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Investigation of sodium copper-phthalocyanine-tetrasulfonate solutions by means of small-angle X-ray scattering
Investigation of Sodium Copper-phthalocyanine-tetrasulfonate Solutions by Means of Small-Angle X-ray Scattering O. K R A T K Y A~D H. O E L S C H L A E G E R Institut fi~r physikalische Chemie der Universit~t Graz, Graz, Austria
Received December 20, 1968; revised May 5, 1969 The size and shape of the associates of sodium Cu-phthalocyanine-tetrasulfonate have been investigated in aqueous solutions by means of small-angle X-ray scattering. Concentration, salt content, and temperature were varied. The smallest associates found consist of 2 molecules, the largest of more than 20 molecules. We propose oblique piles of different height for the shape of the associates. The heat of association has been estimated from the temperature dependence of the scattering curves.
III. PARTIAL SPECIFIC VOLUME
I. INTRODUCTION In aqueous solution most dyes form associates. Their size and shape depend on concentration, temperature, and electrolyte addition. Such associates have been investigated by light absorption (1-3), conductivity (4), etc. Our team was the first to study the problem by means of small-angle X-ray scattering (5-7). This paper deals with the investigation of sodium Cuphthalocyanine-tetrasulfonate (CuPC; Fig. I). With this dye Ahrens has found associates up to tetramers with the help of light absorption spectra (3). We expected to obtaia information also about larger associates.
This quantity is very important for the determination of particle weight by means of the small-angle X-ray scattering method. It has been determined at different concentrations of dye and salt from the densities of the solutions. For that purpose we employed a precision method developed in our working group (8), which allows the determination of the density of only 1 cm 3 of a liquid with a relative error of 10-6. The density of the solid substance was determined by the floating method in a bromoform-xylene mixture. Table I shows the results. We see that does not depend on dye concentration but on the salt content of the solution. We interpret this dependence as a volume contraction of the solution, caused by the electrolyre character of the dye. If the solvent already contains electrolytes, the contraction is diminished. The ~ of the solid dye is considerably larger than that of the dissolved dye. One reason may be that the molecules in the crystal cannot occupy an ideally dense lateral packing. This is also corroborated by the hygroscopy of the substance, which will take up about 10 % of water in air.
II. THE SAMPLE CuPC is a blue dye. Its formula is C32H12NsO12Na4Cu and its molecular weight M1 = 985. It is not known which one of the two equivalent positions the S08Na groups occupy. To prepare the solutions, the hygroscopic substance was dried at 100°C in vacuum over P~O5 and then weighed. At 20°C the solubility lies above 5 % in water and about 0.1% in NaC1 solution (0.8%). Concentrations are given in grams/100 ml solution or equivalently in per cent.
Journal of Colloid and Interface Science, VoI. 31, No. 4, December 1969 49O
SODIUM
COPPER-PHTHALOCYANINE-TETRASULFONATE
•
H
C
o
N
491
was determined with the help of a calibrated lupolen platelet (12). The smallest measured scattering angle waso20 = 0.028; that means a resolution of 550 A.
%
o
SOLUTIONS
V. A SHORT OUTLINE OF THE SMALLANGLE X-RAY SCATTERING METHOD
@ o Q5
Designations: t_ ,
,
.
,
O
i
. . . .
5
i
,
,
,
~0
,
, tg
'
v'
'-
A
FIG. 1. Sodium eopper-phthaloeyanine-tetrasulfonate (CuPC).
TABLE PARTIAL
SPECIFIC SALT
CNaCL
I
VOLUME
CONTENT
CCuPC
V AT I)IFFERENT AT
20°C
(gm/lO0 ml)
(gm/ lOO ml)
(ml/gm)
0 0 0.5 0.5 0
0.5 0.8 0.5 1.0 Solid
0.451 0.452 0.461 0.461 O.56
IV. EXPERIMENTAL METHODS The measuring device is that generally used in our working group: an X - r a y tube with Cu anode and line-shaped focus, which is shorter than the diameter of the tube window and therefore gives an "opening" line-shaped primary beam, furthermore a collimation system practically free of disturbing scattering (9), an automatic step scanning device (10), and a proportional counting tube with a pulse height discriminator set to Cu-Ka radiation (1.54 A). The whole equipment was installed in an airconditioned room at 21.3 ° =t= 0.3°C and 50 % ~ 5 % relative humidity. The solutions were contained in Mark capillaries; for measurements at higher temperature the capillaries were inserted into a euvet kept at constant temperature by an ultrathermostat. The scattering curves were corrected for the collimation error b y means of a computer program developed in our working group (11 ). The intensity of the primary beam P0
M-R-Mq--
particle weight (gram-mole-i). radius of gyration (Angstroms). weight of the cross section (gramo __1 mole -i. Angstrom ). R~ radius of gyration of the cross section o (Angstroms). a-distance between sample and registering plane (era). m-distance between the counter tube slit and the center of gravity of the primary beam in the registering plane (cm). 2 0 - - scattering angle 20 = m/a for small angles. P 0 - - intensity of 1 em of the line-shaped primary beam in the registering plane after attenuation by the sample. I0-scattering intensity at zero angle. l(m)--scattering intensity as a function of ~%.
D-c-zi-p2-Oi--
thickness of the sample (em). concentration of the solute (grams/ I00 ~). electron moles per 1 gm solute. electron moles per 1 ml solvent. partial specific volume of the solute (milliliters gm -i).
According to Guinier the angular dependence of the scattering intensity of particles can be approximated near zero angle by a Gaussian curve (13), In practice log I(m) is plotted versus m ~. The limiting slope tan a at m 2 = 0 gives the radius of gyration of the particle according to R = 0.644 a t x / / t ~ - a; o.644
=
Journal of Colloid and Interface Science,
Vol.
31, No.
4, December
1969
492
KRATKY AND OELSCHLAEGER
By means of the limiting tangent I0 is extrapolated, which is generally not accessible to direct measurement. The particle weight is obtained from the "absolute intensity," that is, the ratio of I0 and Po (14). M=
21 X 1023~ I0 cD(zl -- ~1 1'2)2 P6"
With polydisperse systems we obtain instead the weight average of M and the z-average
of R ~ (15). The cross section of elongated particles can be determined in a similar manner (16). This time log ( m I ( m ) ) is plotted against m2. The limiting slope tan a at m2 = 0 yields the radius of gyration of the cross section.
Rq = 0.526 a ~¢/t-~ a; 0.526 -- ~
~ ~l~-ge
By extrapolation to m2 = 0 we determine now ( m I ( m ) ) 0 and the particle weight per o 1 A length. 27.3 X 10~a ( m I ( m ) ) o Mq = cD (zl -- ~1 P~)2 Po The method is strictly valid only for infinitely long rods but gives satisfactory results also with much shorter particles (17).
b) The dissolved particles should be independent of each other with regard to position and orientation. Hence, generally a concentration series is measured and extrapolated to c = 0. With CuPC this method is not possible, because the size of the particles depends on the concentration. However, here the existence of a certain short-range order is probable, owing to electrostatic forces. This will lead to interparticle interferences and thus cause too small scattering intensities at smallest angles, as is seen clearly in Fig. 2. For that reason the measured particle weights and radii of gyration can be regarded only as lower limits. To keep the error low we have avoided dye concentrations above 1%. Some of our results (see Section IX B, C, E) seem to indicate that the error will not considerably exceed 15 %. We have not yet found a satisfactory correction method. We believe, however, that despite these limitations our measurements offer valuable information. Furthermore, the cross-section data will hardly be affected by interparticle interferences. c) In the solutions we have studied, associates of various size exist in equilibrium. Hence we could obtain only average values of M and R (15). We have tried to overcome the resulting difficulties by using model systems (20). d) The structure of the solvent should be independent of the dissolved substance.
VI. PREREQUISITES FOR THE EVALUATION OF THE X-RAY MEASUREMENTS The accuracy of the determination of mass, size, and shape of dissolved particles depends upon the extent to which certain prerequisites are fulfilled. a) The dissolved particles should have a uniform electron density. Otherwise, one will obtain the correct particle weight, but errors will arise in the determination of the radius of gyration and of the shape. Fluctuations of electron density in small ranges cause weak additional scattering, which can be eliminated by subtracting the constant tail end of the scattering curve (18, 19).
0.05
0.~
~
2~
FIG. 2. S c a t t e r i n g c u r v e s of C u P C in 0.3% N a C I s o l u t i o n , w i t h c o l l i m a t i o n error. O - - 0 . 4 % C u P C ,
A--0.6% CuPC, [:]--1% CuPC, O--1.5% CuPC (Nos. 21-24 of Table V).
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
SODIUM
COPPER-PHTIIALOCYANINE-TETRASULFONATE TABLE
INTERPOL&TED
c ~ c 1 (gm/100 ml) (ml/gm)
VALUES
II
OF V FOR DIFFERENT
0 0.451
0.1665 0,454
Comparing the partial specific volume of dissolved electrolytes with the value for the pure substance, we notice that the ions are surrounded by a shell of denser solvent. Since our dye associates are polyelectrolytes, this well-known effect will influence Io, M, R, and ~. If the solvate shells of different particles are dearly separated, the shell will be included in I0 and R. With regard to M, however, the variations of I0 and ~ cancel out (20). So only R is falsified. If the solvate shells penetrate each other, we shall obtain approximately correct values for R, but M will be inexact. To take account of this effect we have employed for different salt concentrations different values for ~ (Table II), obtained by interpolation of measured values (Table I). e) In solutions containing salt the ions are possibly accumulated in the surroundings of the associates. This would influence mainly M and the cross-section data. The effect should depend on the salt concentration. According to our measurements the dependence is not very distinct. We have therefore limited ourselves to a rather qualitative treatment (Section IX, D). Satisfactory theoretical and experimental methods applicable to the problems in Section YI, D and E have been developed recently (21) in connection with deoxyribonucleic acid. They hold generally for polyelectrolytes in electrolyte solutions. The application to our problems, however, encounters two obstacles. First, we are not in a position to prepare solutions differing in salt content and having constant size distribution of the associates. Secondly, it will be difficult to carry out the required osmotic experiments with particles as small as dye molecules. Nevertheless adaptation might be possible.
493
SOLUTIONS
SALT
CONCENTRATIONS
0.3 0.457
AT 20°C
0.5 0.461
0.7 0.465
VII. REMARKS ON TttE INTERPRETATION OF TIlE SCATTERING CURVES Figure 3 shows typical scattering curves in the Guinier plot. We notice a characteristic decrease of the innermost portion of the curves. This phenomenon has been discussed in Section VI, B. It is not found with salt concentrations above 0.3 %. This may have two reasons: the increasing anisotropy of the particles will bring about a decrease in interparticle interferences; in addition, the scattering curves of strongly anisotropic particles rise considerably in the inner portion and will compensate thereby the visible effect of interferences on the shape of the curves. In all cases the steepest possible tangent was used for the extrapolation to Io and for the determination of R. Since its position will depend somewhat on fluctuations in small ranges of the curves, we have also used the comparison of experimental curves with the best fitting theoretical scattering curves of our collection (mostly ellipsoids or elliptic cylinders) as a means to determine Io and R (17). Thus we could utilize a larger range of the scattering curve whereby the spread of the values has been reduced. For interpretation it is important that the scattering curves converge at larger angles. From this behavior we may conclude that the cross sections of the elongated particles do not vary widely. Figure 4 shows several examples of cross-section functions in the Guinier plot. At the highest concentration we get an ideal Guinier range; with the other measured series we must depend on the steepest tangent. V I I I . T A B L E S OF T H E
RESULTS
We have measured 53 scattering curves of solutions of CuPC. The following parameters were varied: dye concentration (0.05 %
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 196~
494
K R A T K Y AND O E L S C H L A E G E R
:I
2,5 "~-~
1.0
-2
0,0
1110 .3
2110 -3
3.10-~ ~
(2~,) 2
FIG. 3. Guinier plot of scattering curves, corrected for collimation error, of solutions containing 0.4% C u P C and (1)--0.7% NaC1, (2)--0.5% NaC1, (3)--0.3% NaC1, (4)--0.1665% NaC1, (5)-0% NaC1 (Nos. 53, 41, 21, 14, 3, from Tables I I I -
VII).
~'.1o-;-
2"~0 -3
6'.1o -3
F I G . 4 . Cross-section functions of solutions containing 0.4% C u P C and (1)--0.7% NaC1, (2)-0.5% NaC1, (3)--0.3% NaC1, (4)--0.1665% NaC1, (Nos. 53 41, 21, 14 from Tables I V - V I I ) ; Guinier plot.
TABLE III RESULTS OF THE X-RAY MEASUREMENTS: 0% NACL
No.
T (°C)
U~
•-~
(gm/lO0ml)
CCuPC
M
1 2 3 4 5 6 7 8 9 10 11
21.2
0
20.7
0
0.0987 0.245 0.493 0.987 2.16 1.0 0.8 1.0 0.8 1.0 0.8
1830 2170 2490 3780 6570 3510 3170 3020 2900 2960 2610
35.0 50.0
~
1.86 2.20 2.53 3.84 6.67 3.56 3.22 3.07 2.94 3.00 2.65
3.46 4.82 6.42 14.8 44.5 12.7 10.4 9.4 8.7 9.0 7.0
R (A)
R: (A9
9.0 9.0 9.2 10.2 12.7 9.6 9.3 9.4 9.1 9.5 9.1
81 81 85 104 161 92.0 86.5 88.5 83.0 90.0 83.0
Mq
Rq (A)
T A B L E IV RESULTS
OF THE X-RAY
0.1665% N A C ~ ,
MEASUREMENTS:
No.
T (°C)
~NaCl (gm/lO0 ml)
CCuPG (gm/lO0 ml)
M
i
~
R (A)
R~ (~2)
Mq
Rq (A)
12 12F 13 13F 14 14F 15 15F 16 16F 17 17F
21.2
0.1665
0.1
3470 3340 4080 4020 5090 4830 5690 5330 7050 6680 8010 7990
3.52 3.39 4.14 4.08 5.17 4.90 5.78 5.41 7.16 6.78 8.13 8.11
12.4 11.5 17.2 16.6 26.8 24.0 33.5 29.2 51.3 46.0 66.0 65.7
10.3 10.2 10.2 10.1 11.5 10.8 11.8 11.6 12.9 12.3 14.2 14.7
106 104 104 102 132 117 139 135 166 151 202 216
142 ---158 -145 -172 -189 --
6.3 ---6.2 -5.8 -6.3 -6.8 --
0.2 0.4 0.6 1.0 1.5
Journal of Colloid and Interface Science, Vol. 31, No. 4, D e c e m b e r 1969
495
SODIUM COPPEt~-PHTHALOCYANINE-TETRASULFONATE SOLUTIONS TABLE V ~:~ESULTS OF THE X-RAY MEASURE~IENTS:0.3% NACL No.
T (°C) (gm/IO0 z~actmO (gin~190 cc.Pcml)
18 18F 19 19F 20 20F 21 21F 22 22F 23 23F 24 24F 25 26 27 28 29 30 31 32 33 34 35 36 37
21.2
0.3
0.05 0.1 0.2 0.4 0.6 1.0 1.5
21.5 35.0 50.0 20.7 35.0 50.0 21.2
1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0
M
~
~
R (A)
R2 (~2)
~q
Rq (3)
5250 5000 4990 5300 6670 6350 7950 7720 8690 8590 10050 9750 10640 10440 9950 8960 8270 6900 6010 5710 8870 8180 6800 5910 6010 5020 9460
5.33 5.08 5.07 5.38 6.77 6.45 8.07 7.84 8.82 8.72 10.2 9.9 10.8 10.6 10.1 9.1 8.4 7.0 6.1 5.8 9.0 8.3 6.9 6.0 6.1 5.1 9.6
28.4 25.8 25.7 28.9 45.9 41.6 65.1 61.5 77.8 76.1 104 98.0 116 112 102 83,3 70.7 49,2 36.6 33.2 81.6 68.3 47.8 35.5 36.6 26.4 92.3
12.0 11.7 12.0 12.1 13.5 11.8 13.9 13.3 14.5 14.2 15.2 14.8 15.2 15.6 15.4 15.0 13.5 10.6 9.7 9.2 14.4 14.6 12.4 11.7 12.2 11.1 15.0
144 137 144 146 182 139 193 177 210 202 231 219 231 243 237 225 182 112 94 84.5 207 213 154 137 149 123 225
----232 -204 -236 -202 -200 -221 219 187 186 197 171 197 197 183 181 178 165 193
----7.05 -6.8 --= 7.4 -6.9
to 2 % ) , NaC1 c o n c e n t r a t i o n (0 to 0 . 7 % ) , a n d t e m p e r a t u r e (20 ° to 50°C). I n T a b l e s I I I to V I I , each n u m b e r corres p o n d s to a s c a t t e r i n g curve. T h e letter " F " after t h e n u m b e r m e a n s t h a t t h e values of this line h a v e b e e n o b t a i n e d b y comparison w i t h theoretical s c a t t e r i n g curves. T h e t e m p e r a t u r e T is g i v e n i n °C, the concent r a t i o n c i n g r a m s / 1 0 0 ml or e q u i v a l e n t l y i n o p e r cent, R a n d Rq i n A n g s t r o m s . g is defined b y g = M / M 1 . R a n d M are of course average values a n d will be m a r k e d b y a b a r w h e n confusion is possible. P a r t i c u l a r p a r t i cles consisting of i molecules of dye are d e s i g n a t e d b y a s u b s c r i p t i, m e a n i n g t h e degree of association. M # M 1 = i. ~ is therefore t h e m e a n degree of association. W e h a v e a l r e a d y m e n t i o n e d which sorts of m e a n v a l u e s will occur ( S e c t i o n V ) . P a r t i c u l a r d e s i g n a t i o n s w o u l d be t r o u b l e s o m e . M s is
7,0 -7.3 7.6 6.6 7.0 6.9 6.5 6.7 6.7 6.4 6.3 6,3 6.0 6.8
t h e particle weight per 1 A length. A b a r i n a line m e a n s t h a t t h e v a l u e has n o t b e e n d e t e r m i n e d . I f a v a l u e is left o u t t h e figure f r o m t h e p r e v i o u s line still holds. N u m b e r s 1-5 i n T a b l e I I I are from L e d w i n k a (6) a n d h a v e b e e n slightly corrected according to reference 22. IX. DISCUSSION OF THE RESULTS A. PREI~IMINAR¥ REMAI~K W e do n o t a i m a t a n u n a m i b i g u o u s a n d final i n t e r p r e t a t i o n . T h e following considera t i o n s will o n l y b r i n g some order i n t o t h e r a t h e r i n v o l v e d p h e n o m e n a . T o this e n d we use t h e m o d e l system, developed i n referenee 20, which should serve our purpose, a l t h o u g h it is n o t q u i t e suitable. A t first we a s s u m e t h a t t h e associates h a v e t h e shape of o b l i q u e piles (Fig. 5). This is suggested b y t h e weak v a r i a t i o n of t h e cross section of t h e
Journal of Colloid and Interface Science, ¥ol. 31, No, 4, December 1969
496
KRATKY AND OELSCHLAEGER TABLE VI RESULTS OF THE X-RAY MEASUREMENTS:0.5% I~ACL
No.
T (°c)
38 38F 39 39F 4O 40F 41 41F 42 42F 43 43F 44 45 46 47 48 49
21.2
(gm/lOO ~ )
CCuPC
M
0.03
9950 10050 10440 10050 10640 10540 13300 13200 15960 14870 19210 18820 15460 13690 12210 10640 9950 8270
0.5
0.1 0.2 0.4 0.6 1.0 1.0 0.5 1.0 0.5 1.0 0.5
20.7
35.0 50.0
TABLE
~
10.1 10.2 10.6 10.2 10.8 10.7 13.5 13.4 16.2 15.1 19.5 19.1 15.7 13.9 12.4 10.8 10.1 8.4
VII
T
50 51 52 53
21.2
CNaCL
CeuPC
0.7
0.1 0.15 0.25 0.4
(gm/lO0 ml) (gm/lO0 ml)
Rq
Mq
(~)
247 245 254 263
7.7 7.6 7.8 7.9
associates (see S e c t i o n I X , D ) a n d b y t h e c r y s t a l s t r u c t u r e of C u - p h t h a l o c y a n i n e (23).
15.7 17.3 15.9 17.6 16.9 19.9 19.2 26.5 20.8 27.7 25.2
247
--
--
299 253 310 286 396 369
220 -191 -205 -201 -240 -227 211 211 192 192 192
7.2 -7.1 -7.0 -6.8 -7.4 -7.3 7.1 7.1 6.7 6.7 6.7
702
433 767 635 449 384 331 282 269 213
19.6 18.2 16.8 16.4 14.6
Mq
Rq (A)
210
7.3
= 4 Kc +
fb2.
[2]
( H e r e K is t h e association c o n s t a n t , c~ t h e n u m b e r c o n c e n t r a t i o n of associates consistin g of i d y e molecules, n t h e degree of assoc i a t i o n of a possible s u b u n i t ) (20). D e v i a tions f r o m a s t r a i g h t line i n d i c a t e t h a t t h e a s s o ci at i o n c o n s t a n t s are e i t h e r n o t e q u a l or n o t c o n s t a n t . I n p r i n c i p l e all t h e successive a s s o ci at i o n c o n s t a n t s could be o b t a i n e d b y t h e m e t h o d of S t e i n e r (24). H o w e v e r , t h e
/J
]3. CONCENTRATION DEPENDENCE OF THE DEGREE OF ASSOCIATION
J
W e p l o t ~ a g a i n s t c (Figs. 6, 7). I f all a ssoc ia ti o n c o n s t a n t s of t h e f o r m
ki~ - ci+~
R2 (A~)
21.2
-2
0.7% NAC~ (oc)
102 104 112 104 116 114 182 180 264 227 379 364 245 193 154 116 102 70.8
R (A)
the equation
l~ESULTS OF THE X - R A Y MEASUREMENTS:
No.
~
J J
[1]
CiCk
are e q u a l ( S c h u l z - F l o r y d i s t r i b u t i o n ) , this p l o t yields a s t r a i g h t line, t h e slope of w h i c h gives t h e a s s o c i a t i o n c o n s t a n t s , a c c o r d i n g to
FIG. 5. Proposed model of CuPC associates. The lines are the projection of the planes of molecules.
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
SODIUM
COPPER-PHTHALOCYANINE-TETRASULFONATE
SOLUTIONS
497
determination of a greater number of con- curve cannot be extrapolated readily to stants would require very exact measure- c = 0 and g = 2. The reason might be t h a t ments. We resort therefore to qualitative the measurements at concentrations below considerations and regard the slope of the 0.1% are not very reliable. For the shape of curves as a measure for the actual associa- the curve we assume therefore a straight tion constants. line. 0% NaCl (Table I I I ; Figs. 6 and 7). The 0.7% NaC1 (Table V I I ) . The scattering extrapolation to c = 0 yields a degree of curves of this series rise so steeply at the association of about 2. This agrees with the smallest angles that neither M nor R could results of Ahrens (3), who determined, by be determined. Certainly M and R are means of light absorption measurements, larger than in the other series and show the that a significant amount of monomer exists usual concentration dependence. only at very low concentrations (below 0.01%). This agreement is one of the bases C . R A D I U S OF G Y R A T I O N AND D E G R E E OF ASSOCIATION of our paper (see Section VI, B). At higher concentrations he finds an equilibrium beFigures 8-11 show the connection between tween di- and tetramers, which is, according /~2 and ~2 for different salt concentrations. to our measurements, not very well deFigure 12 combines the data of Figs. 8-ii. marcated. Higher associates than tetramers We again assume oblique piles with a are certainly present. We believe that the Sehulz-Flory distribution. In this ease the absorption spectra of tetramers and higher equation from reference 20 holds: associates show no very pronounced differences and that at higher dye concentra= ~ +~_ ~ 2n2 + 1 . [31 tions the accuracy of the absorption experi3 ments is limited. (here n is the degree of association of a subFrom the curvature we may conclude that unit, R1 the radius of gyration of the the association "constants" rise with increasing concentration. This could be con- monomer, a the distance between the nected with the facts that electrolyte addi- centers of adjacent molecules; see Fig. 5). If the system were monodisperse, the followtion strongly enhances the association constants and that the dye itself is a strong ing equation would be valid: electrolyte. The slopes of the following 2 R 2 = R12 + a (i2 _ i ) . [41 curves seem to support this point of view. 0.1665% NaCl (Table IV; Fig. 7); o 0.3% NaC1 (Table V; Fig. 7). The curves From [3] we get a = 2.5 to 2.8 A, from [4] show a much greater slope, corresponding to a = 4.3 to 4.8 A. The real distribution is greater association constants. We can as- probably somewhat narrower t h a n a Schulzsume that CuPC will behave more ideally at Flory distribution, but certainly not monohigher salt concentrations. The shape of the disperse. We therefore regard a value of curve indicates that with larger associ- a , = 3 to 3.5 A as the most probable one. ates the association constants K ~ become R1 is also available from [3]. We put n = 2 smaller. This would mean that the distribu- according to the results of Ahrens and obtion of the degrees of association would be tain R1 = 8.7 A. We shall return to these narrower than a Schulz-Flory distribution. values later. However, we must not forget t h a t the shape I t is noticeable that the four straight lines of the curves is affected b y interparticle of Fig. 12 are not too far from forming a interferences (see Section VI, B). common curve. This means t h a t all the 0.5% NaCl (Table VI; Fig. 7). This possible changes, caused by different conJournal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
498
KRATKY AND OELSCHLAEGER possible errors are limited to a tolerable order of magnitude. 20
D. ---,* c ['/o]
1
CROSS SECTION AND SHAPE OF THE ASSOCIATES
2
£~G. 6. Concentration dependence of the degree of association of CuPC in water (Table I I I , Nos. 1-7).
A c c o r d i n g to M i t t e l b a c h (17) cross-section d a t a f r o m cylindrical bodies are sufficiently exact, if R/Rq > 1.5. W i t h regard to °/ 200
4OO T2
//
T
S
j
2<
/ / 0.5 % NaC{
I
/
V
//o 20C
10C
y//~ /
/
r T2 0.5
I -.--,, c [°/ol
FZG. 7. Concentration dependence of the degree of association of CuPC at different salt concentrations (all measurements at 21 ° 4- 0.3°C from Tables III-VI).
5O
FIG. 9. Relation between mean degree of association and mean radius of gyration: 0.1665% NaCI (Table', IV).
o Z(
20C 10C
J
oo
_._,T 2
lb0 ..... T 2
5O
FIG. 8. Relation between mean degree of association and mean radius of gyration: 0% N a C 1 (Table III).
Fin. 10. Relation between mean degree of association and mean radius of gyration: 0.3% NaC1 (Table V). r
centrations of dye and salt and b y t e m p e r a t u r e variations (concerning interparticle interferences, extension and composition of t h e solvate shells, electrostatic association, shape of the associates, size distribution), c o m p e n s a t e each other to a degree with regard to the relation b e t w e e n / ~ and ~2, or shift t h e p o i n t along the curve only. This plot seems to increase the probability t h a t
~OOili L
----*T ~ 2a0
l?ie. 11. Relation between mean degree of association and mean radius of gyration: 0.5% NaCI (Table VI).
Journal of Colloid and Interface Science, VoL 31, No. 4, December 1969
SODIUM C O P P E R - P H T H A L O C Y A N I N E - T ETRA SU LFO N A TE SOLUTIONS
the mean value character of R we choose instead a ratio of R/Rq > 2. With this restriction we obtain values of Mq from 200 to 250 (see tables), corresponding to Rq between 7 and 7.8 A (determined according to Fig. 13). We believe that the variation is small enough to be explained by a modification of the proposed model. One possibility would be the accumulation of ions in the surroundings of an associate. We are not in the position to decide, however, whether Mq is correlated with the salt concentration or with the degree of association. We shall now give a review of all available data concerning cross section and shape. R ~ W e use 7 A < R~ < 7.8 A. Mq---We use 200 < M~ < 250. Rt--may be estimated from the structure of the molecule. For this purpose the electron density differences of particular regions
of the molecule against water had to be estimated. For that we needed the densities of these regions, essentially that of the central atom, of the surrounding organic groups, and of the sulfonie acid groups with its sodium ions. These data can be computed from the S of dissolved CuPC, of the solid Cu-phthalocyanine, and of the metalfree phthalocyauine. The latter data we took from reference 25. Thus we have obtained o R1 > 7.5 A. The uncertainty towards higher values is due to the fact that the position of the sodium ions and the extension of the soivate shells are not known. Besides, RI is determined mainly by the central distance of the sulfonate groups (8.5 A). RI--8.7 A from Fig. 12. a--is obtained from MI/Ma. 3.9 & < o a < 4.9A. a*--has been estimated from the dependence between/~2 and ~2 (Section IX, C; Fig.
~.
12). 3 ~ < a* < 3.5
50[
T
/.
100
200
Fro. 12. Relation between m e a n degree of association and mean radius of gyration for all investi-
gated salt concentrations; data were compiled from Figs. 8-11. I
499
d--is the distance between the planes of adjacent molecules (see Fig. 5). The structure of Cu-phthaloeyanine crystals shows that d is certainly larger than 3.4 ~_ (23), because the CuPC molecule carries charged groups, which furthermore do not lie in the plane of the molecule, d--can also be estimated from 9, if the area F of the single molecule is estimated from the molecular structure. This procedure yields F = 190 to 230 ~2 and (with ~ = 0.46 mI/ o 2 gm) d = 4 t o 3 . 3 A . Between the various quantities the following relations are valid: 2
R22 = i 62
R
12 + ~a - , .
M1 --;
~..~
a = M~ 22
100
200 ~
d
Mq
-
a
FIG. 13. I~elation between radius of gyration and weight of the cross section (Mq and Rq) at different salt concentrations: X--0.1665% NaC1, 0--0.3% NaC1, A--0.5% NaC1, [2--0.7% NaC1 (all measurements at 21 ° =t= 0.3°C from Tables IV-VII).
[5]
[61
cos ~;
[7]
( R ~ 2 _ cos 2 ~ + N] 2
i
Is]
We shall now calculate our model (Fig. 5). We shall consider a* later.
Journal of Colloid and Inter/ace Science,
Vol.
31, N o .
4 D e c e m b e r 1969
500
KRATKY AND OELSCHLAEGER
d>3.4A ) 3.9A < a < 4.92~
[71 c o s ~ > 0 . 7 9 } > [S]> ~ < 8 . 4 A o 7.8A > Rq > 7A 3.9A < a < 4.9AJ
With this calculation we have kept in mind that Mq and Rq, resp. a and Rq, are correlated, as is shown by Fig. 13. R~ = 7 correspondsotO a = 4.9 A and Rq = 7.8 -~ to a = 3.9 A. The value for R2 obtained in this way agrees l~oorly with the directly measured one (9 A) (TableoIII). From R.~ = 9 A we obtain R1 = 8.8 A, according to [3] or from Fig. 12 R1 = 8.7 A, with is of course practically identical but which is too large compared with the value estimated from the molecular structure (R~ > 7.5 A). This will mean either that the central distance of the sodium ions is about 20 A or that the distance between the molecule centers of the o dimer is at least 6.5 A. It seems more probable that in salt-free solutions particularly pronounced hydrate shells and perhaps several larger associates formed by electrostatic forces are present. We have still to consider a*. The difference between a = 3.9 to 4.9 A and a* = 3 to 3.5 ~_ requires a modification of the proposed model, a results from M1 and Mq, a* from the relation b e t w e e n / ~ and ~2. We assume that a* is too small. Hence we infer either that the associates are bent or that lateral association may occur (Fig. 14). Besides, we see that the curve in Fig. 12 gets flatter with increasing ~. This may
>
ever, with the shape of the concentration dependence. With larger associates the interparticle interferences influence R more strongly than M. Lateral association occurs more frequently with larger associates. This is confirmed by the fact that, in the case of precipitation, lateral association becomes evident. Besides, this would also explain the fact that Mq and Rq are somewhat enhanced with increasing degree of association. E. TEMPERATURE DEPENDENCE OF THE SCATTERING CURVES AND HEAT OF ASSOCIATION
Dye associates become smaller with increasing temperature and decreasing concentration (Fig. 15). Thereby M and R decrease too. All in all, the intensity is reduced in the whole inner portion of the scattering curve. By comparing the concentration dependence and the temperature dependence we can estimate the heat of association for the single association step (20). In other words, under certain restrictions (see reference 20), it will be possible to compensate a change of
100I %
lnean:
The larger associates are less polydisperse than the smaller ones. This disagrees, how/ /
/ -
-*~
-
/.
/ \\ (
s
/ _
f
--
so
2 . 1 0 *2
.
/.-10 -2
6.1@2 ~
2..0,
FI~. 15. Comparison of temperature dependence and concentration dependence of scattering curves, with collimation error, of CuPC in 0.3% NaCl: (1)--1.0% CuPC, 20.7°C; (2)--0.5%, 20.7°C;
(s)--1.0%, 35°c; (4)--0.5%, 35°c; (5)--1.0%, FIG. 14. Possible shape of larger associates.
50°C; (6)--0.5%, 50°C; (Nos. 31-36 of Table V).
Journal of Colloid and Interface Science, V o l . 31, N o . 4, D e c e m b e r 1969
SODIUM COPPER-PHTHALOCYANINE-TETRASULFONATE SOLUTIONS temperature by a change of concentration in such a way that the distribution of the degree of association remains unchanged. This means, furthermore, that the scattering curve, divided by c, will also remain unchanged whether it is corrected for collimation error or not. We need therefore two scattering curves, which coincide if referred to the same concentration. From the two pairs (c, T) and (c', T') the heat of association W1 is obtained according to [9]. in (c/c') (T - T')
A In c -
AT
W1 -
R T ~"
[9]
Such pairs (c, T) and (c', T') are found either directly or better yet by interpolation from measured series. For this purpose we have measured four series of scattering curves at different salt concentrations. Each series consists of two concentrations, each one measured at three temperatures. These are: Nos. 6-11 in Table III, nos. 25-36 in Table V, and Nos. 44-49 in Table VI. One of these series of scattering curves (with collimation error and referred to the same concentration) is shown in Fig. 8. For the evaluation we assume that S does not depend on temperature. To determine the heat of association we compare the temperature dependence at two concentrations at a fixed scattering angle. The temperature is plotted versus the scattering intensity. For each concentration we obtain a curve. In Fig. 8 such a pair of curves is drawn. The abscissa difference between the two curves is the AT of the above formula. For each series we deterrrfined AT at several scattering angles. Under ideal conditions the same value would be shown all along the curves. But practically too small a AT is obtained in the inner portion, since the curve is more falsified there at higher concentrations. In the subsequent range, AT is approximately constant. This range is used for the determination of AT. At still larger angles the curves converge, so that AT cannot be determined there.
501
From the values of AT obtained in this way we get the following values for W1 : - - W1 = 5-7 keal/mole
CNaC1 = 0 ~0
0.3 % 0.3 % 0.5 %
11 kcal/mole 12 keal/mole 13 keal/mole
The first value does not fit into the picture. This is connected with the fact that the association constants depend considerably on the dye content, if the solution does not contain any other electrolytes. This point has been discussed above (Section IX, ]3). The other values agree within the margin of error. Thus we obtain: - W 1 = 12 =h 1 keN/mole. We should mention, however, that this value gives only an order of magnitude, because our method is rather sensitive to errors and furthermore the assumptions used in reference 20 are not completely appropriate. We cannot exclude therefore systematic deviations, despite the good agreement at different salt concentrations. Besides, a qualitative estimation of the influence of interparticle interferences upon the inner portion of the scattering curves appears possible, since here scattering curves of two systems with the same distribution of the degrees of association but different concentrations can be measured. In this method, however, the temperature dependence of the interparticle interferences is not taken into consideration. In any case, our measurements seem to corroborate our assumption that the error caused by interparticle interferences will not exceed 15% for the determination of the degree of association. ACKNOWLEDGMENT We wish to t h a n k t h e C I B A AG, Basel, for suggesting this i n v e s t i g a t i o n , as well as for its s u p p o r t and for the s u p p l y of t h e purified samples. We wish also to t h a n k t h e Osterreichischer F o r s c h u n g s r a t for help w i t h t h e a p p a r a t u s . REFERENCES 1.
I~A~BINOVITCI~,E., A.ND EPSTEIN, L., J . Am. Chem. Soc. 63, 69 (1941).
Journal of Colloid and Interface ,%ience, Vol. 31, No. 4, December 19G9
502
KRATKY AND 0ELSCHLAEGER
2. SCEEIDE, G., Z. Elektrochem. 52, 283 (1948). 3. AHRENS, U., Dissertation, Philipps-Universitiit, Marburg, 1962. 4. MILICEVIC, B., AND EIGENMANN, G., Helv. Chim. Aeta 47, 1039 (1964). 5. KRATKY, 0., MITTELBACH, 1°., PILZ, I., SCHMITZ, ~o. j., AND WAWRA, H., unpublished. 6. LEDWINKA, H., Dissertation, University of Graz, Austria, 1966. 7. KRATKY, O., LEDWINKA, H., AND PILZ, I., Ber. Bunsenger. physikal. Chemic 70, 904 (1966); Makrom. Chem. 105, 171 (1967); KRATKY, O., I°ILZ, I., AND LEDWINKA, H., Monatsh. Chem. 98, 227 (1967). 8. STAmNGEI~, H., LEOeOLD, H., AND KaATlZY, 0., Monatsh. Chem. 98, 436 (1967); KRATKY, O., LEOPOLD, H., AND STABINGER, H., Z. Angew. Physik 27, 273 (1969). 9. KI~ATI~Y, 0., Z. Elektroehem. 58, 49 (1954); ibid. 62, 56 (1958); KI~ATI~y,0., AND SKAI~A, Z., ibid. 62, 73 (1958). 10. KI~ATKY, CI-I., AND KR~TKY, 0., Z. Instrumentenkunde 72, 302 (1964); LEOI~OLD,I~I., Elektronil~ 14, 359 (1965). 11. I{RA~ICV,O., POl~OD, G., ANI) SKALA, Z., Acta Phys. Austriaca 13, 76 (1960); HEINE, S., AND ROPPEnT, J., ibid. 15, 148 (1962); HEINE, S., ibid. 16, 144 (1963). 12. I4~RATKY, O., PILZ, I., AND SCIIMITZ, 1°. J., J. Colloid and Interface Sci. 9.1, 24 (1966); PILZ, I., AND I{RATXY, 0., ibid. 9.4, 211 (1967). Pilz, I., ibid. 30, 140 (1969).
13. GUIN~ER, A., AND FOURN]~% G., "Small Angle Scattering of X-rays." Wiley, !~ew York, and Chapman & Hall, London, 1955. 14. KnATKY, O., Poaon, G., AND KAHovEe, L., Z. Elektrochem. 55, 53 (1951). 15. MITTELBACtt, P., AND POROD, G., Kolloid-Z. 202, 46 (1965). 16. •RATKY, O., AND POROD, G., Acta Phys. Austriaca 2, 133 (1948); POnOE, G., ibid. 2, 255 (1948) ; KR~TKY, 0., AND POROD, G , in H. A. Stuart, ed., "Die Physik der Hochpolymeren," Vol. II, p. 515. Springer Verlag, Berlin, 1953. 17. MITTELDACIL P., Acta Phys. Austriaea 19, 57 (1964). 18. LUZZATI, V., WITZ, J., AND NICOLAIEF].~',A., J. Mol. Biol. 3, 367 (1961). 19. STUI-IRMANN, H. •., AND KIRSTE, B.. G., Z. Physik. Chemi. (Leipzig) IN. F.] 46, 247 (1965); ibid. 56, 334 (1967). 20. OELSCI-ILAEGEI~,H., J. Colloid and Interface Sci. 31, 503 [1969). 21. CASASSA, E. F., ANn EISENSEI~G, H., Advan. Protein Chem. 19, 287 (1964); EISENDERO, l-I., AND COHEN, G., J. Mol. Biol. 37, 355 (1968). 22. ZIPPER, P., Dissertation, University of Graz, Austria, 1969. 23. HONIGMANN, B., LENN]~, I-I.-U., AND SCHR6DEL, R., Z. Krist. 122, 185 (1965). 24. STEINER, R. F., Arch. Biochem. Biophys. 39, 334 (1952). 25. RomNsoN, J. M., J. Chem. Soc. (London) 1936, 615.
Journal of Colloidand Interface Science, VoL 31, No. 4, December1969
Received December 20, 1968; revised May 5, 1969 The size and shape of the associates of sodium Cu-phthalocyanine-tetrasulfonate have been investigated in aqueous solutions by means of small-angle X-ray scattering. Concentration, salt content, and temperature were varied. The smallest associates found consist of 2 molecules, the largest of more than 20 molecules. We propose oblique piles of different height for the shape of the associates. The heat of association has been estimated from the temperature dependence of the scattering curves.
III. PARTIAL SPECIFIC VOLUME
I. INTRODUCTION In aqueous solution most dyes form associates. Their size and shape depend on concentration, temperature, and electrolyte addition. Such associates have been investigated by light absorption (1-3), conductivity (4), etc. Our team was the first to study the problem by means of small-angle X-ray scattering (5-7). This paper deals with the investigation of sodium Cuphthalocyanine-tetrasulfonate (CuPC; Fig. I). With this dye Ahrens has found associates up to tetramers with the help of light absorption spectra (3). We expected to obtaia information also about larger associates.
This quantity is very important for the determination of particle weight by means of the small-angle X-ray scattering method. It has been determined at different concentrations of dye and salt from the densities of the solutions. For that purpose we employed a precision method developed in our working group (8), which allows the determination of the density of only 1 cm 3 of a liquid with a relative error of 10-6. The density of the solid substance was determined by the floating method in a bromoform-xylene mixture. Table I shows the results. We see that does not depend on dye concentration but on the salt content of the solution. We interpret this dependence as a volume contraction of the solution, caused by the electrolyre character of the dye. If the solvent already contains electrolytes, the contraction is diminished. The ~ of the solid dye is considerably larger than that of the dissolved dye. One reason may be that the molecules in the crystal cannot occupy an ideally dense lateral packing. This is also corroborated by the hygroscopy of the substance, which will take up about 10 % of water in air.
II. THE SAMPLE CuPC is a blue dye. Its formula is C32H12NsO12Na4Cu and its molecular weight M1 = 985. It is not known which one of the two equivalent positions the S08Na groups occupy. To prepare the solutions, the hygroscopic substance was dried at 100°C in vacuum over P~O5 and then weighed. At 20°C the solubility lies above 5 % in water and about 0.1% in NaC1 solution (0.8%). Concentrations are given in grams/100 ml solution or equivalently in per cent.
Journal of Colloid and Interface Science, VoI. 31, No. 4, December 1969 49O
SODIUM
COPPER-PHTHALOCYANINE-TETRASULFONATE
•
H
C
o
N
491
was determined with the help of a calibrated lupolen platelet (12). The smallest measured scattering angle waso20 = 0.028; that means a resolution of 550 A.
%
o
SOLUTIONS
V. A SHORT OUTLINE OF THE SMALLANGLE X-RAY SCATTERING METHOD
@ o Q5
Designations: t_ ,
,
.
,
O
i
. . . .
5
i
,
,
,
~0
,
, tg
'
v'
'-
A
FIG. 1. Sodium eopper-phthaloeyanine-tetrasulfonate (CuPC).
TABLE PARTIAL
SPECIFIC SALT
CNaCL
I
VOLUME
CONTENT
CCuPC
V AT I)IFFERENT AT
20°C
(gm/lO0 ml)
(gm/ lOO ml)
(ml/gm)
0 0 0.5 0.5 0
0.5 0.8 0.5 1.0 Solid
0.451 0.452 0.461 0.461 O.56
IV. EXPERIMENTAL METHODS The measuring device is that generally used in our working group: an X - r a y tube with Cu anode and line-shaped focus, which is shorter than the diameter of the tube window and therefore gives an "opening" line-shaped primary beam, furthermore a collimation system practically free of disturbing scattering (9), an automatic step scanning device (10), and a proportional counting tube with a pulse height discriminator set to Cu-Ka radiation (1.54 A). The whole equipment was installed in an airconditioned room at 21.3 ° =t= 0.3°C and 50 % ~ 5 % relative humidity. The solutions were contained in Mark capillaries; for measurements at higher temperature the capillaries were inserted into a euvet kept at constant temperature by an ultrathermostat. The scattering curves were corrected for the collimation error b y means of a computer program developed in our working group (11 ). The intensity of the primary beam P0
M-R-Mq--
particle weight (gram-mole-i). radius of gyration (Angstroms). weight of the cross section (gramo __1 mole -i. Angstrom ). R~ radius of gyration of the cross section o (Angstroms). a-distance between sample and registering plane (era). m-distance between the counter tube slit and the center of gravity of the primary beam in the registering plane (cm). 2 0 - - scattering angle 20 = m/a for small angles. P 0 - - intensity of 1 em of the line-shaped primary beam in the registering plane after attenuation by the sample. I0-scattering intensity at zero angle. l(m)--scattering intensity as a function of ~%.
D-c-zi-p2-Oi--
thickness of the sample (em). concentration of the solute (grams/ I00 ~). electron moles per 1 gm solute. electron moles per 1 ml solvent. partial specific volume of the solute (milliliters gm -i).
According to Guinier the angular dependence of the scattering intensity of particles can be approximated near zero angle by a Gaussian curve (13), In practice log I(m) is plotted versus m ~. The limiting slope tan a at m 2 = 0 gives the radius of gyration of the particle according to R = 0.644 a t x / / t ~ - a; o.644
=
Journal of Colloid and Interface Science,
Vol.
31, No.
4, December
1969
492
KRATKY AND OELSCHLAEGER
By means of the limiting tangent I0 is extrapolated, which is generally not accessible to direct measurement. The particle weight is obtained from the "absolute intensity," that is, the ratio of I0 and Po (14). M=
21 X 1023~ I0 cD(zl -- ~1 1'2)2 P6"
With polydisperse systems we obtain instead the weight average of M and the z-average
of R ~ (15). The cross section of elongated particles can be determined in a similar manner (16). This time log ( m I ( m ) ) is plotted against m2. The limiting slope tan a at m2 = 0 yields the radius of gyration of the cross section.
Rq = 0.526 a ~¢/t-~ a; 0.526 -- ~
~ ~l~-ge
By extrapolation to m2 = 0 we determine now ( m I ( m ) ) 0 and the particle weight per o 1 A length. 27.3 X 10~a ( m I ( m ) ) o Mq = cD (zl -- ~1 P~)2 Po The method is strictly valid only for infinitely long rods but gives satisfactory results also with much shorter particles (17).
b) The dissolved particles should be independent of each other with regard to position and orientation. Hence, generally a concentration series is measured and extrapolated to c = 0. With CuPC this method is not possible, because the size of the particles depends on the concentration. However, here the existence of a certain short-range order is probable, owing to electrostatic forces. This will lead to interparticle interferences and thus cause too small scattering intensities at smallest angles, as is seen clearly in Fig. 2. For that reason the measured particle weights and radii of gyration can be regarded only as lower limits. To keep the error low we have avoided dye concentrations above 1%. Some of our results (see Section IX B, C, E) seem to indicate that the error will not considerably exceed 15 %. We have not yet found a satisfactory correction method. We believe, however, that despite these limitations our measurements offer valuable information. Furthermore, the cross-section data will hardly be affected by interparticle interferences. c) In the solutions we have studied, associates of various size exist in equilibrium. Hence we could obtain only average values of M and R (15). We have tried to overcome the resulting difficulties by using model systems (20). d) The structure of the solvent should be independent of the dissolved substance.
VI. PREREQUISITES FOR THE EVALUATION OF THE X-RAY MEASUREMENTS The accuracy of the determination of mass, size, and shape of dissolved particles depends upon the extent to which certain prerequisites are fulfilled. a) The dissolved particles should have a uniform electron density. Otherwise, one will obtain the correct particle weight, but errors will arise in the determination of the radius of gyration and of the shape. Fluctuations of electron density in small ranges cause weak additional scattering, which can be eliminated by subtracting the constant tail end of the scattering curve (18, 19).
0.05
0.~
~
2~
FIG. 2. S c a t t e r i n g c u r v e s of C u P C in 0.3% N a C I s o l u t i o n , w i t h c o l l i m a t i o n error. O - - 0 . 4 % C u P C ,
A--0.6% CuPC, [:]--1% CuPC, O--1.5% CuPC (Nos. 21-24 of Table V).
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
SODIUM
COPPER-PHTIIALOCYANINE-TETRASULFONATE TABLE
INTERPOL&TED
c ~ c 1 (gm/100 ml) (ml/gm)
VALUES
II
OF V FOR DIFFERENT
0 0.451
0.1665 0,454
Comparing the partial specific volume of dissolved electrolytes with the value for the pure substance, we notice that the ions are surrounded by a shell of denser solvent. Since our dye associates are polyelectrolytes, this well-known effect will influence Io, M, R, and ~. If the solvate shells of different particles are dearly separated, the shell will be included in I0 and R. With regard to M, however, the variations of I0 and ~ cancel out (20). So only R is falsified. If the solvate shells penetrate each other, we shall obtain approximately correct values for R, but M will be inexact. To take account of this effect we have employed for different salt concentrations different values for ~ (Table II), obtained by interpolation of measured values (Table I). e) In solutions containing salt the ions are possibly accumulated in the surroundings of the associates. This would influence mainly M and the cross-section data. The effect should depend on the salt concentration. According to our measurements the dependence is not very distinct. We have therefore limited ourselves to a rather qualitative treatment (Section IX, D). Satisfactory theoretical and experimental methods applicable to the problems in Section YI, D and E have been developed recently (21) in connection with deoxyribonucleic acid. They hold generally for polyelectrolytes in electrolyte solutions. The application to our problems, however, encounters two obstacles. First, we are not in a position to prepare solutions differing in salt content and having constant size distribution of the associates. Secondly, it will be difficult to carry out the required osmotic experiments with particles as small as dye molecules. Nevertheless adaptation might be possible.
493
SOLUTIONS
SALT
CONCENTRATIONS
0.3 0.457
AT 20°C
0.5 0.461
0.7 0.465
VII. REMARKS ON TttE INTERPRETATION OF TIlE SCATTERING CURVES Figure 3 shows typical scattering curves in the Guinier plot. We notice a characteristic decrease of the innermost portion of the curves. This phenomenon has been discussed in Section VI, B. It is not found with salt concentrations above 0.3 %. This may have two reasons: the increasing anisotropy of the particles will bring about a decrease in interparticle interferences; in addition, the scattering curves of strongly anisotropic particles rise considerably in the inner portion and will compensate thereby the visible effect of interferences on the shape of the curves. In all cases the steepest possible tangent was used for the extrapolation to Io and for the determination of R. Since its position will depend somewhat on fluctuations in small ranges of the curves, we have also used the comparison of experimental curves with the best fitting theoretical scattering curves of our collection (mostly ellipsoids or elliptic cylinders) as a means to determine Io and R (17). Thus we could utilize a larger range of the scattering curve whereby the spread of the values has been reduced. For interpretation it is important that the scattering curves converge at larger angles. From this behavior we may conclude that the cross sections of the elongated particles do not vary widely. Figure 4 shows several examples of cross-section functions in the Guinier plot. At the highest concentration we get an ideal Guinier range; with the other measured series we must depend on the steepest tangent. V I I I . T A B L E S OF T H E
RESULTS
We have measured 53 scattering curves of solutions of CuPC. The following parameters were varied: dye concentration (0.05 %
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 196~
494
K R A T K Y AND O E L S C H L A E G E R
:I
2,5 "~-~
1.0
-2
0,0
1110 .3
2110 -3
3.10-~ ~
(2~,) 2
FIG. 3. Guinier plot of scattering curves, corrected for collimation error, of solutions containing 0.4% C u P C and (1)--0.7% NaC1, (2)--0.5% NaC1, (3)--0.3% NaC1, (4)--0.1665% NaC1, (5)-0% NaC1 (Nos. 53, 41, 21, 14, 3, from Tables I I I -
VII).
~'.1o-;-
2"~0 -3
6'.1o -3
F I G . 4 . Cross-section functions of solutions containing 0.4% C u P C and (1)--0.7% NaC1, (2)-0.5% NaC1, (3)--0.3% NaC1, (4)--0.1665% NaC1, (Nos. 53 41, 21, 14 from Tables I V - V I I ) ; Guinier plot.
TABLE III RESULTS OF THE X-RAY MEASUREMENTS: 0% NACL
No.
T (°C)
U~
•-~
(gm/lO0ml)
CCuPC
M
1 2 3 4 5 6 7 8 9 10 11
21.2
0
20.7
0
0.0987 0.245 0.493 0.987 2.16 1.0 0.8 1.0 0.8 1.0 0.8
1830 2170 2490 3780 6570 3510 3170 3020 2900 2960 2610
35.0 50.0
~
1.86 2.20 2.53 3.84 6.67 3.56 3.22 3.07 2.94 3.00 2.65
3.46 4.82 6.42 14.8 44.5 12.7 10.4 9.4 8.7 9.0 7.0
R (A)
R: (A9
9.0 9.0 9.2 10.2 12.7 9.6 9.3 9.4 9.1 9.5 9.1
81 81 85 104 161 92.0 86.5 88.5 83.0 90.0 83.0
Mq
Rq (A)
T A B L E IV RESULTS
OF THE X-RAY
0.1665% N A C ~ ,
MEASUREMENTS:
No.
T (°C)
~NaCl (gm/lO0 ml)
CCuPG (gm/lO0 ml)
M
i
~
R (A)
R~ (~2)
Mq
Rq (A)
12 12F 13 13F 14 14F 15 15F 16 16F 17 17F
21.2
0.1665
0.1
3470 3340 4080 4020 5090 4830 5690 5330 7050 6680 8010 7990
3.52 3.39 4.14 4.08 5.17 4.90 5.78 5.41 7.16 6.78 8.13 8.11
12.4 11.5 17.2 16.6 26.8 24.0 33.5 29.2 51.3 46.0 66.0 65.7
10.3 10.2 10.2 10.1 11.5 10.8 11.8 11.6 12.9 12.3 14.2 14.7
106 104 104 102 132 117 139 135 166 151 202 216
142 ---158 -145 -172 -189 --
6.3 ---6.2 -5.8 -6.3 -6.8 --
0.2 0.4 0.6 1.0 1.5
Journal of Colloid and Interface Science, Vol. 31, No. 4, D e c e m b e r 1969
495
SODIUM COPPEt~-PHTHALOCYANINE-TETRASULFONATE SOLUTIONS TABLE V ~:~ESULTS OF THE X-RAY MEASURE~IENTS:0.3% NACL No.
T (°C) (gm/IO0 z~actmO (gin~190 cc.Pcml)
18 18F 19 19F 20 20F 21 21F 22 22F 23 23F 24 24F 25 26 27 28 29 30 31 32 33 34 35 36 37
21.2
0.3
0.05 0.1 0.2 0.4 0.6 1.0 1.5
21.5 35.0 50.0 20.7 35.0 50.0 21.2
1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0 0.5 1.0
M
~
~
R (A)
R2 (~2)
~q
Rq (3)
5250 5000 4990 5300 6670 6350 7950 7720 8690 8590 10050 9750 10640 10440 9950 8960 8270 6900 6010 5710 8870 8180 6800 5910 6010 5020 9460
5.33 5.08 5.07 5.38 6.77 6.45 8.07 7.84 8.82 8.72 10.2 9.9 10.8 10.6 10.1 9.1 8.4 7.0 6.1 5.8 9.0 8.3 6.9 6.0 6.1 5.1 9.6
28.4 25.8 25.7 28.9 45.9 41.6 65.1 61.5 77.8 76.1 104 98.0 116 112 102 83,3 70.7 49,2 36.6 33.2 81.6 68.3 47.8 35.5 36.6 26.4 92.3
12.0 11.7 12.0 12.1 13.5 11.8 13.9 13.3 14.5 14.2 15.2 14.8 15.2 15.6 15.4 15.0 13.5 10.6 9.7 9.2 14.4 14.6 12.4 11.7 12.2 11.1 15.0
144 137 144 146 182 139 193 177 210 202 231 219 231 243 237 225 182 112 94 84.5 207 213 154 137 149 123 225
----232 -204 -236 -202 -200 -221 219 187 186 197 171 197 197 183 181 178 165 193
----7.05 -6.8 --= 7.4 -6.9
to 2 % ) , NaC1 c o n c e n t r a t i o n (0 to 0 . 7 % ) , a n d t e m p e r a t u r e (20 ° to 50°C). I n T a b l e s I I I to V I I , each n u m b e r corres p o n d s to a s c a t t e r i n g curve. T h e letter " F " after t h e n u m b e r m e a n s t h a t t h e values of this line h a v e b e e n o b t a i n e d b y comparison w i t h theoretical s c a t t e r i n g curves. T h e t e m p e r a t u r e T is g i v e n i n °C, the concent r a t i o n c i n g r a m s / 1 0 0 ml or e q u i v a l e n t l y i n o p e r cent, R a n d Rq i n A n g s t r o m s . g is defined b y g = M / M 1 . R a n d M are of course average values a n d will be m a r k e d b y a b a r w h e n confusion is possible. P a r t i c u l a r p a r t i cles consisting of i molecules of dye are d e s i g n a t e d b y a s u b s c r i p t i, m e a n i n g t h e degree of association. M # M 1 = i. ~ is therefore t h e m e a n degree of association. W e h a v e a l r e a d y m e n t i o n e d which sorts of m e a n v a l u e s will occur ( S e c t i o n V ) . P a r t i c u l a r d e s i g n a t i o n s w o u l d be t r o u b l e s o m e . M s is
7,0 -7.3 7.6 6.6 7.0 6.9 6.5 6.7 6.7 6.4 6.3 6,3 6.0 6.8
t h e particle weight per 1 A length. A b a r i n a line m e a n s t h a t t h e v a l u e has n o t b e e n d e t e r m i n e d . I f a v a l u e is left o u t t h e figure f r o m t h e p r e v i o u s line still holds. N u m b e r s 1-5 i n T a b l e I I I are from L e d w i n k a (6) a n d h a v e b e e n slightly corrected according to reference 22. IX. DISCUSSION OF THE RESULTS A. PREI~IMINAR¥ REMAI~K W e do n o t a i m a t a n u n a m i b i g u o u s a n d final i n t e r p r e t a t i o n . T h e following considera t i o n s will o n l y b r i n g some order i n t o t h e r a t h e r i n v o l v e d p h e n o m e n a . T o this e n d we use t h e m o d e l system, developed i n referenee 20, which should serve our purpose, a l t h o u g h it is n o t q u i t e suitable. A t first we a s s u m e t h a t t h e associates h a v e t h e shape of o b l i q u e piles (Fig. 5). This is suggested b y t h e weak v a r i a t i o n of t h e cross section of t h e
Journal of Colloid and Interface Science, ¥ol. 31, No, 4, December 1969
496
KRATKY AND OELSCHLAEGER TABLE VI RESULTS OF THE X-RAY MEASUREMENTS:0.5% I~ACL
No.
T (°c)
38 38F 39 39F 4O 40F 41 41F 42 42F 43 43F 44 45 46 47 48 49
21.2
(gm/lOO ~ )
CCuPC
M
0.03
9950 10050 10440 10050 10640 10540 13300 13200 15960 14870 19210 18820 15460 13690 12210 10640 9950 8270
0.5
0.1 0.2 0.4 0.6 1.0 1.0 0.5 1.0 0.5 1.0 0.5
20.7
35.0 50.0
TABLE
~
10.1 10.2 10.6 10.2 10.8 10.7 13.5 13.4 16.2 15.1 19.5 19.1 15.7 13.9 12.4 10.8 10.1 8.4
VII
T
50 51 52 53
21.2
CNaCL
CeuPC
0.7
0.1 0.15 0.25 0.4
(gm/lO0 ml) (gm/lO0 ml)
Rq
Mq
(~)
247 245 254 263
7.7 7.6 7.8 7.9
associates (see S e c t i o n I X , D ) a n d b y t h e c r y s t a l s t r u c t u r e of C u - p h t h a l o c y a n i n e (23).
15.7 17.3 15.9 17.6 16.9 19.9 19.2 26.5 20.8 27.7 25.2
247
--
--
299 253 310 286 396 369
220 -191 -205 -201 -240 -227 211 211 192 192 192
7.2 -7.1 -7.0 -6.8 -7.4 -7.3 7.1 7.1 6.7 6.7 6.7
702
433 767 635 449 384 331 282 269 213
19.6 18.2 16.8 16.4 14.6
Mq
Rq (A)
210
7.3
= 4 Kc +
fb2.
[2]
( H e r e K is t h e association c o n s t a n t , c~ t h e n u m b e r c o n c e n t r a t i o n of associates consistin g of i d y e molecules, n t h e degree of assoc i a t i o n of a possible s u b u n i t ) (20). D e v i a tions f r o m a s t r a i g h t line i n d i c a t e t h a t t h e a s s o ci at i o n c o n s t a n t s are e i t h e r n o t e q u a l or n o t c o n s t a n t . I n p r i n c i p l e all t h e successive a s s o ci at i o n c o n s t a n t s could be o b t a i n e d b y t h e m e t h o d of S t e i n e r (24). H o w e v e r , t h e
/J
]3. CONCENTRATION DEPENDENCE OF THE DEGREE OF ASSOCIATION
J
W e p l o t ~ a g a i n s t c (Figs. 6, 7). I f all a ssoc ia ti o n c o n s t a n t s of t h e f o r m
ki~ - ci+~
R2 (A~)
21.2
-2
0.7% NAC~ (oc)
102 104 112 104 116 114 182 180 264 227 379 364 245 193 154 116 102 70.8
R (A)
the equation
l~ESULTS OF THE X - R A Y MEASUREMENTS:
No.
~
J J
[1]
CiCk
are e q u a l ( S c h u l z - F l o r y d i s t r i b u t i o n ) , this p l o t yields a s t r a i g h t line, t h e slope of w h i c h gives t h e a s s o c i a t i o n c o n s t a n t s , a c c o r d i n g to
FIG. 5. Proposed model of CuPC associates. The lines are the projection of the planes of molecules.
Journal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
SODIUM
COPPER-PHTHALOCYANINE-TETRASULFONATE
SOLUTIONS
497
determination of a greater number of con- curve cannot be extrapolated readily to stants would require very exact measure- c = 0 and g = 2. The reason might be t h a t ments. We resort therefore to qualitative the measurements at concentrations below considerations and regard the slope of the 0.1% are not very reliable. For the shape of curves as a measure for the actual associa- the curve we assume therefore a straight tion constants. line. 0% NaCl (Table I I I ; Figs. 6 and 7). The 0.7% NaC1 (Table V I I ) . The scattering extrapolation to c = 0 yields a degree of curves of this series rise so steeply at the association of about 2. This agrees with the smallest angles that neither M nor R could results of Ahrens (3), who determined, by be determined. Certainly M and R are means of light absorption measurements, larger than in the other series and show the that a significant amount of monomer exists usual concentration dependence. only at very low concentrations (below 0.01%). This agreement is one of the bases C . R A D I U S OF G Y R A T I O N AND D E G R E E OF ASSOCIATION of our paper (see Section VI, B). At higher concentrations he finds an equilibrium beFigures 8-11 show the connection between tween di- and tetramers, which is, according /~2 and ~2 for different salt concentrations. to our measurements, not very well deFigure 12 combines the data of Figs. 8-ii. marcated. Higher associates than tetramers We again assume oblique piles with a are certainly present. We believe that the Sehulz-Flory distribution. In this ease the absorption spectra of tetramers and higher equation from reference 20 holds: associates show no very pronounced differences and that at higher dye concentra= ~ +~_ ~ 2n2 + 1 . [31 tions the accuracy of the absorption experi3 ments is limited. (here n is the degree of association of a subFrom the curvature we may conclude that unit, R1 the radius of gyration of the the association "constants" rise with increasing concentration. This could be con- monomer, a the distance between the nected with the facts that electrolyte addi- centers of adjacent molecules; see Fig. 5). If the system were monodisperse, the followtion strongly enhances the association constants and that the dye itself is a strong ing equation would be valid: electrolyte. The slopes of the following 2 R 2 = R12 + a (i2 _ i ) . [41 curves seem to support this point of view. 0.1665% NaCl (Table IV; Fig. 7); o 0.3% NaC1 (Table V; Fig. 7). The curves From [3] we get a = 2.5 to 2.8 A, from [4] show a much greater slope, corresponding to a = 4.3 to 4.8 A. The real distribution is greater association constants. We can as- probably somewhat narrower t h a n a Schulzsume that CuPC will behave more ideally at Flory distribution, but certainly not monohigher salt concentrations. The shape of the disperse. We therefore regard a value of curve indicates that with larger associ- a , = 3 to 3.5 A as the most probable one. ates the association constants K ~ become R1 is also available from [3]. We put n = 2 smaller. This would mean that the distribu- according to the results of Ahrens and obtion of the degrees of association would be tain R1 = 8.7 A. We shall return to these narrower than a Schulz-Flory distribution. values later. However, we must not forget t h a t the shape I t is noticeable that the four straight lines of the curves is affected b y interparticle of Fig. 12 are not too far from forming a interferences (see Section VI, B). common curve. This means t h a t all the 0.5% NaCl (Table VI; Fig. 7). This possible changes, caused by different conJournal of Colloid and Interface Science, Vol. 31, No. 4, December 1969
498
KRATKY AND OELSCHLAEGER possible errors are limited to a tolerable order of magnitude. 20
D. ---,* c ['/o]
1
CROSS SECTION AND SHAPE OF THE ASSOCIATES
2
£~G. 6. Concentration dependence of the degree of association of CuPC in water (Table I I I , Nos. 1-7).
A c c o r d i n g to M i t t e l b a c h (17) cross-section d a t a f r o m cylindrical bodies are sufficiently exact, if R/Rq > 1.5. W i t h regard to °/ 200
4OO T2
//
T
S
j
2<
/ / 0.5 % NaC{
I
/
V
//o 20C
10C
y//~ /
/
r T2 0.5
I -.--,, c [°/ol
FZG. 7. Concentration dependence of the degree of association of CuPC at different salt concentrations (all measurements at 21 ° 4- 0.3°C from Tables III-VI).
5O
FIG. 9. Relation between mean degree of association and mean radius of gyration: 0.1665% NaCI (Table', IV).
o Z(
20C 10C
J
oo
_._,T 2
lb0 ..... T 2
5O
FIG. 8. Relation between mean degree of association and mean radius of gyration: 0% N a C 1 (Table III).
Fin. 10. Relation between mean degree of association and mean radius of gyration: 0.3% NaC1 (Table V). r
centrations of dye and salt and b y t e m p e r a t u r e variations (concerning interparticle interferences, extension and composition of t h e solvate shells, electrostatic association, shape of the associates, size distribution), c o m p e n s a t e each other to a degree with regard to the relation b e t w e e n / ~ and ~2, or shift t h e p o i n t along the curve only. This plot seems to increase the probability t h a t
~OOili L
----*T ~ 2a0
l?ie. 11. Relation between mean degree of association and mean radius of gyration: 0.5% NaCI (Table VI).
Journal of Colloid and Interface Science, VoL 31, No. 4, December 1969
SODIUM C O P P E R - P H T H A L O C Y A N I N E - T ETRA SU LFO N A TE SOLUTIONS
the mean value character of R we choose instead a ratio of R/Rq > 2. With this restriction we obtain values of Mq from 200 to 250 (see tables), corresponding to Rq between 7 and 7.8 A (determined according to Fig. 13). We believe that the variation is small enough to be explained by a modification of the proposed model. One possibility would be the accumulation of ions in the surroundings of an associate. We are not in the position to decide, however, whether Mq is correlated with the salt concentration or with the degree of association. We shall now give a review of all available data concerning cross section and shape. R ~ W e use 7 A < R~ < 7.8 A. Mq---We use 200 < M~ < 250. Rt--may be estimated from the structure of the molecule. For this purpose the electron density differences of particular regions
of the molecule against water had to be estimated. For that we needed the densities of these regions, essentially that of the central atom, of the surrounding organic groups, and of the sulfonie acid groups with its sodium ions. These data can be computed from the S of dissolved CuPC, of the solid Cu-phthalocyanine, and of the metalfree phthalocyauine. The latter data we took from reference 25. Thus we have obtained o R1 > 7.5 A. The uncertainty towards higher values is due to the fact that the position of the sodium ions and the extension of the soivate shells are not known. Besides, RI is determined mainly by the central distance of the sulfonate groups (8.5 A). RI--8.7 A from Fig. 12. a--is obtained from MI/Ma. 3.9 & < o a < 4.9A. a*--has been estimated from the dependence between/~2 and ~2 (Section IX, C; Fig.
~.
12). 3 ~ < a* < 3.5
50[
T
/.
100
200
Fro. 12. Relation between m e a n degree of association and mean radius of gyration for all investi-
gated salt concentrations; data were compiled from Figs. 8-11. I
499
d--is the distance between the planes of adjacent molecules (see Fig. 5). The structure of Cu-phthaloeyanine crystals shows that d is certainly larger than 3.4 ~_ (23), because the CuPC molecule carries charged groups, which furthermore do not lie in the plane of the molecule, d--can also be estimated from 9, if the area F of the single molecule is estimated from the molecular structure. This procedure yields F = 190 to 230 ~2 and (with ~ = 0.46 mI/ o 2 gm) d = 4 t o 3 . 3 A . Between the various quantities the following relations are valid: 2
R22 = i 62
R
12 + ~a - , .
M1 --;
~..~
a = M~ 22
100
200 ~
d
Mq
-
a
FIG. 13. I~elation between radius of gyration and weight of the cross section (Mq and Rq) at different salt concentrations: X--0.1665% NaC1, 0--0.3% NaC1, A--0.5% NaC1, [2--0.7% NaC1 (all measurements at 21 ° =t= 0.3°C from Tables IV-VII).
[5]
[61
cos ~;
[7]
( R ~ 2 _ cos 2 ~ + N] 2
i
Is]
We shall now calculate our model (Fig. 5). We shall consider a* later.
Journal of Colloid and Inter/ace Science,
Vol.
31, N o .
4 D e c e m b e r 1969
500
KRATKY AND OELSCHLAEGER
d>3.4A ) 3.9A < a < 4.92~
[71 c o s ~ > 0 . 7 9 } > [S]> ~ < 8 . 4 A o 7.8A > Rq > 7A 3.9A < a < 4.9AJ
With this calculation we have kept in mind that Mq and Rq, resp. a and Rq, are correlated, as is shown by Fig. 13. R~ = 7 correspondsotO a = 4.9 A and Rq = 7.8 -~ to a = 3.9 A. The value for R2 obtained in this way agrees l~oorly with the directly measured one (9 A) (TableoIII). From R.~ = 9 A we obtain R1 = 8.8 A, according to [3] or from Fig. 12 R1 = 8.7 A, with is of course practically identical but which is too large compared with the value estimated from the molecular structure (R~ > 7.5 A). This will mean either that the central distance of the sodium ions is about 20 A or that the distance between the molecule centers of the o dimer is at least 6.5 A. It seems more probable that in salt-free solutions particularly pronounced hydrate shells and perhaps several larger associates formed by electrostatic forces are present. We have still to consider a*. The difference between a = 3.9 to 4.9 A and a* = 3 to 3.5 ~_ requires a modification of the proposed model, a results from M1 and Mq, a* from the relation b e t w e e n / ~ and ~2. We assume that a* is too small. Hence we infer either that the associates are bent or that lateral association may occur (Fig. 14). Besides, we see that the curve in Fig. 12 gets flatter with increasing ~. This may
>
ever, with the shape of the concentration dependence. With larger associates the interparticle interferences influence R more strongly than M. Lateral association occurs more frequently with larger associates. This is confirmed by the fact that, in the case of precipitation, lateral association becomes evident. Besides, this would also explain the fact that Mq and Rq are somewhat enhanced with increasing degree of association. E. TEMPERATURE DEPENDENCE OF THE SCATTERING CURVES AND HEAT OF ASSOCIATION
Dye associates become smaller with increasing temperature and decreasing concentration (Fig. 15). Thereby M and R decrease too. All in all, the intensity is reduced in the whole inner portion of the scattering curve. By comparing the concentration dependence and the temperature dependence we can estimate the heat of association for the single association step (20). In other words, under certain restrictions (see reference 20), it will be possible to compensate a change of
100I %
lnean:
The larger associates are less polydisperse than the smaller ones. This disagrees, how/ /
/ -
-*~
-
/.
/ \\ (
s
/ _
f
--
so
2 . 1 0 *2
.
/.-10 -2
6.1@2 ~
2..0,
FI~. 15. Comparison of temperature dependence and concentration dependence of scattering curves, with collimation error, of CuPC in 0.3% NaCl: (1)--1.0% CuPC, 20.7°C; (2)--0.5%, 20.7°C;
(s)--1.0%, 35°c; (4)--0.5%, 35°c; (5)--1.0%, FIG. 14. Possible shape of larger associates.
50°C; (6)--0.5%, 50°C; (Nos. 31-36 of Table V).
Journal of Colloid and Interface Science, V o l . 31, N o . 4, D e c e m b e r 1969
SODIUM COPPER-PHTHALOCYANINE-TETRASULFONATE SOLUTIONS temperature by a change of concentration in such a way that the distribution of the degree of association remains unchanged. This means, furthermore, that the scattering curve, divided by c, will also remain unchanged whether it is corrected for collimation error or not. We need therefore two scattering curves, which coincide if referred to the same concentration. From the two pairs (c, T) and (c', T') the heat of association W1 is obtained according to [9]. in (c/c') (T - T')
A In c -
AT
W1 -
R T ~"
[9]
Such pairs (c, T) and (c', T') are found either directly or better yet by interpolation from measured series. For this purpose we have measured four series of scattering curves at different salt concentrations. Each series consists of two concentrations, each one measured at three temperatures. These are: Nos. 6-11 in Table III, nos. 25-36 in Table V, and Nos. 44-49 in Table VI. One of these series of scattering curves (with collimation error and referred to the same concentration) is shown in Fig. 8. For the evaluation we assume that S does not depend on temperature. To determine the heat of association we compare the temperature dependence at two concentrations at a fixed scattering angle. The temperature is plotted versus the scattering intensity. For each concentration we obtain a curve. In Fig. 8 such a pair of curves is drawn. The abscissa difference between the two curves is the AT of the above formula. For each series we deterrrfined AT at several scattering angles. Under ideal conditions the same value would be shown all along the curves. But practically too small a AT is obtained in the inner portion, since the curve is more falsified there at higher concentrations. In the subsequent range, AT is approximately constant. This range is used for the determination of AT. At still larger angles the curves converge, so that AT cannot be determined there.
501
From the values of AT obtained in this way we get the following values for W1 : - - W1 = 5-7 keal/mole
CNaC1 = 0 ~0
0.3 % 0.3 % 0.5 %
11 kcal/mole 12 keal/mole 13 keal/mole
The first value does not fit into the picture. This is connected with the fact that the association constants depend considerably on the dye content, if the solution does not contain any other electrolytes. This point has been discussed above (Section IX, ]3). The other values agree within the margin of error. Thus we obtain: - W 1 = 12 =h 1 keN/mole. We should mention, however, that this value gives only an order of magnitude, because our method is rather sensitive to errors and furthermore the assumptions used in reference 20 are not completely appropriate. We cannot exclude therefore systematic deviations, despite the good agreement at different salt concentrations. Besides, a qualitative estimation of the influence of interparticle interferences upon the inner portion of the scattering curves appears possible, since here scattering curves of two systems with the same distribution of the degrees of association but different concentrations can be measured. In this method, however, the temperature dependence of the interparticle interferences is not taken into consideration. In any case, our measurements seem to corroborate our assumption that the error caused by interparticle interferences will not exceed 15% for the determination of the degree of association. ACKNOWLEDGMENT We wish to t h a n k t h e C I B A AG, Basel, for suggesting this i n v e s t i g a t i o n , as well as for its s u p p o r t and for the s u p p l y of t h e purified samples. We wish also to t h a n k t h e Osterreichischer F o r s c h u n g s r a t for help w i t h t h e a p p a r a t u s . REFERENCES 1.
I~A~BINOVITCI~,E., A.ND EPSTEIN, L., J . Am. Chem. Soc. 63, 69 (1941).
Journal of Colloid and Interface ,%ience, Vol. 31, No. 4, December 19G9
502
KRATKY AND 0ELSCHLAEGER
2. SCEEIDE, G., Z. Elektrochem. 52, 283 (1948). 3. AHRENS, U., Dissertation, Philipps-Universitiit, Marburg, 1962. 4. MILICEVIC, B., AND EIGENMANN, G., Helv. Chim. Aeta 47, 1039 (1964). 5. KRATKY, 0., MITTELBACH, 1°., PILZ, I., SCHMITZ, ~o. j., AND WAWRA, H., unpublished. 6. LEDWINKA, H., Dissertation, University of Graz, Austria, 1966. 7. KRATKY, O., LEDWINKA, H., AND PILZ, I., Ber. Bunsenger. physikal. Chemic 70, 904 (1966); Makrom. Chem. 105, 171 (1967); KRATKY, O., I°ILZ, I., AND LEDWINKA, H., Monatsh. Chem. 98, 227 (1967). 8. STAmNGEI~, H., LEOeOLD, H., AND KaATlZY, 0., Monatsh. Chem. 98, 436 (1967); KRATKY, O., LEOPOLD, H., AND STABINGER, H., Z. Angew. Physik 27, 273 (1969). 9. KI~ATI~Y, 0., Z. Elektroehem. 58, 49 (1954); ibid. 62, 56 (1958); KI~ATI~y,0., AND SKAI~A, Z., ibid. 62, 73 (1958). 10. KI~ATKY, CI-I., AND KR~TKY, 0., Z. Instrumentenkunde 72, 302 (1964); LEOI~OLD,I~I., Elektronil~ 14, 359 (1965). 11. I{RA~ICV,O., POl~OD, G., ANI) SKALA, Z., Acta Phys. Austriaca 13, 76 (1960); HEINE, S., AND ROPPEnT, J., ibid. 15, 148 (1962); HEINE, S., ibid. 16, 144 (1963). 12. I4~RATKY, O., PILZ, I., AND SCIIMITZ, 1°. J., J. Colloid and Interface Sci. 9.1, 24 (1966); PILZ, I., AND I{RATXY, 0., ibid. 9.4, 211 (1967). Pilz, I., ibid. 30, 140 (1969).
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Journal of Colloidand Interface Science, VoL 31, No. 4, December1969