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A study of dyestuff aggregation. I. Determination of dye particle sizes by light scattering
A Study of Dyestuff Aggregation I. Determination of Dye Particle Sizes by Light Scattering A. DATYNER, A. G. FLOWERS, AYD M. T. PAILTHORPE School o f Textile Technology, University o f New South Wales, P.O. Box 1, Kensington, Australia 2033 Received February 14, 1979; accepted July 12, 1979 The particle sizes of three related azo dyestuffs have been determined by light scattering employing a tunable laser as the source of monochromatic light. The extent and mode of aggregation of the dyes are discussed.
1.2. measurements can be taken at temperatures near the boiling point of water, which is technologically relevant; 1.3. no concentration changes occur during the measurement, which is relatively quick. However, a number of solutions varying in concentration have to be prepared to permit extrapolation to zero concentration and great care has to be exercised in the preparation of the solutions for measurement. One of the reasons for the neglect of light scattering was probably the difficulty of generating adequately intense monochromatic light of a variety of wavelengths. Thus Alexander and Stacey (3) used "red and infrared" rather than monochromatic radiation and doubts have been cast on the validity of their results (4). Frank (5) used two neighboring yellow lines of a mercury vapor source for the examination of Orange II (C.I. Acid Orange 7) and benzopurpurine 4B (C.I. Direct Red 2), two of the dyes examined by Alexander and Stacey (3). Sivarajan (6) used a carbon arc to examine six direct dyes and a Pointolite lamp with a red filter (7) for benzopurpurine 4B alone. The results of all these workers for benzopurpurine 4B, in the presence of similar salt concentrations and at similar temperatures, differ considerably. Benderet and Meyer (8)
1. I N T R O D U C T I O N
Many dyestuffs, of low solubility in water, present difficulties in their application to wool and it is thought that these difficulties are associated with either (a) the formation of aggregates (1) which, due to their large size, can enter the fiber but slowly and cannot distribute easily through the fiber, or, (b) the high affinity of such dyes for the fiber which makes it difficult for the adsorbed dye to be desorbed and readsorbed to achieve a uniform distribution. Despite its technological interest, the aggregation of such dyes has hardly been examined and the present series of papers describes an investigation of dye aggregation in aqueous solution, at temperatures up to 95°C, by means of light scattering, and some preliminary conclusions are drawn about the relationships between dye structure and aggregation. The methods available for the measurement of aggregation have been reviewed by Duff and Giles (2). Of these methods, light scattering has hardly been employed, despite a number of advantages not possessed by any of the other methods: 1.1. its suitability for the measurement of relatively large particles such as highly aggregated dyes; 71
Journal of Colloidand Interface Science, Vol. 74, No. 1. March 1980
0021-9797/80/030071-09502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved.
72
DATYNER, FLOWERS, AND PAILTHORPE
used the sodium D-line in their examination of C.I. Direct Yellow 4, a stilbene dye, which may form a cis-isomer on irradiation and it is difficult to draw conclusions from their work. It is not suggested here that the variety of light sources used is the sole cause of the differences in results, but that the type of sources used (except perhaps the sodium D-line) did not assist the acquisition of reliable results. Tunable lasers are available now and provide powerful monochromatic radiation for light-scattering measurement. 2. EXPERIMENTAL 2.1. LIGHT-SCATTERING MEASUREMENTS
2.1.1. Light-Scattering Instrument A light-scattering photometer (SOFICA, Strasbourg, France) has been modified by removing the mercury vapor light source and collimating optics and replacing them with a laser (Control Laser, Model 554 AK), the output of which is tunable by selecting the appropriate Littrow prism and output mirrors, to give a choice of 15 discrete wavelengths ranging from 674.6 to 454.5 nm. A wavelength of 568.2 nm was used for the measurements described in this paper. The all-line output of the laser, as used, is approximately 3 W. The output intensity is servoloop stabilized to better than 1% over 24 hr. In addition, the laser input intensity to the SOFICA is sampled by a beam splitter and reference photomultiplier in the usual way. The laser output is predominantly horizontally polarized and it was therefore passed through a mica half-wave plate followed by a polarizer to yield a vertically polarized beam. This is followed by a mode selector and finally a lens to focus the beam at the center of the scattering cell.
2.1.2. Light-Scattering Theory In the present work, Rayleigh scattering of dye solutions was measured. General light-scattering equation (9) (cgs Journal of Colloid and Interface Science,
Vol. 74, No. 1, March 1980
units have been used in this work):
K*c Ro
_ _
-
l Mv¢ _ _
.p-i(O
)
+ 2A2c + 3A3c z + . . . .
[1]
where
/ dns ~2 -4 -1 K* = 47r2n~[--~c ) hv Na
[2]
for vertically polarized light. c = Concentration, A2, Aa = virial coefficients, no = refractive index of solvent, and dnJdc = specific refractive index increment of the dye. In those cases where light is absorbed by the dye, a small correction to (dnJdc) is necessary (10).
dns 12 -d-c--c]
=
(dn ]~
\"~-c]~ + (
2.303Xv,x 47r ) z'
[3]
where (dn/dc)m = refractive index increment measured on the differential refractometer, Xv = wavelength in vacuo, Na = Avogadro's number, and P-'(O) = particle-scattering function. For particles with a diameter less than one-tenth of a wavelength, the particlescattering function is approximately 1 (9) and is taken to be 1 in this work. ex = Extinction coefficient at the laser wavelength employed. Ro = Rayleigh ratio at concentration c and angle 0 for vertically polarized light. At a measuring angle of 90° and assuming a Fresnel coefficient of zero, the Rayleigh ratio becomes (9) RT R90 = ~ (G(solution)"10OD /ns\ z
-- G
DYESTUFF
index of the solution, and nv = refractive index of the oil bath (silicone oil). The 10°° in Eq. [4] corrects for the small amount of light absorbed by the dye at the measurement wavelength. 2.1.3.
Use o f S o d i u m Chloride
In the present study of aggregation, it was found necessary to work in saline solutions of the dyes. When the work first commenced, aqueous solutions of the dyes were used and it was found that aggregation equilibria were highly variable and particularly sensitive to small amounts of electrolyte, which was very difficult to remove by the method of recrystallisation employed (from ethanol/water) (4). In order to gain reproducible experimental results, it was necessary to work in a solution of known salt concentration. Since salt is present both in the commercial dyestuff itself and in the dyeing recipe, the use of salt in the light-scattering solutions is a logical step. In addition, salt is used in diffusion work and hence the presence of salt in the light-scattering work will allow direct comparison of results from the two techniques. The salt concentration used in this work is 0.03 M sodium chloride. The presence of salt in the light-scattering solution requires that Eq. [2] above be modified as follows (9): K*
=
L WL=,,
47r2n2)t-4N -1[{ On o
v
a
+
IOn) (Oc;) -4-3-, --
1=
,
[5]
where c'~ = concentration of salt, c = concentration of dye, p = pressure, and /zs = chemical potential of other diffusible species. By combining Eqs. [2] and [5] it can be shown (9) that
M* =MF1 +
L
(On/Oc)~=,v
(Oc'=I k -Oc - Jr= J
'
161
where M* = apparent molecular weight, M = true molecular weight.
73
AGGREGATION
TABLEI Rayleigh ratio for toluene (R~,~ × 10~) Temperature (°C)
488 nm
568.2 nm
25
3.92
1.93
55 75
3.37 3.00
1.66 1.48
95
2.69
1.32
By applying the theory of the Donnan membrane equilibrium (9), (Oc'=/Oc)~= may be estimated as M= Oc /~=
M
at high ionic strength or low charge density, where Ms = molecular weight of salt, M = molecular weight of polyelectrolyte of net valence Z. For a monosulphonated dye of molecular weight 600 and aggregation number N, the particle molecular weight will be 500N while the net valence will be N. A typical value for (On/Oc)c=,~ is 0.36 ml/g (see Table III) while the value for (On/ Oc~)c,p at 0.03 M NaC1 is 0.12 mug. By substituting these values in Eqs. [6] and [7], it can be seen that the true molecular weight is underestimated by approximately 2%. This error is negligible in relation to the combined errors involved in the measurement (ca. 15%) and hence has been neglected. This finding is in agreement with the findings of Orofino and Flory (11). 2.1.4. R a y l e i g h R a t i o f o r Toluene
The Rayleigh ratio for toluene (Rg0,,) at 25°C, for a range of wavelengths is given by Cantow (12). For vertically polarized light we have (13) Rgo,v = Rgo.u" - -
2
1 +p~
,
[8]
where p, is the depolarization constant for toluene. Values o f p , at various wavelengths are given by Cantow (12). The Rayleigh ratio for toluene, at higher temperatures, was cap Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
74
DATYNER, FLOWERS,AND PAILTHORPE TABLE II
employed. The interferometer was calibrated against aqueous sucrose solutions. For the dye solutions, the refractive index increment was determined by injecting a sample taken from the light-scattering cell into a differential refractometer (Waters, Model 401). The instrument had been calibrated with appropriate sucrose solutions at each measurement temperature. The upper limit of temperature in the Model 401 is 75°C. The refractive index increment at 95°C was calculated from the value at 75°C, using expansivity corrections, which scarcely affect the second decimal place of dn/dc. The refractive index of the solutions used was measured in an Abb6 refractometer.
DyestuffStructures x o H
N
X
X
I.
X = X' = SO3Na
II.
X = H
X'
X' = S03Na
OH
//
\\
2.3. MATERIALS
X
III.
X = X' = H
Y = S03Na
IV.
X = X' = S03Na
Y = n-C4H 9
V.
X = X' - S O ~ a
Y = n-C8HI7
VI.
X = S03Na
Y = n-CqH 9
X' = H
culated from the expression (14)
Rgo,u
_ 27r2n~kT ( O n ]o. 6 + 6pu h4kT \ Op ]W 6 -- 7pu '
[9]
where KT is the isothermal compressibility of toluene. Values of Rg0,v, calculated by the above method, taking due account of temperature and wavelength dependent variables, are given in Table I for the two principal wavelengths used in this and later work. 2.2.
REFRACTIVE
INDEX
Sodium chloride and sucrose were analytical grade reagents and were used without further purification. Analytical grade toluene was distilled before use. All water was first filtered and deionized and then distilled before use. Dow Corning 702 silicone oil was vacuum distilled before use. Sodium dodecylsulphate (Henkel and Cie GmbH Dusseldorf, 99.99% pure) was used without further purification. The 12-tungstosilicic acid was L.R. grade and purified according to the method of Matijevic and Kerker (15). Dyes I (C.I. Acid Red 41) and II (C.I. Acid Red 88) were purified by successive recrystallizations from water/ethanol until the absorbance of a standard weight/ volume solution was maximized. Dyes IV and V were synthesized in these laboratories as described by Datyner et al. (16). The structures of the four dyes used are given in Table II. No fluorescence could be detected from solutions of these dyes when excited at the measurement wavelength. The spectrofluorophosphorimeter employed is described elsewhere (17).
INCREMENT
For transparent solutions (sodium dodecylsulphate and 12-tungstosilicic acid), an interferometer (Zeiss, Model L36000) was Journal of Colloid and Interface Science, Vol. 74, No. I, March 1980
2.4 METHODS Dyestuff, 10 mg, was pasted with a few drops of cold water, followed by making up
DYESTUFF AGGREGATION to approximately 60 ml with boiling water. Solutions for measurement were prepared by taking aliquots of the above solution and making them up to 50 ml with boiling water. When other components were required, e.g., salt or dispersing agents, they were added to the water. The solutions were then placed in an oven, at the required temperature, for 1 hr, to reach thermal equilibrium. They were then filtered, while in the oven, into the light-scattering cells through a 0.45-/xm filter (Millipore, type HA) in an all-glass apparatus. The amount of light scattered at the chosen wavelength was then measured relative to that of toluene. The concentration of dyestuff in the scattering cell was then determined colorimetrically in a thermostated cell holder in a spectrophotometer (Cary, Model 15). The refractive index increment of the same solution was measured as described in 2.2. 3. RESULTS 3.1. SPECIFIC REFRACTIVE INDEX INCREMENTS Values determined for the specific refractive index increments of the compounds studied are given in Table III. The value found for 12-tungstosilicic acid is in good agreement with the value of 0.091 ml/g determined by Kratohvil et al. (18) while the value of 0.120 ml/g for sodium dodecyl-
TABLE III Specific Refractive Index Increments~
Compound
12-Tungstosilicic acid in 3.0 M NaCI Sodium dodecyl sulphate (above the c.m.c.) Dye I (C.I. Acid Red 41) Dye II (C.I. Acid Red 88) Dye IV in 0.03 M NaC1 Dye V in 0.03 M NaC1
a X = 568.2 nm.
75 12lO8-
K (cC~c___.~) RgO%0 cmc 6x 105 4-
// Nw=60+5
(C-Come) x 103g m1-1
FIG. 1. Debye Plot for sodium dodecylsulphate at 25°C in 0.03 M NaCI. sulphate is in good agreement with the value of 0.117 ml/g published by Parfitt and Wood (19). 3.2.
CALIBRATION
CHECKS
3.2.1. 12-Tungstosilicic Acid 12-Tungstosilicic acid in 3.0 M NaC1, as described by Kratohvil et al. (18), was used as a convenient standard for the aqueous system. 12-Tungstosilicic acid, which has a formula weight of 2879, was found to have a molecular weight of 2890 +_ 100, as determined in the described experimental arrangement. 3.2.2. Sodium Dodecylsulphate Sodium dodecylsulphate was used to test the calibration of the instrument for highermolecular-weight species. The results are shown in Fig. 1, where the method of presentation is that of Debye (20). The number of molecules per micelle so determined is 60 _+ 5, which is in good agreement with the results of Kodama et al. (21) and Huisman (22).
Measurement temperature (°C)
dn/dc
25
0.094
3.3. DYE I (C.I. ACID RED 41)
25 25 25 55 55
0.120 0.350 0.360 0.340 0.330
This dye is a tetrasulphonated dye molecule, and known to be monodisperse in aqueous solution (23). Therefore, at the limit of sensitivity and dye concentration used in this work, no significant excess scattering should be observed for a solution of the dye
(mUg)
Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
76
DATYNER, FLOWERS, AND PAILTHORPE 1-5-
A mathematically convenient, theoretical, probability distribution function which will demonstrate this is the Schultz-Zimm distribution. For a system of particles following the Schultz-Zimm distribution
1.0-
Kc x 105 R90
an+l
N w = 370 +- 50
P(r) -
05-
[10]
.r n.e -at,
F(n + 1)
C xlOSg rnl "I
where P(r) is the probability density for the occurrence of a particle of radius r and n and a are distribution coefficients. It may be shown that
FIG. 2. Dye II at 25°C.
]Qw
=
4/37TP
M
compared with solvent and this was found to be the case. 3.4. DYE I I
(C.I.
x A C I D R E D 88)
The degree of association of Dye II has been determined by diffusion (24) and by polarography (25) at 25°C and found to range between 2 and 5, depending upon concentration. At higher temperatures this dye dissociates and becomes a unimer at 50°C (26) (Fig. 2). Light-scattering measurements yield an aggregation number of 370 _+ 50. Frank (5) found that for Orange II (Dye III in Table II) the aggregation number varies with temperature and concentration and reaches a value of 110 at 5°C. Since Orange II has a sulphonated benzene ring while Dye II has a sulphonated naphthalene ring, it would be expected that Orange II would be more soluble in water and less aggregated than Dye II. The aggregation numbers determined by light-scattering and diffusion-based methods are quite different for Dye II. It must be remembered however that diffusion-based methods give a number average aggregation number, while light scattering gives a weight average aggregation number. Diffusion- and light-scattering-based determinations will only agree for a monodisperse system of particles. For a polydisperse system, on the other hand, the values will be quite different. Journalof Colloidand InterfaceScience, Vol. 74, No. 1, March 1980
Na
(n + 6)(n + 5)(n + 4) , a~ Na
]QD = 4/37rP ~
[11]
F/3 ,
a 3
[12]
where Nw = weight average aggregation number, No = diffusion-determined aggregation number, p = density of dye, and M = molecular weight of dye. Equations [11] and [12] may be readily solved for n and a since we know Nw and No. By substitution of n and a in Eq. [10] the distribution curve may be calculated for different values ofr and such a curve for Dye II is shown in Fig. 3.
-0-7-
('~
-0.6-
~
"r'p~ 1 -
°n+1 ~
rn
-or
e
for n = 1-170435 a = 0.196/.8!
"0-5" -04p(r) .0.3-0.2o.1-
o
lO
20
30
40
50
60
70
r
FIo. 3. Distribution of particle radius of Dye II
at 25°C.
77
DYESTUFF AGGREGATION
3.5. DYES IV aND V
I 10_
Dyes IV and V (Table II) were studied as examples of dye structures which fall midway between Dye II and the more complex dyes chosen for later study. Both of these dyes contain disulphonated naphthalene, which is hydrophilic, and n-butyl (Dye IV) and n-octyl (Dye V) substituted benzene rings which are hydrophobic. It was expected that these dyes would be surface active and possibly form micelles, but surface tension measurements showed that micelles do not form within the concentration range studied (<10-4 g m1-1) at 55°C. This temperature was chosen because at lower temperatures the dyes flocculated. 3.5.1. Dye I V
The results for Dye IV are given in Fig. 4. The aggregation number is 52 +_ 10. This dye has two sulphonate groups, one more than Dye II, and hence one would expect that Dye IV would be more readily soluble in water and have a lower aggregation number than Dye II. This was found to be the
K ~ c x105 R90
x x x
5~
= 52 +- 10
I
0
~
1'0 C x 105 g m1-1
FIG. 4. D y e IV in 0.03 M NaCI at 55°C.
case. Duff et al. (25), using polarography, determined a value of N = 3000, at 25°C, for Dye VI (Table II), which has one less sulphonate group than Dye IV and would be expected to be more highly aggregated than Dye IV. 3.5.2. Dye V
Dye V contains an n-octyl chain where Dye IV had an n-butyl chain. The results are given in Fig. 5. It can be seen from the
4- x
I
3
x x Ix
Kc: x 106
t
RgO 2
\\
x x
x
x
o
;
~
~
X
~
~
~
G
'~
C x 10 5 g n~ -1
FIG. 5. D y e V in 0.03 M N a C I at 55°C. - - - , T h e o r e t i c a l c u r v e . Journal of Colloid and Interface Science, Vol. 74, No. I, March 1980
78
DATYNER, FLOWERS, AND PAILTHORPE
results' profile that the particle size varies with concentration (9). Since there is no evidence of micelle formation (closed association) from surface tension measurements, an open association process must be taking place. The simplest open association model is one in which association proceeds stepwise with the same association constant at each step, viz: ~1 w = (M1)M~ (Ma)M,
+
k MII + M1 ~-- Mm, k Mn-1 + M1 ~-Mn. For such a distribution of particles the weight average molecular weight is
(M11)M~l + . . .
+ (Mll)M,1
which can be reduced to [Mw]2 = [MI]2 +
k
M~ + M I ~ MI,,
4k[Md2c,
where k is the molar association constant and c is the molar concentration of dye. Figure 5 shows the theoretical curve for k = 3 × 10TM 1 mo1-1 and 2A2 = 6 x 10-3 ml g-1. The fit is quite good considering that the same association constant was assumed for each step. Since aggregation varies with concentration, one can only calculate an aggregation number corresponding to a certain concentration. For example, to take a concentration midway in the range examined, say, 4 × 10-Sg m1-1, the aggregation number predicted by the model is not less than 2200, because the model underestimates the aggregation number at high dye concentrations. 4. CONCLUSION
The light-scattering method can be successfully applied to the study of dyestuff aggregation in aqueous solution when dyestuff aggregation is so high that it cannot be assessed in any other way. Dye II has an aggregation number of 370 at 25°C. Dye IV, which is of similar structure, but has an additional sulphonic acid group, has an aggregation number of 52 at 55°C. In Dye V, the increase in size of the alkyl chain from n-butyl (Dye IV) to n-octyl (Dye V) in the hydrophobic part of the molecule caused a dramatic increase in both the Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
(M,)M~
+ • • • (Mn)Mn
+
...
+ • • •
degree of aggregation and the concentration dependence of aggregation. Aggregation numbers determined by lightscattering methods will only agree with diffusion determinations for a monodisperse system. When the solution is polydisperse, light-scattering measurements will always give values higher than those of diffusionbased methods. A combination of information obtained from light-scattering and diffusion measurements permits an estimation of the polydispersivity of the system. ACKNOWLEDGMENTS This work was supported by a grant from the Wool Research Trust Fund on the recommendation of the Australian Wool Corporation, to whom the authors wish to express their thanks, as well as to Mrs. J. Krawets and Messrs. G. Blythe and N. Buchsbaum for assistance with experimental work. REFERENCES 1. Peters, R. H., "Textile Chemistry," Vol. III. Elsevier, London, 1975. 2. Duff, D. G., and Giles, C. H., in " W a t e r " (F. Franks, Ed.), Vol. 4, p. 169. Plenum, New York, 1975. 3. Alexander, P., and Stacey, K. A., Proc. Roy. Soc. Ser. A 212, 274 (1952). 4. Vickerstaff, Th., "The Physical Chemistry of Dyeing," Oliver & Boyd, Edinburgh/London, 1954. 5. Frank, H. P., J. Colloid Sci. 12, 480 (1957). 6. Sivarajan, S. R., J. Indian Inst. Sci. 34, 75 (1952). 7. Sivarajan, S. R. ,J. Indian lnst. Sci. 36, 282 (1954). 8. Benderet, A., and Meyer, P., Bull. Soc. Chim. France 53 (1953). 9. Huglin, M. B., "Light Scattering from Polymer
DYESTUFF AGGREGATION
10. 11. 12. 13. 14. 15. 16. 17. 18.
Solutions," Academic Press, London/New York, 1972. Latimer, P., and Dudley Bryant, F., J. Opt. Soc. Amer. 55, 1554 (1965). Orofino, T. A., and Flory, P. J., J. Phys. Chem. 63, 283 (1959). Cantow, H. J., MakromoL Chem. 18-19, 367 (1956). Anacker, E. W., Rush, R. M., and Johnson, J. S., J. Phys. Chem. 68, 81 (1964). Coumou, D. J., Mackor, E. L., and Hijmans, J., Trans. Faraday Soc. 60, 1539 (1964). Matijevic, E., and Kerker, M., J. Amer. Chem. Soc. 81, 5560 (1959). Datyner, A., Delaney, M. J., and Holliger, H., Aust. J. Chem. 24, 1845 (1971). Pailthorpe, M. T., J. Phys. E. 8, 194 (1975). Kratohvil, J. P., Oppenheimer, L. E., and Kerker, M., J. Phys. Chem. 70, 2834 (1966).
79
19. Parfitt, G. D., and Wood, J. A., Kolloid Z. Z. Polym. 229, 27 (1969). 20. Debye, P., J. Colloid Sci. 3, 407 (1948). 21. Kodama, M., Kubota, Y., and Miura, M., Bull. Chem. Soc. Japan 45, 2953 (1972). 22. Huisman, H. F., Kon. Ned. Akad. Wetensch. Proc. Ser. B. 67, 388 (1964). 23. °Craven, B. R., and Datyner, A., in "Proceedings, IVth International Congress on Surface Active Substances," Vol. III, p. 545. 1964. 24. Craven, B. R., Datyner, A., and Kennedy, J. F., Aust. J. Chem. 24, 723 (1971). 25. Duff, D. G., Kirkwood, D. J., and Stevenson, D. M., J. Soc. Dyers Colourists 93, 303 (1977). 26. E1-Mariah, Afaf A. R., E1-Sabbagh, I. E., and Labib, A., Dokl. Akad. Nauk SSSR 234, 72 (1977).
Journal of Colloidand Interface Science, Vol. 74, No. 1, March1980
1.2. measurements can be taken at temperatures near the boiling point of water, which is technologically relevant; 1.3. no concentration changes occur during the measurement, which is relatively quick. However, a number of solutions varying in concentration have to be prepared to permit extrapolation to zero concentration and great care has to be exercised in the preparation of the solutions for measurement. One of the reasons for the neglect of light scattering was probably the difficulty of generating adequately intense monochromatic light of a variety of wavelengths. Thus Alexander and Stacey (3) used "red and infrared" rather than monochromatic radiation and doubts have been cast on the validity of their results (4). Frank (5) used two neighboring yellow lines of a mercury vapor source for the examination of Orange II (C.I. Acid Orange 7) and benzopurpurine 4B (C.I. Direct Red 2), two of the dyes examined by Alexander and Stacey (3). Sivarajan (6) used a carbon arc to examine six direct dyes and a Pointolite lamp with a red filter (7) for benzopurpurine 4B alone. The results of all these workers for benzopurpurine 4B, in the presence of similar salt concentrations and at similar temperatures, differ considerably. Benderet and Meyer (8)
1. I N T R O D U C T I O N
Many dyestuffs, of low solubility in water, present difficulties in their application to wool and it is thought that these difficulties are associated with either (a) the formation of aggregates (1) which, due to their large size, can enter the fiber but slowly and cannot distribute easily through the fiber, or, (b) the high affinity of such dyes for the fiber which makes it difficult for the adsorbed dye to be desorbed and readsorbed to achieve a uniform distribution. Despite its technological interest, the aggregation of such dyes has hardly been examined and the present series of papers describes an investigation of dye aggregation in aqueous solution, at temperatures up to 95°C, by means of light scattering, and some preliminary conclusions are drawn about the relationships between dye structure and aggregation. The methods available for the measurement of aggregation have been reviewed by Duff and Giles (2). Of these methods, light scattering has hardly been employed, despite a number of advantages not possessed by any of the other methods: 1.1. its suitability for the measurement of relatively large particles such as highly aggregated dyes; 71
Journal of Colloidand Interface Science, Vol. 74, No. 1. March 1980
0021-9797/80/030071-09502.00/0 Copyright © 1980by Academic Press, Inc. All rights of reproduction in any form reserved.
72
DATYNER, FLOWERS, AND PAILTHORPE
used the sodium D-line in their examination of C.I. Direct Yellow 4, a stilbene dye, which may form a cis-isomer on irradiation and it is difficult to draw conclusions from their work. It is not suggested here that the variety of light sources used is the sole cause of the differences in results, but that the type of sources used (except perhaps the sodium D-line) did not assist the acquisition of reliable results. Tunable lasers are available now and provide powerful monochromatic radiation for light-scattering measurement. 2. EXPERIMENTAL 2.1. LIGHT-SCATTERING MEASUREMENTS
2.1.1. Light-Scattering Instrument A light-scattering photometer (SOFICA, Strasbourg, France) has been modified by removing the mercury vapor light source and collimating optics and replacing them with a laser (Control Laser, Model 554 AK), the output of which is tunable by selecting the appropriate Littrow prism and output mirrors, to give a choice of 15 discrete wavelengths ranging from 674.6 to 454.5 nm. A wavelength of 568.2 nm was used for the measurements described in this paper. The all-line output of the laser, as used, is approximately 3 W. The output intensity is servoloop stabilized to better than 1% over 24 hr. In addition, the laser input intensity to the SOFICA is sampled by a beam splitter and reference photomultiplier in the usual way. The laser output is predominantly horizontally polarized and it was therefore passed through a mica half-wave plate followed by a polarizer to yield a vertically polarized beam. This is followed by a mode selector and finally a lens to focus the beam at the center of the scattering cell.
2.1.2. Light-Scattering Theory In the present work, Rayleigh scattering of dye solutions was measured. General light-scattering equation (9) (cgs Journal of Colloid and Interface Science,
Vol. 74, No. 1, March 1980
units have been used in this work):
K*c Ro
_ _
-
l Mv¢ _ _
.p-i(O
)
+ 2A2c + 3A3c z + . . . .
[1]
where
/ dns ~2 -4 -1 K* = 47r2n~[--~c ) hv Na
[2]
for vertically polarized light. c = Concentration, A2, Aa = virial coefficients, no = refractive index of solvent, and dnJdc = specific refractive index increment of the dye. In those cases where light is absorbed by the dye, a small correction to (dnJdc) is necessary (10).
dns 12 -d-c--c]
=
(dn ]~
\"~-c]~ + (
2.303Xv,x 47r ) z'
[3]
where (dn/dc)m = refractive index increment measured on the differential refractometer, Xv = wavelength in vacuo, Na = Avogadro's number, and P-'(O) = particle-scattering function. For particles with a diameter less than one-tenth of a wavelength, the particlescattering function is approximately 1 (9) and is taken to be 1 in this work. ex = Extinction coefficient at the laser wavelength employed. Ro = Rayleigh ratio at concentration c and angle 0 for vertically polarized light. At a measuring angle of 90° and assuming a Fresnel coefficient of zero, the Rayleigh ratio becomes (9) RT R90 = ~ (G(solution)"10OD /ns\ z
-- G
DYESTUFF
index of the solution, and nv = refractive index of the oil bath (silicone oil). The 10°° in Eq. [4] corrects for the small amount of light absorbed by the dye at the measurement wavelength. 2.1.3.
Use o f S o d i u m Chloride
In the present study of aggregation, it was found necessary to work in saline solutions of the dyes. When the work first commenced, aqueous solutions of the dyes were used and it was found that aggregation equilibria were highly variable and particularly sensitive to small amounts of electrolyte, which was very difficult to remove by the method of recrystallisation employed (from ethanol/water) (4). In order to gain reproducible experimental results, it was necessary to work in a solution of known salt concentration. Since salt is present both in the commercial dyestuff itself and in the dyeing recipe, the use of salt in the light-scattering solutions is a logical step. In addition, salt is used in diffusion work and hence the presence of salt in the light-scattering work will allow direct comparison of results from the two techniques. The salt concentration used in this work is 0.03 M sodium chloride. The presence of salt in the light-scattering solution requires that Eq. [2] above be modified as follows (9): K*
=
L WL=,,
47r2n2)t-4N -1[{ On o
v
a
+
IOn) (Oc;) -4-3-, --
1=
,
[5]
where c'~ = concentration of salt, c = concentration of dye, p = pressure, and /zs = chemical potential of other diffusible species. By combining Eqs. [2] and [5] it can be shown (9) that
M* =MF1 +
L
(On/Oc)~=,v
(Oc'=I k -Oc - Jr= J
'
161
where M* = apparent molecular weight, M = true molecular weight.
73
AGGREGATION
TABLEI Rayleigh ratio for toluene (R~,~ × 10~) Temperature (°C)
488 nm
568.2 nm
25
3.92
1.93
55 75
3.37 3.00
1.66 1.48
95
2.69
1.32
By applying the theory of the Donnan membrane equilibrium (9), (Oc'=/Oc)~= may be estimated as M= Oc /~=
M
at high ionic strength or low charge density, where Ms = molecular weight of salt, M = molecular weight of polyelectrolyte of net valence Z. For a monosulphonated dye of molecular weight 600 and aggregation number N, the particle molecular weight will be 500N while the net valence will be N. A typical value for (On/Oc)c=,~ is 0.36 ml/g (see Table III) while the value for (On/ Oc~)c,p at 0.03 M NaC1 is 0.12 mug. By substituting these values in Eqs. [6] and [7], it can be seen that the true molecular weight is underestimated by approximately 2%. This error is negligible in relation to the combined errors involved in the measurement (ca. 15%) and hence has been neglected. This finding is in agreement with the findings of Orofino and Flory (11). 2.1.4. R a y l e i g h R a t i o f o r Toluene
The Rayleigh ratio for toluene (Rg0,,) at 25°C, for a range of wavelengths is given by Cantow (12). For vertically polarized light we have (13) Rgo,v = Rgo.u" - -
2
1 +p~
,
[8]
where p, is the depolarization constant for toluene. Values o f p , at various wavelengths are given by Cantow (12). The Rayleigh ratio for toluene, at higher temperatures, was cap Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
74
DATYNER, FLOWERS,AND PAILTHORPE TABLE II
employed. The interferometer was calibrated against aqueous sucrose solutions. For the dye solutions, the refractive index increment was determined by injecting a sample taken from the light-scattering cell into a differential refractometer (Waters, Model 401). The instrument had been calibrated with appropriate sucrose solutions at each measurement temperature. The upper limit of temperature in the Model 401 is 75°C. The refractive index increment at 95°C was calculated from the value at 75°C, using expansivity corrections, which scarcely affect the second decimal place of dn/dc. The refractive index of the solutions used was measured in an Abb6 refractometer.
DyestuffStructures x o H
N
X
X
I.
X = X' = SO3Na
II.
X = H
X'
X' = S03Na
OH
//
\\
2.3. MATERIALS
X
III.
X = X' = H
Y = S03Na
IV.
X = X' = S03Na
Y = n-C4H 9
V.
X = X' - S O ~ a
Y = n-C8HI7
VI.
X = S03Na
Y = n-CqH 9
X' = H
culated from the expression (14)
Rgo,u
_ 27r2n~kT ( O n ]o. 6 + 6pu h4kT \ Op ]W 6 -- 7pu '
[9]
where KT is the isothermal compressibility of toluene. Values of Rg0,v, calculated by the above method, taking due account of temperature and wavelength dependent variables, are given in Table I for the two principal wavelengths used in this and later work. 2.2.
REFRACTIVE
INDEX
Sodium chloride and sucrose were analytical grade reagents and were used without further purification. Analytical grade toluene was distilled before use. All water was first filtered and deionized and then distilled before use. Dow Corning 702 silicone oil was vacuum distilled before use. Sodium dodecylsulphate (Henkel and Cie GmbH Dusseldorf, 99.99% pure) was used without further purification. The 12-tungstosilicic acid was L.R. grade and purified according to the method of Matijevic and Kerker (15). Dyes I (C.I. Acid Red 41) and II (C.I. Acid Red 88) were purified by successive recrystallizations from water/ethanol until the absorbance of a standard weight/ volume solution was maximized. Dyes IV and V were synthesized in these laboratories as described by Datyner et al. (16). The structures of the four dyes used are given in Table II. No fluorescence could be detected from solutions of these dyes when excited at the measurement wavelength. The spectrofluorophosphorimeter employed is described elsewhere (17).
INCREMENT
For transparent solutions (sodium dodecylsulphate and 12-tungstosilicic acid), an interferometer (Zeiss, Model L36000) was Journal of Colloid and Interface Science, Vol. 74, No. I, March 1980
2.4 METHODS Dyestuff, 10 mg, was pasted with a few drops of cold water, followed by making up
DYESTUFF AGGREGATION to approximately 60 ml with boiling water. Solutions for measurement were prepared by taking aliquots of the above solution and making them up to 50 ml with boiling water. When other components were required, e.g., salt or dispersing agents, they were added to the water. The solutions were then placed in an oven, at the required temperature, for 1 hr, to reach thermal equilibrium. They were then filtered, while in the oven, into the light-scattering cells through a 0.45-/xm filter (Millipore, type HA) in an all-glass apparatus. The amount of light scattered at the chosen wavelength was then measured relative to that of toluene. The concentration of dyestuff in the scattering cell was then determined colorimetrically in a thermostated cell holder in a spectrophotometer (Cary, Model 15). The refractive index increment of the same solution was measured as described in 2.2. 3. RESULTS 3.1. SPECIFIC REFRACTIVE INDEX INCREMENTS Values determined for the specific refractive index increments of the compounds studied are given in Table III. The value found for 12-tungstosilicic acid is in good agreement with the value of 0.091 ml/g determined by Kratohvil et al. (18) while the value of 0.120 ml/g for sodium dodecyl-
TABLE III Specific Refractive Index Increments~
Compound
12-Tungstosilicic acid in 3.0 M NaCI Sodium dodecyl sulphate (above the c.m.c.) Dye I (C.I. Acid Red 41) Dye II (C.I. Acid Red 88) Dye IV in 0.03 M NaC1 Dye V in 0.03 M NaC1
a X = 568.2 nm.
75 12lO8-
K (cC~c___.~) RgO%0 cmc 6x 105 4-
// Nw=60+5
(C-Come) x 103g m1-1
FIG. 1. Debye Plot for sodium dodecylsulphate at 25°C in 0.03 M NaCI. sulphate is in good agreement with the value of 0.117 ml/g published by Parfitt and Wood (19). 3.2.
CALIBRATION
CHECKS
3.2.1. 12-Tungstosilicic Acid 12-Tungstosilicic acid in 3.0 M NaC1, as described by Kratohvil et al. (18), was used as a convenient standard for the aqueous system. 12-Tungstosilicic acid, which has a formula weight of 2879, was found to have a molecular weight of 2890 +_ 100, as determined in the described experimental arrangement. 3.2.2. Sodium Dodecylsulphate Sodium dodecylsulphate was used to test the calibration of the instrument for highermolecular-weight species. The results are shown in Fig. 1, where the method of presentation is that of Debye (20). The number of molecules per micelle so determined is 60 _+ 5, which is in good agreement with the results of Kodama et al. (21) and Huisman (22).
Measurement temperature (°C)
dn/dc
25
0.094
3.3. DYE I (C.I. ACID RED 41)
25 25 25 55 55
0.120 0.350 0.360 0.340 0.330
This dye is a tetrasulphonated dye molecule, and known to be monodisperse in aqueous solution (23). Therefore, at the limit of sensitivity and dye concentration used in this work, no significant excess scattering should be observed for a solution of the dye
(mUg)
Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
76
DATYNER, FLOWERS, AND PAILTHORPE 1-5-
A mathematically convenient, theoretical, probability distribution function which will demonstrate this is the Schultz-Zimm distribution. For a system of particles following the Schultz-Zimm distribution
1.0-
Kc x 105 R90
an+l
N w = 370 +- 50
P(r) -
05-
[10]
.r n.e -at,
F(n + 1)
C xlOSg rnl "I
where P(r) is the probability density for the occurrence of a particle of radius r and n and a are distribution coefficients. It may be shown that
FIG. 2. Dye II at 25°C.
]Qw
=
4/37TP
M
compared with solvent and this was found to be the case. 3.4. DYE I I
(C.I.
x A C I D R E D 88)
The degree of association of Dye II has been determined by diffusion (24) and by polarography (25) at 25°C and found to range between 2 and 5, depending upon concentration. At higher temperatures this dye dissociates and becomes a unimer at 50°C (26) (Fig. 2). Light-scattering measurements yield an aggregation number of 370 _+ 50. Frank (5) found that for Orange II (Dye III in Table II) the aggregation number varies with temperature and concentration and reaches a value of 110 at 5°C. Since Orange II has a sulphonated benzene ring while Dye II has a sulphonated naphthalene ring, it would be expected that Orange II would be more soluble in water and less aggregated than Dye II. The aggregation numbers determined by light-scattering and diffusion-based methods are quite different for Dye II. It must be remembered however that diffusion-based methods give a number average aggregation number, while light scattering gives a weight average aggregation number. Diffusion- and light-scattering-based determinations will only agree for a monodisperse system of particles. For a polydisperse system, on the other hand, the values will be quite different. Journalof Colloidand InterfaceScience, Vol. 74, No. 1, March 1980
Na
(n + 6)(n + 5)(n + 4) , a~ Na
]QD = 4/37rP ~
[11]
F/3 ,
a 3
[12]
where Nw = weight average aggregation number, No = diffusion-determined aggregation number, p = density of dye, and M = molecular weight of dye. Equations [11] and [12] may be readily solved for n and a since we know Nw and No. By substitution of n and a in Eq. [10] the distribution curve may be calculated for different values ofr and such a curve for Dye II is shown in Fig. 3.
-0-7-
('~
-0.6-
~
"r'p~ 1 -
°n+1 ~
rn
-or
e
for n = 1-170435 a = 0.196/.8!
"0-5" -04p(r) .0.3-0.2o.1-
o
lO
20
30
40
50
60
70
r
FIo. 3. Distribution of particle radius of Dye II
at 25°C.
77
DYESTUFF AGGREGATION
3.5. DYES IV aND V
I 10_
Dyes IV and V (Table II) were studied as examples of dye structures which fall midway between Dye II and the more complex dyes chosen for later study. Both of these dyes contain disulphonated naphthalene, which is hydrophilic, and n-butyl (Dye IV) and n-octyl (Dye V) substituted benzene rings which are hydrophobic. It was expected that these dyes would be surface active and possibly form micelles, but surface tension measurements showed that micelles do not form within the concentration range studied (<10-4 g m1-1) at 55°C. This temperature was chosen because at lower temperatures the dyes flocculated. 3.5.1. Dye I V
The results for Dye IV are given in Fig. 4. The aggregation number is 52 +_ 10. This dye has two sulphonate groups, one more than Dye II, and hence one would expect that Dye IV would be more readily soluble in water and have a lower aggregation number than Dye II. This was found to be the
K ~ c x105 R90
x x x
5~
= 52 +- 10
I
0
~
1'0 C x 105 g m1-1
FIG. 4. D y e IV in 0.03 M NaCI at 55°C.
case. Duff et al. (25), using polarography, determined a value of N = 3000, at 25°C, for Dye VI (Table II), which has one less sulphonate group than Dye IV and would be expected to be more highly aggregated than Dye IV. 3.5.2. Dye V
Dye V contains an n-octyl chain where Dye IV had an n-butyl chain. The results are given in Fig. 5. It can be seen from the
4- x
I
3
x x Ix
Kc: x 106
t
RgO 2
\\
x x
x
x
o
;
~
~
X
~
~
~
G
'~
C x 10 5 g n~ -1
FIG. 5. D y e V in 0.03 M N a C I at 55°C. - - - , T h e o r e t i c a l c u r v e . Journal of Colloid and Interface Science, Vol. 74, No. I, March 1980
78
DATYNER, FLOWERS, AND PAILTHORPE
results' profile that the particle size varies with concentration (9). Since there is no evidence of micelle formation (closed association) from surface tension measurements, an open association process must be taking place. The simplest open association model is one in which association proceeds stepwise with the same association constant at each step, viz: ~1 w = (M1)M~ (Ma)M,
+
k MII + M1 ~-- Mm, k Mn-1 + M1 ~-Mn. For such a distribution of particles the weight average molecular weight is
(M11)M~l + . . .
+ (Mll)M,1
which can be reduced to [Mw]2 = [MI]2 +
k
M~ + M I ~ MI,,
4k[Md2c,
where k is the molar association constant and c is the molar concentration of dye. Figure 5 shows the theoretical curve for k = 3 × 10TM 1 mo1-1 and 2A2 = 6 x 10-3 ml g-1. The fit is quite good considering that the same association constant was assumed for each step. Since aggregation varies with concentration, one can only calculate an aggregation number corresponding to a certain concentration. For example, to take a concentration midway in the range examined, say, 4 × 10-Sg m1-1, the aggregation number predicted by the model is not less than 2200, because the model underestimates the aggregation number at high dye concentrations. 4. CONCLUSION
The light-scattering method can be successfully applied to the study of dyestuff aggregation in aqueous solution when dyestuff aggregation is so high that it cannot be assessed in any other way. Dye II has an aggregation number of 370 at 25°C. Dye IV, which is of similar structure, but has an additional sulphonic acid group, has an aggregation number of 52 at 55°C. In Dye V, the increase in size of the alkyl chain from n-butyl (Dye IV) to n-octyl (Dye V) in the hydrophobic part of the molecule caused a dramatic increase in both the Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980
(M,)M~
+ • • • (Mn)Mn
+
...
+ • • •
degree of aggregation and the concentration dependence of aggregation. Aggregation numbers determined by lightscattering methods will only agree with diffusion determinations for a monodisperse system. When the solution is polydisperse, light-scattering measurements will always give values higher than those of diffusionbased methods. A combination of information obtained from light-scattering and diffusion measurements permits an estimation of the polydispersivity of the system. ACKNOWLEDGMENTS This work was supported by a grant from the Wool Research Trust Fund on the recommendation of the Australian Wool Corporation, to whom the authors wish to express their thanks, as well as to Mrs. J. Krawets and Messrs. G. Blythe and N. Buchsbaum for assistance with experimental work. REFERENCES 1. Peters, R. H., "Textile Chemistry," Vol. III. Elsevier, London, 1975. 2. Duff, D. G., and Giles, C. H., in " W a t e r " (F. Franks, Ed.), Vol. 4, p. 169. Plenum, New York, 1975. 3. Alexander, P., and Stacey, K. A., Proc. Roy. Soc. Ser. A 212, 274 (1952). 4. Vickerstaff, Th., "The Physical Chemistry of Dyeing," Oliver & Boyd, Edinburgh/London, 1954. 5. Frank, H. P., J. Colloid Sci. 12, 480 (1957). 6. Sivarajan, S. R., J. Indian Inst. Sci. 34, 75 (1952). 7. Sivarajan, S. R. ,J. Indian lnst. Sci. 36, 282 (1954). 8. Benderet, A., and Meyer, P., Bull. Soc. Chim. France 53 (1953). 9. Huglin, M. B., "Light Scattering from Polymer
DYESTUFF AGGREGATION
10. 11. 12. 13. 14. 15. 16. 17. 18.
Solutions," Academic Press, London/New York, 1972. Latimer, P., and Dudley Bryant, F., J. Opt. Soc. Amer. 55, 1554 (1965). Orofino, T. A., and Flory, P. J., J. Phys. Chem. 63, 283 (1959). Cantow, H. J., MakromoL Chem. 18-19, 367 (1956). Anacker, E. W., Rush, R. M., and Johnson, J. S., J. Phys. Chem. 68, 81 (1964). Coumou, D. J., Mackor, E. L., and Hijmans, J., Trans. Faraday Soc. 60, 1539 (1964). Matijevic, E., and Kerker, M., J. Amer. Chem. Soc. 81, 5560 (1959). Datyner, A., Delaney, M. J., and Holliger, H., Aust. J. Chem. 24, 1845 (1971). Pailthorpe, M. T., J. Phys. E. 8, 194 (1975). Kratohvil, J. P., Oppenheimer, L. E., and Kerker, M., J. Phys. Chem. 70, 2834 (1966).
79
19. Parfitt, G. D., and Wood, J. A., Kolloid Z. Z. Polym. 229, 27 (1969). 20. Debye, P., J. Colloid Sci. 3, 407 (1948). 21. Kodama, M., Kubota, Y., and Miura, M., Bull. Chem. Soc. Japan 45, 2953 (1972). 22. Huisman, H. F., Kon. Ned. Akad. Wetensch. Proc. Ser. B. 67, 388 (1964). 23. °Craven, B. R., and Datyner, A., in "Proceedings, IVth International Congress on Surface Active Substances," Vol. III, p. 545. 1964. 24. Craven, B. R., Datyner, A., and Kennedy, J. F., Aust. J. Chem. 24, 723 (1971). 25. Duff, D. G., Kirkwood, D. J., and Stevenson, D. M., J. Soc. Dyers Colourists 93, 303 (1977). 26. E1-Mariah, Afaf A. R., E1-Sabbagh, I. E., and Labib, A., Dokl. Akad. Nauk SSSR 234, 72 (1977).
Journal of Colloidand Interface Science, Vol. 74, No. 1, March1980