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Dye diffusion in anisotropic polyamide fibres
Journal of Membrane Science, 15 (1983) 171-180 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
DYE DIFFUSION
I.D. RATTEE Department
IN ANISOTROPIC
POLYAMIDE
171
FIBRES*
and S. SO of Colour Chemistry,
Leeds
University,
Leeds LS2 9JT (Gt. Britain)
(Received September 27, 1982; accepted in revised form January 4, 1983)
Summary Radioactive tracer techniques have been used to study the diffusion of three dyes in polyamide fibres produced under different conditions. It has been shown that drawn nylon fibres have a surface barrier layer which limits diffusion. The permeability of the layer is reduced by drawing, and varies with drawing conditions. The dependence of dye diffusion on concentration, ionic size and draw ratio is less in the surface than in the bulk of the fibre, but variations in dyeing behaviour have been shown to follow surface rather than bulk diffusion characteristics.
Introduction
The use of isotopically labelled anionic dyes in the study of tracer or exchange diffusion in polyamide films under conditions of uniform concentration was developed several years ago [ 1,2]. The technique was later developed to enable such studies to be carried out on textile fibres rather than model substrates, enabling data relating to wool [ 3] and nylon fibres [ 41 to be reported. In the latter investigation, it was shown that drawn nylon fibres exhibit radial anisotropy and possess a surface which is more difficult to penetrate than the bulk of the fibre. The tracer diffusion method provides the only way by which concentration dependent diffusion coefficients in anisotropic media can be examined. In normal diffusion studies involving anions adsorbed on to polyamides, the nonlinearity of the adsorption isotherm combined with diffusion potential factors leads to a concentration dependent diffusion coefficient, which consequently varies at each point along the concentration gradient of the diffusing dye [ $6 1. Thus the diffusion coefficient varies with radial distance and if there is, in addition, radial anisotropy also leading to a varying diffusion coefficient, it is impossible to separate the two effects. Using tracer methods, diffusion can be studied in the absence of a concentration gradient, allowing anisotropic effects *Based on a paper presented at the IUPAC Symposium on Interrelations between Processing, Structure and Properties of Polymeric Materials, August 29-September 2, 1982, Athens, Greece.
0376-7388/83/$03,00
0 1983
Elsevier Science Publishers B.V.
172
to be examined. The conditions of ionic migration along a concentration and diffusion potential gradient are different from those in a tracer diffusion experiment, and the magnitude of the diffusion coefficients will vary as a consequence of differences in the probability factors. Nevertheless the general analysis remains unaffected. The experimental methods are described elsewhere [ 2-41. Essentially, polyamide fibres equilibrated with non-labelled dye in aqueous solution are brought into contact with an otherwise identical but labelled dyebath, and the rate of exchange followed by suitable means. By using the 3sS isotope in the preparation of sulphonated acid dyes in conjunction with liquid scintillation counting, the system can be readily analysed. Based on the analysis of the data, a diffusion coefficient relating to the bulk of the fibre and a surface admittance coefficient can be calculated. The method is based on the treatment of surface limited diffusion by Newman [7] and first used in the study of dye diffusion in fibres by Medley and Andrews [ 9,101. For diffusion across a surface boundary into a cylinder, Newman’s treatment gives [ 81: Mt
r=
m
1-c
00
4L:
exp (-fliDt/a2) P;(P;
n=l
(1)
+ L:)
where Mt/M_ is the relative achievement of the equilibrium adsorption (or exchange) after time t; on values are the roots of Jo(&) = 0; D is the bulk diffusion coefficient; a is the radius and L, is a dimensionless coefficient such that
in which a is the surface admittance coefficient Ly=
Mb Db Ma 6 -
defined by (3)
-
Mb/M, is the equilibrium partition coefficient governing the distribution of the diffusing ions or molecules between the surface barrier phase and the bulk of the fibre; 6 is the thickness of the barrier layer and Db is the related diffusion coefficient. For short times, eqn. (1) gives the approximate solution, Mt ii--
2cKt = a
8 - ii
aw (7~D)l”
+ *.. (4)
in which the second term is small. Thus, under appropriate conditions, Mt/M, is directly proportional to t, and from the slope of the relationship (Ymay be calculated. The definition o a “short time” may be derived from the relationship between Mt/M, and t1$‘. This is found to be initially concave prior to be-
173
coming linear. The period of initial concavity defines the period of applicability of eqn. (4). The linear portion of the Mt/M, vs. t”’ relationship has a slope which is related to L 1.For large values of L, there is no marked concavity in the relationship, and the initial average slope (i.e. when Mt/M, < 0.1) is 4~(D/na’) which agrees with Crank’s relationship for a cylindrical fibre with no surface barrier [8]. However, for 0.7 > Mt/M, > 0.1,the average slope is 4(7~D/a’). For smaller values of L1 the slope falls below this value. However, it is relatively insensitive to the value of L, until L, < 10.In Fig. 1 the relationship between the slope of ~((Dt/aZ) vs. Mt/M, is shown as a function of L,.It is easily shown that the error in D introduced by assuming the slope to be l/(nD/az) is less than 10% for L1 = 10 and less than 5% for L1 = 20. The order of magnitude of L1 may be calculated from the value of cy (obtained from “short time” data) and an estimated D value (using slope = -\/(nD/a*)) together with a. Thus an estimate can be made of the validity of making the simplifying assumption that L1 is large, or whether L, needs to be determined.
051 . 20
Ll
Fig. 1. Sensitivity of the slope of d(Dt/a2)
vs. IM,/M,
to L,
30
174
Medley and Andrews [9] have described the use of the approximate equation, Mt -= M,
4
2
Dt
71(32-L,
which allows IL1 to be estimated from the negative intercept on the Mt/M, axis. This method is perhaps the less satisfactory, due to the large errors resulting when the intercept is small and the lack of any independent estimate of 01. Nevertheless, it has been used to produce useful information [ 3,4]. The present investigation has been concerned with an examination of the effect of draw ratio and drawing conditions on the bulk diffusion and surface admittance coefficients of Nylon 66 fibres and an investigation of the concentration dependence of the two factors. Experimental Nylon 66 fibres were supplied by I.C.I. (Fibres Division) in the form of 28 filament yarns with an amine end group content of 3.02 X lo-’ equivalent/ kg. The yarns were drawn at 65% R.H. under identical conditions to draw ratios of 0, 2.0, 2.5, and 3.0. For the study of the effect of drawing conditions a second series of yarns was obtained from the same source with a draw ratio of 3.42, achieved with a variety of drawing speeds and ceramic pin temperatures. Before use, the yarns were preset at 70°C for 270 minutes without tension in water.
-0
-0,s”
N=N
-03s
Dye 2
OH
N=N
Dye 3
88 ;b,-
Fig. 2. The dyes used in the experiments;
* indicates isotopic labelling with 35s.
175
Exchange experiments were carried out using three dyes employed in earlier studies [ 2,4], shown in Fig. 2. The apparatus and experimental procedures have been described elsewhere [ 1,3,4]. Comparative dyeing experiments were carried out using the yarns drawn under different conditions by dyeing samples together at 60°C in a single dyebath containing C.I. Direct Blue 71, a dye commonly employed to show up differences in dyeing behaviour. A dyeing time of 10 minutes at 70°C was used in order to maximise differences in initial adsorption and minimise redistribution or levelling of the dye. The colour strength was determined using a Zeiss RF3 spectrophotometer, the data from which were used to compute the value of L in accordance with the C.I.E. LAB system. In this context, L is, of course, not the same as the diffusional L1 used by Newman, Crank, etc. The C.I.E. L term is related to reflectance, so that it becomes smaller as the colour strength of a dyeing increases. Results
The values of D and QIwere calculated in each case from 12-14 separate data points giving an error in D of approximately 10% and in cr of approximately 5%. The results of the diffusion measurements are shown in Tables 1-4. TABLE 1 The effect of draw ratio on D and 01(0 = 0.66; Dye No. 2) Draw ratio
0 2.0 2.5 3.0
D (lo-‘6
m”/sec)
97.3 20.8 4.32 1.22
a (m/set) very large 1.7 x 10-q 5.0 x 10--‘O 2.0 x lo-‘0
TABLE 2 The effect of adsorbed dye concentration 0
D (lo-‘6
m*/sec)
on D and ~1(draw ratio 3.0) 01 (lo-‘*
Dye No. 1
0.2 0.41 0.53 0.60 0.70
0.43 1.51 1.86 2.78 3.24
0.97 1.75 1.87 2.50 2.95
Dye No. 2
0.60
0.38
0.500
m/set)
176 TABLE 3 Values of D as a function of draw ratio with varying 0 (Dye No. 2) Draw ratio
0
D (lo-‘”
2.0
0.55 0.78 0.82 0.88
19.2 25.4 25.9 28.9
2.5
0.49 0.70 0.79 0.86
3.32 5.40 5.51 5.92
3.0
0.40 0.62 0.70 0.92
0.97 1.27 1.30 1.32
m’/sec)
TABLE 4 Effect of drawing conditions Sample
1 2 3 4 5 6 7
on D and OL(0 = 0.6; Dye No. 1; draw ratio = 3.42)
Feed roll speed (m/min)
Draw roll speed (m/min)
Ceramic pin ;f;perature
D (10-l”
61 121 210 210 210 121 61
208 415 720 720 720 415 208
unheated a unheated unheated 70 110 110 110
1.11 2.42 2.41 2.37 2.38 2.05 2.40
m2 /see)
a (lo-”
m/set)
1.05 2.18 2.13 1.70 1.55 2.13 1.50
a Although the ceramic pin was unheated, the drawing process leads to frictional heating and Sample 1 is expected to have been drawn at a lower temperature than Samples 2 and 3 because of this.
Dye concentrations have been shown in terms of the function 0, which is the fractional electrostatic saturation of the fibre. 0 is calculated from e=
Dye concentration absorbed in equivalents/kg Amine end group concentration in equivalents/kg
(6)
The results of the competitive dyeing experiments are shown in Fig. 3 which shows acu as a function of L. The diffusional parameter UCY was used since the fibres varied slightly in diameter, giving surface area variations proportional to this radius.
177
1.8-
1.0.
0.8. 23
24
25 L values
Fig. 3. Variation of
acy
26
27
28
C I.E. LAB system
with L (lightness: C.I.E. LAB system).
Discussion Nylon samples produced with a draw ratio below 3 show variability along the fibre length, giving rise to diameter variations and, it may be supposed, differences in polymer orientation of a kind sufficient to render diffusion data obtained with such fibres less certain. At higher degrees of drawing, i.e. 2 3, fibre uniformity is achieved and sample variation effects are much less apparent. The effects of sample variation for draw ratios < 3 was most evident in relation to the values of the surface admittance coefficients. The results are nevertheless sufficiently reliable to permit a reasonable comparison to be made between D and (Yvalues at different draw ratios. A general inspection of Tables 1-4 shows that taking into account the radius of the fibres (2 low5 m), the values of L always exceed 10, justifying the use of the limiting slope approximation for the calculation of D. From Table 1 it can be seen that increasing draw ratio reduces both D and cr but after the very large effect on ~1which occurs when drawing commences, the effect of drawing on D is rather greater than it is on (11.Thus the ratio D/a falls with draw ratio as shown previously [4]. The concentration dependence of the two coefficients is illustrated for Dye No. 1 in Table 2. The D values clearly tend towards an upper limiting value as
178 TABLE 5 The effect of adsorbed dye concentration 8
0.20 0.41
0.53 0.60 0.70
D/a (lo-’
on
D/a (draw ratio 3.0; Dye No. 1)
m)
4.47 8.63
9.95 11.12 10.98
similar studies, using a moderately CWtdline PolYamide film substrate [ 21. The variation of D/a with 0 shows the relative sensitivity of the two coefficients to concentration; this is shown in Table 5. Since both D and a increase with 8, the increase of D/a with 0 signifies that the bulk diffusion coefficient is more concentration dependent than is the surface admittance coefficient. The effect of dye anion size on the two diffusional parameters can also be seen from Table 2. The value of D/o may be calculated for 0 -” 0.6 for Dyes I and 2, giving values of 1.11 X lO-‘j m and 7.56 X 10d7 m, respectively. Since D and a both decrease with the size of the diffusing ion, the fdl in D/a with size shows that D is the more sensitive factor. The effect of concentration in the case of Dye No. 1 could be explained on the basis of a lower diffusional free volume in the surface as compared with the bulk. The concept of a diffusional free volume is based on the suggestion that since the diffusion of a large dye ion involves migration by means of large voids, not all of the free volume is available for the diffusional process. As the diffusional free volume is increasingly occupied by the diffusing ions, the concentration dependence of the diffusion coefficient diminishes [ 2,111. Since the diffusional free volume is, in part, defined by the size of the diffusing ions, the effect can be easily demonstrated. In Fig. 4(a), the results of earlier work 1111, based on Dyes 1, 2 and 3, are shown; the upper limiting effect can be seen clearly. In Fig. 4(b) the results are reported in accordance with a suggestion by Iijima [ 121, which produces a single concentration relationship for the diffusion of the three dyes. The value occupation of the diffusional free of DIDmax is related to the proportional volume for each dye and thus eliminates the size variable. It is clear that, if the concentrations of the dye in the surface and bulk phases are the same, then given a higher degree of orientation in the surface, the occupation of the diffusional free volume will be higher, giving a lower concentration dependence. However, this is unlikely to be the only explmaCon Of the difference between the two phases, since the effect of size on D/Q_ is not entirely consistent with orientation differences alone and electrostatic or charge factors may be involved. has heen ohsewed
before
in
179
p-7.0 -
[by
_
-0.9
P
0.2
0.4
e
0.6
0.8
1.0
Fig. 4. Variation of tracer diffusion coefficients with adsorbed dye concentration; values vs. 8; (b) relative D values (D/D,,) VS. 0,
(a) D
Apart from the result obtained at a low drawing speed and pin temperature, the results of the study of the effect of drawing conditions show that the value of the bulk diffusion coefficient is remarkably insensitive to this factor, and that the observed differences in dyeing behaviour reflected in the values of L cannot be explained on the basis of the general diffusion properties of the polymer. On the other hand, the surface admittance coefficient shows marked variation, and as Fig. 3 shows, there is a good correspondence between surface admittance and dyeing characteristics. Clearly, more work is needed to determine the relationship of drawing and spinning conditions to the surface admittance coefficient, but it is clear that variations in the latter arising from production variables are of direct technical significance. Acknowledgement The authors wish to thank Dr. J.H. Nobbs of the Department Chemistry for assistance in the analysis of the data.
of Colour
References 1 G. Chantrey and I.D. Rattee, Tracer diffusion of chloride ions in Nylon 6 film, J. Sot. Dyers Colour., 85 (1969) 618.
180 2 G. Chantrey and I.D. Rattee, The tracer diffusion of dye anions in Nylon 6 film, J. Appl. Polym. Sci., 18 (1974) 105. 3 D.K. Al-Hariri, J.A. Coates and I.D. Rattee, Surface barrier effects in wool dyeing, II, J. Sot. Dyers Colour., 95 (1979) 432. 4 J.A. Coates, V. Ellard and I.D. Rattee, Tracer diffusion studies of anions in Nylon 66 fibres, J. Sot. Dyers Colour., 96 (1980) 14. 5 R.H. Peters, J.H. Petropoulos and R. McGregor, A study of the diffusion of dyes in polymer films by a microdensitometric technique, J. Sot. Dyers Colour., 77 (1961) 704. 6 M.E. Hopper, R. McGregor and R.H. Peters, Some observations on the concentration dependence of diffusion coefficients of acid dyes in nylon, J. Sot. Dyers Colour., 86 (1970) 117. 7 A.B. Newman, The drying of porous solids, Trans. Amer. Inst. Chem. Eng., 17 (1931) 203, 310. 8 J. Crank, The Mathematics ‘of Diffusion, The Clarendon Press, Oxford, 1956. 9 J.A. Medley and M.W. Andrews, The effect of a surface barrier on uptake rates of dye into wool fibres, Text. Res. J., 29 (1959) 398. 10 J.A. Medley and M.W. Andrews, The kinetics of wool dyeing - Some effects of alcohols on wool dyeing rates, Text. Res. J., 30 (1960) 855. 11 G. Chantrey and I.D. Rattee, The influence of polymers and dye characteristics on diffusion in Nylon 66, J. Appl. Polym. Sci., 18 (1974) 93. 12 T. Iijima, Personal communication.
DYE DIFFUSION
I.D. RATTEE Department
IN ANISOTROPIC
POLYAMIDE
171
FIBRES*
and S. SO of Colour Chemistry,
Leeds
University,
Leeds LS2 9JT (Gt. Britain)
(Received September 27, 1982; accepted in revised form January 4, 1983)
Summary Radioactive tracer techniques have been used to study the diffusion of three dyes in polyamide fibres produced under different conditions. It has been shown that drawn nylon fibres have a surface barrier layer which limits diffusion. The permeability of the layer is reduced by drawing, and varies with drawing conditions. The dependence of dye diffusion on concentration, ionic size and draw ratio is less in the surface than in the bulk of the fibre, but variations in dyeing behaviour have been shown to follow surface rather than bulk diffusion characteristics.
Introduction
The use of isotopically labelled anionic dyes in the study of tracer or exchange diffusion in polyamide films under conditions of uniform concentration was developed several years ago [ 1,2]. The technique was later developed to enable such studies to be carried out on textile fibres rather than model substrates, enabling data relating to wool [ 3] and nylon fibres [ 41 to be reported. In the latter investigation, it was shown that drawn nylon fibres exhibit radial anisotropy and possess a surface which is more difficult to penetrate than the bulk of the fibre. The tracer diffusion method provides the only way by which concentration dependent diffusion coefficients in anisotropic media can be examined. In normal diffusion studies involving anions adsorbed on to polyamides, the nonlinearity of the adsorption isotherm combined with diffusion potential factors leads to a concentration dependent diffusion coefficient, which consequently varies at each point along the concentration gradient of the diffusing dye [ $6 1. Thus the diffusion coefficient varies with radial distance and if there is, in addition, radial anisotropy also leading to a varying diffusion coefficient, it is impossible to separate the two effects. Using tracer methods, diffusion can be studied in the absence of a concentration gradient, allowing anisotropic effects *Based on a paper presented at the IUPAC Symposium on Interrelations between Processing, Structure and Properties of Polymeric Materials, August 29-September 2, 1982, Athens, Greece.
0376-7388/83/$03,00
0 1983
Elsevier Science Publishers B.V.
172
to be examined. The conditions of ionic migration along a concentration and diffusion potential gradient are different from those in a tracer diffusion experiment, and the magnitude of the diffusion coefficients will vary as a consequence of differences in the probability factors. Nevertheless the general analysis remains unaffected. The experimental methods are described elsewhere [ 2-41. Essentially, polyamide fibres equilibrated with non-labelled dye in aqueous solution are brought into contact with an otherwise identical but labelled dyebath, and the rate of exchange followed by suitable means. By using the 3sS isotope in the preparation of sulphonated acid dyes in conjunction with liquid scintillation counting, the system can be readily analysed. Based on the analysis of the data, a diffusion coefficient relating to the bulk of the fibre and a surface admittance coefficient can be calculated. The method is based on the treatment of surface limited diffusion by Newman [7] and first used in the study of dye diffusion in fibres by Medley and Andrews [ 9,101. For diffusion across a surface boundary into a cylinder, Newman’s treatment gives [ 81: Mt
r=
m
1-c
00
4L:
exp (-fliDt/a2) P;(P;
n=l
(1)
+ L:)
where Mt/M_ is the relative achievement of the equilibrium adsorption (or exchange) after time t; on values are the roots of Jo(&) = 0; D is the bulk diffusion coefficient; a is the radius and L, is a dimensionless coefficient such that
in which a is the surface admittance coefficient Ly=
Mb Db Ma 6 -
defined by (3)
-
Mb/M, is the equilibrium partition coefficient governing the distribution of the diffusing ions or molecules between the surface barrier phase and the bulk of the fibre; 6 is the thickness of the barrier layer and Db is the related diffusion coefficient. For short times, eqn. (1) gives the approximate solution, Mt ii--
2cKt = a
8 - ii
aw (7~D)l”
+ *.. (4)
in which the second term is small. Thus, under appropriate conditions, Mt/M, is directly proportional to t, and from the slope of the relationship (Ymay be calculated. The definition o a “short time” may be derived from the relationship between Mt/M, and t1$‘. This is found to be initially concave prior to be-
173
coming linear. The period of initial concavity defines the period of applicability of eqn. (4). The linear portion of the Mt/M, vs. t”’ relationship has a slope which is related to L 1.For large values of L, there is no marked concavity in the relationship, and the initial average slope (i.e. when Mt/M, < 0.1) is 4~(D/na’) which agrees with Crank’s relationship for a cylindrical fibre with no surface barrier [8]. However, for 0.7 > Mt/M, > 0.1,the average slope is 4(7~D/a’). For smaller values of L1 the slope falls below this value. However, it is relatively insensitive to the value of L, until L, < 10.In Fig. 1 the relationship between the slope of ~((Dt/aZ) vs. Mt/M, is shown as a function of L,.It is easily shown that the error in D introduced by assuming the slope to be l/(nD/az) is less than 10% for L1 = 10 and less than 5% for L1 = 20. The order of magnitude of L1 may be calculated from the value of cy (obtained from “short time” data) and an estimated D value (using slope = -\/(nD/a*)) together with a. Thus an estimate can be made of the validity of making the simplifying assumption that L1 is large, or whether L, needs to be determined.
051 . 20
Ll
Fig. 1. Sensitivity of the slope of d(Dt/a2)
vs. IM,/M,
to L,
30
174
Medley and Andrews [9] have described the use of the approximate equation, Mt -= M,
4
2
Dt
71(32-L,
which allows IL1 to be estimated from the negative intercept on the Mt/M, axis. This method is perhaps the less satisfactory, due to the large errors resulting when the intercept is small and the lack of any independent estimate of 01. Nevertheless, it has been used to produce useful information [ 3,4]. The present investigation has been concerned with an examination of the effect of draw ratio and drawing conditions on the bulk diffusion and surface admittance coefficients of Nylon 66 fibres and an investigation of the concentration dependence of the two factors. Experimental Nylon 66 fibres were supplied by I.C.I. (Fibres Division) in the form of 28 filament yarns with an amine end group content of 3.02 X lo-’ equivalent/ kg. The yarns were drawn at 65% R.H. under identical conditions to draw ratios of 0, 2.0, 2.5, and 3.0. For the study of the effect of drawing conditions a second series of yarns was obtained from the same source with a draw ratio of 3.42, achieved with a variety of drawing speeds and ceramic pin temperatures. Before use, the yarns were preset at 70°C for 270 minutes without tension in water.
-0
-0,s”
N=N
-03s
Dye 2
OH
N=N
Dye 3
88 ;b,-
Fig. 2. The dyes used in the experiments;
* indicates isotopic labelling with 35s.
175
Exchange experiments were carried out using three dyes employed in earlier studies [ 2,4], shown in Fig. 2. The apparatus and experimental procedures have been described elsewhere [ 1,3,4]. Comparative dyeing experiments were carried out using the yarns drawn under different conditions by dyeing samples together at 60°C in a single dyebath containing C.I. Direct Blue 71, a dye commonly employed to show up differences in dyeing behaviour. A dyeing time of 10 minutes at 70°C was used in order to maximise differences in initial adsorption and minimise redistribution or levelling of the dye. The colour strength was determined using a Zeiss RF3 spectrophotometer, the data from which were used to compute the value of L in accordance with the C.I.E. LAB system. In this context, L is, of course, not the same as the diffusional L1 used by Newman, Crank, etc. The C.I.E. L term is related to reflectance, so that it becomes smaller as the colour strength of a dyeing increases. Results
The values of D and QIwere calculated in each case from 12-14 separate data points giving an error in D of approximately 10% and in cr of approximately 5%. The results of the diffusion measurements are shown in Tables 1-4. TABLE 1 The effect of draw ratio on D and 01(0 = 0.66; Dye No. 2) Draw ratio
0 2.0 2.5 3.0
D (lo-‘6
m”/sec)
97.3 20.8 4.32 1.22
a (m/set) very large 1.7 x 10-q 5.0 x 10--‘O 2.0 x lo-‘0
TABLE 2 The effect of adsorbed dye concentration 0
D (lo-‘6
m*/sec)
on D and ~1(draw ratio 3.0) 01 (lo-‘*
Dye No. 1
0.2 0.41 0.53 0.60 0.70
0.43 1.51 1.86 2.78 3.24
0.97 1.75 1.87 2.50 2.95
Dye No. 2
0.60
0.38
0.500
m/set)
176 TABLE 3 Values of D as a function of draw ratio with varying 0 (Dye No. 2) Draw ratio
0
D (lo-‘”
2.0
0.55 0.78 0.82 0.88
19.2 25.4 25.9 28.9
2.5
0.49 0.70 0.79 0.86
3.32 5.40 5.51 5.92
3.0
0.40 0.62 0.70 0.92
0.97 1.27 1.30 1.32
m’/sec)
TABLE 4 Effect of drawing conditions Sample
1 2 3 4 5 6 7
on D and OL(0 = 0.6; Dye No. 1; draw ratio = 3.42)
Feed roll speed (m/min)
Draw roll speed (m/min)
Ceramic pin ;f;perature
D (10-l”
61 121 210 210 210 121 61
208 415 720 720 720 415 208
unheated a unheated unheated 70 110 110 110
1.11 2.42 2.41 2.37 2.38 2.05 2.40
m2 /see)
a (lo-”
m/set)
1.05 2.18 2.13 1.70 1.55 2.13 1.50
a Although the ceramic pin was unheated, the drawing process leads to frictional heating and Sample 1 is expected to have been drawn at a lower temperature than Samples 2 and 3 because of this.
Dye concentrations have been shown in terms of the function 0, which is the fractional electrostatic saturation of the fibre. 0 is calculated from e=
Dye concentration absorbed in equivalents/kg Amine end group concentration in equivalents/kg
(6)
The results of the competitive dyeing experiments are shown in Fig. 3 which shows acu as a function of L. The diffusional parameter UCY was used since the fibres varied slightly in diameter, giving surface area variations proportional to this radius.
177
1.8-
1.0.
0.8. 23
24
25 L values
Fig. 3. Variation of
acy
26
27
28
C I.E. LAB system
with L (lightness: C.I.E. LAB system).
Discussion Nylon samples produced with a draw ratio below 3 show variability along the fibre length, giving rise to diameter variations and, it may be supposed, differences in polymer orientation of a kind sufficient to render diffusion data obtained with such fibres less certain. At higher degrees of drawing, i.e. 2 3, fibre uniformity is achieved and sample variation effects are much less apparent. The effects of sample variation for draw ratios < 3 was most evident in relation to the values of the surface admittance coefficients. The results are nevertheless sufficiently reliable to permit a reasonable comparison to be made between D and (Yvalues at different draw ratios. A general inspection of Tables 1-4 shows that taking into account the radius of the fibres (2 low5 m), the values of L always exceed 10, justifying the use of the limiting slope approximation for the calculation of D. From Table 1 it can be seen that increasing draw ratio reduces both D and cr but after the very large effect on ~1which occurs when drawing commences, the effect of drawing on D is rather greater than it is on (11.Thus the ratio D/a falls with draw ratio as shown previously [4]. The concentration dependence of the two coefficients is illustrated for Dye No. 1 in Table 2. The D values clearly tend towards an upper limiting value as
178 TABLE 5 The effect of adsorbed dye concentration 8
0.20 0.41
0.53 0.60 0.70
D/a (lo-’
on
D/a (draw ratio 3.0; Dye No. 1)
m)
4.47 8.63
9.95 11.12 10.98
similar studies, using a moderately CWtdline PolYamide film substrate [ 21. The variation of D/a with 0 shows the relative sensitivity of the two coefficients to concentration; this is shown in Table 5. Since both D and a increase with 8, the increase of D/a with 0 signifies that the bulk diffusion coefficient is more concentration dependent than is the surface admittance coefficient. The effect of dye anion size on the two diffusional parameters can also be seen from Table 2. The value of D/o may be calculated for 0 -” 0.6 for Dyes I and 2, giving values of 1.11 X lO-‘j m and 7.56 X 10d7 m, respectively. Since D and a both decrease with the size of the diffusing ion, the fdl in D/a with size shows that D is the more sensitive factor. The effect of concentration in the case of Dye No. 1 could be explained on the basis of a lower diffusional free volume in the surface as compared with the bulk. The concept of a diffusional free volume is based on the suggestion that since the diffusion of a large dye ion involves migration by means of large voids, not all of the free volume is available for the diffusional process. As the diffusional free volume is increasingly occupied by the diffusing ions, the concentration dependence of the diffusion coefficient diminishes [ 2,111. Since the diffusional free volume is, in part, defined by the size of the diffusing ions, the effect can be easily demonstrated. In Fig. 4(a), the results of earlier work 1111, based on Dyes 1, 2 and 3, are shown; the upper limiting effect can be seen clearly. In Fig. 4(b) the results are reported in accordance with a suggestion by Iijima [ 121, which produces a single concentration relationship for the diffusion of the three dyes. The value occupation of the diffusional free of DIDmax is related to the proportional volume for each dye and thus eliminates the size variable. It is clear that, if the concentrations of the dye in the surface and bulk phases are the same, then given a higher degree of orientation in the surface, the occupation of the diffusional free volume will be higher, giving a lower concentration dependence. However, this is unlikely to be the only explmaCon Of the difference between the two phases, since the effect of size on D/Q_ is not entirely consistent with orientation differences alone and electrostatic or charge factors may be involved. has heen ohsewed
before
in
179
p-7.0 -
[by
_
-0.9
P
0.2
0.4
e
0.6
0.8
1.0
Fig. 4. Variation of tracer diffusion coefficients with adsorbed dye concentration; values vs. 8; (b) relative D values (D/D,,) VS. 0,
(a) D
Apart from the result obtained at a low drawing speed and pin temperature, the results of the study of the effect of drawing conditions show that the value of the bulk diffusion coefficient is remarkably insensitive to this factor, and that the observed differences in dyeing behaviour reflected in the values of L cannot be explained on the basis of the general diffusion properties of the polymer. On the other hand, the surface admittance coefficient shows marked variation, and as Fig. 3 shows, there is a good correspondence between surface admittance and dyeing characteristics. Clearly, more work is needed to determine the relationship of drawing and spinning conditions to the surface admittance coefficient, but it is clear that variations in the latter arising from production variables are of direct technical significance. Acknowledgement The authors wish to thank Dr. J.H. Nobbs of the Department Chemistry for assistance in the analysis of the data.
of Colour
References 1 G. Chantrey and I.D. Rattee, Tracer diffusion of chloride ions in Nylon 6 film, J. Sot. Dyers Colour., 85 (1969) 618.
180 2 G. Chantrey and I.D. Rattee, The tracer diffusion of dye anions in Nylon 6 film, J. Appl. Polym. Sci., 18 (1974) 105. 3 D.K. Al-Hariri, J.A. Coates and I.D. Rattee, Surface barrier effects in wool dyeing, II, J. Sot. Dyers Colour., 95 (1979) 432. 4 J.A. Coates, V. Ellard and I.D. Rattee, Tracer diffusion studies of anions in Nylon 66 fibres, J. Sot. Dyers Colour., 96 (1980) 14. 5 R.H. Peters, J.H. Petropoulos and R. McGregor, A study of the diffusion of dyes in polymer films by a microdensitometric technique, J. Sot. Dyers Colour., 77 (1961) 704. 6 M.E. Hopper, R. McGregor and R.H. Peters, Some observations on the concentration dependence of diffusion coefficients of acid dyes in nylon, J. Sot. Dyers Colour., 86 (1970) 117. 7 A.B. Newman, The drying of porous solids, Trans. Amer. Inst. Chem. Eng., 17 (1931) 203, 310. 8 J. Crank, The Mathematics ‘of Diffusion, The Clarendon Press, Oxford, 1956. 9 J.A. Medley and M.W. Andrews, The effect of a surface barrier on uptake rates of dye into wool fibres, Text. Res. J., 29 (1959) 398. 10 J.A. Medley and M.W. Andrews, The kinetics of wool dyeing - Some effects of alcohols on wool dyeing rates, Text. Res. J., 30 (1960) 855. 11 G. Chantrey and I.D. Rattee, The influence of polymers and dye characteristics on diffusion in Nylon 66, J. Appl. Polym. Sci., 18 (1974) 93. 12 T. Iijima, Personal communication.