theory of dyeing-f. jones
TRANSCRIPT
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THE THEORY OF DYEING
15
The Theory
of
Dyeing
F.
JONES
Department of Colorir Chemistry and Dyeing, University of Leeds, Leeds LS2
9JT
Introduction
Previous reviews of research work directed toward
a
greater
understanding
of
the way in which dye molecules are transferred
from th e dyeing medium to the polymer
or
substrate phase have
stressed that
a
unified fundamental theory, applicable to all
dyeing processes, is still
far
f rom
a
reality and may never be
attained. The main reason for this is that in any dyeing process
there are many variable parameters, some
or
all of which are
mutually dependent. T o achieve any progress in such studies, it is
necessary to control these parameters
so
that the effect
of
each
on
the dyeing system can be determined. This may not always be
possible. Thus, altering the dye concentration within an aq ueous
dyebath in order
to
study the concentration changes of dye
within a substrate may, even where
all
other conditions can be
maintained constant, produce
a
change in the structure
of
the
solvent and
a
possible alteration in th e nature of the dye species
partaking in dyeing.
Some
of
these variable parameters in the molecular dyeing
theory for ionic and non-ionic systems have been discussed
recently by McGregor a nd Peters
1).
Structural features of both
dye and polymer which may influence the thermodynamics and
the kinetics of dyeing includ e:
I ) the nature, conce ntration, distribution and degree of ionisation
of
ionisable groups in the dye in the solvent and subs trate phases
(2)
the molecular and ionic interaction s of all the species present in
both phases
(3)
the volume fraction, configuration and distribution
of
both
the crystalline and th e amorphous regions, and the degree
of
ionisa-
tion
of
ionisable groups, in the s ubstr ate
4)
the existence of reversible and non-reversible stresses within
the polymer before
and
during coloration
5 )
structural changes
in
the solvent distributed betwaen the
two
phases.
Since these changes are not independent, the researcher has to
adopt several simplifications and use model experiments where
variables can be contro lled.
The
results obtained in this manner can be compared with
calculated results obtained from theoretical models utilising th e
same number of variables. Model systems can therefore be used
only
to
illustrate specific poin ts in dyeing theory. One su ch model
(2) ,
used to illustrate the equilibrium values and kinetics
of
dyeing of non-ionic dyes, is based on simple mixing theory in
which dye molecules may be treated as occupying mean positions
in a quasi-crystalline
or
liquid (substrate) lattice. The funda-
mental concept
is
identical with that
(3)
describing the thermo-
dynamic behaviour of non-ionic solutes in which the solute
structure in the solvent is com parab le with that
of
a supercooled
liquid. It can thus be shown that the partial molar enthalpy of
solution,
AE,
of disperse dyes in the fibre is directly related t o th e
melting point of the dye according to the expression
where
4
and
4
represent the site fraction
of
the dye at tempera-
tures T and
Tm,
the dyeing temperature and melting point,
respectively. The value 0,,, may be obtained by extrapolation.
Eqn
1
is equally valid for th e solution
of
disperse dyes in water.
As certain non-ionic dyes can exist as metastable liquids
at
temperatures as low as 20°C
4),
the possibility
of
interpretation
inherent within this model m ay fruitfully bear fu rther examina-
tion. The model
is,
however, subject to serious limitations. It
applies only to ideal systems, i.e. those
of
low equilibrium dye
concentration, and can
be
applied only when it is known that
water plays
no
part in determining the equilibrium saturation
value
of
the dye in the substrate. More recent work
5 )
on the
adsorption
of
azobenzene and p-nitroaniline vapo urs by subs-
trate films in the presence and in the absence
of
unsaturated
water vapour has shown that the equilibrium saturation values
of
these compounds in second ary cellulose acetate are inversely
related to the amount
of
water vapour absorbed.
The
simple
binary mixing theory
of
dyeing may be more successfully
applied to hydrophobic polymers such as polypropylene, where
water plays an insignificant role in the abs orpti on
of
dye.
By using the same basic assumptions
( 2 ) .
with regard to the
state and distribution of dye within the polymer, and applying
phenomenological equations, it can also be shown from this
model that the kinetics
of
dyeing of hydrophobic fibres can be
expressed by
C =
S[I -exp(-8r)l
. 2)
where
Cr
s the total amoun t
of
dye absorbed at time
t ,
S
is the
solubility
of
the dye within the fibre and
8
is
a
rate constant.
Comparison
of
experimental rates of dyeing with Eqn 2 for
assumed values
of
shows good agreement, although this
expression does not ta ke into account
a n y
localised variation
of
activities existing at surfaces an d phase boundaries.
Much published research
on
dyeing and coloration is directed
towards the further understanding of practical commercial
processes, and comparatively little
is
published on what is
sometimes regarded
as
academic dyeing theory. Many experi-
mental results from the former group would be
of
more value to
the theoretician
if
the chemical structures and purity
of
additives
in the dyeing process, dyes and polymers could be disclosed and
the conditions during dyeing systematically defined. Although
much is published, this review has therefore had to be limited
to
salient pape rs in which these restriction s have been met.
Dyeing theory is concerned with the thermodynamics and
kinetics
of
processes occurring within th e dyebath, the interaction
between dyeing species and the internal an d external surfaces of
fibres, transfer from these surfaces by diffusion processes to
equilibrium positions within the substrate and the behaviour of
dyes once this type
of
equilibrium has been achieved. It is
proposed therefore to discuss recent advances in dyeing theory
under these headings and to include recent work carried out in
less conventional systems, such as heat-fixation methods. Since
coloration with reactive dyes entails simultaneous physical
absorption and chemical reactions within the dyebath an d within
the substrate, this topic will be considered separately, although
this division is somewhat unreal. By this means it is hoped t hat
the reader will
be
given a more comprehensive view
of
dyeing
theory without any artificial division based on s ubst rate types.
State
of
Dyes
in Solutions
and
Dispersions
Concepts concerning the structural nature
of
water
(6),
the
presence
of
cavities a nd ice-like clusters
of
water molecules that
are not ‘inter-cluster’ hydrogen-bonded, and the influence of
solutes in changing these structures have meant tha t ideas
on
the
structure
of
aque ous dye solutions h ave been modified in recent
years. This has been particularly relevant to studies of the
phenomenon of association of dye species in the solution.
Coates
7)
has surveyed the forces of interaction between like
ionic species which can lead to d imerisation an d higher degrees of
association and has discussed this process from its thermo-
dynamic and kinetic aspects. Although the standa.rd free-energy
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REVIEW
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IN COLORATION; JONES
change involving both enthalpy change and entropy change in the
dimerisation for any dye can be determined from the equilibrium
constant governing the reversible formation of dimer from two
monomeric species and its temperature dependence, the values
obtained in practice depend on the accuracy of the means by
which the equilibrium constant is obtained.
Thus,
to
a first approximation the dimerisation of a number of
ionised monosulphonated dyes and of some positively charged
basic dye cations is accompanied by standard entropy changes of
from - 0 to -20 cal deg-1 mole-1. This decrease is made up in
part by a
loss
in translational entropy of the monomeric ion and in
part by a gain in entropy of the water. This gain of entropy by the
solvent is due to the probable decrease in the structural order of
the water promoted more effectively in the vicinity of a mono-
meric ion than in the region of
a
dimeric species. Conversely,
entropy values obtained for non-ionic dye vapours, which exist
mainly
in
the form of dimers
a),
show that, under anhydrous
conditions, the decrease in entropy related to dimer formation is
only of the order of -1.0 to
-2.0
cal deg-1 mole-1. This
decrease is therefore much less than that generally observed for
dimerisation in solution. It must, however, be pointed out that
association in the vapour is between molecules that, although
polarisable, do not possess a fully developed charge. It appears
then that the structural nature of water promotes association and
explains the large equilibrium shift towards monomer formation
at high temperatures, since the structure of the solvent is strongly
dependent on temperature. If association of dye molecules were
dependent only on the forces of interaction contributing to
hydrophobic bonding, then the phenomenon would also be
observed in other solvents. Since association is much less marked
in organic solvents of low dielectric constant, it can be concluded,
at least for basic dyes possessing a non-localised positive charge
9), that increased water-water interactions overcome the
repulsion forces acting between dye ions of similar charge.
The possibility that dye ions associate in solution is very real
and, if this is not taken into account, errors in determining such
parameters as ionisation constants can be considerable. The
problem can be overcome to some extent by using very dilute dye
solutions, where the probability of collision may reasonably be
expected to be low. Even so, self-associationoccurs at concentra-
tions as low as one milligram of dye anion per litre of solution
(10). In determining ionisation constants for a number of
monosulphonated 00'-dihydroxyazo mordant dyes, it was
necessary to use mixtures of dioxan and water to overcome
association effects and extrapolate the ionisation constants to
values for pure water. It was then possible to compare the effect
of association on the ionisation constant related to the ionisation
of the first hydroxyl group in these dyes. This is increased when
association occurs. Under more alkaline conditions both
hydroxyl groups are ionised and association is minimised or
eliminated since the repulsion forces between the trivalent fully
ionised entities are much larger.
The influence of additives such as urea
I I ) ,
formamide
(12),
N-alkylacylamides
(13)
and alcohols
(9)
on the structure and
properties of dye solutions has recently been studied. It is
generally accepted that additives of this type induce disorientation
of the water structure in the vicinity of the dye ion, thereby
reducing aggregation attributed to
loss
of hydrophobic interaction.
It has been pointed
ou t
14) that this mechanism has not been
conclusively proved, although no doubt a decrease in dye-dye
interaction by the action of urea on dye solutions does occur, and
leads to increased rates of dyeing. The swelling action on protein
substrates and reduction of hydrophobic interaction in the
substrates by urea also contribute to an increase in the rates of
dyeing, thus illustrating the interdependence of parameters
mentioned earlier.
Non-ionic disperse dyes possess very low solubilities n aqueous
dispersions at the dyeing temperature, and association, which
may occur in.the absence of formally charged structures, may be
very difficult to detect by conventional means. Anomalies in
rates of dyeing found by McDowell and Weingarten
15)
n
applying four pure disperse dyes to polyester material have, on
the other hand, been interpreted in terms of an increase in
particle size of the dye, leading to lower aqueous solubility. This
reasoning assumes that the rate of dyeing
is
directly related to the
concentration of dissolved dye molecules. When the pure dye is
pretreated in boiling water, the rate of dyeing in some cases
decreases and in others increases. These authors had earlier
16)
drawn attention to the classical equation relating solubility to
particle size and molecular weight, viz.
3)
where S, is the mean solubility of a particle of radius r,
y
is the
free surface energy,
p
is the density of the solid and
S
is the
minimum solubilitywhen the particle size
is
increased. There must
be a maximum value of r for the condition Sr =S nd this can be
shown 17) to be approximately
10-2
pm, which is much less than
the mean radius of disperse dye particles. Further, the anomalies
in rates of dyeing were inconsistent, and it is now suggested that
the inconsistency may be explained by the formation of different
structural modifications
of
the solid dye during dyeing. These
modifications could be verifiable from X-ray diffraction data.
That this possibility has not been put forward by the authors is
surprising, since in another context 18) it is stated that X-ray
diffraction data are obtained as a matter of routine.
Solid-state transitions and polymorphic changes occurring
through solution and recrystallisation mechanisms are well
established in non-ionic dyes and pigments. In azo pigments
transitions occur on heating the pigment in an aqueous environ-
ment 19), and Apperley (20)has recently studied the influence of
surface-active agents on the morphology of
C.I.
Disperse Yellow
3
at the coupling stage.If such changes are occurring
in
dyebaths,
then further research on specific systems from this aspect may
throw considerable light on anomalous results obtained in
dyeing research.
J h e t i c s of
Dyeing
Diffusion processes in dyeing are essentially those describing
the mass transfer of dye from the external aqueous phase to the
interior of the substrate, and the distribution of dye within this
substrate up to its saturation equilibrium value. A complete
description of transfer mechanisms should therefore include
possible formation of a boundary layer in proximity to the fibre
within the aqueous phase, the boundary conditions at the inter-
face between this layer and the fibre, a possible diffusion layer
between the interface and the fibre interior, and the mechan-
ism by which the dye is transferred to the centre of the fibre.
When possible changes with respect to concentration and the
effect
of
additives other than dyes in the above phases are con-
sidered, in relation to structural changes occurring within the
substrate, it can be seen that the overall dyeing mechanism is very
complex. Fundamental studies of rates of dyeing are therefore,
where possible, limited to conditions that will allow assessment of
transfer processes with a minimum of dependent parameters.
Weisz and Zollinger
(21)
have considered the transfer of dye in
solution within substrate capillaries in which partial sorption or
immobilisation of the diffusant occurs. In this model, where
sorption of this type is reversible, he apparent diffusion coefficient
DA s defined by
. 4)
where
P
is the fraction of the substrate accessible to diffusion
processes,b is a tortuosity constant, which is less than
4 3 ,
Cf/C,
is the ratio of the total concentration
of
dye,
Cj;
per unit
volume
of fibre to an external dyebath concentration
C,,,
at equilibrium.
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THE THEORY OF DYEING
17
n
is the equilibrium partition coefficient between the mobile
portion of the internal dye concentration and the external dye
concentration, and
D
is the true diffusion coefficient
of
the
mobile
dye molecules within th at region of the su bstra te accessible
to diffusive motion. T he co nstant
a
depends on the particular
form
of
the absorption isotherm and falls within the range
1
* l a6 depending on the affinity of th e dye in th e system.
Eqn 4 is of general applicability and has been applied to an
earlier model for diffusion in cellulose
(22)
when the dye is
considered to be migrating along water-filled pores with simul-
taneous adsorption. By assuming that t he accessibility parameter,
P,
an
be
equated with a fractional uptake
of
water by th e fibre
and that the dye concentration is the same in the internal and
external aqueous phases, i.e.
n
=1, for dyes
of
high affinity where
a
approaches
1
‘6,
the eq uation ha s been successfully applied t o
previously published results on diffusion. Although there must be
some reservation on the assumed values
of
n and
a,
t is interest-
ing to observe that, for a direct dye, the value of th e true diffusion
coefficient, D,
of
the m obile dye molecules within the fibre is very
similar in magnitude to the value fo r th e diffusion coefficient of
dye molecules within the bulk aqu eous phase. It i s concluded that
for this dye the pore model with partial dye sorptio n is adeq uate
to account for the kinetics of dye transpo rt. Agreement is not as
good for acid dyes on nylon, but, with further assumptions abo ut
the aqueous solubility of disperse dyes, values for D obtained
from the general Eqn
4
for disperse dyes applied to polyesters and
cellulose acetates closely follow the
D
values for diffusion in
water alone.
Th e general applicability of this equa tion ca nno t, however, be
substantiated until further quantitative dat a on dye solubility and
free aqueous diffusion coefficients have been obtained. Very
little recent information is available on t he latter. Murfet
(23)
has
determined the relative diffusivity
of
C.I. Acid Red
1
using
a
vertical diffusion cell with
a
sintered-glass membrane. A lthough
the true aqueous diffusivity of the dye cannot
be
determined,
since the tortuosity and effective area of the sinter are not
amenable to absolute measurement, it is interesting to n ote tha t
relative diffusivity decreases in t he presence of urea, in co ntras t
with the fact that ur ea causes an increase in the rate of dyeing of
this dye on wool
14). One possible interpretation is that urea
accelerates dyeing by influencing other parameters such as the
structure
of
the boundary layer and the substrate, while having an
opposing effect on th e migration
of
dye in the internal aqueous
phase.
Although Fick‘s equations are often used as
a
basis for
diffusion studies, it is now accepted that theoretically determined
rate curves are comparatively insensitive to initial and boundary
conditions and to differential equations used in their derivation.
To
gain more detailed information on t he diffusion mechanisms,
it is necessary to obta in concentration-distance profiles, usually
by cross-sectioning fibres or films and determining dye distribu-
tion by microdensitometry. This has been done
( 2 4 )
for the
dyeing of various polymer films with disperse dyes in the presence
and in the absence
of
carriers. That in conventional dyeing
processes there are at least three components-dye, sub strate and
solvent-leads
to
a complex situation. Th e addition of carrier is
a
further complication. Even with the simplest systems rates
of
dyeing cannot be adequately dealt with in Fickian terms, since
the latter are expressly concerned with a binary system.
According to McGregor
et al. (24) ,
each component will
occupy
a
definite fraction
of
the fibre phase,
so
that, when
restrictions are imposed on this total volume, we might expect
that a n inward flow or volume flux of dye would
be
accompanied
by an outward flow
of
dyebath medium and that these opposing
flows might interact. This relative motion
of
molecules in
a
multi-component system can cause
a
change in volume or a
hydrodynamic bulk flow
of
the system. It becomes necessary
then, particularly at high diffusant concentrations, t o correct the
measured diffusion
flow
to take account of any hydrodynamic
transfer of the component under investigation. This could be
achieved by taking into account
a
frame
of
reference within
which the diffusion process is measured. T he reference frame may
be delineated in several ways. By conducting diffusion experi-
men ts in pre-swollen fibres
or films,
t can be assumed that no
furth er change in volume occurs o n dyeing, and he re the reference
frame is fixed with respect to the surface of the fibre
or
film.
Under these conditions Fick‘s laws do appear to apply and
reference-frame effects may become important only in carrier
dyeing and in dyeing fibres that have not been pre-swollen.
Irreversible changes in polyester structures have recently been
observed
(25)
n carrier dyeing with disperse dyes.
A method f or determining concentration-distance profiles
without cross-sectioning an d thereby standardising the frame-of-
reference effects still furth er ha s been developed by Blacker and
Patterson (26). The m ethod utilises the continuou s changes in
transmitted monochromatic light when
a
dyed filament, of
circular cross-section, is scanned across its longitudinal axis by
moving th e filament across
a
narrow slit. A microspectrophoto-
meter is used for this purpose, the results being suitable for
com pute r calculation to determine the dye distribution across the
fibre. Changes in profile shap e for
a
number of disperse dyeings
on polyester and nylon 6.6 filaments over
a
range
of
dyeing times
were obtained. The profile shape and the observation that in all
cases
a
time-dependent increasing surface concentration
of
dye
occurs showed that th e rate of transpo rt of dye to a boundary
just within the surface
of
the substrate
is
no higher than that at
which dye is transferred
to
the interior. It is also interesting to
observe that fo r nylon
6.6
this latter rate
is
extremely high, even
durin g the initial stages of dyeing, since horizo ntal profiles were
obtained. This behaviour is difficult
to
interpret unless it is
assumed either that th e subs trate is behaving like
a
liquid or th at
the driving force
for
diffusion is
a
variation in activity and not
concentration
of
the diffusing species.
When the dye and the substrate possess charges
o f
opposite
sign, which usually applies to t he nylon-acid dye system und er
acid conditions, the charge on the fibre becomes increasingly
negative during dyeing. This happens in the dyeing of nylon
with Orange I (C.I. Acid Orange 7), the surface potential
becoming increasingly more negative
as
dye concentrations both
within
( 2 7 )
and on the surface
( 2 8 )
increase. The initial surface
potential depends on the history
of
the substrate. Bell
( 2 9 )
has
found that rates of dyeing
of
acid dyes on nylon 6.6 are directly
proportional to the surface area and the saturation equilibrium
value
of
the dye on th e substrate. Th e latter values ar e considered
to be directly related to ami ne end-group con tent, bu t, in contrast
with Suzawa a nd Saito’s results
(28) ,
it is assumed that there is
no possibility of adsorption
of
dye on the surface. Bell’s con-
clusions must therefore be taken with som e reservation, p articu-
larly when it is noted th at dye concentrations in the fibre phase
were estimated solely on the basis of changes in dye concentration
occurring within the dyebath.
When the ion and the substrate are oppositely charged,
interaction between species can lead t o additional factors in the
interpretation
of
molecular diffusion processes. Some attention
has been paid to this problem by Mayer
(30)
in the dyeing
of
acrylic fibres (negative sites) with cationic basic dyes under
commercial conditions. Diffusion is satisfactorily achieved only
below a certain temperature and strict temperature control is
necessary t o achieve
a
reasonable rate of dyeing consistent with
levelness. Above this maximum temperature, bond formation,
represented by salt linkage, inhibits the attainment of adequate
rates
of
diffusion. Information to investigate this problem in
a
fundamental way is, however, lacking a t present.
A generalised treatment for explaining non -Fickian behaviour
has been given recently
(31) .
This type of diffusion, usually
attributed to substrate changes, can also occur when a second
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independent process such as a n immobilising chemical reaction
is superimposed with a comparable time scale. The presence of
blind pores acting as diffusant sinks in a porous subs trate can
also have this effect. Anomalous diffusion may also arise in
systems in which thermody namic diffusion coefficients, theo-
retically determined from practical diffusion coefficients an d
diffusant solubility, depend both on activity and on penetration
distance
in
such a way that activity and distance variables canno t
be separately assessed. Solutions to this general problem require
a large amount
of
computation and are wcrthwhile only
in
particular circumstances.
The molecular interpretation of diffusion of dyes in polymeric
systems is based on the strong dependence of the apparent
diffusion coefficients D A on temperature, which often follows a
simple Arrhenius eq uatio n, viz.
D A -
Do exp - E / R T )
. . 5 )
where
D,,
s a pre-exponential
or
proportionality constant and E
is the activation energy of diffusion. This energy is required by
the diffusing molecule to enable it
to
jump from one absorption
site
to
a vacant neighbour. The pre-exponential factor is related
to
the jum p distance and entropy
of
diffusion. For more hydro-
phobic fibres, the activation energy
of
diffusion is related to the
energy
of
hole formation
within
the polymer which allows the
dye molecule to diffuse.
I n
this respect it has been observed
(32)
that the activation energy
of
diffusion for disperse dyes
in
unmodified polypropylene
is
higher (by approximately
14
kcal/
mole) than that observed when the same dyes are applied
to
cellulose acetate. T he difference may be du e t o the temperature
dependence of interchain bonding
in
polypropylene and to the
swelling of cellulose acetate caused by absorbed water.
In
confirmation,
it
has previously been found that deso rption from
vapour-dyed polypropylene film occurs simply on cooling,
whereas desorption from vapour-dyed cellulose acetate occurs
only in
the presence
of
water vapour.
I t
is therefore possible that
at high temperatures diffusion into polypropylene is a process
simply of mixing.
Thermodynamics of Dyeing Processes
When diffusion is allowcd to contitwe
unt i l
n o further dye is
absorbed, the dye-substrate-solvent system can be considered
to be
i n
a state of dynamic equilibrium p rovided th at the physicril
and chemical forces appertaining to the processes of adsorption
are completely reversible, there being, for instance, n o perm anent
change in the structure of the substrate during dyeing. The
variation
with
temperature of the amount
of
dye absorbed at
equilibrium (the equilibrium sorption value) allows thermo-
dynamic quantities such as the standard affinity or free-energy
change, and heat and entropy of dyeing to be determined.
Application of these concepts to dyeing systems, however,
requires certain assumptions about the ideal behaviour
of
the dye
species in the solvent, the internal solution and substrate phases.
Assumptions have also
to
be made abo ut the internal o r available
volume in the substrate within which absorp tiono ccurs .
The free-energy change,
lc n
the transfer
of
one mole of dye
from
its standard state
in
solution
to
its standard state
in
the
fibre is given by
. . 6)
where lF is the standard enthalpy or heat-content change
in
the
process and
15
s the corresponding entrop y change. Th e stan-
dar d stat e of the dye may be arbitrarily defined for both phases.
Energies
of
bonding between dye and substrate for different dyes
may
be
compared only on this basis within the limits
of
the above
assumptions. High heats o f bonding between dye and substrate
molecules indicate a large change
in
entropy or decrease
in
randomness
of
dye molecules on absorption, but
it
has been
pointed out
( 3 3 )
that such correlations may be spurious when
LIZ'
nd
.IF'
re obtained from the same set
of
data, and con-
firmation is required by mathematical transformation.
i c
~
lF
- - T A T
lyer
el a/ ( 3 4 )
have applied Eqn
6
to show that a relation
between
A H '
and
4 3
does exist in the dyeing
of
cellulose with
Chlorazol Sky Blue
FF C.1.
Direct Blue
1
and that
4Ec
alues
increase with increasing size of alkali-metal cations present
during absorption. Calculated values
of
activity
of
the dye in
solution were used together with a variable substrate-volume
parameter defined previously
35)
as the product of the surface
area available for dye sorption and the thickness
of
the diffuse
double layer existing between the bulk dyebath phase and the
oute r surface of cellulose.
As A i r
ncreases in this manner there
is a corresponding increase
in
the value
of
the entrop y change
uhic h is considered t o be due t o different packing arrangements
of dye molecules at the surface of the substrate. The interpreta-
tion of these results, however, in terms of a breakdown in water
structure
in
the vicinity of the cellulose in the presence
of
large
cations (as is done by the authors) must be treated cautiously,
since thermodynamic data are concerned only with differences
in initial and final states and can give no information on the
mechanism by which the final sta te is appro ached . It is interesting
in this connection to note th at, in the dyeing
of
cellulose with the
leuco ani on of a non-sym metrical vat dye-a process similar to
the application
of
direct dyes-stacking or associ ation
of
the dye
anion occurs on the fibre, and this leads to an oxidised dyeing
in which associates are present before oxidation
(36).
More attention has been paid recently to research on the
dyeing
of
wool an d nylon with acid dyes. Interaction has generally
been considered as electrostatic bonding between dye anion
and positively charged sites such as protonated amine groups
existing
in
the substrate under acid conditions. This conclusion
has been deduced from studies of sorption isotherms where no
further increase in dye sorption beyond the value equivalent
to
the number
of
charged sites has been obtained. T he possibility
that van der Waals forces arising from dipole-induced dipole
interaction an d dispersion forces also operate must not be exclu-
ded. Possible substrate changes, particularly when the attainment
of equilibrium is prolonged, leading to the exposure of sites at
which interaction with dye anions may occur, must also be con-
s
dered.
One approech to reduce the number of these parameters
(37)
has been to study the absorption of dye anions that normally
have no substantivity for cellulose, by a cellulose substrate
modified by conversion of some of the hydroxyl groups to
8-aminoethyl groups. Any dye bonding occurring should there-
fcre be specific
to
the amino groups. Thermodynamic affinities
and heats of dyeing show that t he dye anion has interacted with
the protonated amin o group. Changes in accessibility compared
with unmodified cellulose are shown to be negligible, but the
modification reaction in which polyethyleneimines having
substantivity for the substrate
(38)
are formed may lead
to
a
substrate
in
which more than one type
of
adsorption site
is
present. The assumption of lack of substantivity of these acid
dyes for cellulose and their precise mode
of
interaction with
amin o groups have been called into question 39), but in a simpler
system
( 4 0 ) ,
when the same dyes have been applied to amino-
polypropylene under acid conditions, the correlation between
protonated amino groups and equilibrium sorption values has
been explained on the basis
of
a simple ion-exchange model.
Although Langmuir-type adsorption isotherms indicate
a
probable stoichiometric relation, amounts of dye absorbed over
and above th e limiting value (overdyeing) give rise to Freundlich-
type isotherms. This phenomen on is attributed t o th e presence. of
associated dye species within the dyebath. Theoretical expressions
describing differences
in
the two types of isotherm for acid dyes
on nylon depend not only on the degree
of
association of dye in
the dyebath but also
on
the equilibrium established between
sorbed and mobile dye anions within the polymer phase 41).
This latter type
of
equilibrium behaviour has been considered
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THE THEORY OF DYEING
19
by Marshall
42),
particularly for Orange I1 applied to a wool
substrate at the isoelectric point. By using
a
model based on
DoMan equilibrium partition and applying the condition
of
electrical neutrality in internal and external solutions, variations
in dye-sorption isotherms can be attributed to the influence
of
dye Concentration
on
the equilibrium between absorbed dye and
mobile dye in the internal solution. In approximating estimated
values of this equilibrium constant over a range of concentra-
tions, it was necessary to vary th e equilibrium constant to give the
best fit to the experimentally determined isotherms. This variation
may be used to determine the activity coefficient and hence th e
degree of association
of
the dyes within the internal aqueous
phase, and, when this w as calculated, the values of the activity
coefficient were similar to thos e calculated for the external dye-
bath phase.
In the thermodynamics
of
dyeing hydrophobic fibres with
disperse dyes, isotherms that are linear up to th e point of satura-
tion with respect to the dyebath phase are usually obtained.
Since most disperse dyes have very limited solubility in water,
even at the dyeing temperature, experimental difficulties arise in
determining whether such solutions a re monomolecularly dis-
persed or contain associated species. Recent research by
McDowell and Weingarten
18)
has no t revealed any conclusive
results on this point, but it was shown that at
120°C
non-linear
isotherms could
be
obtained with 1 amino-4-hydroxyanthra-
quinone on polyester film. The isotherms were linear up to the
saturation solubility of the dye in the aqueo us phase, the gradual
approach to
a
maximum value for up take within th e film beyond
this point being attributed to changes in the substrate. Th e heats
and entropies of dyeing
for
a
number of dyes, when determined
from absorption isotherms, were higher than the values deter-
mined from the temperature coefficient of the ratio of solubilities
of the dye in polyester to the solubilities in water. In thermo-
dynar+ c terms this difference is explained
43)
by the Fact that
the heat of dyeing determined from sorption isotherms is an
integral heat of dyeing where the total heat evolved is due not
only to the interaction between dye and subs trate molecules but
also, in the later stages, to the interaction between entering dye
molecules and substrate that already contains dye molecules.
The heat of dyeing obtained f rom solubility ratios approaches the
value for a heat of interaction between dye molecules and
a
substrate containing dye. In the limit th e difference between the
two is equal to
RT,
which at 150°C (the maximum dyeing tem-
perature used) is 0.84 kcal/mole. T he experimentally determined
difference is greater tha n this value an d lies in th e range 1.78-4.45
kcal/mole
for
the dyes considered. Two contributory causes are
possible. The first is that association of dye could
occur
in the
substrate and the second that contributions to the experimentally
determined heats of solution of the dyes in water may arise fro m
heats of solid-state transitions occurring in the dye-solid suspen-
sion. Whether disperse dyes are associated in the substrate is
still an open question
(see
below) and the possibility of solid-
state transitions occurring in disperse dye suspensions needs to
be more fully investigated.
Chemical Reaction with Substrates and Fibres
Although use is made of conventional physico-chemical
concepts in elucidating the mechanisms
of
reaction
of
coloured
compounds with substrates, discussion of the subject has been
arbitrarily divorced from normal dyeing theory in the past
since reactive-dyeing mechanisms involve no t only interaction by
physical ionic and dipole-induced dipole and dispersion forces
but also formation of covalent bonds with the substrate. With
reactive dyes, simultaneous hydrolysis
of
the dye by water in
both external and internal phases can occur. The resultant
changes in chemical structure
of
both dye and substrate during
dyeing therefore lead
to
more complex mechanisms of abso rptio n
and fixation.
Rattee has recently reviewed
44)
the chemistry
of
these
reactions from
a
kinetic stan dpoint. I n view of the heterogeneous
nature of the dyeing process, the initial model system used has
been one in which a homogeneous reaction phase-soluble
reactive dye, soluble alcohol acting a s the sub strate and water-
is considered. Reaction of dye with alcohol is analogous with
fixation
of
dye o n cellulose. The fixation a nd hydrolysis reactions
are bimolecular, although the total reaction norm ally behaves as
a
pseudo-unimolecular reaction because water and alcohol are
present in excess. It can be shown that, under conditions where
the alcohol is very slightly ionised, th e ratio
of
the rate constants
of fixation and hydrolysis, i.e. the reactivity ratio, Z, must
be
cons tant at any temperature an d be independent of pH co nditions.
At higher pH values, the ionisation of the alcohol may become
significant and th e reactivity rat io in this case is no longer con-
stant but depend s on pH. W hen the model is extended
to
include
cellulose, which contains ionisable primary and secondary
alcoholic groups, the situation becomes more complex, since
reactions may proceed at different rates in the fibre and
in
the
aqueous phase. The distribution of dye between the two phases
assumes
a
greater significance und er these conditions and the rate
of
diffusion into the fibre also plays a part. Hydrolysis occurs
both in th e dyebath and in the internal water phase, but for the
purpose of this discussion the latter effect can be shown to be
minimal. Simultaneous reaction
of
the dye with the fibre and
diffusion
of
the dye within the fibre can be accommodated by
applying
a
simplified Danckwerts’ equation
44) i,n
which the
efficiency of fixation E, defmed as the ratio of th e rate of reaction,
dfldr, to the rate of hydrolysis, dhldt, is given by
where
[ D ] F
s the con stant surface dye concentration,
[Ills
is the
dye concentration in the dyebath,
Z
is the previously mentioned
reactivity ratio, [C-] is the concentration
of
ionised hydroxyl
groups in the cellulose and KH
is
the bimolecular hydrolysis
constant. The apparent argument therefore is that the prime
factor determining the efficiency
of
fixation is the ratio
[ D ] F / [ D ] , ,
the substantivity ratio. The diffusion coefficient, D, and the
reactivity ratio have only minor effects,
as
d o
pH
conditions.
The last-named play
a
secondary role since the hydroxyl-ion
concentration i n th e external phase
([OH -I,,)
influences the value
of [C-1.
Strictly, this hydroxyl-ion concentration is related to the
hydroxyl-ion concentration within the internal aqueous phase
and the situation is in practice more difficult to interpret.
Changing the pH
of
the dyebath will cause
a
more
or
less
negative potential to develop at the substrate surface and,
where the surface potential becomes more negative, mutual
anionic repulsion between the surface and dye anion will cause
the value of
[D]F
to decrease.
Assuming that the dyebath
concentration is constant, the substantivity ratio will also
decrease. This effect, however, can
be
mitigated by increasing
the pH, which causes an increase in the diffusion coefficient.
Fro m a practical point of view, therefore, any process that leads
to a high degree of exhaustion
of
the dye will tend to give
a
high
substantivity ratio and consequently improve the overall efficiency
of the dyeing operation. It is interesting to observe 46) that the
influence
of
urea in improving the efficiency
of
reactive dyeing
cannot be due solely to an increase in dye solubility, since this
effect would reduce the substantivity ratio where the amount
of
bonded dye
[ D ] F
s unchanged. Improved efficiency is therefore
attrib uted to a n increase in the diffusion coefficient on increasing
the concentration
of
dye in the bath.
Practical confirmation of the validity of th e modified Danck-
werts’ equation
7 )
cannot be obtained under conditions where
dye hydrolysis and fixation occur simultaneously. Sumner
and
Taylor
47)
have attempted to overcome this problem in a
serni-quantitative way by considering the dyeing behnviour of
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REVIEW OF PROGRESS IN COLORATION; JONES
reactive dyes when hydrolysis is at a m inimum. This occurs under
slightly acid conditions for reactive dyes on cellulose. If, now , the
dyeing behaviour of dyes containing non-reactive residues but
similar in structure t o reactive dyes is observed over a ra nge of
pH values, it can be assumed that the changes in affinity and
rates of diffusion of these inert dyes will be paralleled by similar
but theoretical changes occurring with the reactive dyes. The
affinity and diffusion coefficients of
t he
latter can therefore be
determined over a p H range by extrapolation.
For
two out of the
three dyes examined in this way, calculated values of D increased
and values of
[ D ] F
decreased with increasing alkalinity. In
contrast, the third dye exhibited a minimum in its D values and
a ma xi mu m f or [ D l ~ a tH
I 1 *5 .
Hydrolysis in the dyebath of dichlorotriazine reactive dyes in
which
the
chromogen is linked to the reactive residue through an
imino group may no t be a simple second-order reaction b ut may
be complicated by the presence
of
a deprotonated imino form
(-i;j:)Bxisting as a result of acid-base equilibrium between the
latter and the imino form (-NH-) itself
(48).
The products of
hydrolysis of each form
will
be identical, although the rate
constants for hydrolysis for each fo rm will differ. These constants
and the acid-base equilibrium constant cannot be determined
without a knowledge of the activity coefficients
of
each species.
Products
of
activitycoefficientsand rateconstants can, however, be
approximated by computer processes. When this approximation
is carried out, the derived activation energies of hydrolysis are
found
to
depend on temperature with a maximum curvature at
30°C. This illustrates a comm on feature either in the dye struc-
tures
or
in the system as
a
whole. Th e observation
of
a minimum
in the mean activity coefficient in solutions
of
Orange
11
at this
temperature (49) determined by differential vapour-pressure
manometry is relevant in this context and may indicate structural
changes in the aqueous solvent in the vicinity
of
t he
dye anion
at this temperature.
More recently, the emphasis in reactive-dyeing theory has
shifted towards protein substrates and the investigation of sub-
structures within the protein that can react with the dye. The
elucidation
of
reaction mechanisms is more difficult than with
cellulose, since reactions are possible with a greater number
of sites of different types, the possibility of fibre degradation
is higher and fibre morphology is more complex. Very little
quantitative information was available until S hore, in an a dm ir-
able series of papers 50) and adopting the approach previously
taken for the reaction of dyes with cellulose, examined the r ate
of
reaction of a monoch lorotriazine dye with a number of model
compound s related
in
structure
to
the amino-acid residues
in
pro-
teins. If it is assumed t ha t the reactivities or dissociation constants
of
the groups
in
the protein are unaffected by their neighbours
then their reaction rates and activation energies will be com-
parable with those of model compo und s in aqueous solutions.
By such comparison the order of relative reactivity in water-
soluble proteins is cysteine thiol
>
N-terminal amino > histidine
> imidazolyl, etc., down to lysine amino and serine alcoholic
groups. This assumes that the availability of
t he
groups in the
protein to the reactive dye is equally as great as their availability
as model com pou nds in a homogeneous solution, but this
is
not
very likely. By extending the s tudy
51)
o include water-insoluble
proteins of known composition the most important groups to
react
were again shown to be the cysteine thiol, the primary amin o
groups
of
lysine and N-terminal amino-acid residues.
It
is
important to note that the thiol groups are reactive over the
whole pH range, whereas primary amino groups exert an influ-
ence only under alkaline conditions. Conditions with respect to
p H
in
kinetic a nd therm odynamic studies will differ from those
adop ted in t he reactive dyeing of cellulose. It is not possible then
to
adopt comparative techniques such as those
of
Sumner and
Taylor 47),
since the dye reacts readily un der n eutral
or
slightly
acid conditions.
By using
a
mixture of hydrolysed and reactive dye and applying
an equation resulting from a combination of Danckwerts
equa tion an d Hill s equation for diffusion into an infinite cylinder
with the condition of a satur ated fibre surface, Shore has shown
52)
that under acid conditions the diffusion coefficient of both
dye species increases with pH . Abov e p H 4.0 eaction of the dye
with wool predom inates a nd below this p H reactive dye preferen-
tially hydrolyses. Under neutral conditions the reactivity of the
dye for a wool substrate was less than the theoretical level,
suggesting that there m ay be specific chemical hindrance to the
reaction in the solid phase. A similar observation had been made
previously in comparing the rate constants for reaction of
a
dye
with a w ater-soluble alcohol an d with cellulose
(53).
Independent confirmation that hydrolysis of reactive dyes is
minimised i n
the
pH range
4-6
had been given by Lewis and
Seltzer
54) .
In the pad-batch dyeing
of wool
at roo m temperature
with dichlorotriazines under weakly acid conditions, the degree
of fixation app roach ed unity, particularly in the presence of
additives such as sodium metabisulphite. It is considered that th e
high rate
of
reaction may be due to th e formation
of
thiol groups
in the wool arising from the reduction of disulphide bonds. It
may also be ad ded that in the absen ce of reducing agents, under
acid conditions, protonation of the triazine nitrogen atoms may
increase the activity
of
the dichlorotriazine dye and allow
increased reaction with un-ionised thiol groups. Simultaneously,
the hydrolysis reaction would be minimal since a very low con-
centration of hydroxyl ion would be present.
The
specific
reaction with thiol groups in model compounds and substrates
requires furthe r investigation.
CHROME MORDANTING
Although not usually regarded as reactive dyeing in any sense,
the chrome mordanting of wool also entails direct chemical
reaction of the chromium with the fibre. Chromium is usually
applied as a hexavalent cation, in which form it is able
to
diffuse
into the wool. During application, the effect of heat accelerates
the reduction to trivalent chromium, probably by the action of
the substrate. The
Cr(1II)
can then react with the wool at
a
comparatively low rate. Hartley
55)
has considered the possible
reaction sites, reaction being excluded at amin o, thiol or phenolic
groups
56),
and concludes from pH changes during absorption
and from spectral data that the ionised carboxyl groups
in the
wool
take part in
the
formation of metal complexes.
This reaction is interpreted in terms
of a
prob able first-order
nucleophilic reaction whereby the presence of at least one
strongly negative ligand, e.g. sulphate, in a water-saturated
6-co-ordinated chromium cation facilitates the loss of a water
ligand. Thi s
loss
occurs as the rate-controlling step in the reaction
by the displacement
of
charge from the strongest negative ligand
to the central metal cation. The resultant penta-co-ordinated
transition-state entity is then in a sterically favourable orientation
to react with an ionised carboxyl group in the substrate. In
support
of
this reasoning, the more negative ligand remains
co-ordinated with the chromium after reaction. Although this
proposed mechanism still leaves room for 1
I
dye-chromium
complexes to be formed by ligand replacement, the existence
of
this type
of
complex in wool has never been proved. Th e forma-
tion of 2:l dyeechromium complexes requires displacement of
a
wool-carboxyl-ligand, and furthe r research is necessary.
High-temperature Dyeing under Anhydrous Conditions
The process of padding a fibrous material with a dispersion
of
a
non-ionic dye, drying and then heating the treated fibre to
a
high (190-220°C) temperature
for
a
short period to produce a
dyeing is by now familiar. The greatest use of such a process,
e.g. the Thermosol method, is in the coloration of polyester-
cellulose mixtures to dye the polyester component. Dyeing occurs
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THE
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DYEING
21
under high-temperature anhydrous conditions. The mechanisms
by w hich dye molecules
are
transferred from the solid particle
to
the substrate have been variously described as particle dissolution
in the substrate 57),
a
partial co ntact mechanism 58)
or
an
evaporation and dye-vapour absorption process
(59).
By similar
but independent experiments Datye 60) nd Sumner
et al
61)
have shown that, on padding and drying, the dye particles and
solution are preferentially ta ken u p by the cellulose component,
whereas in the fixation stage the dye
is
preferentially absorbed
by the polyester component. It follows, therefore, that the
vaporisation
of
the dye plays an imp ortant pa rt in the transfer
mechanism. Contribution s
to
the dyeing mechanism by transfer
of dye across dyed and undyed fibres throu gh sites of contact o r
by transfer through t he medium
of
additives may or may not be
relatively important.
Both Sumner
et
al
and Datye have found that dispersing
agents or migration inhibitors have no effect on the rate of
transfer. By determining the amount
of
dye absorbed when the
polyester subst rate is placed at various fixed distances from the
source of dye, an approximately linear relation between the
amoun t absorbed an d distance is found, from which the amoun t
absorbed a t zero distance, i.e. w hen th e dye sou rce and polyester
are in contact, can be extrapolated. Since there is good agreement
between these extrapolated values and those experimentally
determined, for a number of disperse dyes over
a
range
of
temperatures, Sumner
et al.
conclude that a single transfer
mechanism, viz. by vaporisation and absorption of dye vapour,
is adequate t o explain the amo unt
of
dye absorbed. Confirmation
is given from linear plots
of
ln[D]/, where [D]/ is the amount
of dye absorbed in unit time, against reciprocal temperature,
It is assumed that the rate of abso rptio n is controlled specifically
by the rate
of
diffusion d[D],/dt of the dye vap our in air. The
rate is directly related to the diffusion coefficient in air,
D
nd
to the vapour pressure
of
the dye
p
and inversely related to the
distance x between source and substrate, i.e.
. . . 8)
Sincc In
D
is proportional to reciprocal temperature and by
applying the Clausius-Clapeyron relation between
p
and
T,
Ean 8 mav be exmessed as
In(d[D],/dr)
In
D
+
Inp
- n x
In(d[D],/dr)
In K +
C
n x --
where K,
C
and
N
are constants and
L
is the latent heat of
sublimation
of
the dye at
a
total pressure of one atmosphere.
Plots
of
In[rate of transfer] or ln[D]+ at unit time against
1/T
should therefore be linear and of negative slope independent of
x .
This has been fou nd experimentally to
be
the
case
even when the
value
of x
is zero. On the other hand, the relation between [D]/
and
x
determined by Daty e
60)
as mor e curvilinear and extra-
polation to
zero
distance could lead to results indicative of an
additional small contribution by a direct contact mechanism.
Dyeing by application
of
unsaturated dye vapour
to
both
polyester and nylon substrates at high temperature has been
adequately dem onstrated 62). t is of interest t o observe
5 )
hat,
when model comp oun ds such as p-nitroaniline an d azobenzene
are applied to cellulose acetate by vapour-absorption methods
in the presence of unsaturated water vapour, the sorption
equilibrium values decrease as t he con centration
of
water vapour
within the substrate increases. Since sorption occurs under
equilibrium conditions, the decrease cannot be attributed to a
reduced rate of dye transfer by th e presence of water vapour, but
is possibly due to increased competition fo r sites between sorb ate
and water or
to
changes in subst rate structu re influenced by the
presence
of
water. In conventional dyeing, the amount
of
water
present in the substrate cannot be controlled in this way. The
comparatively high saturation values and their rapid attainment
obtained in high-temperature fixation or solvent-dyeing processes
may therefore
be
explained by the absence
of
water in addition
to
the high thermal energy
of
both dye and substrate molecules.
It h as been noted recently 63) hat the total amount
of
a
dye
in
a
mixture absorbed by the substrate under heat-fixation
conditions can be less tha n tha t absorbed when the dye is applied
separately and tha t long er fixation times a re required. In view of
these observations, it is possible that the vapour pressure of the
dye solid is reduced to that of a more stable polymorph, the
solid-solid transition taking place more readily
in
the presence
of
a second vapour component. Th e question of the heat stability
and the possibility of structural transitions
of
disperse dye
particles under conditions
of
high-temperature fixation requires
furthe r investigation, since n o research has been published in this
field.
The Physical State
of
Dyes
in
Polymers
U p o this point we have considered t he state
of
dyes in solution
and the kinetics and thermodynamics of dye transfer from the
dyebath to the substrate. Since this transfer process is dynamic
in natu re, it is possible that fur ther changes in the physical state
of the dye molecules in the polymer can take place outside the
environment
of
the transfer medium and more particularly when
the dyed material is heated, washed or exposed
to
light. It is
generally accepted tha t changes
in
colour occurring in the soaping
of vat and azoic dyeings can be attributed to the formation of
aggregates within the cellulose and some evidence has already
been given 36) hat association of vat-dye anions takes place
within the substrate during dyeing.
At present, it is not known with any real certainty whether
disperse dyes in hydrophobic sub strates exist as monomolecular
dispersions or whether they associate to fcrm large
or
small
aggregates. Giles
et
al.
have drawn attention
to
this probleni and
consider tha t associates
of
non-ionic dye molecules are present in
dyed nylon, polyester and cellulose acetates. Thcy base their
conclusions on two main arguments. Firstly (64,
65)
by measur-
ing the rate
of
fading,
as
expressed by changes in optical density
of
the dyed subs trate with time when exposed to light, the ord er
of
the fading reaction can be classified according to whether the
rate
of
fading changes approximately exponentially or linearly
with time. Some dyes may fade according to a combination
of
these orders of reaction, w hereas other (ano malo us) dyes exhibit
an initial increase in the optical density
of
the dyed film.
These
differences in reaction order
or
ra te
of
fiiding are attributed to
the presence and growth
of
aggregates
o f
dyc molecules within
the
film
on exposure to light. Secondly
6 6 ) ,
or those dyes con-
taining two absorpticn bands
in
th e visible region
of
their spectra,
the ratio of the molar extinction coefficientsof each band increa-
ses with increase in dye concentration
in
solution. Changes
in
the
ratio are related to changes
in
the degree of association as the
concentration
of
dye is varied. F rom similar changes in the spec-
tra of dyed hydrophobic films arid dyed films exposed to light
for different periods, it is concluded by analogy that such films
contain both monomolecularly dispersed and aggregated dye
molecules and that the average aggregation number increases as
fading proceeds.
It has been pointed ou t
67)
hat, since the spectrophotometric
technique used to examine dyed films utilises monochromatic
light that is partially plane-polarised, changes
in
extinction ratios
may be due to dichroic effects within the
film.
It has also been
observed 26) hat the dichroic orientation factor
of
dyed
filaments increases as the amount of dye present increases, since
the dye molecules first occupy the least oriented parts of the
substrate and th e zones
of
higher orientation are occupied only
at higher concentrations
of
dye.
If
t he
aggregation number
of
the dye increases during fading,
then there must b e
a
contribution to rates of fading from a dye-
migration mechanism. By studying the change in the dichroic
orientation factor of dyed polyester films with temp erature, any
reversible dye migration taking place as
a
consequence
of
heat
treatment would
be
indicated by
a
reversible change in the
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REVIEW
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JONES
dichroic orientation factor. Nakayama e t
al (68)
have shown
that, provided the amorphous polymer structure does not change
irreversibly, the orientation factor is in fact reversible. It is
concluded that, even
if
dye migration occurs at higher tempera-
tures, the dye molecule reverts to the same type
of
absorption
site on cooling.
The view that disperse dyes are at least initially monomolecu-
larly dispersed
in
hydrophobic fibres is favoured by Husy e t al.
69).
In
their more recent experiments they qualitatively show that
exposure to light of cellulose acetate dyed with an azo disperse
dye
in
which a trans+ rearrangement can take place is
accompanied by contractions in the dimensions of the substrate.
With dyes that
do
not undergo this phototropic change, the
dimensions
of
the substrate remain unchanged. These results
indicate a close interaction between dye and substrate molecules
which is favoured more by
a
molecular dispersion than by an
associated state.
Conclusions
A
reading of this review will show that no new theories of
dyeing have been postulated and that a comprehensive theory of
dyeing is still far from reality. In
a
recent survey, Valko (70)
suggests that, whereas thermodynamic studies of dyeing can
make useful contr ibutions to the general theories ofintermolecu-
lar forces, diffusion processes and the influenceof parameters such
as concentration, temperature, electrolyte concentration and
polymer structure
on
these processes remain largely uninvesti-
gated and would be
of
greater relevance to application methods.
As is shown in this review, however, when equilibrium studies are
carried out and assessed
in
conjunction with the growing amount
of information
o n
the structure of water and aqueous solutions,
their relevance to dyeing theory should not be underestimated.
Dyeing theory has been previously retarded by lack of knowledge
about non-ideal behaviour, but it is now possible, e.g. by differen-
tial manometry or vapour-pressure osmometry, to determine the
mean activity coefficients
of
dyes in solution. This may be the
first
step
in
determining activity coefficients of dyes in the
internal aqueous phase and inthesubstrate. Finally,muchresearch
is still needed on the heat stability
of
dye dispersions and solids
and on the thermodynamics and kinetics of heat-fixation
processes.
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