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Kirkwood—Alder transition in monodisperse latexes. I. Nonaqueous systems
Kirkwood-Alder Transition in Monodisperse Latexes I. NonaqueousSystems~ AKIRA KOSE Institute for Applied Optics, 22-17 Hyakutdn-cho 3, Shinjuku-ku, Tokyo, Japan AND
SEI HACHISU Institute for Optical Research, Kyoiku University, 22-17 Hyakunin-cho 3, Shinjuku-ku, Tokyo, Japan Received June 14, 1973; accepted October 4, 1973 Spontaneous phase separation phenomenon in a nonaqueous monodisperse latex system is studied to verify the Kirkwood-Alder transition in colloid systems. The nonaqueous system might be suitable for our purpose, because both electrical double layers and van der Waals force effect could be negligible therein. Polymethyl methacrylate latex cross-linked with divinylbenzene was dried and then dispersed in benzene at various concentrations. The phase separation occurs in certain particle concentration ranges, depending upon the degree of the cross-linking. The values of the concentration at which the phase separation starts are in the range of from 0.105 to 0.195 by measured volume fraction; smaller values correspond to lower degrees of cross-linking. Correction of the measured volume fractions for the swelling of the particles gives values very close to 0.5, which are independent of the degree of the cross-linking.This is in good agreement with the value 0.497 predicted by Alder, Hoover, and Young EJ. Chem. Phys. 49, 3688 (1968)]. In the phase-separated state the ordered phase which forms a sediment exhibits a beautiful opal-like iridescence (demonstrating the existence of polycrystalline structure), while the disordered state is rather translucent and gives weakly iridescent scattering, which would be attributed to the presence of spacial local order, that is, the liquid-like structure. Experimental evidence seems to support the conclusion that the phase separation which occurs in monodisperse latexes cannot be explained by the DLVO theory but could be attributable to the Kirkwood-Alder transition ill a hard sphere system. INTRODUCTION Order formation of particles in monodisperse latexes has attracted the interest of a n u m b e r of authors because of the beautiful iridescence from the ordered arrays of the particles, and in some works the p h e n o m e n o n of coexistence of the ordered and disordered phases was pointed out. Luck and Wesslau (1), and Luck, Klier and Wesslau (2), first to observe the 1 Presented in part at the 25th Symposium on Colloid and Interface Science held in Fukuoka, Japan, November 1972.
coexistence, seem to have regarded it as a result of some attractive force between the particles. Later, Vanderhoff et al. (3), observed this p h e n o m e n o n as a rapid appearance of all iridescent sediment in a deionized dilute latex, t h a t is, within 1-2 wk, the particles of some samples settled into a packed layer, leaving a thin clear s u p e r n a t a n t layer, and stated t h a t the ion exchange increased the rate of compacting of these particles into packed arrays. Krieger and Hiltner (4), in their studies of the Bragg reflection from the ordered latex, have
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Journal of Colloidand InterfaceScience.Vol. 46. No. 3, March 1974
Copyright • 1974by AcademicPress, Inc. All rights of reproductionin any form reserved.
KIRKWOOD-ALDER
TRANSITION IN LATEX. I
found the coexistence of the two phases as an abnormal behavior of the changes in center-tocenter distance between latex particles, and stated that, at intermediate electrolyte levels, ordered and disordered phases coexist at equilibrium; the volume fractions of the coexisting phases are functions of the ionic strength. They have suggested the introduction of the theory of globular protein cluster formation proposed by Kirkwood and Mazur. The authors and a collaborator have reported in a previous paper (5) that aqueous monodisperse latexes, under certain conditions, spontaneously separate into two phases, one of which has a disordered structure and looks milky white, while tile other has an ordered structure that is more concentrated than the disordered one and is iridescent in its appearance provided that the distance between the particles is comparable in length with visible light wavelength. The authors have concluded that this cannot be explained by the DLVO theory but could be interpreted by the idea of the Kirkwood-Alder transition (6-8). In the field of physics, one of the most fundamental and interesting themes is a subject of transition between liquid and solid state, that is, whether or not the transition from liquid to solid state is possible in the absence of attractive potential. Kirkwood (9) discussed that in hard sphere systems the transition may occur when the volume fraction of the particles is exceeded by a certain value. Later on, Alder and Wainright (7) showed in their computer experiments using molecular dynamics method that in a two-dimensional system consisting of 870 discs, the phase transition begins at A/Ao = 1.3 (A is the area per disc, A0 is area per disc at close packing) and is completed at A/Ao = 1.43. Alder, Hoover, and Young (8) predicted for hard sphere systems that the transition starts at about 0.5 and is completed at about 0.55 by volume fraction. In our previous experiments a phase transition took place at considerably smaller volume
461
fractions than the predicted values. This was attributed to the larger effective volume of the particles because of the presence of electrical double layers around the particles. For further confirmation of the accordance between theory and experiments, it is desirable to observe this phenomenon in other systems which more nearly simulate the hard sphere system. As examples of this kind, two types of systems can be suggested from the colloid chemical point of view; one is the class of latex dispersed in nonpolar liquids such as hydrocarbons, and the other is aqueous latexes with high electrolyte concentrations which are stabilized by nonionic surfactants. As to nonaqueous latex systems, extensive studies have been carried out by Papir and Krieger (10), and Hiltner, Papir and Krieger (11). They showed that cross-linked polystyrene latexes could be redispersed in a number of organic liquids having different physical properties, and observed that the latexes in some polar organic media (aromatic) gave beautiful iridescence, whereas in nonpolar media the latexes did not give diffraction maxima despite stable dispersions being formed. They concluded that the order is attributed to electrostatic repulsion between particles as a result of partial dissociation of ionic surface groups. The authors have found that both crosslinked polystyrene and cross-linked polymethyl methacrylate latexes give iridescent dispersions in nonpolar solvents such as benzene, toluene, and carbon tetrachloride if some care is taken in the preparation of the dispersion. In the present paper, phase separation in a nonaqueous latex, polymethyl methacrylate (PMMA) particles in benzene, is studied. The polymer was cross-linked to prevent the particles from dissolving into the medium. This system is considered to possess neither electrical nor van der Waals interactions, and is considered to be an excellent model for the hard sphere system.
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KOSE AND HACHISU EXPERIMENTAL
solution of the latex particles as described later. However, the regular trends in the sample Methyl Methacrylate (MM A )--Divinyl benzene latexes indicate that the cross-linking was (D V B ) Copolymer/Benzene Latex made, at least, in proportion to the amount of Cosss-linked PMMA in benzene was chosen DVB. The trends were confirmed qualitatively from a number of combinations of polymers by the fact that the greater the DVB content and nonaqueous solvents, because of ease of the greater the refractive index of the particles preparation, the nonpolarity of benzene, and and the less the degree of swelling, and vice the excellent optical properties of the system. v e r s a . The refractive indices of the particles and In St-DVB latexes, the swelling and dissolumedium in this system are so close to each other tion were appreciably smaller. that the latex looks almost transparent, when Particle diameters determined by electron observed under diffused light, which greatly microscopy are shown in the fourth column in facilitates observations. The phase separation Table I. The polymerized latexes, containing could easily be detected by the appearance of ca. 0.2 (by volume fraction) polymer, were tiny iridescent flecks in the suspension, and purified by deionization using a mono-bed ion furthermore, the three-dimensional mosaic ion exchange resin (Robin and Haas MB-3) structure of the ordered phase was clearly obin as much as 50% by volume of the latexes; served to have an opal-like appearance. Anthe resin was removed completely by repeated other merit of MMA-DVB copolymer is its centrifugation. high density (ca. 1.19), which makes the "phase A purified latex was vacuum dried to conseparated" crystals precipitate faster and prostant weight at room temperature. A small motes "spatial" separation of the two phases. amount of precisely weighed dried latex was Among the other systems, the styrene- placed in a test tube equipped with a screw cap divinyl benzene (St-DVB) copolymer/benzene with Teflon packing. A 10-15 ml quantity of system has the particular merit that the re- benzene was added and the tube was vigorsemblance in molecular structure between the ously shaken by a shaking device. Ill about 1 hr particles and medium assures that the van der complete dispersion was obtained. Then, a Waals interaction is almost nil. A few observa- sufficient quantity of benzene was added to tions using this system, which will be reported attain a total volume of 20 ml. In this preparaelsewhere, gave almost the same results as were tion, when the tube was allowed to stand obtained with the MMA-DVB copolymer/ quietly after the addition of benzene, the benzene system, indicating that with regard to dried latex at the bottom became swollen into van der Waals force the situation is the same a translucent gel and very slowly dispersed by in the two systems. diffusion into the upper liquid to form a concentration gradient. In about 1 mo the gel dispersed completely. It was remarkable Monodisperse latexes of PMMA cross-linked that ill the lower part of this gradient there withDVB were prepared by emulsion polymeri- appeared an ordered structure with an opalzation. The degrees of cross-linking were 2.5, like iridescence as shown schematically in 5, 10, and 15% by volume (20% cross-linking Fig. 1, which remained until just before comyielded nonspherical particles). The described plete dispersion. This phenonemon, which is values of the degrees of the cross-linking are referred to below, was important and useful volume percentages of DVB content on a because it served as a reliable measurement of monomer basis. It is questionable that all the the quality of the sample under preparation. molecules of the added I)VB have functioned For some uncertain reasons, some monodiseffectively as cross-linking agents, considering perse latexes dispersed in a nonaqueous solthe relatively high degree of swelling and dis- vent were sometimes noniridescent although
Preparation of Samples and Observation
Journal of Colloid and Interface Science, Vol. 46, No. 3, M a r c h 1974
KIRKWOOD-ALDER TRANSITION IN LATEX, I they had had high monodispersity and suitable particle sizes. The results of such experiment were very confusing and led us to a wrong conclusion. Such defective latexes were easily determined by this smlple test because they did not give the opal-like appearance in the concentration gradient. This is probably due to the presence of the impurities such as inorganic salts and/or oligomers of methyl methacrylate, because the anomaly did not occur when the latexes were thoroughly purified, using an ion exchange resin. Papir and Krieger (10) and Hiltner, Papir, and Krieger (11) stated that St-DVB copolymer latexes in benzene and in toluene and such as those having low dielectric constant did not give diffraction maxima, and the latexes in methanol did not give a stable suspension. Probably, these results were due to watersoluble impurities. ~ Suspensions thus obtained were almost clear when viewed under diffuse light, and the more transparent in appearance the less the degree of cross-linking. Suspensions of varying solid content ranging from 0.02 to 0.25 by measured volume fraction at an interval of 0.02 were prepared for each latex having a different degree of cross-linking. The measured volume fraction denotes volume fraction obtained from dry weight and the specific gravities of the polymer, and benzene (PMMA: 1.19 and benzene: 0.87, respectively). The effects of swelling and dissolution of the particles will be described later. The samples thus prepared were placed on a rack in increasing order of concentration and were immersed in water for the convenience of observation. The observation was made in a dark room under the illumination of a horizontal beam of white light. Virtually complete equilibrium was attained in about 1 wk and the iridescent phase appeared in all of the tubes except in those containing suspensions of lowest volume fractions (Fig. 2). In the phase separating tube iriI n o u r case b o t h c r o s s - l i n k e d p o l y s t r y r e n e a n d c r o s s l i n k e d P M M A l a t e x e s in m e t h a n o l g a v e s t a b l e a n d iridescent suspensions.
.~
0~
~
~.~
"~
o~
i
5"~
463
m
u
~o
o~ 0~c~
~v
¢9
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
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KOSE AND ,HACIIISU
I m
~--'-~-1 I Transparent ~---I ~:1 2 Turbid, --- -----I colorless . . . .
!ill :i~!.! :ill
colored ~i;';:;~;] 4 Iridescent 5~ 3~', flecks
No. I
colored 6 Translucent, colored
0.02-0.06
"i "i "2
itl,
, , :' ,
2
3
4
0.07-0,11
state.
descence appeared, at first, along the inner wall of the tube as a vertical and specular reflecting color band and then as tiny glistening iridescent flecks came in the suspension as shown schematically in Fig. 3a. These flecks settled slowly and finally formed an iridescent and more transparent sediment with well-defined horizontal boundary. On the other hand, when suspending medium having greater specific gravity than latex particles such as dichloromethane (sp gr 1.33) is used instead of benzene, the iridescent crystallines formed in the bulk of the suspension moved toward the upper portion to form the iridescent layer at the top of the suspension. F r o m this fact, the particle
5 0,12-0.|3
Particle Volume
FIG. 1. Schmatic representation of a feature of MMADVB copolymer/benzene latex in the nonequilibrium
a
//A ///
"'" ;:i; ~5
5 Turbid, ::'"
///'
I ///~
I
!:!~~ T!:.: ;2;
i
u
r",5
6
7
8
0,14-0,16
Fraction(measured)
FIG. 2. Schematic representation of features of samples in the equilibrium, Sample V: 5~o crosslinking. ~ : Disordered portion; ~ . : Colored scattering portion; ~ - / - ~ : Ordered portion. No. 1-2: (0.02-0.06 by volume fraction) turbid, colorless. No. 3-4:(0.07-0.11 by volume fraction) turbid, colored. No. 5-6:(0.12--0.13 by volume fraction) phase separation was occurred. No. 7-8: (0.14--0.16 by volume fraction) entire body was in crystalline state. concentration of the crystalline portion is considered to be greater than that of the disordered portion. For the 50-/0 cross-linked case the general features in the final equilibrium state were as follows. I n the samples of the lowest polymer content (0.02-0.06 by volume fraction), which were noniridescent, the entire body of the
b
c
,\\\\~,~ ,//hl/!/!
.S.
FIG. 3a. Schematic representation of a sample in iridescent state. Sample V (5% cross-linking) (1) reflected light is orange; (2) reflected light is green. (b) Observation arrangement. (W) water; (MC) microcrystal; (0 and 0') Bragg angles for the different net planes; (L.S.) light source, parallel beam of white light. (c) Schematic representation of the relation among light source, reflecting crystal net planes and observing position. (L.S.) light source, parallel beam of white fight; (B.S.) beam splitter; (1) reflected light is orange; (2)green; (3)invisible. J o u r n a l o f C o l l o i d a n d I n t e r f a c e S c i e n c e , Vol. 46, No. 3, March 1974
KIRKWOOD-ALDER
465
TRANSITION IN LATEX. I
suspension was turbid due to the Tyndall scattering. In the second lowest group (0.070.11), the turbidity was somewhat stronger and the scattered light was tinted with iridescent color which changed as the direction of the observation changed. In the moderately concentrated samples (0.22-0.13),8 phase separation was observed; the ordered phase was a beautiful sediment packed with a number of small crystals with net planes reflecting iridescent colors,4 and the supernatant disordered phase had the same appearance as the second lowest group, that is, the scattered light was tinted. It is remarkable that the sediment, which was more concentrated than the supernatant portion, was significantly more transparent than the supernatant; this can be explained by the interference effect of the light by the ordered structure. The opal-like appearance indicated that the ordered phase had a polycrystalline structure. In the most concentrated group, the entire body of the suspensions were in the ordered state, with an appearance similar to the sediments in the phase-separated samples. As the polymer content increased the iridescent colors had a tendency to shift toward shorter wavelengths, and the polycrystalline structure became finer (individual crystals became smaller) and finally disappeared to give smooth rainbow colors. Critical values of polymer content for the appearance of colored scattering (C1) and for the phase separation (C2) are given in the fifth and sixth columns of Table I. These values cannot directly be compared with Alder-I-Ioover-Young's (8) prediction because the polymer particles must have been appreciably swollen and furthermore been T h e concentration range in which the two phases coexist was very narrow. T h e samples in the range shown in Fig. 2 were prepared b y careful dilution of ~a more concentrated entirely crystallized latex a t an interval less t h a n a 0.02 volume fraction. 4 T h e opal-like appearance observed in the course of preparation was due to the fact t h a t in the concentration gradient there was a region in which the concentration was adequate for the crystallization.
partly dissolved, releasing noncross-linked linear molecules into the medium. Therefore, for comparison with the prediction, the effective volume fraction of the particles ¢ should be used instead of the measured volume fraction C. This is shown in the following section. D E T E R M I N A T I O N OF T H E E F F E C T I V E V O L U M E F R A C T I O N (0)
The effective volume fraction (¢) can be determined from the intrinsic viscosity if we assume that the particles retain their spherical form after swelling (Fig. 4) and partial dissolution. Furthermore, it is also assumed that the swelling ratio ~ (ratio of swollen to unswollen volume) of the particles remains constant regardless of the extent of dilution of the latex, and the particles deform negligibly in the shear flow encountered in the viscosity measurements. Thus, ¢ is related to the measured volume fraction C by a simple equation q~ = ~.C. Considering the partial dissolution, the factor may not be the simple "swelling ratio" but also includes the effects of dissolution. At this point, however, we do not need to go further into this complexity but are satisfied with the constancy of ~. Viscosity of the latex is expressed by an extended Einstein equation as ~
= 2 + 2.5(~c) + ~ ( ~ c ) ~ . . . .
Then, 2
lira (~/~- 2 ) - = 2.5~. C~0
C
Denoting intrinsic viscosity by E~, becomes E@/2.5. Next, in obtaining ~r = ~suspension/'qmedium, correction of ~]med.has to be made for the effect of the dissolution. The viscosity of the medium ~/med. in this case, is not equal to that of pure benzene but is the viscosity of the benzene solution of the polymer eluted from the particles, and is no longer constant but decreases as the dilution continues. Therefore, 7Jrned. should be measured after each ~,~usp. measurement. However, because the Ubbelohde inter-
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KOSE AND HACHISU
FIG. 4. Electron micrograph of 5% cross-linked PMMA latex particles once suspended and swollen in benzene. A small drop of the diluted benzene suspension was dried on a carbon-coated nitrocellulose film and then observed. Considering the bond rupture, swelling and consequent dissolution which the particle must have experienced in benzene the sphericity is surprising. Thus, the swollen particles (in benzene) are presumed to have retained good sphericity.
nal dilution viscometer was used in our experiment, measuring ~med. after each ~/,usp. measurement was very difficult. Hence, the relative viscosity of the medium was determined as a function of C, the particle volume fraction of the suspension, independently of nsusp, measurement. A supernatant solution was obtained by centrifugation 5 from a latex of moderate concentration ( C - - 0 . 0 5 for example) and nmed. It is of interest that when a uniformly dispersed latex suspension having 5% solid content was subjected to centrifugation, it separated into six different phases; transparent supernatant, colorless turbid, colored turbid, iridescent fleck, colored turbid, and colored translucent phase in order from the top to the bottom of the suspension. This feature of the sample was identical to that in the nonequilibrium state as shown in Fig. 1.
was measured using an Ubbelohde viscometer at exactly the same degrees of dilution corresponding to those employed in the */su~p.measurement. Here an assumption was made that the fraction of the soluble portion of a crosslinked P M M A latex particle is constant regardless of the degree of dilution. This was ascertained in relatively few numbers of cases. The relative viscosity of the suspension and of the medium, based on the pure benzene, versus C curves are shown in Fig. 5. In Fig. 6 is shown a plot of ( ~ s u s p . / ~ m e d . - - 1)/C versus C. Intrinsic viscosities thus obtained are listed in the eighth column in Table I. The values of ~ thus obtained for different cross-linked latexes are given in the ninth column of Table I. In the 10th column are the critical values for coloration of scattered light
Journal of Colloid and Interface Science, VoL 46, No. 3, March 1974
467
KIRKWOOD-ALDER TRANSITION IN LATEX. I
in the effective volume fraction obtained from the values in the fifth column by multiplication with the respective ¢ values. In the l l t h column are given the critical values of the phase separation and in the last column those of the entire crystallization, although these values are not exact. OBSERVATION OF IRIDESCENCE
3O
2O
c
Study of the iridescence gives valuable information about the structure in monodisperse latexes. Spectroscopic investigations are under way in our laboratory. Here, a brief description is made of its qualitative character. The features of the crystalline body in a test tube were mentioned earlier and depicted in Fig. 3 for the case of a 50-/0 cross-linked latex.
I0
0
I
0
0.01
I
I
I
I
0.02
0.03
0.04
0.05
Volume Fraction (C)
FIG. 6. Reduced viscosity of Sample V latex suspension as a function of measured volume fraction of latex particles, where ~ = relative viscosity of the suspension/relative viscosity of the medium.
4
When observed by backward reflection as shown in Fig. 3a, b and c, four typical features were: (a) a bright orange colored band at the center of the tube along the inner surface and parallel to the axis, (b) two green bands at the symmetric positions with respect to the orange band, (c) a number of brilliant orange colored flecks (1-2 m m in diameter) in the bulk of the suspension and (d) a few number of green colored flecks. The above observation can be explained according to fcc model as follows:
A
% 2
B
1
0
0.01
0.02
0.03
0.04
0.05
Volume Froction (C)
FIO. 5. Relative viscosity based on pure benzene versus measured particle volume fraction curves of latex suspension and its medium. (A) The relative viscosity curve of Sample V/benzene suspension, where ~Tr(suspension) ~ ~susp./~Tpurebenzelxe; (B) the relative viscosity curve of the medium, the supernataut solution separated from Sample V latex suspension, as a function of the particle volume fraction of the suspension. For this curve the values on abscissa do not mean the volume fractions of the eluted polymer, but were determined from the value of the measured particle volume fraction of latex suspension from which the supernatant solution had been separated and each corresponding degree of dilution. In this case, ~/r(medium) ~/medium/~Tpure benzene.
Let the center to center distance be D, the diameter of the swollen particles be D~ and the real diameter of the unswollen particles be Dr. Assuming that the volume fraction of the swollen particles is 0.55 in compliance to the predicted values of Alder, Hoover and Young (8), the relation between D and Ds is D3
0.74 = 1.345
-
D~8
[-17
0.55
where 0.74 is the volume fraction of particles at close packed state, then
D/D~ =
(1.345)t = 1.10.
Journal of Colloid and Interface Science, Vol. 46, No. 3, Marcl~ ~:97%
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KOSE AND HACHISU
Since the swelling ratio is 4.2 for Sample V, D. = (4.2)LDr = 1.61"D~.
[2]
Combining Eqs. [1] and F2], D = 1.10 X 1.61 X D~ = 1.77.D~.
[3]
The distances between net planes are, d(m> = (])½.D, d<2oo) = \ 2 /
'
[+3
d(22o) = ½"D. Reflection from (100) and (110) are destroyed by geometric structure factor effect. Substituting Eq. [-3] in to Eq. I-4-] and using the values of 1380/~ for D~ the lattice distances become din1) = 0.82 X 1.77 X 1380 = 2002, d(~00) = 0.71 X 1.77 X 1380 = 1734, ['5-]
The scattered light from the supernatant phase was faintly colored and changed with change of angle of the observation, e.g., from red (backward), via green (at right angle to the incident direction) to blue. This corresponds to the X-ray halo obtained with liquid, and indicates presence of local spacial order or liquid-like structure in the latex suspension. The data given ill Table I indicate that the liquid-like structure begins to appear at about 0.25 by volume fraction. Another possible explanation of this coloration would be the presence of tiny crystallites suspending in disordered phase (2) or Mie scattering. However, the authors would favor the liquid structure view, because the state of coloring does not change upon quiet standing for more than 6 mo and upon slight dilution the colored phase disappeared, resulting in a colorless turbid phase. If the color is of Mie type, it would not disappear upon dilution.
d~2~0) = 0.50 X 1.77 X 1380 = 1221.
CONCLUSION
The average refractive index is very close to 1.50 and Bragg equation for the first order interference is
Since, in the present system, both the van der Waals and the electric interaction do not play a significant role, the spontaneous phase separation into the ordered and disordered phase, with ordered phase being more concentrated, cannot be explained by any theory other than the Kirkwood-Alder transition. The obtained values of ¢, scattering around 0.5, for the start of separation are in good accord with Alder, Hoover and Young's (8) prediction. Thus, the phase separation in monodisperse latexes has been explained; we no longer need to assume the attractive interaction of electrical double layers in concentrated systems. At the same time, the Kirkwood-Alder theory can be said to have been substantiated by the experimental evidence. Another observation, the iridescent scattering from the disordered phase seems to indicate the presence of a local spacial order that is characteristic of the liquid structure. The monodisperse latex has now been found to be an excellent model system for the study of structure of liquid as well as of solid systems.
X = 2 n d sin0 = 3d,
where 0 = 90, n = 1.50, and d's are given in Eq. ['5]. Peak wavelengths are X(m) = 6000 A
(orange),
X(200) = 5200 )t
(green),
Xc~20) -= 3660/~, upper two values corresponding to orange and green, respectively, and the third one is invisible. From these data, the orange color at the center of the tube is considered to correspond to the reflection from the (111) plane of the fcc lattice which is in accordance with Luck, Klier, and Wesslau's (2) results and our observations (12), and green from the (200). As described earlier, due to its regular structure, the crystalline sediment looks more transparent in spite of its higher particle densities.
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
KIRKWOOD-ALDER TRANSITION LN LATEX. I ACKNOWLED GMENT The authors express their sincere thanks to Dr. M. Wadati and Professor Dr. M. Toda for the valuable discussion in the theoretical field. Also, we thank Mrs. T. Kitayama for carrying out the preparation of latex samples. REFERENCES i. LUCK, W., AND r~VESSLAU, H., "Festschrift Carl Wurster." Gesamtherstellung Johannes Wiesbecket, Frankfurt am Main, W. Germany, 1960. 2. LUCK, W., KLIER, M., AND WESSLAU, H., Ber. Bunsenges. Phys. Chem. 67, 75, 84 (1963). 3. VANDE~I~O~,J. W., VAN DEN Hut, H. J., TAUSlC, R. J. M., AND OVEgBEEK, J. T. G., in "Clean Surfaces: Their preparation and Characterization for Interfacial Studies" (G. Goldfinger, Ed.). p. 15. Dekker, New York, 1970.
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4. KRIEGER,I. M., AND HILTN~.R, P. A., in "Polymer Colloids" (R. M. Fitch, Ed.) p. 63. Plenum, New York, 1971. 5. I-IACHISU, S., KOBAYASHI, Y., AND KOSE, A., J. Colloid Interface Sci. 42, 342 (1973). 6. ~TADATI,M., AND TODA, M. t J. P.~ys. So6. Japan 32, 1147 (1972). 7. AI.DE~, B. J., A~CDWAI2WmH~,T. E., Phys. Rev. 127, 359 (1962). 8. ALDER,B. J., HOOVER, W. G., AND YOUNG,D. A., J. Chem. Phys. 49, 3688 (1968). 9. KIRKWOOD,J. G., J. Chem. Phys. 7, 919 (1939). 10. P~a~m, Y. S., A:~D KRIEOER, I. M., Y. Colloid Interface Sci. 34, 126 (1970). ii. HILTNER, P. A., PAPIR, Y. S., AND KRIEGER, I. M., J. Phys. Chem. 75, 1881 (1971). 12. KOSE, A., OZAICI,M. ANDTAKANO,K., KOBAYASHI, Y., AND HACmSU, S., J. Colloid Interface Sci. 44, 330 (1973).
Journal of Colloid and Interface Science. Vol. 46, No. 3, March 1974
SEI HACHISU Institute for Optical Research, Kyoiku University, 22-17 Hyakunin-cho 3, Shinjuku-ku, Tokyo, Japan Received June 14, 1973; accepted October 4, 1973 Spontaneous phase separation phenomenon in a nonaqueous monodisperse latex system is studied to verify the Kirkwood-Alder transition in colloid systems. The nonaqueous system might be suitable for our purpose, because both electrical double layers and van der Waals force effect could be negligible therein. Polymethyl methacrylate latex cross-linked with divinylbenzene was dried and then dispersed in benzene at various concentrations. The phase separation occurs in certain particle concentration ranges, depending upon the degree of the cross-linking. The values of the concentration at which the phase separation starts are in the range of from 0.105 to 0.195 by measured volume fraction; smaller values correspond to lower degrees of cross-linking. Correction of the measured volume fractions for the swelling of the particles gives values very close to 0.5, which are independent of the degree of the cross-linking.This is in good agreement with the value 0.497 predicted by Alder, Hoover, and Young EJ. Chem. Phys. 49, 3688 (1968)]. In the phase-separated state the ordered phase which forms a sediment exhibits a beautiful opal-like iridescence (demonstrating the existence of polycrystalline structure), while the disordered state is rather translucent and gives weakly iridescent scattering, which would be attributed to the presence of spacial local order, that is, the liquid-like structure. Experimental evidence seems to support the conclusion that the phase separation which occurs in monodisperse latexes cannot be explained by the DLVO theory but could be attributable to the Kirkwood-Alder transition ill a hard sphere system. INTRODUCTION Order formation of particles in monodisperse latexes has attracted the interest of a n u m b e r of authors because of the beautiful iridescence from the ordered arrays of the particles, and in some works the p h e n o m e n o n of coexistence of the ordered and disordered phases was pointed out. Luck and Wesslau (1), and Luck, Klier and Wesslau (2), first to observe the 1 Presented in part at the 25th Symposium on Colloid and Interface Science held in Fukuoka, Japan, November 1972.
coexistence, seem to have regarded it as a result of some attractive force between the particles. Later, Vanderhoff et al. (3), observed this p h e n o m e n o n as a rapid appearance of all iridescent sediment in a deionized dilute latex, t h a t is, within 1-2 wk, the particles of some samples settled into a packed layer, leaving a thin clear s u p e r n a t a n t layer, and stated t h a t the ion exchange increased the rate of compacting of these particles into packed arrays. Krieger and Hiltner (4), in their studies of the Bragg reflection from the ordered latex, have
460
Journal of Colloidand InterfaceScience.Vol. 46. No. 3, March 1974
Copyright • 1974by AcademicPress, Inc. All rights of reproductionin any form reserved.
KIRKWOOD-ALDER
TRANSITION IN LATEX. I
found the coexistence of the two phases as an abnormal behavior of the changes in center-tocenter distance between latex particles, and stated that, at intermediate electrolyte levels, ordered and disordered phases coexist at equilibrium; the volume fractions of the coexisting phases are functions of the ionic strength. They have suggested the introduction of the theory of globular protein cluster formation proposed by Kirkwood and Mazur. The authors and a collaborator have reported in a previous paper (5) that aqueous monodisperse latexes, under certain conditions, spontaneously separate into two phases, one of which has a disordered structure and looks milky white, while tile other has an ordered structure that is more concentrated than the disordered one and is iridescent in its appearance provided that the distance between the particles is comparable in length with visible light wavelength. The authors have concluded that this cannot be explained by the DLVO theory but could be interpreted by the idea of the Kirkwood-Alder transition (6-8). In the field of physics, one of the most fundamental and interesting themes is a subject of transition between liquid and solid state, that is, whether or not the transition from liquid to solid state is possible in the absence of attractive potential. Kirkwood (9) discussed that in hard sphere systems the transition may occur when the volume fraction of the particles is exceeded by a certain value. Later on, Alder and Wainright (7) showed in their computer experiments using molecular dynamics method that in a two-dimensional system consisting of 870 discs, the phase transition begins at A/Ao = 1.3 (A is the area per disc, A0 is area per disc at close packing) and is completed at A/Ao = 1.43. Alder, Hoover, and Young (8) predicted for hard sphere systems that the transition starts at about 0.5 and is completed at about 0.55 by volume fraction. In our previous experiments a phase transition took place at considerably smaller volume
461
fractions than the predicted values. This was attributed to the larger effective volume of the particles because of the presence of electrical double layers around the particles. For further confirmation of the accordance between theory and experiments, it is desirable to observe this phenomenon in other systems which more nearly simulate the hard sphere system. As examples of this kind, two types of systems can be suggested from the colloid chemical point of view; one is the class of latex dispersed in nonpolar liquids such as hydrocarbons, and the other is aqueous latexes with high electrolyte concentrations which are stabilized by nonionic surfactants. As to nonaqueous latex systems, extensive studies have been carried out by Papir and Krieger (10), and Hiltner, Papir and Krieger (11). They showed that cross-linked polystyrene latexes could be redispersed in a number of organic liquids having different physical properties, and observed that the latexes in some polar organic media (aromatic) gave beautiful iridescence, whereas in nonpolar media the latexes did not give diffraction maxima despite stable dispersions being formed. They concluded that the order is attributed to electrostatic repulsion between particles as a result of partial dissociation of ionic surface groups. The authors have found that both crosslinked polystyrene and cross-linked polymethyl methacrylate latexes give iridescent dispersions in nonpolar solvents such as benzene, toluene, and carbon tetrachloride if some care is taken in the preparation of the dispersion. In the present paper, phase separation in a nonaqueous latex, polymethyl methacrylate (PMMA) particles in benzene, is studied. The polymer was cross-linked to prevent the particles from dissolving into the medium. This system is considered to possess neither electrical nor van der Waals interactions, and is considered to be an excellent model for the hard sphere system.
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
462
KOSE AND HACHISU EXPERIMENTAL
solution of the latex particles as described later. However, the regular trends in the sample Methyl Methacrylate (MM A )--Divinyl benzene latexes indicate that the cross-linking was (D V B ) Copolymer/Benzene Latex made, at least, in proportion to the amount of Cosss-linked PMMA in benzene was chosen DVB. The trends were confirmed qualitatively from a number of combinations of polymers by the fact that the greater the DVB content and nonaqueous solvents, because of ease of the greater the refractive index of the particles preparation, the nonpolarity of benzene, and and the less the degree of swelling, and vice the excellent optical properties of the system. v e r s a . The refractive indices of the particles and In St-DVB latexes, the swelling and dissolumedium in this system are so close to each other tion were appreciably smaller. that the latex looks almost transparent, when Particle diameters determined by electron observed under diffused light, which greatly microscopy are shown in the fourth column in facilitates observations. The phase separation Table I. The polymerized latexes, containing could easily be detected by the appearance of ca. 0.2 (by volume fraction) polymer, were tiny iridescent flecks in the suspension, and purified by deionization using a mono-bed ion furthermore, the three-dimensional mosaic ion exchange resin (Robin and Haas MB-3) structure of the ordered phase was clearly obin as much as 50% by volume of the latexes; served to have an opal-like appearance. Anthe resin was removed completely by repeated other merit of MMA-DVB copolymer is its centrifugation. high density (ca. 1.19), which makes the "phase A purified latex was vacuum dried to conseparated" crystals precipitate faster and prostant weight at room temperature. A small motes "spatial" separation of the two phases. amount of precisely weighed dried latex was Among the other systems, the styrene- placed in a test tube equipped with a screw cap divinyl benzene (St-DVB) copolymer/benzene with Teflon packing. A 10-15 ml quantity of system has the particular merit that the re- benzene was added and the tube was vigorsemblance in molecular structure between the ously shaken by a shaking device. Ill about 1 hr particles and medium assures that the van der complete dispersion was obtained. Then, a Waals interaction is almost nil. A few observa- sufficient quantity of benzene was added to tions using this system, which will be reported attain a total volume of 20 ml. In this preparaelsewhere, gave almost the same results as were tion, when the tube was allowed to stand obtained with the MMA-DVB copolymer/ quietly after the addition of benzene, the benzene system, indicating that with regard to dried latex at the bottom became swollen into van der Waals force the situation is the same a translucent gel and very slowly dispersed by in the two systems. diffusion into the upper liquid to form a concentration gradient. In about 1 mo the gel dispersed completely. It was remarkable Monodisperse latexes of PMMA cross-linked that ill the lower part of this gradient there withDVB were prepared by emulsion polymeri- appeared an ordered structure with an opalzation. The degrees of cross-linking were 2.5, like iridescence as shown schematically in 5, 10, and 15% by volume (20% cross-linking Fig. 1, which remained until just before comyielded nonspherical particles). The described plete dispersion. This phenonemon, which is values of the degrees of the cross-linking are referred to below, was important and useful volume percentages of DVB content on a because it served as a reliable measurement of monomer basis. It is questionable that all the the quality of the sample under preparation. molecules of the added I)VB have functioned For some uncertain reasons, some monodiseffectively as cross-linking agents, considering perse latexes dispersed in a nonaqueous solthe relatively high degree of swelling and dis- vent were sometimes noniridescent although
Preparation of Samples and Observation
Journal of Colloid and Interface Science, Vol. 46, No. 3, M a r c h 1974
KIRKWOOD-ALDER TRANSITION IN LATEX, I they had had high monodispersity and suitable particle sizes. The results of such experiment were very confusing and led us to a wrong conclusion. Such defective latexes were easily determined by this smlple test because they did not give the opal-like appearance in the concentration gradient. This is probably due to the presence of the impurities such as inorganic salts and/or oligomers of methyl methacrylate, because the anomaly did not occur when the latexes were thoroughly purified, using an ion exchange resin. Papir and Krieger (10) and Hiltner, Papir, and Krieger (11) stated that St-DVB copolymer latexes in benzene and in toluene and such as those having low dielectric constant did not give diffraction maxima, and the latexes in methanol did not give a stable suspension. Probably, these results were due to watersoluble impurities. ~ Suspensions thus obtained were almost clear when viewed under diffuse light, and the more transparent in appearance the less the degree of cross-linking. Suspensions of varying solid content ranging from 0.02 to 0.25 by measured volume fraction at an interval of 0.02 were prepared for each latex having a different degree of cross-linking. The measured volume fraction denotes volume fraction obtained from dry weight and the specific gravities of the polymer, and benzene (PMMA: 1.19 and benzene: 0.87, respectively). The effects of swelling and dissolution of the particles will be described later. The samples thus prepared were placed on a rack in increasing order of concentration and were immersed in water for the convenience of observation. The observation was made in a dark room under the illumination of a horizontal beam of white light. Virtually complete equilibrium was attained in about 1 wk and the iridescent phase appeared in all of the tubes except in those containing suspensions of lowest volume fractions (Fig. 2). In the phase separating tube iriI n o u r case b o t h c r o s s - l i n k e d p o l y s t r y r e n e a n d c r o s s l i n k e d P M M A l a t e x e s in m e t h a n o l g a v e s t a b l e a n d iridescent suspensions.
.~
0~
~
~.~
"~
o~
i
5"~
463
m
u
~o
o~ 0~c~
~v
¢9
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
464
KOSE AND ,HACIIISU
I m
~--'-~-1 I Transparent ~---I ~:1 2 Turbid, --- -----I colorless . . . .
!ill :i~!.! :ill
colored ~i;';:;~;] 4 Iridescent 5~ 3~', flecks
No. I
colored 6 Translucent, colored
0.02-0.06
"i "i "2
itl,
, , :' ,
2
3
4
0.07-0,11
state.
descence appeared, at first, along the inner wall of the tube as a vertical and specular reflecting color band and then as tiny glistening iridescent flecks came in the suspension as shown schematically in Fig. 3a. These flecks settled slowly and finally formed an iridescent and more transparent sediment with well-defined horizontal boundary. On the other hand, when suspending medium having greater specific gravity than latex particles such as dichloromethane (sp gr 1.33) is used instead of benzene, the iridescent crystallines formed in the bulk of the suspension moved toward the upper portion to form the iridescent layer at the top of the suspension. F r o m this fact, the particle
5 0,12-0.|3
Particle Volume
FIG. 1. Schmatic representation of a feature of MMADVB copolymer/benzene latex in the nonequilibrium
a
//A ///
"'" ;:i; ~5
5 Turbid, ::'"
///'
I ///~
I
!:!~~ T!:.: ;2;
i
u
r",5
6
7
8
0,14-0,16
Fraction(measured)
FIG. 2. Schematic representation of features of samples in the equilibrium, Sample V: 5~o crosslinking. ~ : Disordered portion; ~ . : Colored scattering portion; ~ - / - ~ : Ordered portion. No. 1-2: (0.02-0.06 by volume fraction) turbid, colorless. No. 3-4:(0.07-0.11 by volume fraction) turbid, colored. No. 5-6:(0.12--0.13 by volume fraction) phase separation was occurred. No. 7-8: (0.14--0.16 by volume fraction) entire body was in crystalline state. concentration of the crystalline portion is considered to be greater than that of the disordered portion. For the 50-/0 cross-linked case the general features in the final equilibrium state were as follows. I n the samples of the lowest polymer content (0.02-0.06 by volume fraction), which were noniridescent, the entire body of the
b
c
,\\\\~,~ ,//hl/!/!
.S.
FIG. 3a. Schematic representation of a sample in iridescent state. Sample V (5% cross-linking) (1) reflected light is orange; (2) reflected light is green. (b) Observation arrangement. (W) water; (MC) microcrystal; (0 and 0') Bragg angles for the different net planes; (L.S.) light source, parallel beam of white light. (c) Schematic representation of the relation among light source, reflecting crystal net planes and observing position. (L.S.) light source, parallel beam of white fight; (B.S.) beam splitter; (1) reflected light is orange; (2)green; (3)invisible. J o u r n a l o f C o l l o i d a n d I n t e r f a c e S c i e n c e , Vol. 46, No. 3, March 1974
KIRKWOOD-ALDER
465
TRANSITION IN LATEX. I
suspension was turbid due to the Tyndall scattering. In the second lowest group (0.070.11), the turbidity was somewhat stronger and the scattered light was tinted with iridescent color which changed as the direction of the observation changed. In the moderately concentrated samples (0.22-0.13),8 phase separation was observed; the ordered phase was a beautiful sediment packed with a number of small crystals with net planes reflecting iridescent colors,4 and the supernatant disordered phase had the same appearance as the second lowest group, that is, the scattered light was tinted. It is remarkable that the sediment, which was more concentrated than the supernatant portion, was significantly more transparent than the supernatant; this can be explained by the interference effect of the light by the ordered structure. The opal-like appearance indicated that the ordered phase had a polycrystalline structure. In the most concentrated group, the entire body of the suspensions were in the ordered state, with an appearance similar to the sediments in the phase-separated samples. As the polymer content increased the iridescent colors had a tendency to shift toward shorter wavelengths, and the polycrystalline structure became finer (individual crystals became smaller) and finally disappeared to give smooth rainbow colors. Critical values of polymer content for the appearance of colored scattering (C1) and for the phase separation (C2) are given in the fifth and sixth columns of Table I. These values cannot directly be compared with Alder-I-Ioover-Young's (8) prediction because the polymer particles must have been appreciably swollen and furthermore been T h e concentration range in which the two phases coexist was very narrow. T h e samples in the range shown in Fig. 2 were prepared b y careful dilution of ~a more concentrated entirely crystallized latex a t an interval less t h a n a 0.02 volume fraction. 4 T h e opal-like appearance observed in the course of preparation was due to the fact t h a t in the concentration gradient there was a region in which the concentration was adequate for the crystallization.
partly dissolved, releasing noncross-linked linear molecules into the medium. Therefore, for comparison with the prediction, the effective volume fraction of the particles ¢ should be used instead of the measured volume fraction C. This is shown in the following section. D E T E R M I N A T I O N OF T H E E F F E C T I V E V O L U M E F R A C T I O N (0)
The effective volume fraction (¢) can be determined from the intrinsic viscosity if we assume that the particles retain their spherical form after swelling (Fig. 4) and partial dissolution. Furthermore, it is also assumed that the swelling ratio ~ (ratio of swollen to unswollen volume) of the particles remains constant regardless of the extent of dilution of the latex, and the particles deform negligibly in the shear flow encountered in the viscosity measurements. Thus, ¢ is related to the measured volume fraction C by a simple equation q~ = ~.C. Considering the partial dissolution, the factor may not be the simple "swelling ratio" but also includes the effects of dissolution. At this point, however, we do not need to go further into this complexity but are satisfied with the constancy of ~. Viscosity of the latex is expressed by an extended Einstein equation as ~
= 2 + 2.5(~c) + ~ ( ~ c ) ~ . . . .
Then, 2
lira (~/~- 2 ) - = 2.5~. C~0
C
Denoting intrinsic viscosity by E~, becomes E@/2.5. Next, in obtaining ~r = ~suspension/'qmedium, correction of ~]med.has to be made for the effect of the dissolution. The viscosity of the medium ~/med. in this case, is not equal to that of pure benzene but is the viscosity of the benzene solution of the polymer eluted from the particles, and is no longer constant but decreases as the dilution continues. Therefore, 7Jrned. should be measured after each ~,~usp. measurement. However, because the Ubbelohde inter-
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
466
KOSE AND HACHISU
FIG. 4. Electron micrograph of 5% cross-linked PMMA latex particles once suspended and swollen in benzene. A small drop of the diluted benzene suspension was dried on a carbon-coated nitrocellulose film and then observed. Considering the bond rupture, swelling and consequent dissolution which the particle must have experienced in benzene the sphericity is surprising. Thus, the swollen particles (in benzene) are presumed to have retained good sphericity.
nal dilution viscometer was used in our experiment, measuring ~med. after each ~/,usp. measurement was very difficult. Hence, the relative viscosity of the medium was determined as a function of C, the particle volume fraction of the suspension, independently of nsusp, measurement. A supernatant solution was obtained by centrifugation 5 from a latex of moderate concentration ( C - - 0 . 0 5 for example) and nmed. It is of interest that when a uniformly dispersed latex suspension having 5% solid content was subjected to centrifugation, it separated into six different phases; transparent supernatant, colorless turbid, colored turbid, iridescent fleck, colored turbid, and colored translucent phase in order from the top to the bottom of the suspension. This feature of the sample was identical to that in the nonequilibrium state as shown in Fig. 1.
was measured using an Ubbelohde viscometer at exactly the same degrees of dilution corresponding to those employed in the */su~p.measurement. Here an assumption was made that the fraction of the soluble portion of a crosslinked P M M A latex particle is constant regardless of the degree of dilution. This was ascertained in relatively few numbers of cases. The relative viscosity of the suspension and of the medium, based on the pure benzene, versus C curves are shown in Fig. 5. In Fig. 6 is shown a plot of ( ~ s u s p . / ~ m e d . - - 1)/C versus C. Intrinsic viscosities thus obtained are listed in the eighth column in Table I. The values of ~ thus obtained for different cross-linked latexes are given in the ninth column of Table I. In the 10th column are the critical values for coloration of scattered light
Journal of Colloid and Interface Science, VoL 46, No. 3, March 1974
467
KIRKWOOD-ALDER TRANSITION IN LATEX. I
in the effective volume fraction obtained from the values in the fifth column by multiplication with the respective ¢ values. In the l l t h column are given the critical values of the phase separation and in the last column those of the entire crystallization, although these values are not exact. OBSERVATION OF IRIDESCENCE
3O
2O
c
Study of the iridescence gives valuable information about the structure in monodisperse latexes. Spectroscopic investigations are under way in our laboratory. Here, a brief description is made of its qualitative character. The features of the crystalline body in a test tube were mentioned earlier and depicted in Fig. 3 for the case of a 50-/0 cross-linked latex.
I0
0
I
0
0.01
I
I
I
I
0.02
0.03
0.04
0.05
Volume Fraction (C)
FIG. 6. Reduced viscosity of Sample V latex suspension as a function of measured volume fraction of latex particles, where ~ = relative viscosity of the suspension/relative viscosity of the medium.
4
When observed by backward reflection as shown in Fig. 3a, b and c, four typical features were: (a) a bright orange colored band at the center of the tube along the inner surface and parallel to the axis, (b) two green bands at the symmetric positions with respect to the orange band, (c) a number of brilliant orange colored flecks (1-2 m m in diameter) in the bulk of the suspension and (d) a few number of green colored flecks. The above observation can be explained according to fcc model as follows:
A
% 2
B
1
0
0.01
0.02
0.03
0.04
0.05
Volume Froction (C)
FIO. 5. Relative viscosity based on pure benzene versus measured particle volume fraction curves of latex suspension and its medium. (A) The relative viscosity curve of Sample V/benzene suspension, where ~Tr(suspension) ~ ~susp./~Tpurebenzelxe; (B) the relative viscosity curve of the medium, the supernataut solution separated from Sample V latex suspension, as a function of the particle volume fraction of the suspension. For this curve the values on abscissa do not mean the volume fractions of the eluted polymer, but were determined from the value of the measured particle volume fraction of latex suspension from which the supernatant solution had been separated and each corresponding degree of dilution. In this case, ~/r(medium) ~/medium/~Tpure benzene.
Let the center to center distance be D, the diameter of the swollen particles be D~ and the real diameter of the unswollen particles be Dr. Assuming that the volume fraction of the swollen particles is 0.55 in compliance to the predicted values of Alder, Hoover and Young (8), the relation between D and Ds is D3
0.74 = 1.345
-
D~8
[-17
0.55
where 0.74 is the volume fraction of particles at close packed state, then
D/D~ =
(1.345)t = 1.10.
Journal of Colloid and Interface Science, Vol. 46, No. 3, Marcl~ ~:97%
468
KOSE AND HACHISU
Since the swelling ratio is 4.2 for Sample V, D. = (4.2)LDr = 1.61"D~.
[2]
Combining Eqs. [1] and F2], D = 1.10 X 1.61 X D~ = 1.77.D~.
[3]
The distances between net planes are, d(m> = (])½.D, d<2oo) = \ 2 /
'
[+3
d(22o) = ½"D. Reflection from (100) and (110) are destroyed by geometric structure factor effect. Substituting Eq. [-3] in to Eq. I-4-] and using the values of 1380/~ for D~ the lattice distances become din1) = 0.82 X 1.77 X 1380 = 2002, d(~00) = 0.71 X 1.77 X 1380 = 1734, ['5-]
The scattered light from the supernatant phase was faintly colored and changed with change of angle of the observation, e.g., from red (backward), via green (at right angle to the incident direction) to blue. This corresponds to the X-ray halo obtained with liquid, and indicates presence of local spacial order or liquid-like structure in the latex suspension. The data given ill Table I indicate that the liquid-like structure begins to appear at about 0.25 by volume fraction. Another possible explanation of this coloration would be the presence of tiny crystallites suspending in disordered phase (2) or Mie scattering. However, the authors would favor the liquid structure view, because the state of coloring does not change upon quiet standing for more than 6 mo and upon slight dilution the colored phase disappeared, resulting in a colorless turbid phase. If the color is of Mie type, it would not disappear upon dilution.
d~2~0) = 0.50 X 1.77 X 1380 = 1221.
CONCLUSION
The average refractive index is very close to 1.50 and Bragg equation for the first order interference is
Since, in the present system, both the van der Waals and the electric interaction do not play a significant role, the spontaneous phase separation into the ordered and disordered phase, with ordered phase being more concentrated, cannot be explained by any theory other than the Kirkwood-Alder transition. The obtained values of ¢, scattering around 0.5, for the start of separation are in good accord with Alder, Hoover and Young's (8) prediction. Thus, the phase separation in monodisperse latexes has been explained; we no longer need to assume the attractive interaction of electrical double layers in concentrated systems. At the same time, the Kirkwood-Alder theory can be said to have been substantiated by the experimental evidence. Another observation, the iridescent scattering from the disordered phase seems to indicate the presence of a local spacial order that is characteristic of the liquid structure. The monodisperse latex has now been found to be an excellent model system for the study of structure of liquid as well as of solid systems.
X = 2 n d sin0 = 3d,
where 0 = 90, n = 1.50, and d's are given in Eq. ['5]. Peak wavelengths are X(m) = 6000 A
(orange),
X(200) = 5200 )t
(green),
Xc~20) -= 3660/~, upper two values corresponding to orange and green, respectively, and the third one is invisible. From these data, the orange color at the center of the tube is considered to correspond to the reflection from the (111) plane of the fcc lattice which is in accordance with Luck, Klier, and Wesslau's (2) results and our observations (12), and green from the (200). As described earlier, due to its regular structure, the crystalline sediment looks more transparent in spite of its higher particle densities.
Journal of Colloid and Interface Science, Vol. 46, No. 3, March 1974
KIRKWOOD-ALDER TRANSITION LN LATEX. I ACKNOWLED GMENT The authors express their sincere thanks to Dr. M. Wadati and Professor Dr. M. Toda for the valuable discussion in the theoretical field. Also, we thank Mrs. T. Kitayama for carrying out the preparation of latex samples. REFERENCES i. LUCK, W., AND r~VESSLAU, H., "Festschrift Carl Wurster." Gesamtherstellung Johannes Wiesbecket, Frankfurt am Main, W. Germany, 1960. 2. LUCK, W., KLIER, M., AND WESSLAU, H., Ber. Bunsenges. Phys. Chem. 67, 75, 84 (1963). 3. VANDE~I~O~,J. W., VAN DEN Hut, H. J., TAUSlC, R. J. M., AND OVEgBEEK, J. T. G., in "Clean Surfaces: Their preparation and Characterization for Interfacial Studies" (G. Goldfinger, Ed.). p. 15. Dekker, New York, 1970.
469
4. KRIEGER,I. M., AND HILTN~.R, P. A., in "Polymer Colloids" (R. M. Fitch, Ed.) p. 63. Plenum, New York, 1971. 5. I-IACHISU, S., KOBAYASHI, Y., AND KOSE, A., J. Colloid Interface Sci. 42, 342 (1973). 6. ~TADATI,M., AND TODA, M. t J. P.~ys. So6. Japan 32, 1147 (1972). 7. AI.DE~, B. J., A~CDWAI2WmH~,T. E., Phys. Rev. 127, 359 (1962). 8. ALDER,B. J., HOOVER, W. G., AND YOUNG,D. A., J. Chem. Phys. 49, 3688 (1968). 9. KIRKWOOD,J. G., J. Chem. Phys. 7, 919 (1939). 10. P~a~m, Y. S., A:~D KRIEOER, I. M., Y. Colloid Interface Sci. 34, 126 (1970). ii. HILTNER, P. A., PAPIR, Y. S., AND KRIEGER, I. M., J. Phys. Chem. 75, 1881 (1971). 12. KOSE, A., OZAICI,M. ANDTAKANO,K., KOBAYASHI, Y., AND HACmSU, S., J. Colloid Interface Sci. 44, 330 (1973).
Journal of Colloid and Interface Science. Vol. 46, No. 3, March 1974