D. L . UNDERWOOD AND H . J . WHITE, J R . 75 THE KINETICS OF ABSORPTION OF WATER AND AQUEOUS SOLUTES BY DRY VISCOSE CELLULOSE BY H. B. MANN AND T. H. MORTON CourtauIds Ltd., Textile Research Laboratory, Bocking, Braintree, Essex Received 16th June, 1953 In pad-dyeing fabrics, the final result depends on the amount of dye taken up during the very short time the fabric is immersed in the dye liquor. The rate of water and dye absorption is thus of great technical importance and interest. The kinetics of absorption by single viscose filaments havc been studied in thrce aspects : kinetics of wetting, kinetics of the absorption of simple solutes such as inorganic salts and urea on wetting the fibre in aqueous solutions, and the kinetics of dye absorption on wetting the fibre in a solution containing dye.The wetting of the fibre is a comparatively rapid process taking about 10 sec for com- pletion at 20" C . The rate of wetting is dependent both on fibre dimensions and tem- perature ; it is approximately proportional to surface area, and the rate of increase with temperature corresponds to an activation energy of about 7 kcal/mole. Simple inorganic salts, urea, glycerol, and sucrose are taken up by the fibre proportionately rather slower than water on immersion of the fibre in the corresponding aqueous solution. The absorption of a direct cotton dye on wetting the fibre in aqueous solution follows a different course. Very little dye is absorbed during the period of wetting, thc dye being presumably concentrated in solution at the interface of the swelling fibrc ; thcreafter redistribution of the dyestuff occurs by well-understood diffusion mechanisms.The foundations for a scientific study of the physical chemistry involvcd in dyeing wllulosic materials with direct cotton dyes were laid in 1933 by Neale and Stringfellow 1 and by Boulton, Delph, Fothergill and Morton.2 Since then, a great deal of further work has been carried out by a number of workers and the mechanism of this process is now iargely understood.3 Little or no systematic work has, however, been done on the mechanism of the application of these same dyes to cotton and viscose rayon by the so-called pad-dyeing process; such a study is timely, since this process is increasingly uscd commercially. The pad-dyeing process differs in a number of respects from the more conventional methods of dyeing which havc already been studied in detail.In the conventional methods the fibres arc immersed at a relatively high tem- perature in a dyebath comprising a large volume of a relatively dilute dye solution containing salt and the dye allowed to diffusc slowly from the solution into the bulk of thc fibres : a commercial dyeing may take some hours. In pad-dyeing, however, thc fibres (in fabric form) are passed rapidly (1-5 sec) through a relatively concentrated dyc solution at a comparativcly low temperature and thc excess dyc solution removed immediatcly by passing the fabric through a mangle, dye solution corresponding approximately to the imbibition of the fibre only being76 KINETICS OF ABSORPTION retained.The impregnated fabric is then given a short after-treatment-c.g. steaming-during which the dye diffuses from the periphery into the interior of the individual fibres. In order to investigate thc various mechanisms involved it is convenient to consider the process in a number of stages : (i) absorption of solvent (normally water), (ii) absorption of solutes present (other than dye), (iii) absorption of dye, (iv) penetration of dye into the fibre during stcaming. During the prescnt investigation, the kinetics of the first three of thesc processes have been considercd. As in all the previous investigations into the physical chemistry of dyeing processes, the experimental conditions were chosen for ease of interpretation of the results rather than for their similarity to the conditions which are operative in commercial practice.In the present work, the substrate (viscose rayon) has been studied in the form of regenerated cellulose sheet and as single ends of con- tinuous filament yarn of low twist; the results represent as far as possible the kinetics of absorption by a simple cellulose lamina or filament rather than the absorption by a cornplicatcd aggregate of fibres, where mechanical retention of solvent and solutes may involve considerable complications. All fibres are composed of long polymolecular chains whose axes correspond approximatcly to the length of the fibre. There are regions-the crystallites- in which the molecular chains are in a state of comparatively high order and in which the intermolecular forces are sufficiently high to prevent penetration by water molecules.The molecular chains in the remaining amorphous regions are, however, much more randomly arranged, the intermolecular forces being cor- respondingly reduced. In cellulosic fibres in particular, the molecular chains are composed of large numbers of glucose units, the chains themselves being largely held together by H-bonding between the hydroxyl groups of these units; when these fibres are immersed in water, the osmotic forces are sufficiently large to overcome the weaker intermolecular forces in the amorphous regions and cause the molecular chains to move apart, thus permitting the entry of water molecules ; X-ray techniques, however, show that the more ordered regions of the fibre are not penetrated by water molecules.It is this swelling of the amorphous regions of the fibre in the aqueous dyebath which produces capillary spaces between the molecular chains sufficiently large for the entry of the dye molecules during dyeing. The majority of dyc molcculcs are far too large to penetrate the fibre in the absencc of this swelling. Previously it has been assumed that the swelling of thc fibre in water occurs practically instantaneously and this is probably true for viscosc rayon at the tcmperatures used in normal dyeing (- 95" C). In pad-dyeing, however, where the temperature of the dyebath is much lower and the time of immersion very small, the rate of wctting of the fibre must clearly be considered in any proposed mechan- ism for the absorption of solutes from the padding bath.Since no results on the ratc of wctting of cellulosic fibres with liquid water are available, an invcstigation into the kinetics of this process was clearly desirable. THE KINETICS OF ABSORPTION OF LIQUID WATER BY VISCOSE RAYON EXPERIMENTAL MATERIALS.-Regenerated cellulose sheet (standard " 600 " quality Cellophane), of thickness 4 x 10-3 cm ; continuous filament viscose yarns-current production of 150/72, 100/40, 150/40, 200/40, 150/27, 300/50. (A viscose yarn, 9000 m of which weigh 150 g and which is composed of 72 filaments, is briefly described as 150/72 viscose. The twist in thesc yarns is vcry low, ca. 1 t.p.i. so that the individual filaments are rclativcly free.)H . B . MANN AND T . H . MORTON 77 Since one would expect the rate of wetting to be very sensitive to the presence of spinning lubricants, etc., great care was taken to remove any such contaminant froin the yarns before carrying out the wetting experiments.Similar precautions were taken to wash the regenerated cellulose sheet free from the hygroscopic plasticizing glycerine. All the materials used were conditioned (at 65 % r.h.) and had, therefore, an initial moisture regain of ca. 13 %. PROCEDURE.-FOr the yarns, the experimental procedure adopted for the rate-of- wetting determinations consisted of padding, mangling, collecting, and determining the weight of watcr taken up. This process was carried out on a single end of yarn and it is convenient to describe the experimental details of the three operations separately.(i) Padding.-The padding bath comprised a trough containing a hollow glass roller, 2 in. in diameter, partially submerged in the padding liquor. The yarn passed through a scrics of guides, round the glass roller a specified number of times, and thence to the manglc. The wetting time, taken as the time between the yarn entering the padding bath and passing through the mangle nip, was varied by changing the number of wraps of the yarn on the glass roller; it can readily be computed from the mangle speed and the length of wetted yarn. During the operation, the roller was rotated manually, so that the tension in the yarn was virtually zero, since thc observed water absorption is, to some extent, dcpcndcnt on yarn tension. (ii) Mmgling.-The mangle was of the small laboratory type, power-driven at a constant speed of 4.3 in./scc ; the loading of the 4-in.diam. rolls (covered with rubber of 80 Shore hardness) was adjusted by weighting to 50 Win. width of the rolls. In order to obtain efficient removal of surplus water from the padded yarn it was nccessary to cover the mangle rolls with two thicknesses of a spun viscose rayon fabric and to in- corporate a wetting agcnt (Teepol, 2 ml/l.) in the padding liquor. The wetting agent served the dual purpose of assisting the removal of surplus water from the yarn by wetting- out the spun rayon fabric covering the rolls and of ensuring adequate wetting of the yarn in its passage through the padding bath. The first of these functions of the wetting agent was found to be the most important, since the equilibrium water take-up was lower in the presence of wetting agent than without it.The apparent rate of wetting too was some- what lower in the presence of wetting agent, although the lowcring of the rate of wetting was less marked than that of the equilibrium absorption. Both of these observations indicate that, in the absence of the wetting agent, the yarn was still being wetted by un- removed surplus water after mangling. Under the conditions specified, the " complete wetting " value approximated, for all except the finest filament yarn, to the normal im- bibition figure found by the standard centrifuge method ; the absorptions of the finest yarns tended to be higher, due, no doubt, to inefficient removal of surplus water under the mangling conditions used in these experiments.(iii) Collection of yam-In order to avoid errors due to drying of the padded and mangled material during collection, the yarn was taken up on a bobbin composed of two discs, 2 in. in diameter, machined from 8 in. Perspex sheet, mounted on a glass axle (1 in. diam.). The axle was rotated manually to provide the variation in speed necessary as the yarn builds up between the discs. The separation of the discs was adjusted to approximately the diameter of the wet yarn under test. In this way, each layer of yarn betwecn the discs was only able to air-dry for a very small fraction of a second before being covered by the succeeding layer of wet yarn. The distance between the take-up mechanim and the mangle was reduced as far as practicable (to approximately 1 in.) and undcr these conditions the total drying time was very small.Experiments in which the distance between the mangle and the collection apparatus was greatly increased (up to about 3 ft) confirined that errors due to drying under the former conditions could be neglected. When approximately 0.3-0.4 g of yarn had accumulated between the Perspex discs, the mangle was stopped, the yarn broken and the discs held over an open weighing bottle. Withdrawal of the glass axle caused the small coil of yarn to fall into the bottle which was immediately restoppered and wcighed. This procedure was again found to be vcry effcctivc in preventing drying errors. The yarn was then dried at 105°C and reweighed, and the watcr up-take (as g/103 dry cellulose) calculated and plotted against the time of wetting.With regenerated cellulose sheet, the ratc of wetting was much slower than with yarn ; samplcs of the shcet could therefore be imniersed in the padding bath for a selected period ; thc surface water removed by careful blotting between two sheets of blotting paper ; and the wet samplc transfcrrcd immcdiately to a weighing bottle, weighed, dried and reweighed as before.78 KINETICS OF ABSORPTION RESULTS ABSORPTION OF WATER AT 20" C.-Thc results for a selection of the yarns and for thc regenerated cellulose sheet are presented graphically in fig. 1. These and other experi- mental data permit the conclusion that, in the early stages of wetting, the amount of water absorbed is approximately proportioiial to the square root of time of wetting ; this COII- clusion is consistent with the hypothesis that the water sorption process is a diffusion, of comparatively uncomplicated nature, characterized by a diffusion coefficiciit of the order of 10-6-10-7 cm2/sec. hme t (sec) I---- 0 10 20 FIG.1 .-Dcpendence of sorption on A 1501'72 1 ;!?:\:: viscose rayon, D 300/50 i E ccllulose sheet ; temp. 20" C time. The tinies of half-wetting of thc six yarns and the regenerated cellulose sheet, obtained by interpolation from graphs of amount of water present against time, are givcn in table 1. In calculating the values for timc of half-wetting givcn in table 1, due allowance was made for the initial moisture content. As an approximation, it is concluded that the rate of wetting of normal viscose ccllulose is proportional to the specific surface area of the fibre or film.TABLE l.-RATE OF WETTING AT 20" c material 150/72 100/40 150/40 200/40 150127 300/50 regenerated cellulose sheet approx. surface nrca (103 cmz/g) 5.0 4.5 3.5 3.2 3.0 2.8 0.4 time of half-wetting (sec) 0.6 0-7 1.0 1.2 1.1 1.2 5.9 EFFECT OF TEMPERATURE.-The regenerated cellulose sheet and yarns 1 OO/40, 150/40, 300/50 were selected for these experiments. The experimental procedure used was the same as that adopted in the previous work, cxccpt that the temperaturc of the padding water was controlled a1 either 0" or 40" C, the former by the addition of crushed ice to the bath as required. Results are given in table 2.H. B . MANN AND T. H. MORTON TABLE 2.-EFFECT OF TEMPERATURE ON THE RATE OF WETTING OF VJSCOSE CELLULOSE time of activation matcrial temp."C half-wett ing energy 100/40 0 1.7 (S=) (kcal/rnole) 20 0.7 7.1 40 0.25 150/40 0 3.0 20 1.0 7.8 40 0.6 300/50 0 3.3 20 1.2 7.4 40 0.6 regenerated 0 15.9 40 3.1 cellulose sheet 20 5.9 6.9 79 It is found that the plot of the logarithm of the time of half-wetting against the reciprocal of the absolute temperature is linear-within the limits of accuracy of the experiments. The integrated form of the Arrhenius equation may be applied to calculate an energy of activation of the wetting process : whcre t 2 and tl are the times of half-wetting at the absolute temperatures T2 and T1 and AE is thc activation energy. Values of AE are given in table 2. King and Cassie4 have examined the rate of absorption of water vapour by wool fibres and have attributed the low ratcs of absorption which they observed to the nccessity of dissipating the hcat of absorption (some 750 cal/g of dry wool). It is not thought, how- ever, that the present unexpectedly low rates of wetting can be attributed to heating effects, since these experiments have almost certainly been carried out under isothcrmal conditions, and it is concluded that the measured rates of water absorption do, in fact, depend on the rate of diffusion of Iiquid water through regenerated viscose cellulose.THE KINETICS OF ABSORPTION OF SOME SIMPLE SOLUTES PROM AQUEOUS SOLUTION Before carrying out the main work of this section it was ascertained that none of the simpler solutes listed in table 3 had any significant eflect upon the rate TABLE 3.-RATE OF PENETRATION OF SOLU'TES INTO REGENERATED CELLULOSE SHEET AT 0" c solute (water) NaCl Na2S04 Na2C03 CaC12 Na3P04 AIC13 urea glycerine sucrose time or half- COIIC.g/f . pcnetration (see) I 50 50 50 50 50 50 100 100 100 (16) 20 26 30 27 26 32 18 30 40 of water absorption, although some changes in the equilibrium absorpiion were found, espccially when working with solutions of high concentration. The rates of penetration at 0" C into regenerated cellulose shect of a numbcr of simple solutes have been measured. The experimental procedure was similar to that detailed above, cxcepting that the amount of solute absorbed was also determined (the inorganic salts conductimetrically, urca by Kjeldahl analysis for nitrogen, and glycerine and swrose80 KINETICS OF ABSORPTION by weighing).Graphs were again constructed of mass of solute absorbcd (per unit mass of cellulose) against timc, and the timc of half-penetration intcrpolated as before. Rcsults arc given in table 3. THE KINETICS OF ABSORPTION OF A DIRECT COlTON DYE FROM AQUEOUS SOLUTION The rates of absorption of a direct cotton dye were measured under various conditions, both on regenerated cellulose sheet and on somc of the viscosc yarns mentioned above. The experimental procedure was analogous to that detaiIed in the previous sections, the dye absorbed being estimated colorimetrically after stripping from the viscose sub- strate with aqueous pyridine. Two dyes were investigated : Fast Red K (Colour Index 5 no. 278).Sky Blue FF (Colour Index 5 no. 518). NH2 OH CH3O OCH3 OHNH2 N=N (->- -Nn?O,Na Na03sG3 Na03S They were chosen because of their well-established constitutions and because they are known to possess very dissimilar diffusion coefficients in viscose rayon under conven- A. Fast Red K B. Sky Blue FF 0.2 % dye, 0.5 % NaCl at 20" C ; regenerated cellulose shcet. FIG. 2.-Absorption of Fast Red K and Sky Blue FF. tional dyeing conditions.6 Both dyes were obtained in an electrolyte-free state by aqueous ethanol extraction followed by further purification in an ion-exchange column ; their subsequent purity was checked by determination of sulphated-ash content and con- ductimetric titration for chloride. The effect of a number of variables on the kinetics of dye take-up by dry ccllulose on immersion in the dye solution has been investigated and consequently a very largeH .B . MANN AND T. H. MORTON 81 number of results have been obtained ; for the sake of clarity a selection of the data will bc presented here in graphical form. Before considering in detail the effect of such variables as dye concentration, sodium chloride concentration, temperature, and yarn gg 1 viscose rayon C regenerated celhlose 0.2 % Sky Blue FF, 0.5 %NaCI at 20" C sheet FIG. 3.-Effect of fiIament size. dimensions, it is convenient to summarize the main conclusions which can be drawn from the results obtained : (i) The absorption of a direct cotton dye follows a quite different course from that observed with the simple solutes; a relatively small amount of dye is initially absorbed 150/40 viscose rayon at 20" C A 0.2 %, B 0.1 Sky Blue FF %, NaCl/dye ratio, 2.5.C 0.05 %, D 0.025 % FIG. 4.-Effect of concentration. very rapidly by the cellulose, the amount being apparently independent of the amount of water absorbcd, but a relatively long period elapses before a secondary absorption of dye occurs. (ii) The amount of dye absorbed in this initial stage is very much less than that which would be contained in a quantity of solution equivalent to the quantity of water absorbed.82 KINETICS OF ABSORPTION EFFECT OF Dn-Since the dyes used in this work differ in their respective salt- sensitivities, any comparisons made between them at identical concentrations-both of dye and of salt-are of doubtful value. As a generalization, however, it may be noted that, whilst the secondary absorptions of the two dyes differ considerably, the initial absorptions are very similar (fig.2). Regenerated cellulose sheet, 0.2 % Fast Red K, 0.5 % NaC1. A, 40" C; B, 30" C; C, 0" C FIG. 6.-Effect of temperature, EFFECT OF DENIER.-h fig. 3 are shown the results for two yarns of widely differing denier and for regenerated cellulose sheet. The rates of penetration vary considerably as expected, higher absorptions, both initial and secondary, being associatcd with larger specific surface areas of the substrate. concentration upon the rates of penetration is difficult to assess without a knowledge EFFECT OF DYE CONCENTRATION AT CONSTANT SALT/DYE RA'rro.-The cffect of dyeH. D. MA" AND T. H. MORTON 83 of the equilibrium value of the absorption of dye, but the extent of the initial absorptions varies considerably (fig.4). DF= k(Ds)n, wherc DF =- concentration of dye on fibre, Ds =- concentration of dye in bath. k and 11 are constants, IZ having the value 0.76 for Sky Blue FF under the chosen conditions. The effect of sodium chloride concentration (fig. 5) is seen to be unexpectedly complex in that, at low concentrations, the amount of dye absorbed actually decreases with time over the first minute. EFFECT OF TEMPERATURE.-The effect of temperature upon the extent of the initial dye absorption is small ; the secondary dye absorption, however, is considerably faster at the higher tcn~peratures (fig. 6). Thesc initial absorption values obey the relationship : EFFECT OF SODIUM CHLORIDE CONCENTRATION AT CONSTANT DYE CONCENTRATION.- DISCUSSION The various effects found when a dry cellulosic fibre is immcrsed in water or in a solution of simple solute or dye comprise a group of phenomena more complicated than was anticipated at the beginning of the experimental work.All the observed effects can be unified, and explained at least qualitatively, by a simple working hypothesis. Imagine a dry filament of circular cross-section aaa which is immersed in water. Water and cellulose diffuse into each other, so that within a short time equilibrium is achieved, to give a swollen filament of cross-section bbb. If now the water is replaced by an aqueous solution, the water and cellulose will interact as before, but, unless the solute enters the fibre at the same rate as the solvent, some or all of the solute contained in the region bbb less aau will be " filtered " and left in the form of a highly / - , / ' ,6 FIG. 7.conccntrated solution aiong the periphery 666 ;- this high concentration of solute will tend to equilibrium by diffusion into the yarn or into the bulk of the solution. In general, therefore, an interpretation of the phenomena depends on assigning reasonable approximate values to the diffusion constants characterizing the various aspects of this process. (i) The kinetics of the absorption of water by cellulose (or, alternatively, the diffusion of thc cellulose into water) at 20" C can be characterized by a diffusion coefficient of the order of 10-6-10-7 cmZ/sec. For comparison, the diffusion cocfiicicnts ( x 106) into water may be noted : urea, 8 ; glycerol, 4 ; sucrose, 3 ; and sodium chloride, 9.(ii) If the same diffusion coefficient characterized each of the celluloses, then the rate of wetting should be proportional to the square of the specific surface arca; since approximate proportionality to the first power is found (table l), the diffusion coefficients corresponding to the finer filaments must be rather smaller -i.e. the cellulose must be tougher-than for the coarse filaments and regenerated sheet-a difference corresponding to one already well established for the diffusion of dyes in cellulose. (iii) The effect of temperature on the rate of wetting is about that expected for the mutual interdifiusion of water and a close-packed structure such as swollen ccllulosc ; about half the activation energy of the process-7 kcal/mole--can be attributed to the decrease in the viscosity of water with temperature.(iv) The rate of absorption of water from simple solutions is virtually inde- pendent of the solute and its concentration, as might be cxpected if the rate-deter- mining factor were the interdiffusion of cellulose and water ; the equilibrium value of thc swelling is, howcver, to some extent dependent on the solute and its concentration.84 KINETlCS OF ABSORPTION (v) The rate of absorption of a solute is rather slower than of the water in which it is dissolved (table 3), and it can be assumed that the solutc is rather slower than water in diffusing through swollen cellulose. The relative rates for sodium chloride, urea, glycerol and sucrose are closely paralleled by the respective diffusion Coefficients of these substances in water, quoted above.(vj) The initial absorption of dye is very much less than the amount present in the water absorbed. It is probable that most of the dye retained is absorbed by molecular entanglement in the surface layers of the cellulosc; the data of fig. 3 show that the extent of the surface is an important factor ; and the known value of the diffusion cocfficicnts of the dyes in water or dilute salt solutions, ca. 10-6 cni2/sec, indicates that any concentrated dye solution near the surface of the fibre should come into equilibrium with the bulk of the solution at about the same rate as the fibres swell in water.Thus, persistence of the initial dye absorption for the periods noted in fig. 2 and 3 is good evidence for actual fixation of some dye in the surface layers of the fibre. The drop in the initial absorption with time in a salt-free system (fig 5) is an indication that this surfax-fixed dye may, under certain conditions, diffuse back into the solution as well as into thc bulk of the fibre. (vii) The initial dye absorption increases logarithmically, not linearly, with the dye concentration in the solution; the relationship is, in form, identical with that of the Freundlich adsorption isotherm. The dye molecules swept by the absorbed water into the surface pores of the fibre set up a surface change on the fibre (cf. Crank7) which will tend to reduce the probability of later absorption of succeeding dye, so that a falling-off from proportionality of absorption with concentration is not unexpected.(viii) The secondary stage of the dye absorption is clearly the onset of the normal dycing process, whereby dye molecules are absorbed from solution on to the cellulose surface and from there diffuse into the bulk of the Cellophane. For the two dyes employed, the normal dyeing difyusion coefficients at 90" C in shect cellulose are Fast Red K Sky Blue FF 5 x 10-9 cm2/scc, 1.3 x 10-9 cm2/sec. At 20" C the dye diffusion constants may be expected to be smaller by a factor of ca. 102. These dyeing diffusion coefficients agree generally with the data of fig. 2 so far as the secondary dye absorption is concerned. (ix) The initial dye absorption is virtually independent of temperature (fig. 6) as might be expected if it is due to molecular entrapment of the dye molecules on the fibre surface. The secondary absorption is, however, very dependent on temperature. The data of fig. 6 are consistent with an energy of activation of 17 kcal/mole for the secondary diffusion process ; this value is in good agreement with the generally accepted mean value 3 of 14 kcal/mole for the energy of activa- tion of the diffusion of direct cotton dyes in viscose cellulose. (x) In the preceding paragraphs the working hypothesis has been found to conform qualitatively with each successive aspect of the data considered. It is believed that the hypothesis provides an adequate physical representation of the mechanisms and is capable, at a later stage, of more quantitative treatment ; further, it is proposed to apply this conception to the analysis of the pad-dyeing of fibre aggregates. 1 Neale and Stringfellow, Trans. Fararlay Soc., 1933, 29, 1167. 2 Boulton, Delph, Fothergill and Morton, J . Text. Inst., 1933, 24, P113. 3 Vickerstaff, The Physical Chemistry of Dyeing (Oliver and Boyd, London and 4 King and Cassie, Trans. Faraday SOC., 1940, 36, 445. 5 Colour Index (SOC. Dyers and Col., Bradford, 1st ed., 1924). 6 Neale, J. SOC. Dyers Col., 1936, 52, 252. 7 Crank, J . SOC. Dyers Col., 1947, 63, 412. Edinburgh, 1950).