ion diffusion coefficient had increased 700 times to have a value greater than that for the bromide ions. These results werc explained in terms of the strong a&i.ity of the hydrogen ion for the charged carboxyl groups in the fibre, so that for low concentrations, the proportion of mobile or frec hydrogen ions at any one time is small. As the keratin becomes saturated with acid the proportion of mobile ions increases giving a higher value for the observed or “overall” diffusion coefficient. The intention of the present work is to investigate the behaviour of an anion which has a strong affinity for the polymer, i.e.much greater than that of the halide ions used previously. The free acid of the dye was chosen rather than the sodium salt since the effect of pH changes can be investigated without the addition of another ionic species. The dye chosen (Orange 11) is a typical example of the level acid dyes (i.e. dyes which have oiily a moderate af5nity for keratin). The wool titration data for this dye already exist 16 and there is also little evidence of aggregation in solution of the dye at the temperature of these experiments.M. L. WRIGHT 63 Mcasurements involving keratin in dilute dye solutions are dominated by the high values obtained for the solubility or distribution coefficient. For a moderate affinity dye such as Orange 11 free acid, the solubility at pH 3.5 is approximately 2000, i.e.1 g of wool can practically exhaust 2000 ml of dye solution at this pH. For dyes of higher affinity such as the milling acid type, this effect will be much enhanced; e.g. for Coomassie Milling Scarlet the solubility value is about 105 at pH 6. As can be seen from the titration curves 16 the effect bccomes smaller as the dye solution concentration is increased. Although these values are for equilibrium sorption, the magnitude of the solubility cocfficient can play a very significant part in diffusion studies. Since the diffusion and permeability co- efficients are related by the solubility we find that although the diffusion coefficient may be low for such a system, the flux may be quite high.For example, consider a membrane experiment in which radioactive tracers are used; then the radio- active solution becomes exhausted of active ions while the side originally non- radioactive rapidly becomes radioactive and this reduces the concentration gradient. This may occur before the steady state is established as a low diffusion coefficient indicates that the equilibrium is only slowly established. A second effect is the maintenance of equilibrium between the dye solution and the membrane during diffusion due to the presence of a still layer of unstirred solution at the membrane surface. This phenomenon has been examined by Alexander, Gough and Hudson for the reaction between wool and chlorine 17 and for dyeing experiments ; 18 the magnitude of this effect under the conditions used in the present experiment has been shown to be negligible (see appendix).The problem in both cases, is one of supplying dye to the solution/keratin interface rapidly enough to ensure that diffusion in the polymer is rate controlling; in the present series of expcri- ments to ensure this, it was found necessary to lower the temperature to 60" C to reduce the diffusion coefficient. Both the above effects are more important with wool fibre masses or fabrics than with membranes, due to the difficulties in circulating the solution between the fibres. Also when rates of absorption are measured rather than the steady-state flow the effect is enhanced, as it is de- pendent on the flow rate. For a membrane, thickness 3 x 10-3 cm and D == 10-11 cmz sec-1, it can be shown assuming a " square root of time " law, that the uptake of dye in the first minute is 100 times that passing through per minute in the steady state for equal surface concentrations.The results obtained for the anion self-diffusion coefficient (table 1) indicate a rapid incrcase with concentration especialiy when it is appreciated that they are for only a very limited concentration range near saturation. This is a similar effect to that found for the hydroken ions in the HBr system at saturation. Measurements have also bcen made of the electrical conductivity K of the mem- brane in dye solutions at 60" C at the same concentrations as used in the diffusion measurements, these are shown in table 3. The diffusion cell used for the dye diffusion is of the same diameter as the conductivity apparatus described previously 4 TABLE 3 dye sorption conductivity calculated % PH (Lister and Peters), (ohms-1 cm-1) anion contribution 3.5 0.68 2-9 x 10-7 7-1 % (mmo W) 2 5 0.88 2.2 x 10-6 2 4 % 1.5 (0.9) 2.3 x 10-5 0-8 % and so the diffusion and conductivity results are directly comparable.The mobil- ity u of an ion can be calculated from the sclf-diffusion coefficient using the Einstein relation (u = FD/RT) and thercfore values for the dye anion mobility uD in keratin can be calculated. Also we can write formally K r= I*'8(uH + uD), where 8 is the ionic concentration in the polymer. An estimate of the hydrogen ion mobility ua can therefore be obtained from the membranc conductivity when64 SELF-DIFFUSION OF A DYE taken in conjunction with data for the anion self-diffusion coefficicnt at the same concentration and temperature.This calculation shows that the hydrogen ion mobility is much greater than for the dye anions (see table 3). Although it is seen that the hydrogen ion mobility increases greatly with concentration, the results are not directly comparable with those obtained in the HBr system, after allowing for the difference in temperature between the two sets of experiments. This may be due to the fact that any slight difference in the sorption isotherms would tend to influence strongly the diffusion results in Ihe region of saturation. A conductivity value has also been obtained at 25” C for one concentration, viz. pH 2-5. The conductivity results at 25” C and 60” C indicate that the activation energy is about 10 kcal/mole in this temperature range for the diffusion of hydro- gen ions.As the dye anion contribution is only a small fraction of the con- ductivity, the activation energy for the diffusion of the anion cannot be obtained by this method. (In the present work no direct measurements have yet been made for the anion diffusion at various temperatures.) In a previous paper dealing with the HBr + keratin system, the variation of hydrogen ion mobility with concentration was explained in terms of two energy states for thc hydrogen ions, the majority of ions being strongly bound to sites (8”) and the others existing in a more mobile state (8’). A similar treatment may be applied to the dye anions which gives 8;/(W - 0;) = 0; exp (- AA/RT).Also, the total concentration sorbed is 8 = 8’ $- 8”. The difference in chemical potential at unit activity for the anion in the two states is and @at is the concentration of bound ions at saturation. Then, as before, we assume that the overall mobility of the anions is due to the relatively small “ mobile ” fraction and therefore OUD = 8’$& where uD is the overall mobility and u t D is the mobility of the mobile fraction. Similarly O D D = 6’D’D, where OD and DtD are the cor- responding self-diffusion coefficients and therefore Taking the known value 19 for the affinity of the anion of Orange I1 for keratin as a measure of &’D then a value for D‘,, can be calculated. This value is con- siderably lower than that found from the diffusion of Orange I1 in solution and we must conclude that the steric hindrance of the keratin to diffusion is con- siderable.(The results for D’D are approximately 1000 times smaller than in aqueous solution.) Since the results in this paper are for solution concentrations which give almost saturation acid combination, the value of (8s.t - 8) tends to depend critically on the value chosen for fW. Mobility values will have to be obtained for lower ionic concentrations in the polymer before the theory can be satisfactorily tested for the dye anion. The values obtained for the self- diffusion coefficient, shown in table 1, are not much larger than estimates made for the diffusion coefficient in wool fibres.19 This is surprising because it might have been expected that the results for the wool fibres would be controlled to a great extent by the low diffusion coefficient in the surface layers.The results so far obtained for wool fibres are for the chemical diffusion coefficient of the dye as a whole (zHD). As D$ > D& therefore zHD m 20& since to a first ap- proximation the chemical diffusion coefficient is given by the harmonic mean of the self-diffusion coefficients. In practice the results will be strongly influenced by the concentration dependence of the diffusion coefficient. In the HBr system4 measurements of the membrane potential were uscd to confirm the hydrogen ion mobility value obtained from the self-diffusion and conductivity results. The membrane potential AE is directly related to the mobility ratio in a two-component system, i.c., D~ = (exp A p t D / R T ) D ‘ D / ( O S a * - 8).M.L. WRIGHT 65 Preliminary results for solutions of the dye show that the weaker solution becomes positive confirming that the hydrogen ion mobility is greater than that of the anion. APPENDn<.-The eflect of the unstirred layer may be investigated quantitatively as follows. When the system is at equilibrium consider the steady state flow of radioactive ions through the still layer and the membrane given by (1) where c, 6 refer to the various radioactive concentrations in solution and menlbrane (see fig. 2) and Ds, DM arc the diffusion coefficients in solution and membrane respectively. If the radioactive ions are removed from the right- hand side of the membrane as fast as they arrive then 82 m 0.From the titration curve it is seen that a linear relation between pH and dye ab- sorbed is approximately true in the range pH 3 to 4 and this is given by Ds(C4 - C3)/d = &(dl - &)/AX, FIG. 2. (2) Stirred el 0.33 loglo (c3/3 x 10-6)- At pH 3.5 for a membrane thickness 3 x 10-3 cm, taking Ds = 5 x 10-6 and DM = 10-11 cm2 sec-1 and assuming d = 0.1 cm, graphical solution of eqn. (1) and (2) gives c3 = pH 3.6. The dye con- centration sorbed at the surface would be 064 mmolelg compared with 0-67 mmole/g at equi- librium at pH 3.5. This is a relatively small error under the worst conditions encountered in this series of experiments (viz. S = 2000). In practice the still layer is probably much less than 0.1 cm at 60" C (Alexander and Hudson18 give a value of 0.03 cm at 25" C for stirring at 50 rev/min ; a smaller value still would be obtained at 60" C due to the reduced viscosity). so/uhon I wish to thank Dr. A. B. D. Cassie, Director of Research, for encouragement in this work and the Council of the Wool Industries Research Association for permission to publish. I would like to thank Mr. G. King for discussion and Mr. F. Bond and Miss M. M. Hargreaves for assistance with the experimental work. 1 Speakman and Smith, J. SOC. Dyers Col., 1936, 52, 121. 2 Millson and Turl, Amer. Dyestuf Reporter, 1950, 39, 647. 3 Lindberg, Textile Res. J., 1950, 20, 381. 4 Wright, Trans. Faraday Soc., 1953, 49, 95. 5 Wright, in press. 6 Kressman, J. Physic. Chem., 1952, 56, 118. 7Durrum, J. Amer. Chem. Soc., 1951, 73,4875. 8 Kunkel and Tiselius, J. Gen. Physiul., 1951, 35, 89. 9 Barrer, Difusion in and through Solids (The University Press, Cambridge, 1941), 10 Wright, J . Physic. Chem., in press. 11 Wright, to be published. 12 Lodge, Brit. Assoc. Report, 1886, 389. 13 Bauman and Eichhorn, J. Amer. Chem. Suc., 1947, 69,2830. 14 Sumner, private communication. 15 UltCe, Schooneveldt and Schuringa, Biuchim. Biophys. Acta, 1953, 10, 590. 16 Vickerstaff, Physical Chemistry of Dyeing (Oliver and Boyd, London, 1950). 17 Alexander, Gough and Hudson, Trans. Faraday Sac., 1949,45, 1058, 1109. 18 Alexander and Hudson, Textile Res. J., 1950, 20,48 1. 19 Lister and Peters, this Discussion. p. 18. C