The Physical Chemistry of Dyeing

The Physical Chemistry of Dyeing

FRANCIS JONES

Dept of Colour Chemistry University of Leeds Leeds LS2 9JT

Introduction All dyeing processes entail three fundamental stages: (a) the dissolution or dispersion of the dye in a medium such that it will be readily adsorbed by the fibre, (b) the transport to and adsorption on the surfaces of the fibre and (c) the penetration and diffusion into the individual filaments of the textile. Why a dye is preferentially absorbed from a solution and is retained by the fibre is more difficult to elucidate. What is apparently a simple series of steps becomes much more complicated when factors such as the state of the dye in the dyebath, the nature and role of the solvent, the influence of additives, the possible changes of structure in the fibre during dyeing, the nature of interaction forces between dye and substrate and the possi- bility of multi-stage or heterogeneous mechanisms of diffusion are taken into account. The study of dyeing theories therefore cuts across a number of disciplines including surface and colloid chemistry and polymer chemistry and extends into biological studies.

In view of the number of inter-related parameters, it is not surprising that no unified theory of dyeing has been developed to account for all observed phenomena. This point of view was emphasised in the last Review article [ l ] on this subject and reiterated more recently by Rys and Zollinger [2]. These authors give a concise and mathematically oriented review of models which can be applied to the thermodynamics and kinetics of dyeing processes and which can serve as the starting point for any future studies of more specific systems. Current ideas on interaction forces between dye and polymer molecules derived from thermodynamic and kinetic data have been discussed recently by Rattee [3] , who states that, in addition to progress in the understanding of dye-substrate systems, recent studies are beginning to reveal new problems as well as solutions. Mention should also be made of an earlier (1968) publication by Peters [4], since this appears to be the latest definitive text on diffusion described in terms of model and actual systems. There has remained, however, a strong need for an authoritative and comprehensive text on dyeing theories and it is hoped that the Society of Dyers and Colourists’ publication now in preparation will adequately fill the gap apparent since Vickerstaffs [5] classical work on the subject.

This review, covering the past three years, shows that approximately equal emphasis has been placed on the thermodynamics and the kinetics of dyeing. A growing awareness of the influence of the state of the dye in solution, particularly in the presence of additives, on rates of dyeing, and of problems of aggregation and dye stability is reflected in an increasing number of papers on these topics. Perhaps the two most significant new developments over this period are those of dyeing from organic solvents and the transfer-printing process, in which volatile dye is transferred from a printed paper to a

fabric by dry heat. Although the technical knowledge in both these methods of coloration has progressed very rapidly, the quantitative data necessary for the elucidation of the mechanism of dyeing have still to be determined, particularly in transfer printing. Both these topics are discussed below. I f we consider the fundamental sequences in a dyeing process in their logical order we should first consider the behaviour of dyes in solution.

State of Dyes in Solution and Dispersion It is normally assumed that dye molecules or ions in aqueous solution are adsorbed on the substrate surface and diffuse into the interior of the substrate as individual entities, particularly at low concentrations of dye and at the high temperature of dyeing. A partial explanation of the tendency of ionised dye molecules to concentrate at the solution-fibre interface has been given by Giles and Soutar [6]. Ionised monosulphonated dyes reduce the surface tension of their aqueous solutions, thereby acting as anionic surfactants, and concentrating a t the solution-air interface. The same effect of reducing surface tension has now been observed for di-, tri- and tetra-sulphon- ated dye molecules irrespective of the orientation of the solubilising groups. Since most direct dyes and acid dyes for wool do not contain more than four such groups, it is assumed that all ionised dyes are surface-active. In addition to concentrating at the solution-air interface, it is assgmed that they will also congregate at the solution-fibre interface. On the other hand, as the concentration in the bulk of the solution is increased above a certain limiting value (critical micelle concentration), the dye exclusively forms ionic micelles or aggregates. The surface tension does not decrease further and by implication the micelles do not concentrate or are not adsorbed at the solution-fibre interface.

This aggregation at higher concentrations of dye occurs as a result of two opposing entropy changes: (i) a larger positive entropy change due to the decrease in the ordered structure of the water on association of dye molecules and (ii) a smaller negative entropy change due to the loss of translation and rotation entropy of the monomeric dye molecules in this process. The net entropy change is positive and is the thermodynamic force causing association. Changes in the extent of association in solutions of anionic dyes, as measured by deviations from linearity of Beer’s law plots, have been obtained [7]. It is emphasised that a linear relation between absorbance and concentration is not a necessary criterion for a solution containing only monomolecularly dispersed entities since large aggregates such as pigment particles may also show linear behaviour. From the results of these observations a theory relating Beer’s law deviation to the degree of association in terms of face-to-face stacking of dye ions has been described [8]. The observations have been criticised [9] , however, since the conditions under which such particulate dispersions obey Beer’s law differ from those pertaining to a concentrated solution of dye.

Association of dye molecules in aqueous solution is an extensively observed phenomenon. In reactive-dye solutions,

64 REV. PROG. COLORATION VOL. 4 1973

association does not depend on the nature of the reactive residue [ lo ] . Its effects, however, are to reduce the rate of diffusion and to make the reactive residues less prone to hydrolysis with the medium and less .available for reaction with the fibre [ 1 1 1 . It is now generally accepted that additions of urea to a reactive dyebath reduce the degree of association of the molecules, thereby increasing the number of groups available for reaction with the substrate [ 121 and improving the yield of reacted dye. It had been previously assumed that urea could act simply as a swelling agent for wool fibres, but it has been shown [ 131 that at long 1iquor:goods ratios and low temperatures, a pre-swelling treatment of wool is still required for the application of high-molecular-weight acid dyes in the presence of urea. For acid dyes of lower molecular weight urea causes a disaggregation in solution.

INFLUENCE OF SURFACTANTS ON IONISED DYES The nature of the species formed in solutions of ionised dyes in the presence of surfactants is not clearly presented in current literature. It is accepted that the equilibrium between monomolecular and associated dye ions still exists, but, in addition, structures such as surfactant micelles, dye-containing micelles and ‘complexes’ in which dye ions are associated with a smaller number of surfactant ions or molecules may be present. The actual species that is adsorbed at the fibre surface and diffuses into its interior is even less understood. Specu- lation or suggestion with reference to such entities has been tentative and made indirectly on the basis of changes in dyeing rates 1141 or levelling behaviour [15]. In contrast, a more direct study of the interaction between surfactants and anionic dyes in solution from spectral changes has been carried out by Hughes et al. [I61 and the results have been related to the dyeing of nylon 6.6. Essentially, the action of a cationic surfactant (Dispersol CWL; ICI) on an acid dye containing two ionised sulpho groups is firstly to neutralise the available sulpho groups. As the surfactant concentration is increased above a minimum amount, the 2: 1 surfactant-dye ‘complex’ or salt which is formed dissolves in the micelles of surfactant present in excess. During dyeing only dye ions are absorbed, any surfactant that diffuses more rapidly into the nylon being desorbed. The established equilibria between dye-ion mono- mer, aggregates and surfactant-dye complexes are shifted in favour of the latter as the surfactant is desorbed, and dye ions are adsorbed. At equilibrium any dye present in the solution is in the form of a complex or situated within the micelles. However, the mechanism by which dye is released from the micelle and made available for dyeing has not at present been studied. In fact, a number of questions remain unanswered. I t is suggested as a starting point that the whole system, dye-surfactant-water, over the complete range of concentrations and based on ternary-phase diagrams may give further information on micellar structure which can be related to dyeing theory. This procedure is conventional in studies on surfactants, e.g. the system hexanol-hexadecyltrimethyl- ammonium bromide-water as investigated by Friberg [ 171 .

SURFACTANTS AND NON-IONIC DYES The low solubility of non-ionic dyes in dispersions at the dyeing temperature means that spectrophotometric changes occurring on increasing dye concentration are difficult to detect and of little use in studying possible molecular

associations. The addition of surfactants is known to increase the dye solubility, but again comparatively little is known about the state of the dye molecules under these conditions. Improvements in solubility also depend on the constitution and concentration of the surfactants used [ 181. Hayano and Shinzuka [ 191 have used polarography to determine the aqueous diffusion coefficients of the entities formed on interaction of non-ionic surfactants with non-ionic dye molecules. The size of these entities is of the same order as that of the micelles formed by these reagents above a c.m.c. of M. Since the half-wave potential of the dye is not changed when surfactants are present, the diffusing entity is considered to be a dye-containing micelle and not a complex formed between a dye molecule and a small number of surfactant molecules.

In addition to improving solubility, the presence of dispersing agents may either promote the physical stability of the dye dispersion or in some cases increase the rate of growth of crystals. Both effects have been observed. Biedermann [20] has found that an azo disperse dye based on an aminopyrazole coupling system can be prepared in as many as five different modifications each of different crystallographic structure. In the presence of an anionic dispersing agent each form is sufficiently stable at 80°C to allow the dyeing of cellulose acetate up to equilibrium. The resultant saturation values of the dye depend on the.modification used and range from 0.77 to 5.5 g dye per 100 g undyed fibre. Before this work, the dyeing theory of disperse dyes was confined to a constant partition coefficient based on a single saturation value of dye in the fibre. It now appears that previous results must be re-examined in the light of saturation values being dependent on the type and stability of the crystallographic modification used. Confirmation of Biedermann’s observation has been obtained by Leung [21]. Pretreatment by dry heat of C.I. Disperse Yellow 3 produces a more stable crystallographic modification. Comparison of the mean saturation values showed that those for the two forms differed by as much as 16%. The difference, which is too great to be attributed to experimental error, is not as marked as the differences found by Biedermann, probably because the lattice energies of the two forms of (2.1. Disperse Yellow 3 are not very dissimilar. Other methods of preparing disperse dyes in different modifications have been described by Flores and Jones [22]. It appears also that anionic dispersing agents are much more effective in maintaining dispersion stability than non-ionic dispersants even up to temperatures of 130°C, as judged by improved levelling properties in dyeing polyester fibres [ 151 .

The influence of the crystal structure of dyes on dyeing processes is not confined to disperse dyes. The rate of reduction of vat-dye suspensions depends also on the crystallographic form of the dye and its degree of lattice order, even when differences in particle size have been taken into account. Following the original observations of Barlaro [23] , Arnold [24] has shown that the times of half-reduction of a number of forms of C.I. Vat Orange 5 vary considerably over the range 9.6 to 25 min. Heat treatment at 200”C, which causes an increase in crystal-lattice order without altering particle size, extends the time of half-reduction by factors of from 5 to 20X. It is also interesting to note that in the preparation of one form by crystalhation about 0.1% of the whisker-like crystals are perfectly annular in shape and probably result from a strongly asymmetric screw dislocation [25].

REV. PROG. COLORATION VOL. 4 1973 65

Diffusion and Rates of Dyeing In terms of mechanism, the mass transfer of dye from a solution or suspension to the interior of the fibre takes place in three stages: (i) the transport of dye to the fibre surface from the bulk of the solution, (ii) adsorption thereon and (iii) diffusion into the fibre phase. The detailed mechanism requires a knowledge not only of the nature of the adsorbed and diffusing species but also of the structure and physical state of the substrate, the affinity or partition distribution of the diffusant and the nature of the interaction forces between dye and polymer. It is important to recognise that simple absorption and desorption occurring simultaneously and at equal rates are not characteristic of dyeing systems, which require a partition coefficient greater than unity and strongly in favour of the diffusing species in the polymer phase.

If we consider the first of these three stages it is well known that rates of dyeing can depend on the degree of agitation of the dye solution and that these rates tend to a maximum value when agitation is efficient. It is possible then that a barrier to the transfer of dye from the bulk phase to the fibre surface exists. This barrier can control the dyeing rate when the velocity of dye-liquor close to the surface is low in comparison with the bulk velocity. The problem has been recently studied by Peters et al. [26] who considered velocity changes occurring in the vicinity of methoxymethylnylon films immersed in dye solutions with streamline flow parallel to the plane of the film. The main changes in velocity of flow occur in a direction perpendicular to the plane of the film so that an arbitrary hydrodynamic layer may be chosen in which the velocity changes from zero at the film surface to 99% of the bulk velocity at some distance from the surface. Since the hydrodynamic velocity withn this layer is much less than the bulk velocity, a diffusional boundary layer may be established. This is defined as the region in which the dye concentration changes its value from that at the surface to 99% of the concentration in the bulk liquid phase. The significance of the analysis is that the diffusional boundary layer is much narrower than the hydrodynamic boundary layer and its thickness decreases with increasing rate of flow, thus increasing the rate of transfer of dye to the surface. If it is assumed that the concentration gradient across the boundary layer is linear and the surface-dye concentration is zero, it is possible to apply Ficks first equation using an experimentally determined aqueous diffusion coefficient to determine the thickness SD of the boundary layer. For C.I. Acid Red 13, SD approaches 10-20 X cm at velocities approaching 5 cm S'. For much lower velocities, but still consistent with the rate of flow experienced in package dyeing, Brooks and Nordon [ 271 found mean boundary-layer thicknesses that were considerably less than those of Peters et al. Their results, however, were obtained by a different method utilising the heat flux from an electrically heated wire.

In a brief description of the model developed by Peters et al. [28] on the basis of the above work (as shown in Figure l), diffusion occurs from a solution of concentration C across the boundary layer of thickness SD to the liquid side of the substrate where the dye concentration is c'. In this layer steady-state conditions apply. On the substrate side of the interface where the dye concentration is C* diffusion occurs down a non-linear gradient and is described by Ficks second equation, where the diffusion coefficient, Of, is assumed constant. To solve this equation, two conditions are necessary.

So Jut io+ Solid Phase---- Phase -_ &--- -

k - I

Figure I - Diffusion into a substrate through a diffusional boundary layer SD

Firstly the film must initially contain no diffusant and secondly the rate of supply of molecules through the boundary layer must be equal to or greater than the rate of removal of molecules from the surface to the interior of the film. When the two rates are equal:

where Ds is the aqueous-phase diffusion coefficient and the film surfaces are situated at x=+l. The second condition implies that there is no restriction to diffusion at the interface, whereas there may be restriction in the boundary layer.

By considering an immediate equilibrium between dye concentrations on either side of the interface a constant partition coefficient, K can be defined which is equal to kl o/kO-l, the ratio of the rate constants representing the passage of dye into and out of the interface respectively. Therefore

KC' = C*x=--[ (2)

when dyeing is completed and the whole system has reached equilibrium C* becomes C-, the saturation equilibrium value, and c' becomes C the concentration for an infinte dyebath. From Eqn 2 therefore

KC = c, (3)

If C is the saturation solubility of the diffusant in the bulk liquid phase, K is the thermodynamic equilibrium partition coefficient. Eqn 2 as given here is not however limited to saturation concentrations.

Substituting Eqn 2 and 3 into Eqn 1 gives for the


based on initial slopes, in addition to more direct measurements of structural changes, was able to show that increases in the rate of dyeing of an anionic dye which take place when nylon filaments are heated before dyeing are due to increases in the relative size of the void spaces within the substrate even though the degree of lateral order of the polymer molecules may increase due to thermal effects. Similar observations have been made [31-331 in the disperse dyeing of polyester fibres that have been previously heat-set. The thermal prehistory of nylons and polyesters to some extent controls not only the rate of dyeing but also the related migration and levelling properties of the dye within the substrate. In fact, Beckmann and Langheinrich [34] attempted, by defining a ‘barriness parameter’, to measure such variations in dyeing behaviour. Warwicker’s conclusions indirectly confirm the earlier suggestion [35] that diffusion is controlled by the mobility of polymer-chain segments as indicated by changes in T g , the glass-transition temperature. Tg is directly related to molecular orientation and crystallinity and is usually determined on the dry polymer. In an aqueous environment such as a dyeing system, Tg may be considerably lowered. For example [36], in water-swollen nylon 6 film the Tg may be as low as -10°C. In dyeing with model disperse dyes the activation energy of diffusion showed an abrupt change in value some 30-40 degC above this T g . The difference in temperature is considered to be related to the molecular size of the diffusing molecule and hence to a specific minimum void volume which will allow dye penetration to occur rapidly.

The prevalence of heat-fixation methods of dyeing polyester fibres in which temperatures up to 220°C may be employed has meant a greater awareness of the role of polymer structure on diffusion characteristics in such systems. In addition, the high rate of sorption of dye under these conditions has led to experimental difficulties in determining diffusion coefficients. However, at 210°C the diffusion of disperse dyes into polyester fibres has been found [37] to be Fickian with a concentration-independent diffusion coefficient. This effect is probably due to an adequate volume of void space arising from a high polymer-segment mobility. The effect of heat setting, before heat fixation, on the rate of dyeing of polyester with disperse dyes is to reduce the rate to a minimum value at setting temperatures below the dye- application temperature [38].

With one exception [36] the above conclusions have been deduced from rate-of-dyeing data. The method of determining concentration-distance profiles from cross-sections of dyed film [39] or by using a multiple membrane in the form of a tightly wound roll of film [40] has not been extensively used, even though such methods would contribute much more to our understanding of diffusion mechanisms. A recent example of the former method has been in determining the concentration dependence of the diffusion coefficients of two acid dyes in nylon 6.6 films by Hopper et al. [41]. For both nylon and acrylic polymers the mechanism of diffusion for ionised dyes is usually interpreted in terms of a substrate consisting of a system of pores and channels filled with dye solution, through which the dye ions can diffuse with simultaneous adsorption on and migration over the pore surface. The normalised distribution profiles for the two dyes are shown in Figure 2. They fall into two categories A and B. Curves A were obtained under dyeing conditions such that the instantaneous surface- dye concentration was only 50% of that required to saturate

boundary conditions as x=-1:

or

4 where h = ----

D f 6 D K (4)

This boundary condition also applies to the surface x=+l and it can be seen that the model applies equally well to diffusion in a cylinder or filament during non-steady-state diffusion.

The significance of Eqn 4 becomes apparent when the value assigned to h is considered in relation to dyeing rates. It will depend not only upon the ratio Ds/Df but also on 6~ (the thickness of the boundary layer) and the partition coefficient of the dye. For a film or filament of constant thickness, increasing h will give an increase in dyeing rate. Consequently, decreasing 6~ by increasing the rate of flow will accelerate the dyeing until an upper limit is reached ash-. Above this limit increases in the rate of flow have no further effect, the overall rate of diffusion being controlled solely by rates of diffusion within the substrate.

The main emphasis in recent diffusion studies has been on the third stage of the process, namely the diffusion of dye into the substrate itself. Problems associated with a restrictive boundary-layer barrier can be minimised by using rapid agitation, and the immediate establishment of an equilibrium surface concentration equivalent to the equilibrium saturation value of the dye in the fibre when an infinite dyebath is used appears to be a reasonable assumption to make with respect to surface adsorption. On the other hand, the use of rates of uptake in the initial stages of dyeing and approximations to Ficks second equation such as Eqn 5:

(5)

to determine diffusion coefficients are open to question. Curves of rates of dye uptake cannot be used to distinguish between diffusion coefficients which may or may not be concentration-dependent. Diffusion coefficients determined by these methods are apparent values in that the concentration ct obtained at time t is an integral concentration and does not indicate the distribution of dye across the fibre or film cross-section. Despite these drawbacks, Fickian formalism, represented by apparent diffusion coefficient or initial slopes of Cct against t% plots according to Eqn 5 , can still be used to determine diffusion parameters, as discussed by Milicevic [29], provided that they are .limited to the comparison of different dyes on the same substrate or to the study of the influence of changes in the structure of the substrate on rates of dyeing of a single dye.

Thus Warwicker [30] by using a dye-uptake parameter


x/2dDt

Figure 2 - Dism'bution of C.I. Acid Red 18 (0) and C.I. Acid Red 8 (A) in nylon 6.6 film

the total amino-end-group content. Where complete surface saturation is achieved, sigmoidal curves of the type B were obtained, indicating a marked dependence of the diffusion coefficient on concentration. Addition of electrolyte to the dyebath caused a change in shape of the profile from type B to type A with an attendant reduced dependence of the diffusion coefficient on the dye concentration in the film. To account for these changes and the fact that not all the ionised sites in the substrate are accessible to dye, an accessibility factor was introduced. T h s factor is related to the internal partition coefficient and the number of charges carried by the dye ion. Under acid conditions, protonated amino groups are neutral- ised by anions, usually C1- or formate ions originating from the acid. Such anions are displaced by dye ions so that the concentration-dependent diffusion coefficient should vary according to the number of charges on the dye ion and the nature and rate of outward diffusion of the displaced anion. Confirmation of these observations has been obtained recently from similar but simpler studies in the dyeing of acrylic films with basic dyes where the displaced ion is cationic and the sorption site is negatively charged.

Reference was made in the last review on this subject [42] to the work of Blacker and Patterson (431 in developing a method of determining concentration-distance profiles of dyed filaments without the necessity of cross-sectioning. Further work by Commetto [44] using C.I. Disperse Blue 24 on polyester filament in the absence of carrier has confirmed the time-dependent surface concentration found by Blacker [43] and the sigmoidal nature of the distribution profile. The variation of the diffusion coefficient with Concentration has also been found to be sigmoidal. It is suggested that in the initial stages of dyeing the dye can act as its own carrier, by opening up the polyester structure. Whereas the larger dye molecules would not be absorbed as readily as smaller carrier molecules, once in the fibre the former may open up the structure facilitating penetration of dye molecules which arrive at a later stage in the process.

Thermodynamics in Dyeing Processes The diffusion process in dyeing may be considered complete when there is no longer a net transfer of dye molecules or ions from the dyebath to the fibre. A dynamic equilibrium is then maintained in which the rates of adsorption and desorption are exactly counterbalanced. It is this dynamic equilibrium which plays a major role, particularly for dyes of lower substantivity,

in levelling processes. Under these conditions the distribution of dye between the liquid-dyebath and solid substrate phases can be obtained. The effects of changes in temperature and concentration on this distribution can be used to infer the general nature of the interaction forces between the dye entity and the substrate. Irrespective of the precise definition of these forces, statistical considerations show that the number of dye molecules which take up sufficient thermal energy to overcome the energy of binding with the substrate is proportional to the number adsorbed and the term exp.(-Q/RT). Q is the adsorption energy per mole of dye. Provided no changes such as swelling occur in the substrate during dyeing, the equilibrium partition coefficient between dye in the fibre (C,) and dye in solution (Cs) can be represented by:

where k is a proportionality constant. By creating conditions such that CF, Cs or T remains constant, isosteres, isobars and isotherms, respectively, may be obtained. The isotherm expressed by Eqn 6 is observed in ideal mixing situations where the interaction between dye molecules is comparable with the interaction between dye and substrate molecules [3]. Under these conditions the energy of the dye-substrate bond should then be approximately equal to the geometric mean of the cohesive energy densities of the dye and of the polymer. The cohesive-energy density of either may be described in terms of a solubility parameter, S, which is a measure of the change in energy per unit volume of the material when the component molecules are separated to a distance sufficient to overcome any residual interaction. Whereas 6-values for polymers can be obtained only indirectly from the solubility parameters of effective low-molecular-weight solvents or by calculation, the corresponding values for non-ionic volatile disperse dyes can be obtained from sublimation data [45] and density values. Ibe [46], independently following some earlier work [47], has compared the calculated solubility parameters for some disperse dyes with the solubility parameters of cellulose acetate and polypropylene under anhydrous conditions. Saturation equilibrium values for different dyes increase as the difference in 6-values for the dye and the fibre becomes smaller. When the difference, AS, approaches zero, mixing becomes ideal. Although increases in CF are generally observed, as A6 decreases, more accurate values of the solubility parameter particularly for water-swollen polymer, and the use of experimentally verified solubility parameters of disperse dyes, would allow t h s method to be more widely applied in dyeing theory.

Although it is normal to discuss mechanisms of interaction between dye and substrate as mixing processes as in the solution theory of disperse dyeing, it is also necessary to consider processes of competition for interaction sites in the polymer matrix. This is particularly relevant for those dyeing systems in which both the dye and the polymer contain ionisable groups under the dyeing conditions employed, and in which there may be competition between different types of ions or even water molecules for site occupation. This competition is known as isosteric inhibition of sites. If, in addition, it is accepted that dye-polymer interaction entails possible conformational changes in the dye entity (e.g. cisttrans isomerism or flexibility rearrangements) then it must


be accepted that similar conformational changes may occur in the polymer which may inhibit interaction of competing entities. This type of competition has been referred to as allosteric [48], a suggestion which arose to account for the reduction in rate of dyeing of C.I. Acid Red 66 on wool in the presence of rn-cresol at concentrations less than that required to cause any significant swelling [9]. The allosteric effect was confirmed by using a model system with a-chymotrypsin as the protein substrate [50].

An extended form of Eqn 6 has been put forward by Harris and McGregor [51] as a model to account for the equilibrium sorption behaviour of acid dyes on nylon fibres. Account is taken of additional necessary factors such as differences in electrical potential occurring in the distribution of a dye anion between water and the nylon. The sign and number of charges on the ion are fundamental parameters determining sorption behaviour as are the ionisation charges on and in the fibre. When other factors such as the mechanical work performed and activity coefficient distribution for a specific dye ion between the two phases are considered under the single heading of an ‘apparent standard affinity’ and an arbitrary series of values of k in Eqn 6 is assigned, the sorption behaviour of the dye ion over a range of pH values can be calculated and is shown to be similar to that observed in practice. The model still appears to be extremely complex despite the fact that certain features which influence dyeing, particularly those related to the structure of the polymer, have, of necessity, had to be omitted. It does appear to be adequate to describe [52] the adsorption of dyes on nylon 6 and nylon 6.6 qualitatively.

A similar but simpler approach has also been taken by these authors [53] to describe the sorption behaviour of basic dyes on acrylic fibres. The high substantivity of basic dyes on this substrate plays an important role in diffusion processes and hence their absorption properties are significant. As with anionic dyes on nylons the dyeing process is generally accepted as an ionic-exchange process, in this case the replacement of a proton originating in the sulpho group in the substrate by a dye cation. The equilibrium partition ratio of dye cation between the two phases may also be described by a constant, provided that the distribution of protons is also taken into account. If it is assumed that conditions of electrical neutrality are observed and that the total cation concentration within the fibre is equivalent to the total concentration of ionised acid groups present, the distribution at equilibrium may be expressed in the form of a linear Langmuir isotherm. It has been found that this linearity does not apply over the whole concentration range. At higher dye concentrations within the fibre some ‘overdyeing’ can occur with certain dyes, which is reflected in ‘tailing’ in the isotherm. McGregor and Peters considered that the phenomenon could be explained by the presence of two types of ionisable groups within the substrate arising either from incomplete ionisation or from possible replacement of sulphate groups, as distinct from sulpho groups, by hydroxyl groups under the experimental conditions used. Other workers [S4] have found that decomposition of fibre or dye prevented the determination of saturation equilibrium values. However, the use of an analogous distribution coefficient of the dye between water and butanol and a somewhat sweeping assumption that the diffusion coefficient is inversely proportional to molecular weight allowed the theoretical ion-distribution

mechanism to be applied with some relevance to practical dyeing systems.

One intrinsic factor in systems in which the affinity of the ionic dye is dependent on the presence of charged sites in the polymer is that the surface or zeta potential changes as the ion of opposite charge neutralises sites. Thus the adsorption of increasing amounts of an anionic dye by nylon 6 fibres under acid conditions causes a change in potential from positive to negative owing to the neutralisation of protonated amino groups available for interaction. The final surface potential will therefore depend on the accessibility of dye to reaction sites and hence on the crystallinity of the polymer [55]. The same effect is observed in the dyeing of cellulose or poly(viny1 alcohol) fibres with direct dyes. In the direct dyeing of cellulose the distribution of ions is determined by the negative charge owing to the presence of ionised carboxylic acid [56] groups and the adsorbed dye anions. In earlier studies on the dyeing of cellulose, thermodynamic values of affinity and dye-sorption isotherms were obtained by the application of a constant-volume parameter to allow for regions of the cellulose inaccessible to dye. It is now considered [57] from the measurement of Donnan potentials that a variable volume term should be used. This variable parameter is related to the effective thckness of the electrical double layer present at the cellulose-dye solution interface. The presence of positively charged electrolyte counter ions influences the thickness of the double layer and the volume term varies inversely with the square root of the concentration of counter ion. The existence of the double layer and the electrical surface potential developed when one of the surfaces of the double layer moves relative to the other has been confirmed [58] by streaming- potential experiments. Unfortunately, from the dyeing-theory point of view, a direct comparison of thermodynamic data obtained when constant and variable volume terms are applied has not been made. The problem of relating surface potentials t o a constant or variable volume parameter in dyeing cellulose is, however, made more difficult since both are related to the crystallinity of the cellulose fibres [59].

The application of a volume term has been questioned more recently by McGregor [56] who considers that such a term may be replaced by a practical ionic distribution coefficient for the inorganic ions in the system which can be obtained independently of dye-sorption measurements. The apparent success of earlier theories is possibly due to the adoption of a volume term that was too low but which was countered by the neglect of the ionised carboxyl group in the substrate. The available evidence supports the suggestion that dye-fibre interaction decreases with increasing dye concentration.

A conventional volume term has been used in determining the affinity data for the application of direct dyes of similar and dissimilar structure as binary mixtures [60] . Competition for sites appears greatest when two dyes having considerably different structures are used. Although interaction in solution is also enhanced, in this case the dye ions will require different substrate conformations for maximum dye-substrate interaction. The explanation is thus given in allosteric terms (see above) and it is possible that conformational changes may be induced to different extents by dyes of different structure.

Reactive Dyes In discussing interaction mechanisms in dyeing with reactive


dyes, account has to be taken not only of physical ionic and dispersion forces which influence kinetic and equilibrium values but also the formation of covalent bonds and the competing hydrolysis reactions of the dye with the solvent in both the bulk and the internal aqueous phases. A brief survey was given in the previous review [ l ] on this subject with particular reference to cellulosic substrates. Hildebrand in an extensive review series also includes reaction on protein and nylon fibres [61], diffusion and substantivity [62] , covalent- Jond formation [63] and hydrolysis and removal of hydrolysis products [64]. More recently published data have been directed mainly towards technical application methods [65] . The fundamental aspects in dyeing proteins such as wool and the interaction of different dyes with amino-acid residues in this substrate have been a more recent development. Previous evidence showed that the monochlorotriazinyl reactive group is preferentially bonded with cysteine thiol, N-terminal amino and histidyl groups and to a much less extent with lysyl amino and seryl alcoholic groups. Acid-base equilibria are important since thiol groups are effective over the whole range of pH and primary amino groups can react only under alkaline conditions. When a 0-hydroxyethylsulphonyl sulphate ester is used as the reacting moiety a similar order in the amino-acid group effectiveness is found [66] with the additional fact that the lysyl and histidyl groups form covalent bonds at high acidities. In an assessment [67] of the futation ratios of a number of reactive dyes, each containing the same chromogen but different reactive groups, on wool, it was shown that dyes containing an a-bromoacrylamide or difluoromonochloro- pyrimidyl group gave the highest degree of fiation. A relatively poor fixation ratio was achieved with vinylsulphone or its corresponding sulphate ester, with the former being more reactive. This contrasts with the observation [68] that, on cellulose under alkaline conditions, the vinylsulphone group is less reactive than the sulphate ester. If this is correct then an alternative mechanism to the one normally proposed (which entails the formation of a vinylsulphone as an intermediate step in the reaction sequence) is necessary. The alternative is a direct second-order reaction between the sorbed sulphate ester and the cellulose anion with the anion attacking the 0-carbon atom in the ester as the -OS03- group is removed. In view of earlier remarks about the presence of ionised carboxyl groups in cellulose, it might also be of interest to consider its possible influence in its reaction with labile residues in dyes.

Solvent Dyeing Since the previous review [69] on solvent dyeing, little fundamental work on the theory of this process has been reported. Shipman [70] in more general terms has surveyed some of the solvents and dyes which could be used for dyeing nylon, polyester and acrylic fibres. These dyes are limited to the lower-molecular-weight non-ionic dyes. Reactive disperse dyes may be applied to nylon [71] and reactive dyes to wool provided in this case that a mixture of perchloroethylene and glycerol is used together with a dispersing agent [72]. Metal-complex dyes may also be used for dyeing nylon [73] and basic dyes have been examined on acrylic fibres [74]. A possible way of applying basic dyes is to form a complex between the cationic dye and negatively charged surfactant [75]. It remains to be seen whether any of these processes reach commercial significance.

Economic and other related factors restrict any commercial development mainly to the use of perchloroethylene as the solvent. It is interesting to note that the use of aromatic solvents such as toluene and xylene allows a higher rate of diffusion of dye into polyester film than does perchloroethylene with a saturation equilibrium value of the dye (4-methyl-2- nitrophenylazo-3’-methylpyrazolone) equally as great [76] . These aromatic compounds, however, are ineffective as solvents for a large number of non-ionic dyes. It is usually observed in dyeing from perchloroethylene that, although the rate of dyeing is much higher than from conventional aqueous systems, the partition distribution favours the retention of dye in the solvent with a consequent decrease in the partition coefficient. Datye et al. [76] in an extensive examination of a range of dyes in this solvent show that the thermodynamic behaviour of dyes on polyester film is similar to that found in conventional dyeing systems in that linear absorption isotherms are obtained over wide concentrations of dye. This observation has been confirmed by Katayama et al. [77]. The observed partition coefficients decrease with increasing temperature and, since the enthalpies of solution of dye both in the solvent and in the substrate are positive, the latter being smaller than the former, it has been argued [78] that the enthalpy of absorption of dyeing is also positive, giving rise to an endothermic dyeing process, which is in contrast to conventional dyeing. Linear absorption isotherms were found in every case except with dyes that contained a reactive residue that could possibly react at sites within the substrate. In general, therefore, the similarity in thermodynamic behaviour with that of disperse dyes applied conventionally points to a similar ‘solution’ mechanism of dyeing. The major differences arise in the diffusion mechanism. Diffusion is Fickian and diffusion coefficients, which are greater by a factor of 10 than those determined from the aqueous dyeing of polyester fibres, are independent of concentration of dye in the substrate. The shape of the relative concentration profiles within the substrate is similar to that given by curve A in Figure 2. Also from changes in stirring rates and the qualitative application of Eqn 4 it has been shown [76] that the formation of a diffusional boundary layer either does not occur or has a minimal effect, probably owing to the low viscosity of perchloroethylene at the dyeing temperature.

The increased diffusion coefficient in dyeing from perchloroethylene is probably due to the action of the sorbed solvent in changing the structure of the polyester. This can be shown by X-ray diffraction [78] and is consistent with the finding [73] that dyes are fixed at a higher rate in perchloroethylene vapour than by heat fixation at the same temperature.

The presence of small amounts of water in perchloroethylene causes an additional increase in the rate of uptake of dye [79]. Its effect on the saturation equilibrium value of the dye in the substrate has been studied only semi-quantitatively. To attribute the consequent increase in the distribution coefficient solely to the reduction of solubility of dye in an organic medium containing water [79] is somewhat tenuous. It is possible that a distribution of water between the two phases is rapidly achieved and the water in the polyester phase could cause a breakdown of interchain forces allowing a more ready penetration of dye molecules. Whether the competition between dye and water molecules for possible sites is isosteric or allosteric or both is not at present known.

70 REV, PROG. COLORATION VOL. 4 1973

Transfer Printing The commercial significance of transfer printing is indicated by an estimated [80] forty-fold increase in production by 1975 based on a yardage of 24 million in 1970. Its advantage lies in a completely dry system. A number of papers [81] describing this process have appeared recently. They have been limited to qualitative descriptions of the dyes and substrates used and the conditions required to give the maximum efficiency of transfer.

Studies directed towards the elucidation of the mechanism of dyeing in this process have not yet been carried out, although it is generally accepted that, in both transfer printing and other heat-fixation methods of dyeing, absorption of dye occurs mainly through the vapour phase by volatilisation of the non-ionic dye particles. Thus the choice of dye is restricted to those which have a comparatively high volatility or vapour pressure at the application temperature. The generalisation [82] that dyes of low molecular weights can be used, since they possess higher volatility, although valid, is not a sufficiently sound basis for fundamental research. It is only necessary to consider the wide differences in properties, including volatility, of 1- and 2-aminoanthraquinone to under- stand that these compounds would not be absorbed at the same rate, even though their molecular weights are identical. The nature and orientation of substituent groups in the dyes are also of fundamental importance. I t is surprising therefore that attempts have not so far been made to correlate actual vapour pressures or concentrations of dye in the vapour phase with rates of absorption in transfer printing. Vapour-pressure data and sublimation enthalpies of a wide range of non-ionic disperse dyes and model compounds are already available in current literature [83] . Concentration-distance profiles would furnish evidence whether dyes of higher substantivity cause ring dyeing under transfer-printing conditions and the

results could be related to the ease of penetration of fabric substrates and to the sublimation fastness of the dyeings. Japanese research has indirectly approached this problem by considering the rate of desorption of dye from polyester films at high temperatures and over a range of ambient pressures [84]. This rate was directly dependent on the pressure, increasing to a maximum at pressures below lo-’ Torr. In the initial stages of desorption, for all the dyes examined, an induction period existed in which the rate of desorption was negligible. Ths period increased with increasing ambient pressure and, although the authors attributed the delay to a lower dye concentration present within the burface of the film before and at the commencement of desorption, it may possibly be due to a restriction in the mean free path of the dye molecules, varying with pressure, which could act as the ratecontrolling step. In addition, the rates of desorption and the related apparent diffusion coefficients depended on the physical structure of the polyester and whether outward diffusion was taking place above or below the glass-transition temperature of the polymer. Rates of sublimation from dyed polyester fibres have also been studied by Pechyeva and Golomb [ 8 5 ] , who were able to relate these rates to the structure of the dyes used and in particular to the number of amino groups attached to the anthraquinone nucleus of the dyes and model compounds used.

From the above observations, we must conclude that factors additional to the simple one of molecular weight of dye must be taken into account in studying transfer printing. Vapour pressure, dye and substrate structure, diffusion kinetics, ambient pressures and other factors which may influence any of these parameters must all be studied from a fundamental aspect before a full understanding of the mechanism of transfer printing and heat fixation can be achieved.

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The Physical Chemistry of Dyeing