BERT I L 0 L 0 F S SO N 45 STUDY OF DIFFUSION PROCESSES IN TANNING BY D. M. G. ARMSTRONG* Thc British Leather Manufacturers’ Reseal ch Association, Egham, Surrey Received Gth July, 1953 Whenever two phases are in contact, it is possible, from the apparent mass of one phase immersed in the other, to estimate the amount of matter in that phase and to follow any transport of matter from one phase to the other. The application of a pyknometric method to skin in water or tan solution is discussed. Two concepts are introduced: the specific apparent mass of a protein (shown to be equal to its density increment) and the apparent specific volume of fixed tan. In the diffusion of tannin into skin, part is fixed by the protein and thus there is attrition of the diffusate, and very often sharp diffusing fronts are formed.The theory for this type of diffusion process has been given by Hill and Hermans and it is now applied to tanning; it is found that the apparent mass of skin in tan solution of constant con- centration after correction for small changes in density of the solution, varies with the square root of time. This is verified by experiments with tannin from mimosa (Acacia molfissima) bark and tannic acid. Thc tanning process is shown to be much simpler with Mimosa tannin. The amount of tannic acid which can enter bovine skin reaches a limiting value as the concentration of the tan solution is increased, and it is thus possible that, as concentration increases, the amount of tan fixed decreases. The method used at present in the tannery to estimate the rate of tanning is to cut sections through the leather, since there is generally a sharp boundary between the tanned and untanned part.Mezey 1 followed the movement of this boundary by taking such sections, staining them with dichromate and measuring the distance travelled using a microscope. Stather 2 used this method with several tanning materials and established that the depth of penetration was proportional to the square root of time and also to the square root of the concentration of the tannin. He further found 3 that the quantity of tan fixed by small strips of skin was approximately proportional to the square root of the time that these strips had been in tan solution. Pyknometric methods of analysis, i.e. methods depending on measurements of the density of the material analyzed, have been proposed in particular by Russell 4 for the estimation of sulphate.As early as 1905, Parker and Russell 5 proposed such methods for the estimation of the dry weight of skin and give values of the density of skin and conversion factors for obtaining the weight of dry skin from the apparent mass of the latter in water. Brown and Holmes6 followed the rate of tanning as an undctermined function of the “ surface dry mass ” of the skin being tanned. * present address : The Royal Veterinary College, London, N.W.l.46 DIFFUSION PROCESSES If a piece of skin with water filling the interfibrillary space is immersed in a solution of a tannin, its initial apparent mass in that solution depends on the dcnsity of the latter ; as tannin diffuses into the skin it displaces water and the apparent mass increases. The amount of tannin entering the skin should thus be a function of the apparent mass of the piece and of the density of the solution.The advantage of such a method is that continuous observations can be carried out with a minimum of interference with the system studied (cp. Clack 7 and Wall, Grieger and Childers 8). As tannin enters the skin it combines with the protein, and this must slow down the diffusion. The theory of this type of diffusion process, which may be called diffusion with attrition of the diflusate, has been developed by Hill9 and more recently by Hermans.10 It predicts the formation of a sharp diffusing front moving over a distance proportional to the square root of time and of concentration in agreement with the findings of Stathcr.29 3 In this papcr we invcstigate thc use of pyknometric methods in the study of tanning process and dcduce relations, some of which are similar in form to those given by Adair and Adair 11 in connection with the density increment of proteins.Data obtained by these methods arc then used to show the validity of the Hill- Hermans 99 10 theory for the tanning process. EXPERIMENTAL The tanning materials used were a commercial mimosa extract (from the bark of Acacia rnollisima) in powder form containing 65 mg equiv. of salt as dcterniined using the u '//1 I// //I I/- i. I f 1 (Q) . - / / 1 B ,,, ,,. ' / FIG. 1 .-Experimental details. acid form of the ion exchange resin Zeo Karb 226, and 17 mg equiv.of acid per 100 g of dry extract, and B.D.H. tannic acid containing 120 mg equiv. of acid and 1-5 mg equiv. of salt per 100 g of dry acid. Solutions in distilled water of the required concentration were used. The skin was obtained from an ox and had been treated with cal- cium hydroxide and sodium sulphide to unhair it. It was neutralized by 0.1 M acetate buffer of pH 5, di- alyzed in distilled water and finally dehydrated with acetone which was then evaporated. Rectangular picas of various size up to 5 x 10 cm were cut from the dorsal region, where the thickness was ap- proximately 0-7 cm. Fine holes were drilled at two adjacent corners of the pieces; through these were threaded loops of fine Nylon thread or bent handles of Nichrome wire as shown in fin.1. The pieces were degreased using petroleum ether. After evaporating the latter, they were placed in a beaker of distilled water in a vacuum desiccator which was evacu- ated at the water pump for 6 h, left under a partial vacuum overnight and a further evacuation carried out the next day. In this way all the air could be removed from the pieces as shown by measurement of their apparent mass. The mass of fully soaked pieces, both tanned and untanned, was detcrmined after lightly pressing between' filter paper, yielding " the surface dried mass ". The pieces were immersed in tan solution or water in 1 I. beakers placed in a thermostat at 20 k 0.02" C. In general half an hour was required to attain the temperaturc equilib- rium. Between measurements the pieces were allowed to rest sideways at the bottomD. M.G. ARMSTRONG 47 of the beakers ; in later experiments they were kept isolated from thc sides of the beakers as shown in fig. 1 (b). For measurement of apparent masses, an analytical balance was placed on a table spanning the thermostat tank. The left-hand pan arrestor was removed and a detachable suspension fitted to the bottom of the pan as shown in fig. I@). The loop of Nylon was placcd on a hook at the bottom of the suspension ; for pieces fitted with a Nichrome handle, the latter was kept immersed and passed over a glass hook (the volume of which had been determined) also immersed in the solution and connected to the suspension by fine platinum wire. The density of the solution was calculated from the apparent mass of a glass sinker (calibrated in distilled water at 20" C ) in place of the piece.Ap- parent masses were estimated to thc nearest 0-1 mg but in their measurement, the damping was such that the sensitivity of the balance was reduced from 5 to 1 or 2 divisions per mg ; thus it is unlikely that readings more accurate than 11; 0.15 mg could be obtained. When dealing with dense tan solutions C. > 1.1 g/ml) the pieces were loaded to prevent them from floating, using a small calibrated glass sinker filled with mercury (fig. l(b)). To find the dry mass of skin or leather pieces, these were placed in an air oven at 104 f 1" C for 24 h then weighed in situ by hooking the piece by its handle to a suspension passing through the top of the oven. There was only a further very small percentage loss in mass after 24 h.Before any piece was placed in the oven it was left to dry (on a sheet of polyethylene) at room temperature, protected from the dust. To determine the concentration of soluble tan in the solution a portion was centrifuged for 30 min at 3500 rev/min and the clear solution decanted; portions were transferred to flat weighing bottles, weighed and evaporated to dryness on a water bath. The residue (never > 9 g), after being hcated in the oven at 104" C, was weighed and the density of the remaining centrifugcd solution determined. To investigate the increase in tan fixation with increase in temperature (the "hot pitting " process) the beakers containing pieces of skin in tan solution were sealed with Cellophane painted with molten paraffin wax and then placed in an oven at 37" C .The procedure in a diffusion experiment was then as follows: a piece of skin was weighed in water (then, in some cases, swollen in acid solution) and its apparent mass therein and the density thereof being measured. Its surface dry mass was determined and the piece quickly transferred to the tan solution of known density and concentration. The apparent mass of the piece was then determined at intervals together with the density of the solution. At the end of the experiment, or on transfer to another solution, the piece was surface-dried, weighed and the concentration of the solution determined. The values of specific volume obtained were corrected for air buoyancy effect, using the approximate formula : where v is the corrected specific volume, v* the uncorrected value, pa the density of air and p2 the density of the solution in which the determination of apparent mass was made.The correction is within experimental error. v == V* -1- v*Pa/Pz - paw*', RESULTS AND DISCUSSION We define (i) fixed tan as any tannin material combined with the protein, i.e. no longer in solution; (ii) soluble tan all matter, non-volatile at 104" C, in solution irrespective of whether it includes substances which are not tannin ; (iii) 20" C as standard temperature. 1. THE APPARENT SPECIFIC VOLUME AND DENSITY INCREMENT OF SOLUBLE TAN.- The apparent specific volume urn (as defined by Kraemer 12) can be obtained from the density p2 of the solution and the concentration cST of the tan : where po is the density of water.The unit is ml/g if densities are expressed in g/ml and csr is in g of tan per ml of solution. The density increment kk is defined 11 by the equation p2 = PO + k&,, (1 62) . k . . ir 1 - pov;; (1.3)48 DIFFUSION PROCESSES if v ~ r does not vary with the concentration then k$ is constant and p2 varies I inearly with concentration. In general, vsr is nearly constant for high-molecular weight non-electrolytes. With freshly prepared solutions of tannic acid, VST is constant over a wide range of concentrations as shown in fig. 2, the value being 0.593 ml/g. With mimosa, we have not investigated the change of VST with concentration but have obtained with cST -- 0.118 the value 0.601 3: 0.009 ml/g (standard deviation for 5 determinations).I I c s 7- 0.1 0.2 0.3 0.4 0.5 0-6 FIG. 2.-Values of a , and am from varying concentrations of tannic acid solution. A values of vST for freshly prepared solutions ; 0 values of a, for aged solutions (40 to 60 days) and after use in tannage ; 0 values of am. 2. THE SPECIFIC APPARENT MASS OF SKIN PROTEIN.-when immersed in Water a mass mp of skin protein has an apparent mass m;,o and we define the apparent volume Vp of the protein by the equation, m;, 0 = mP - VP PO? :. m;, o/mp = 1 - vPpo = ki, since up, the apparent specific volume of skin protein, is the ratio of the apparent volume to the mass of the protein. Thus the ratio of the apparent mass of the protein to its mass is equal to its density increment. Since we are dealing with a fibrous protein in such a state that changes in concentration are limited, we call k; the specific apparent mass of the skin protein.From the value of k; and measurement of the apparent mass of a quantity of skin (or any fibrous protein) in water, we can calculate its mass. By weighing pieces of skin after drying at 104" C for 24 h, then in distilled water at 20" C, we obtained kg = 0.3125 f 0.0006 (standard deviation for 6 determinations). Some of these determinations were done by weighing the pieces in water first, then dehydrating, using acetone, drying at 104" C and weighing. In subsequent experiments, the mass of skin protein was obtained from its apparent mass. The value of up corresponding to this value of kg is 0.6890 -+ 04006 ml/g This value is lower than that (0.71 mI/g) calculated for collagen from the specific volume of the amino acid residues by the method of Cohn and Edsall13 using the composition of collagen given by Bowes and Kenten,l4 and is also lower than that of most soluble proteins which varies between 0.70 and 0.75 (Svedberg 15).This is not unexpected in view of the high percentage of amino acids residue with low specific volume present in skin collagen.D. M. G . ARMSTRONG 49 The variation of vp with temperature is not known. However, it is probable that the coefficient of volume expansion is about the same as that of muscle protein (7.4 x 10-4 per deg.) as determined by Wilkie 16 from the apparent mass of frog muscle in Ringer's solution in the temperature range 0-20" C. in contact with an aqueous tan solution, tan is fixed by the protein.We assume that in this fixation, the apparent specific volume of the skin protein remains constant. We do not assume that the apparent specific volume of the tan vpr when fixed and when in solution to be the same and vp varies, since in tanning the amount of tan fixed varies, whereas that of skin remains constant. To determine urn, the mass mrn of tan fixed on a mass mp of skin protein is obtained. We assume that the molality Fin of the tan in solution, in g tan/g water, is the same inside the piece as in the solution outside it ; in other words we con- sider the piece as an aggregate of tanned fibres immersed in a homogeneous tan solution. The surface dry mass of the piece, rnl, is then obtained, and the piece dried and weighed to obtain mDL, the mass of dry leather.3. THE APPARENT SPECIFIC VOLUME OF FIXED TAN.-when skin protein is placed The mass of tan in solution inside the piece is given by and The apparent mass of the piece m;,2 in the solution of density p2 can be con- sidered as equal to the sum of the apparent masses of the skin protein m;, 2 and that of the fixed tan rnA.2. but We now define k&, the specific apparent mass of fixed tan, as k; = 1 - povPT. (3.7) Values of vm for mimosa and tannic acid were obtained from measurements on pieces which had attained equilibrium (or quasiequilibrium) with the tan solution. From pieces tanned in mimosa solution in the concentration range 0.1 1 to 0.1 3 g/g solution of density 1-05 g/ml, of pH 4-1, and containing 50 mg equiv.salt/l. we obtained as value for urn, 0.630 f 0.003 ml/g (7) * ; tanning at pH 3-22 with the same salt concentration, gives a value 0.6270 whilst tanning at pH 3.2 with the salt concentration at 220 mg equiv.11. with KC1, @2 = 1.061), a value 0.6325 was obtained. From pieces in a solution of higher concentration 0.208 g/g solution and density 1.08324, with tannage carried out at pH 3-2 both in the presence and absence of large amounts of undissociated acetic acid (930 mg equiv/l. of solution) we obtained the value 0-6273 f 0.0004 (6) inl/g. With tannic acid, the values ob- tained varied with concentration as shown in fig. 2. Large bulks of concentrated tan solution are difficult to dry and hence pieces tanned in such solution will con- tain large amounts of tan in solution and it is very probable they cannot be dried in 24 h.Thus, to obtain a more accurate value of urn for tannic acid, pieces of skin 5 x 7.5 cm were tanned by the method of Gustavson and Nestvold 17 by im- mersion in concentrated (0.5-0.2 g/ml) acetone solution of tannic acid and each piece then placed in 11. of distilled water, which was changed after 2 days, and * the number in parenthesis refers to the number of determinations.50 D I F F U S I 0 N P R 0 C E S S E S then kept in that same water under toluene for one month, after which the same measurements were carried out to yield a value of vPY for tannic acid of 0-6170 5 0.0013 (8) ml/g. In this way uncertainties of drying were much reduced since there was a minimum amount of soluble tans in the piece.Since vST is smaller than VPY, there should therefore be expansion in the overall volume of the system with tanning. us suppose that we have a piece of skin of surface dried inass ml, and overall volume V1 (obtained from ml, the apparent mass r n ; , ~ , and p2) containing mp of skin protcin, mm of fixed tan, msT of soluble tan, mo of water. Since 4. VARIATION OF APPARENT MASS WITH ENTKY OF TANNING MATERIAL.-kt mo = WI - ~ P v P + mmVm + mST%T)IpO, mi, 2 = k&p f k b m + k h m - (p2 - PO) VI, (4.1) (4.2) SO that for a finite change at constant rnp k&Am, -1- k&Ani, = Am;,, -t 032 -- p0)AVl -I- V1Ap2; (4.4) this expression neglects a term in Ap2AV1, which is lcgitimate since our experi- ments are carried out at constant concentration and thus p2 is nearly constant and changes in V1 during tanning are small.We now define Arnf such that Am? = Am;, 2 + (p2 - PO)AVI -t- W p 2 . (4.5) Am? is thus the change in apparent mass of the piece corrected for changes in volume and density : it is solely a function of the change in tan content of skin. If we start the experiment with no tail in the piece thcn we can write k&nm f kkm, = Am?. (4.6) In most experiments it was found that V1 remained constant; to obtain the curves shown in fig. 4(a) and 5(a), V1 was 12.97 ml originally, 13.22 ml after 1 day, 13.28 ml at the end of the experiment, differenccs which are not significant since the value of V1 depends on how hard the piece is pressed between filter paper before weighing and therefore to obtain values of Am?, AV1 can generaIly be taken as zero.With pieces fitted with Nichrome handle and sinker, the value of V1 used is the combined volume of the piece and all the attachments including the volume of the hook at the end of the suspension. 5. LEATHER ANALYsIS.-The composition of pieces of leather, when quasi- equilibrium conditions have been attained in the tan solution, can be obtained from their apparent mass in that solution, the mass of skin protein having been deduced from the apparent mass of the skin in water. The mass of fixed tan is then to obtain the mass rnsr of soluble tan inside the piece, the weight concentration as, and the surface dried mass of wet leather must be obtained and nkT = Cm1 - h P + ~ m ~ l a s r . (5.2) Q~ is the number of g of soluble tan in 1 g solution and is related to cbT and (5.3) msr as follows : It is assumed in (5.1) and (5.2) that the interfibrillary solution has the same composition as the external solution.- - aST = cST/J)2 GST/(1 -k mST)-D . M. G. ARMSTRONG 51 Values of changes in mpr from one quasi-equilibrium state to another can be obtained by differentiation of (5.1) similarly for changes in nzsT we use which combined with (1.2) followed by differentiation at constant mp yields niST E= (V1 - vmmm - vPmP)cST, k&AmsT == (mm/csT)Ap2 - (p2 - ~0)vrnAmm (5 5 ) (5.6) 6. NON-SOLVENT WATER.II-lt is possible that in tannage in sohtions of high concentration some of the watcr inside the leather does not contain any dissolved tan (called bound water by Cheshire and Holmes 18).If mNs is the mass of this water associated with a given sample mm = ~ I D L - mp - (mi - mDL - mNs)Gsr (6.1) where vo is the specific volume of water. Using these two equations, the two unknowns mm and mNS can be estimated. The accuracy of this estimate requires accurate values of Zn and vm. To allow for variation of vm from sample to sample, the value for the piece used would have to be determined. The best procedure is probably to obtain rnl for the tanned piece then to transfer it to water and allow most of the soluble tan to diffuse out, the amount of the latter being estimated from the value of Am? for that process using (4.9, Amp, being zero and k& being estimated from ZsT and p2. Since tan appears to diffuse continuously from a piece immersed in water, there must at all times be a small amount of tan in solution inside the piece and an allowance should bc made for this, using a suitable application of the diffusion theory.We have not carried out such experiments but have used eqn. (6.2) to estimate the value of mNs for skin protein in solutions of potassium chIoride varying in concentration from 0.5 to 2-5 N. mm is then zero and the amount of non-solvent water varied between 0.33 and 0.39 g per g of dry skin protein which is of the same order as the values found by Eilers and Labout 19 from the change in con- centration in NaCl solutions in contact with skin. (The method of determining mNs from the apparent mass has been used by Neale and Williamson20 with cellulose.) applies to the diffusion into a semi-infinite skin phase bounded by a plane surface in contact with tan solution, with the following boundary conditions : (i) at x = 0, cST = cE at all times, x being the distance measured from the plane surface and normal to it, and cE being the constant external concentration of the tan solution in g/ml solution; (ii) at time t = 0, there are sites in the skin phase where tannin can become fixed to the extent of cm g/ml of the skin; (iii) at t = CO, cST = cE everywhere and all sites are occupied ; (iv) at t = t, x = f this being the plane where cST = 0, i.e.the boundary be- tween the region where all sites are occupied and that where none are. At this boundary the rate of forward diffusion of the tan equals the rate at which the sites are occupied; thus tan cannot diffuse until all sites are occupied D being the diffusion coefficient.7. APPLICATION OF THE DIFFUSION THEORY.-The Hill-Hermans 99 '0 theory -- D(dcs,/d,r)t -- c*df/dt, (7.1)52 D I F F US I 0 N PI< 0 C E S S E S If the boundary moves slowly, then a steady state is cstablished behind it and (7.2) (7.3) dcsT/df = O = DdZCsT/dXz ; CST = cE(1 - x/C$), so that (7.1) can be integrated yielding the amount of tan fixed per unit area of surface u p to time f is f = (2DcE/c,,)’t*; n?P.r/A = c n f , :. mpr = A(2Dc,c,)hi, A being the area of the plane. The amount of tan in solution inside the piece per unit area is (7.4) .’. mST Z= [cE/(2(‘FT)ImFT; (7.8) combining (7.6), (7.8) and (4.6) we finally get (7.9) i.e. Amy is proportional to the square root of time at constant tan concentration. FIG.3.-Diagrams of tanning as a dif- fusion process. These show cross- sections through the skin normal to its surface at different times. The axis OX represents distances measured normally from the surface, whilst OC is used as 0 s x o x o concentration axis, for cm above OX and for cm below. 5 is the distance of the tanned/untanned boundary from the grain c. 7 C, I CW layer and 5’ that from the flesh layer (in practice is generally greater than t’). AmT = A[k& f /~~cE/(2c,)](2Dc,cn)BtP, :bi :M :L (b) shows the end of stage I ; (c) shows the end of stage 11. la ( 6 I ( C ) With skin, thc phase is separated by two parallel planes, at the flesh and grain side respectively. Thus there will be two boundaries moving toward each other until they meet.We may call the period up to that time, which is the period when most of the tan is fixed, the first stage of tanning. At the end of this stage, the concentration of tan in solution in the piece falls linearly from cE on the outside to zero at the meeting plane of the boundaries. Thereafter there is a diffusion of tan until the concentration inside is uniform and equal to cE; this period may be called the second stage of tanning. Subsequently (and perhaps concurrently) there may be a further deposition of tan, which we call the third stage of tanning. Fig. 3 depicts the process. In tlic derivation of (7.9) we have neglected the fact that the whole volume of the protein phase is not available to the diffusion process since a large part of that volume is occupied by skin protein and fixed tan.The volume available to diffusion VD will be VD = Vl - (VP + V*), (7.10) Vl being the volume of the piece of skin, V, and VFT the volumes of protcin and fixed tan respectively. From the definition of en, Crr -:- (mFT),lVLb (7.11) the value of mm being that at the end of stage I : substituting in (7.8) we obtain the value of msr at thc end of stage I , (nrsT) I - - c,v,/2. (7.12)D . M. G. ARMSTRONG 53 To estimatc the magnitude of D we shall make the assumption that the area available to diffusion AD is given by AD 7-z ( vD/ v1)A. (7.13) In our experiments we have used pieces of skin in the form of a rectangular parallelepiped and there will be an effect due to diffusion from the smaller sides of the piece; thus if the latter has dimensions 2, h and 6, b being the thickness, then the initial area available to diffusion will be (7.14) (7.15) Fig.4 shows the curve obtained by plotting values of Am? per g of skin protein (a) an ordinary piece of skin 3.5 x 6.5 cm and protein concentration 0.377 g/ml; (b) for a piece originally of the same size as the other but heat shrunk by heat- ing in distilled water to 67" C then cooled to 20" C (this treatment resulted in a 7 % decrease in overall volume). The tan solution was mimosa of concentration 2(lh + hb + lb)JG/v~, whcreas the final area when the six boundaries meet is approximately 2(1 - b)(h - b) vD/ v1. against days in tan solution for 0.4 FIG. 4.Variation of the apparent mass of tan per gram of skin protein with time.(a) 0 for a normal piece of skin in a mimosa tannin solution of concentration cST = 0.12 g/ml and pH 3.8. (6) A for a heat-shrunk piece of skin in the same solution. 0.1 17 g/ml, pH 3-8, and density 1.046 g/ml, the density remaining fairly constant during the experiment. The curves show that with heat-denatured skin the rate of uptake of tan is much slower. When Amf/m, is plotted against the square root of time (fig. 5) a siiaight line is obtained over a long period of time in agreement with (7.9) for both pieces. The graph for piece (a) shows three points of inflection; one during the first day, the others near the tenth and twenty-fifth days (points A and B on the graph). The first may be due to a dccreasein the area available to diffusion owing to diffusion through the smaller sides of the piece, the next marking the end of the first stage of tanning and the last the end of the second stage.To test this, the apparent mass k&,msr, of tan in solution in the piece at point R was calculated using (5.4) and (5.6) assuming quasi-equilibrium between B and the end of the experiment at F; this is justified by the form of the graph. Since at the end of stage I the amount of tan in solution is half that at the end of54 DIFFUSION PROCESSES stage 11, subtracting half the value of kkm, at B gives the value of Am; at the end of stage I. In this way point A was obtained, marking the end of stage I at a position very near the inflection point (the value of AnzT/m, at the end of stage I is probably higher since we have assumed that all dissolved matter in solu- tion is fixable tannin which is unlikely). Thus it would appear that stage I took 9 days and stage I1 (A to B) 15 to 16 days.The graph for piece (6) shows that the end of stage I had not been reached by the time the experiment was terminated which was verified by cutting a scction normal to the grain of the piece, when it was clear that only about gth of the piece had been tanned; it is well known that the hcat shrinking of skin powder leads to higher tannin fixation and thus from (7.4), if cm increases, the value of for a given length of time t decreases. FIG. S(6) shows a slight inflection which may be due to a secondary proccss of tan deposition, which is located in 5(a) between B and F (corresponding to a third stage of tanning). B (0) F o.’-ooo- o - - o o o ~ -0 F I ~ .5.-Graph of Amf/mp against the square root of time for the same pieces as in fig. 3. The point A marks the estimated end of the 1st stage of tanning; point B the cnd of the 2nd stage. A further example of the uses of the pyknometric method is shown in fig. 6. For these experiments 6 pieces of skin of dimensions 10 x 5 cm were used, They were swollen over three days in a solution of acetic acid, 0.2N in NaCl and of pH 3.2 prior to tanning to eliminate possible complications due to swelling during tanning. The final average skin protein concentration was 0.33 g l d , that before swelling being 0.37 g/ml. Two mimosa solutions were made up to contain the same concentration of extract (ca. 240 g/l.) and the acid and salt concentrations adjusted by addition of HCl and NaCl for solution I and acetic acid and NaOH for solution 11, the follow- ing analysis being obtained after the end of the experiment.P2 -. salt .- . - acid __ solid content mg equiv./l. gll. PH solution I 3.2 150 60 220 1.083 solution I1 3.2 135 930 240 1 a094 SoIution I1 was far more stable than solution I, since far lcss deposit occurs in it. After an initial drop of approximately 0.003, the density of the solutions (and hence, probably the concentration) remained fairly constant. One piece, no. 1, was placed in solution I for 44 days, then transferred t oD . M. G . ARMSTRONG 55 solution I1 in which it remained for 54 days. The solution and piece were then heated for 7 days at 37" C, cooled to 20" C to allow measurements to be carried out, then heated again for seven days.After cooling again to 20" C it was left in solution I1 for a further 5 days, then transferred back to solution I. Piece no. 2 was kept in solution I throughout the whole experiment, being heated in the same way and at the same times as piece no. 1. Piece no. 3 was kept in solution I1 and heated in the same way and at the same times as pieces no. 1 and 2. . It was transferred to solution I at the same time as piece no. 1 was trans- ferred back from solution 11 to solution I. Each of these experiments was done in duplicate. -Tk< end- of stags -K-fm--pkm-lm. .1- was-ta'mi-tas-ccmxi higatpoint -33 @I days). From this the value of Arnf/rnp at the end of stage I was calculated (point A). f . ..5 8io 20 30 $070 /OO f30 Day5 FIG.6.-Plot of Ami/mp against square root of time (in h) : (1) 0 for piece of skin no. 1 in mimosa solution I up to point C and from E to F, in solution I1 from C to E. (2) A for skin no. 2 in solution I throughout. (3) V for skin no. 3 in solution I1 up to point E. Values of Am1 Imp for pieces 2 and 3 are the ordinate values minus 0.125 and 0.25 units respectively. C is the point where transfer to solution I1 was carried out. Using eqn. (5.1), (5.4) and (4.4) it is possible to calculate the value C', which Arnf/mp should have, assuming that there is a complete diffusion process occurring to make the inter- fibrillary solution the same in all respects as solution 11; as the figure shows this value is not attained although Am? increases then decreases again, which implies that some of the tan previously fixed is being dissolved.Between C and D the calculated loss in fixed tan is 2.8 g / 1 0 g of skin protein (2.6 % for thc duplicate). The change in An$ on hot pitting is shown by the curve between D and E, E being 5 days after removal of solution and piece from the oven; from the increase in n4,2 using (5.1) and (5.4), the increase in tan fixed could be estimated. Table 1 gives the calculated values of the amount in g/l@O g of skin protein of fixed tan at various points in the process for the six pieces; the primes refer to duplicates.56 DIFFUSION PROCESSES Table 1 and fig. 6 show that there was no significant difference in tan fixation or uptake brought about by addition of undissociated acetic acid to the solution, either in tanning at 20" C or on hot pitting; its addition to a solution in contact with a piece previously tanned in the absence of this acid led to the dissolution of some of the fixed tan, but this was compensated by an added fixation on hot pitting.Fig. 6 shows that stage I requires 6 or 7 days for pieces 1 and 2, and stage I1 15 to 16 days. The end of stage I for piece 3 has not been estimated since the amount of non-tannins in solution was too high. From the slope of the plot TABLE 1.- piece 1 1' 2 2' 3 3' -AMOUNT OF TAN FIXED PER 1OOg AT POINTS SHOWN ON FIG. 4 B C D D toE F 83-68 85.65 82-85 19.61 1 10.0 86.98 88.69 86.10 19-55 115.6 86.22 I 93.63 12.98 112.2 79-43 89.72 9.50 104.4 - I 88.07 11.72 115.8 - - 93-04 12.96 108.9 the calculated value of mpr at A (assumed equal to the value at B) and the average value of cm of the solution over stage I (obtained from p2), the value of the diffusion coefficient has been calculated using the average of the two values obtained by the use of (7-14) and (7.15) for the area available to diffusion (b being obtained by dividing V.1 by Zh). Thus D = 2.3 x 10-7 cm2/sec and from this a rough estimate of the average radius of the diffusing particles of 9 x 10-7 cm can be obtained by using the Einstein-Sutherland 21.22 equation.2 3 4 5 6 7 8 9 1 0 .0.5 HOUr.5 FIG. 7.4raph of Amf/mp against the square root of time for pieces of skin tanned in solutions of tannic acid of various concentrations : (a) p,, cm = 0.09, p 2 == 1.042, (d) 0, CST = 0.18, p2 = 1.071, pH = 3 ; (e) 0 csr = 0.26, p2 = 1.107, pH = 3 ; cf) 8, pH = 4; (b) A, csr ~ 0 .2 1 , ~2 = 1.082, pH = 4 ; (c) V, CST =0.09, p2 = 1.034, pH = 3 ; CST = 038, p2 = 1.155, pH = 3, (s) A, CST = 0.62, p2 = 1.248, pH = 3. Fig. 7 and 8 show the variation of Ami/mp with the square root of time at different values of concentration of tannic acid (the concentrations remained nearly constant during the experiments). It is seen from fig. 7 that again over ap- preciable parts of the process the same relationship is obeyed, especially at lower concentrations. At very high concentration, curve ( g ) where cST = 0.62 there is an infcction in the curvc after 6 h as if the entry of tan were impeded, possibly due to deposition of fixed tan which reduces the area available to diffusion.Fig. 8 shows that after 2 days or less there is a marked inflection, but that there is still appreciable entry of tan for a long period.D . M. G . ARMSTRONG 57 By calculating the mass of tan in solution msr in the pieces at the end of the expcriments using (5.1) and (5.2), we can obtain the value of half the apparent mass of tan in solution in the piece k&r71,/2 and by dividing by inp and subtracting the result from the final value of Arnf/rnp we get a value of Amf/rnp (that at the points marked H on the curves) which is much higher than the inflection region of the curves. Thus the second slow part of the process cannot be solely due to stagc IT of tanning but involved also a third stage of deposition of fixed tan. It is probable that stage I is very rapid.Thus tanning with tannic acid is a more complicated process than with mimosa tannin. Also by comparison of curves 8(a) and 5(b) where concentrations were nearly equal, it is seen that there is a far greater amount of tan fixed by skin from tannic acid. The nature of the curves obtained with tannic acid is such that since stage I1 and 111 of tanning occur at the samc time it is not possible to estimate the diffusion coefficient by the method used with mimosa. yo, , . . 100 , , , , 200 . , . . 300 ] FIG. 8.Plot of AmT/mp against the square root of time for the whole tanning process, for the same pieces as in fig. 7. For the sake of clarity only the final part of some of the curves are shown. An attcmpt to estimate the value of cm and hence of D by taking values of the dope of the straight portions at two concentrations and assuming cm and D to be constant, thereby giving pairs of simultaneous equations by the use of (7.9), was unsuccessful since cpT probably, and D possibly, vary with concentration.Fig. 8 shows that the value of the apparent mass of tannic acid per gram of skin protein has a limiting value of about 0.78 (at 40 days), whereas one might expect that this apparent mass, and hence the amount of tan in the piece, would increase continuously with increasing concentration, until the whole of the water in the skin had been replaced by tan (when an = 1). Two possible implications can be drawn from this. As the concentlation increases so the amount of tan fixed per gram of protein decreases. Thus for piece ( g ) where the concentration is 0.62 g/ml using (5.1) and (5.2), assuming zlm to be 0.617, the amount of tan fixed per 100 g of skin protein is 81 g ; the corresponding amount of tan in solution was 94 6: and for other pieces, the values were respectively : piece cf) 148 and 59 ; piece (e) 162 and 37 ; piece (b) 137 and 32.Alternatively, as the concentration increases so the amount of non-solvent water increases so that, effectively, the difference between the concentration of the interfibrillary solution and that of the external solution increases.58 SELF-DIFFUSION OF A DYE The author wishes to thank the Director and Council of the British Leather Manufacturers’ Research Association for permission to publish this paper, Dr. M. P. Balfe for valuable discussions and Mr. D. J. Tate for his help in the experi- mental work. 1 Mezey, Collegium Haltingen, 1925, 305. 2 Stathcr, Collegium Haltingen, 1933, 9 and 316. 3 Stather and Laufmann, Collegium Haltingen, 1935, 420. 4 Russell, Znd. Eng. Chem. (Anal.), 1937, 9, 592. 5 Parker and Russell, Manchester, Liverpool and District Tanners’ Federation Year Book 6 Brown and Holmes, private publication, 1937. 7 Clack, A Research on Diflusiion in Liquids (Clack, Aberdeen, 1922). 8 Wall, Griegcr and Childers, J. Amer. Chem. Soc., 1952, 74, 3562. 9 Hill, Proc. Roy. SOC. B, 1929, 1Q4, 39. 10 Hermans, J. Colloid Sci., 1947, 2, 387. 11 Adair and Adair, Proc. Roy. SOC. A, 1946, 190, 341. 12 Kraemer, in Svedberg and Pcdersen, The Ultracentrifuge (Oxford University Press, 1 3 Cohn and Edsall, Proteins, Amino Acids and Peptides (Reinhold, New York, 1943)) 14 Bowes and Kenten, Biochem. J., 1948,43, 358. 15 Svedberg, Proc. Roy. SOC. B, 1939,127, 1. 16 Wilkie, J. Physiol., 1953, 169, 369. 17 Gustavson and Nestvold, Leder, 1951, 121. 1 8 Cheshire and Holmes, J. Znt. SOC. Leather Chem., 1942, 26, 237. Holmes and 19 Eilers and Labout, Symp. Fibrous Proteins (SOC. of Dyers and Colourist, Bradford, 20 Neale and Williamson, Nature, 1953, 171, 844. 21 Einstein, A m . Physilc, 1905, 17, 549 ; 2. Elelctrochem., 1908, 14, 337. 22 Sutherland, Phil. Mag., 1905, 9, 781. (Bolton, 1905), p. 45. 1940), p. 59. p. 370. Lee, J. SOC. Leather Trades Chem., 1949, 33, 21, 122. 1946), p. 30.