The Dyeing of. Cellulosic Fibres. Edited by Clifford Preston P ~DBs~ BRENT SMITH 2610 GLEN BURNlE DR! (919) 781'-io04 RALEIGH, _-_ NC 27607

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1 The Dyeing of Cellulosic Fibres BRENT SMITH 2610 GLEN BURNlE DR! RALEIGH, _-_ NC (919) 781'-io04 Edited by Clifford Preston P ~DBs~ 43 Worshipful Company Society of Dyers

2 - Copyright , by the Dyers Company Publications Trust. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without the prior permission of the copyright - o wners. Published by the Dyers Company Publications Trust, and distributed by the Society of Dyers and Colourists, P 0 Box 244, Perkin House, 82 Grattan Road, Bradford, West Yorkshire BDI 2JB, England. Printed by The Eastern Press Ltd, London and Reading.

3 Dyhig with Vat Dyes (Ulrich Baumgarte) David A Clarke) 1 Fibres (John Shore)

4 dm = k',[d], dr Heterogeneous Systems - Cellulose and Water The homogeneous system described above illustrates the basic ground rules of reactive dyeing. It is now necessary to adapt them to the far more complicated heterogeneous system of cellulose and water. In a two-phase system reaction between two entities can take place only if both are present in the same phase; therefore reaction between dye and cellulose can occur only when the dye has been absorbed into the cellulose phase. Thus any discussion of the kinetics must allow for the rate at which dye is absorbed. The rate of diffusion of a sorbent into a solid medium with which it can react according to first-order kinetics has been considered by Danckwerts [40]. The solution for the dyeing of an infinitely thick plane slab of material in a dyebath of infinite volume can be written in the approximate form shown in Eqn 4.7: (4.7) where dqldt = rate of sorption of reactive dye per unit area of surface, which can be equated to the rate of fixation (since the material is considered infinitely thick and all the dye which enters will be fixed) [DIF = equilibrium concentration of dye at the surface of the material D = diffusion coefficient of the dye in the material - k; = first-order or pseudo-first-order reaction constant for the reaction between dye and substrate. As in the homogeneous system described above, there are two competing reactions and the efficiency of fixation is given by Eqn 4.8: Rate of fixation S(D]F V "F E= - Rate of hydrolysis L[DIs kh where [DIs = concentration of dye in the aqueous phase kh = first-order or psuedo-first-order reaction constant of hydrolysis. (4.8) The constant L, the liquor ratio, defines the difference in amount of the two phases -rrc (usually in terms of litres of dyebath per kilogram of substrate) and S, which defines the surface area of the substrate, is necessary because Danckwert's equation refers to diffusion per square centimetre of surface. It has been demonstrated experimentally [35] that the ratio of the bimolecular constants (RF) for the reaction of dye with the fibre (kf) and with water ( k~) is a constant for a given dye over a wide range of alkaline ph values, thereby confirming that the kinetic relationships in the homogeneous system still apply in the heterogeneous cellulose-water system and that the reactive entity is ionised cellulose. Thus Eqn 4.9 applies:

5 150 DYEING OF CELLULOSIC FIBRES kf/kh = RF (4-9) and hence, since kb= kficell 0-1 and kh = khioh-], Eqn 4.10 can be written: (4.10) where [Cello-] = concentration of ionised cellulose. Eqn 4.8 may therefore be rewritten in the form of Eqn 4.11: I _,'k - (4.11) from which the percentage fixation may be calculated using Eqn 4.4. Again, however, the efficiency of the process is only half of the story. Of equal importance to the practical dyer is the rate at which active dye is used up and hence the time required to complete the dyeing process. The total rate of disappearance of active dye is the sum of the rates of the two competing reactions (Eqn 4.12): where df/dt = rate of reaction of dye with the fibre. Integration of Eqn 4.12 permits calculation of the amount of active dye that has been removed from the bath after a given time, following which Eqn can be used to evaluate how much of this dye will have been fixed to the fibre. It must be emphasised that these equations are in an abbreviated form which applies only under certain conditions. The full equation corresponding to the simple Eqn 4.7 has been given by Danckwerts [a]. Derivations of the equations for efficiency and rate have also been described [41, 421. Although only strictly applicable to the ideal system of an infinitely thick plane slab of material, the validity of these equations in describing the behaviour of dyes in practical dyeing on cellulosic fibres and films has been demonstrated This required the accumulation of considerable data, too laborious a process for a study of all reactive dyes. However, the principles can be used generally to demonstrate the implications of the relevant variables for the practical application of these dyes. 4.6 PRACTICAL IMPLICATIONS OF THE PHYSICAL CHEMISTRY Factors Outside the Dyer's Control Fibre Shape Factor (S) Although not merely a measure of surface area, the fibre shape factor is expressed in SI units as m2/kg. It has been demonstrated that the lower the linear density of the fibre, i.e. the greater the surface area per unit weight, the more efficient is the dyeing. Clearly this would result in poor reproducibility if repeat dyeings were

6 -3-4 Q m a Figure Relationship between substantivity and diffusion coefficient dyes and the ultimate efficiency of fixation depends on kinetic effects rather than on equilibrium. In the theoretical treatment of non-reactive dyes, e.g. direct dyes on cotton, equilibrium sorption is dependent solely on the substantivity ratio at the end of dyeing. Provided the dyeing conditions have been kept constant, this is the result towards which the system has been aiming during the whole period of dyeing. Even if the dyeing conditions are deliberately or accidentally changed during dyeing, the result will be no different provided the final conditions are the same and sufficient time is allowed for the correct equilibrium situation to be achieved. This is because the dye is always free to migrate from dyebath to fibre and vice versa, thus always achieving the correct partition appropriate to any change in the dyeing conditions. Of course, for certain dye-fibre systems, migration may be so poor that the time required to achieve equilibrium may be unrealistically long in the practical sense. Nevertheless theoretically the opportunity always exists..- In reactive dyeing the situation is totally different. The end result, in terms of efficiency of fixation, is the sum of all the separate efficiencies obtaining at each instant of the dyeing time. Even if the dyeing conditions are kept constant after the addition of alkali, the efficiency will change as the dyeing proceeds, because the substantivity ratio progressively changes, penetration of the fibre increases, the

7 4. DYEING WITH REACTIVE DYES 156 dye. All these changes affect the substantivity ratio and hence the efficiency of dyeing at each particular instant of dyeing time. These gradual changes, which are dependent purely on the physical chemistry of the system, should in practice offer no problems in terms of reproducibility because, provided the dyeing sequence is carried out with precision, the changes will occur reproducibly and the end result will be the same. If, however, deliberate or accidental changes are made in the conditions during the fixation sequence which affect any of the important parameters, then the result will be different. This will not be corrected by a subsequent return to normal conditions because the dye is already fixed and is no longer free to migrate. Adequate precision in controlling the dyebath conditions must be exercised at all times if reproducibility is to be achieved, particularly in the application of mixtures of dyes when the component dyes are affected differently by changes in dyeing conditions. 4.8 COMPROMISES NECESSARY IN REACTIVE DYEING All dyeing methods necessitate compromise, between the level of exhaustion and the time required to achieve it, between wet-fastness and level-dyeing properties, between technical performance and cost of different dyeing methods, and so on Essential Variants One way to describe such compromises is to employ a method already published [43, 581. Since Eqns 4.11 and 4.12 each contain seven variables, several assumptions must be made in applying them. The value of RF has been found to vary in the range approximately and so an average value of 0.7 has been used. An average value of 18 would reasonably represent the value of the ratio [CellOftIOH-] for normal ph, electrolyte concentration and applied depth. The value of S was that used previously [43] for a sample of viscose fibre (i.e. 43) and the liquor ratio was taken at 20: 1. This leaves the three dye variables: substantivity ratio, diffusion coefficient and reactivity to hydroxyl ions. Since substantivity ratio and diffusion coefficient are interdependent, the latter can be included as a function of the former. This leaves two variables, substantivity ratio and reactivity, and it is now possible using Eqn 4.11 and an integrated form of Eqn 4.12 to represent the interplay between them. In Figure 4.9 substantivity ratio ([DIF/[Dls) is plotted against reactivity (k'"), both on a logarithmic scale, and curves A-E, calculated using Eqn 4.11, are drawn where constant levels of fixation are obtained when the reaction has been completed. It is clear that any increase in k ' must ~ be accompanied by an increase in [D]F/[D]~ if efficiency is to be maintained at any desired level, and that maximum efficiency will be achieved at high levels of [D]F/[D]~ and IOW levels of k'h. The curves F-L show the values of the two variables necessary to ensure 99% reaction with either the fibre or water in various lengths of'time. It can be seen that a dye of low substantivity requires a greater reactivity than one of high substantivity to complete the reaction in a given time. In the practical situation, both efficiency of dyeing and the time required to reach completion are important. The properties of any dye that is required to give completion in less than 60 min and a fixation

8 4 DYEING WITH REACTIVE DYES log k h Figure Values of substantivity ratio and reactivity required (a) to produce various levels offixation when all the dye has reacted (curves A-E), and (b) to complete reaction in a given time (curves F-L); calculated from Eqns 4.II and 4.12 with RF=0.7, S=43, L=20 and (CellO-]l(OH-]= 18 better than 80% would have to fall in the area above the curves BM andhm. It is clear, therefore, that the more stringent the dyeing requirements the smaller the permissible variation in [DjF/[DIs and krh. Equally, for the average dye, if maximum substantivity and length of time are specified then the fixation efficiency under any particular dyeing conditions is also defined within fairly narrow limits Factors Controllable by the Dyer Although the values of the two variables under consideration are dependent on molecular structure, the dyer does have some control of them by adjusting ph, temperature and salt concentration. PH The effects of changing the ph of application may be illustrated by taking the substantivity vs ph profile of a typical dibasic dye in combination with the reactivity vs ph profile of dye A in Figure 4.7. Using Eqn 4.11 it is possible to predict what the percentage fixation would be if sufficient time was allowed for all the dye to react with either the fibre or water (Figure 4.10, curve A). The efficiency falls as the ph increases; this is due to the increase in reactivity. The rate of fall is accelerated beyond ph 11, since in this region the effect of increased reactivity is reinforced by a drop in substantivity ratio. Curve B shows the fraction of the total dye available that would have reacted in 60 min according to Eqn A ph in excess of 10.5 is

9 1 I I \ PH Curve A Fixation if time sufficient for all the dye to react B Amount of dye reacted in 60 min - C Fixation in 60 min D Amount of dye reacted in 15 min E Fixation in 15 min Figure Effect of time and ph on the amount of dye reacted and amount of dye fixed; calculated for a dibasic dye with a reactivitylpfl profile shown in Figure 4.7, curve A, using other values as for Figure 4.9 necessary before all the dye can be considered, for all practical purposes, to have reacted. Combining curves A and B produces curve C, the fraction of dye that will have reacted with the fibre in 60 min. For this particular dye, under these dyeing conditions and for this time, there is a ph of maximum fixation at approximately ph 9.5 (which does not correspond to the ph of 100% reaction of the dye). The effect of time of dyeing is also of interest. In Figure 4.9 curves D and E illustrate an available dyeing time of 15 min, and it can be seen that the ph of maximum fixation has moved from approximately 9.5 for 60 min to 11.5 for 15 min, with the maximum fixation changing from approximately 83 to 63%. Thus there is a further compromise - a saving of 45 min in time for a 25% loss in level of fixation. With this dye (Figure 4.7, dye A) the choice is available because the reaction can be accelerated by raising the ph, even though efficiency is lost, because little or no increase in rate of reaction results. In some cases the reaction may become slower, while still producing a decrease in efficiency.

10 Figure 4. II - Effect of ph on percentage fixation of dyes of different reactivitylph profiles (dyeing time 60 min); calculated for dibasic dyes with reactivitylp H profiles as shown in Figure 4.7, curves A-C, using other values as for Figure 4.9 The ph of maximum fixation depends on the relative shapes of the substantivity and reactivity vs ph profiles. In Figure 4.11 three dibasic dyes are illustrated which all possess the same substantivity profile as the dye in Figure 4.9 but have reactivities according to curves A, B and C in Figure 4.7. The differences in ph of maximum fixation can be seen in Figure 4.11 (curves A and B), but of equal importance are the shapes of the curves produced. In curve A there is a region (ph ) of relatively small change in fixation, since neither the substantivity nor the reactivity is changing drastically with ph. Above ph 11 the drop in substantivity is reinforced by a marked increase in reactivity. In curve B the sensitivity of reactivity to ph has produced a much sharper peak. For curve C the reverse is true, since over the ph range the reactivity is relatively insensitive to ph. In this latter case the constancy of reactivity means that above ph 11 only the fall in substan- - tivity is affecting the fixation. If a mixture consisted of the three dyes illustrated in Figure 4.11, no single ph value would produce maximum efficiency in all three dyes and yet another compromise would have to be made. In addition the selection of a ph close to that of maximum fixation for one of the ph-sensitive dyes (A or B) would make the other

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