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Langmuir 1993,9, 394-411
Feature Article Recent Study of Polymer Latex Dispersionst Shin Dosho,! Norio Ise,*J Kensaku Ito,ll Satoshi Iwai,* Hiromi Kitano,ll Hideki Matsuoka,! Hiroshi Nakamura,* Hiroya Okumura,* Takashi Ono,! Ikuo S. Sogami,*J Yoshihiro Ueno,*Hiroshi Yoshida,i and Tsuyoshi Yoshiyamal Department of Polymer Chemistry, Kyoto University, Kyoto 606-01, Japan, Department of Physics, Kyoto Sangyo University, Kyoto 603, Japan, Department of Chemical and Biochemical Engineering, Toyama University, Toyama 930, Japan, and Fukui Research Laboratory, Rengo Co. Ltd., 96-11 Asahi, Kanazu-cho, Sakai-gun, Fukui 919-06, Japan Received March 5, 1992. In Final Form: August 28, 1992
The dynamic aspects in latex particle dispersionswere studied using video imagery combined with an image data analyzer and Kossel line analysis. The lattice vibrations and lattice defects in the colloidal crystals were demonstrated. The trajectories of particles in the ordered regions were shown to be quite different from those in coexisting disordered regions. The kinetics of (2D) crystal growth was followed by using the microscopic information(as a density function) and ita Fourier transformation. The process was also followed by the radial distribution functiong(r),which was obtained by direct measuremente of interparticle distances. The Ostwald ripening mechanism was confirmed in the process of crystallization. The 3D crystallizationprocess over a longtime span was investigated by the intrinsic Koeeel imageanalysis. The ordering was found to proceed through several intermediate processes starting with a 2D hexagonal close-packed structure through stages characterized by a strong anisotropy ending with face-centeredcubic structure (fcc) or body-centered-cubic structure (bcc). The implication of the two-state structure (coexistenceof ordered and disorderedregions) was discussed in conjunction with the structure of liquids. The Smoluchowski theory of collisions was tested by measuring the time evolution of dimers (collision products) of latex particles. The 'inside" structure of latex dispersionswas studied by a confocal laser scanning microscope. The interparticle distance was found to be insensitive toward the distance from the glass-dispersion interface, while the crystallization was much easier near the interface than inside the dispersions in ita initial stage. The void structure was found not only near the interface but also inside the dispersions: In some cases, the cross sectionof the void was found to become larger with distance from the interface. The study by the ultra-small-angleX-ray scattering (USAXS)technique confiied the resulta obtained by the Kossel line analysis and also indicated the existence of fcc structures inside the dispersion. The glass-dispersion interface (wall) effect was concluded to be negligible on the interparticle distance. Finally, attention was drawn to the facta that the (purelyrepulsive) DLVO (or Yukawa)potential and the (repulsiveplus attractive) Sogami potential provide almost equally satisfactoryagreements with observed structure factor and g(r)and also with observed shear modulus of latex dispersions. This implies that the DLVO (or Yukawa) potential is not the only correct potential to describe the colloidal behavior. The two-state structure, the observed interparticle distance being smaller than the average spacing, the void structure,the Ostwald ripening mechanism,and the re-entrant phase separationtestify to the existence of a long-range attraction in addition to the widely accepted repuleion. Considering any one ion, we shall find on average more dissimilar than similar ions in its surroundings, an immediate consequence of the electrostatic forces effectiue between the ions. (Debye, P. J. W . ;Hiickel, E. Phys. 2.1923,24,185.) 1. Introduction
About forty years ago, Sir Lawrence Bragg and J. F. Nye deviseda scheme for making a model of metal crystals.1 Their so-calledbubble rafts visualized successfullyvarious phenomena (such aa grain boundaries, point defects, dislocations, recrystallization, and annealing) that had been believed to exist in reality. However one serious disadvantage was inherent in this model; thermal motion 'Dedicated to Professor R. H. Ottewill on the occasion of his retirement. Kyoto University. I Rengo Co. Ltd. 11 Toyama University. Kyoto Sangyo University. (1) Bragg, L.; Nye, J. F. R o c . R. SOC.London 1947,190,474.
*
waa not reproduced. Since this factor is highly important in real systems, this disadvantage is crucial. Recent advances in synthesis techniques of high polymers have allowed us to produce well-characterized monodisperse polymer latex particles. When fairly large (over 0.2 pm in diameter) latices are dispersed into a liquid, their behavior can be seen under an ultramicroscope with the technique developed by Hachisu et al.,2when the refractive index difference between the liquid and the particles is large enough. In other words, the long time scale of the motion of latex particles enables us to make real time observations on various phenomena, which have been impossible for atomic and molecular systems. Since the latices are much smaller than the bubbles, and can be dispersed 'monomolecularly" in liquid (namely, not in contact with each other aa waa the case with the bubbles), the thermal motion can be visualized. Thus the polymer latex dispersions can be expected to be a much more realistic model for atoms and molecules than the bubble rafts. In the present review, recent findings mostly on (2) Kose, A.; Ozaki, M.; Takano, K.; Kobayashi, K.; Hachisu, H. J . Colloid Interface Sci. 1973,44, 330.
0743-7463/93/2409-0394$04.oo/o0 1993 American Chemical Society
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Figure 1. Ordering of polymer latex particles in aqueous dispersion: Latex, SS-45; latex diameter, 0.5pm;number of strong acid groups per particle, 6.5 X lo5(charge density, 13.3 pC/cm2); latex concentration, 2 70. Each white spot is a latex particle. The center-to-center interparticle distance is about 1 pm. Point defects and edge dislocations are clearly seen. Microscope used was a Carl Zeiss Axiomat IAC.
dynamicaspects in the latex dispersionswill be discussed; the rather static nature of ordering phenomenon of latex particles has been reviewed previously.3 2. Study by Reversed-Type Metallurgical Microscopes a. Ordered Structure, Lattice Vibration, and Lattice Defects. The monodisperse latices to be discussed in this paper were synthesized by an (aqueous) emulsion copolymerization of styrene and styrenesulfonate,unless otherwisestated. Becauseof their affinity toward the polymerization medium (water), the ionic (sulfonate and sulfate) groups are believed to exist on the surface of the polystyrene spheres. When suspended in dissociating liquids, the particles are dissociated into negatively charged spheres and (hydrated) protons. In the present article,light water was chosen mostly. In case it was desirable to rule out the influenceof the gravitational sedimentation, a mixture of heavy and light water was adopted. When the latex dispersionscontain a fairly high level of ionic impurities, the particles show almost free motion, as is easily confirmed by microscopy. When the impuritylevel is lowered by methods such as ultrafiltration, the particles are no longer randomly distributed but, surprisingly,show a more or less ordered distribution due to electrostaticinterparticleinteraction,although they are in liquid media. Figure 1 is a micrograph (not an electronmicrograph)showing ordering of latex particles on a horizontalplane in the dispersion. (The micrographs provide compelling evidence for the ordering of latex particles. However, it was not possible to see ordered arrangements by electronmicrographs; probably the organization is destroyed in the freeze-dryingtreatment of dispersions. Thus seeing is not always believing.) The orderedstructurecould be proved to be three-dimensional by laser diffraction analyses4t5and also by shifting the ~~
~~
~~~~
(3) Ise, N. Angew. Chem. 1986,98,323;Angew. Chem., Znt. Ed. Engl. 1986,25,323. (4) Clark, N.A.;Hurd,A.;Ackerson,B.Nature 1979,281,57. Ackerson, B. J.; Clark, N. A. Phys. Reo. Lett. 1981,46, 123. ( 5 )Yoshiyama,T.; Sogami, I.; Ise, N. Phys. Reo. Lett. 1984,53,2153.
focus plane of the microscope,6 It should be clearly understood that the micrographs show the anionic latex particles while the cationic small ions (protons in the present case)exist in the space between the latex particles, though invisible. Thus, Figure 1may be taken to represent a plane of a metal crystal. In our analogy the particles and small ions correspond to metal ions and free electrons in the real crystals, respectively. Figure 1is impressive but misleading, since the actual situation is not at all static as imagined from this figure but highly dynamic. By taking advantageof video imagery and an image data analyzer, various dynamic properties of the particles can be studied. Figure 2 shows the locations of the center of latex particles in the ordered regions in 8.3 s (about 240 points for each parti~le).~ Clearly the particles show (isotropic) thermal motion around the lattice point and the motion is more violent at lower concentrations, as expected. The maximum amplitude of the vibration became larger with decreasing latex concentration;it was about h0.20 of the spacing (about 1pm) under the experimental condition of Figure 2 (at 1% ). Nonetheless,the ordered structure was maintained. Thoughnot evidentfrom Figure 2, an interestingfeature of the oscillation of two adjacent lattice planes can be seen, when the trajectory of the single particle is analyzed as follows: Figure 3a shows the trajectories of three particles in the “perfect”ordered structure obtained in 1 s and Figure 3b represents their displacement-time curves of the three particles decomposed into x: and y directiom8 The displacement-time curves for the three neighboring particles have similar shapes and phases. Although the originalpapefl should be consulted for detail,the influence of the first particle is evident on the third as is seen from Figure 3, but not so on the sixth (about 6 pm away). An interparticle correlation really exists. According to the preliminaryFourier analysisof the curves,this correlation could be reproduced by a vibration with a period of about 1s. Thus the lattice points show a coupled vibration of fast (thermal motion) and slow (motion of lattice plane) modes. It would be interesting to point out an analogy with lattice vibrations in s01ids.~ It is rather difficult to obtain “perfect” lattice structures for the latex dispersions. We can often see Schottky and Frenkel defects and edge dislocations. The coordinates of particle centers around the point defect were determined for 1s, reproduced on a new video frame, and shown in Figure 4. The distribution of particles in the “perfect” structure was isotropic, as is clear from Figure 2, whereas the particles around the Schottky defect (particles 8 to 13) had a tendency to move in a direction toward the defect with a higher probability than in other directions. This seemsto be reasonable sincethe restoring force of the particles along this direction would be smaller because of the lack of particle at the defect than that of those in other directions and in a “perfect” lattice. It is to be recalled that the change of thermal entropy of solid crystals due to point defects is evaluated by the Einstein model with the assumptionthat the frequencyof vibration of atoms along the direction toward the point defect is (6) Ito, K.; Nakamura, H.; Ise, N. J. Chem. Phys. 1986,85,6136. (7) Ito,K.; Nakamura, H.; Yoshida, H.; Ise, N. J. Am. Chem. SOC.1988, 110,6955. (8)Ise, N.; Matauoka, H.; Ito, K.; Yoshida, H. Discuss. Faraday SOC. 1990,90,153. (9) Kittel, C. Introduction to Solid State Physics, 5thed.;John Wiley New York, 1976.
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Figure 2. Location of the center of the particle in the ordered structure in 8.3 s at room temperature: latex, N400 (diameter, 0.4 pm;charge density, 6.9 pC/cm2). The original micrographic picture was taken by a Carl Zeiss microscope and a video system at every l/30
s. After computer treatment, the particle centers in 8.3 s were reproduced in one new frame and photographed.
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Figure 3. Lattice vibrations: latex, N400 (the same as in Figure 2); latex concentration,0.5 9% ;room temperature. Reprinted with permission from ref 8. Copyright 1990 the Royal Society of Chemistry. (a) Trajectory of particles in a 'perfect" lattice in 1 s. Although the picture was omitted, the interparticle distance between two particles was about 1pm. (b) Lattice vibrations in x and y directions. The displacement is plotted against time.
smaller than that in the "perfect" lattice.1° The basic aspect of the entropy calculation appears to be substantiated at least qualitatively by the latex study. Quantitative discussion of existing theories on lattice defects will be made after a large population of lattice defects has been studied. b. Inhomogeneity in Particle Distribution in Macroscopically Homogeneous Dispersions: The TwoState Structure and Void Structure. In highly concentrated dispersionsit is not at all difficult to accept that particledistributionis determinedsimplyby the exclusion volume effect between the particles. Such a situation was depicted in Figure 1 of the previous review." Various properties of such dispersions would be described satisfactorily by the purely repulsive interactions such as the DLVO or Yukawa potential. In dilute dispersions, how(10) For example, see Henderson, B. Defects in Crystalline Solids; Edward Arnold Publishers: London, 1972; Chapter 1. (11)Ise, N.; Matsuoka, H.; Ito,K.; Yoshida, H.; Ymanaka, J. Langmuir 1990,6,2%.
Figure 4. Distribution of particles around a Schottky defect in 1s: latex, SS-45 (the same as in Figure 1);latex concentration, 1.0%; room temperature. The motion of the particles 8,9,12, and 13 is definitely anisotropic while the motion of the particles 10 and 11is apparently isotropic. This is due to the rather short observation period (1s). When the period is extended, particles 10 and 11 also show anisotropic movement. Reprjnted with permission from ref 8. Copyright 1990 Royal Society of Chemistry.
ever, it is definitely incorrect to presume that the ordered structure such as shown in Figure 1 covers the entire dispersion volume. We have observed the two-state structure, namely coexistence of a stable localized, nonspace-fillingstructure with free particles, particularly for highly charged latex p a r t i ~ l e s . ~ J ~ J ~ Figure 5 shows trajectories of latex particles in the ordered and coexisting disordered regions for 11/15s. It is evident that the motion of the disorderedparticles is much more vigorous than that of the particles in the ordered regions to such an extent that the thermal motion of the ordered particle around the lattice points is almost indiscerniblein Figure 5,though fairly substantialasshown in Figure 2. We note that the motion of the particle in the disordered regions can be approximatelydescribed by the (12) Ise, N.; Okubo, T.;Sugimura, M.;Ito, K.;Nolte, H. J. J. Chem. Phys. 1983, 73,536. (13) Yoshiyama, T.; Swami, I. S. hngmuir 1987,3,851.
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.'
. .
Figure 5. Trajectories of latex particles in the ordered (lower part) and coexisting disordered regions (upper part) for 11/15 s: latex, N300 (diameter, 0.3 pm; charge density, 1.3 pClcmz);latex concentration, 2%. The particle centers in 11/15 s, which were photographed by an Olympue microscope from the side of the observation cell and stored in the image data analyzer, were demonstrated in one new frame and connected with lines wing the analyzer. To simplify the picture, not all of the information obtained in 11/15 s was used. The position of the particles in the disordered region at the starting time is shown by open circles and that after 11/15 s by filled circles. The lines without either open or filled circles indicate the three-dimensional,out-of-focusplane movements of particle, which cannot be photographed.
Einstein theory on Brownian motion:14 The root-meansquare displacement, (R2)1/2, of Brownian particles can be determined by microscopic observation under a condition in which the motion is not far out of the focal plane. The observed values have been reported to be in good agreement with the theory at relatively low latex concentrations (Le., 0.1% ! or below) and/or at salt concentrations of 10-2 to 10-3 M.W6 Another type of inhomogeneity of particle distribution is the existence of a void structure. This was first pointed out by Hachisu et aL2 and recently observed by us and Kesa~amoorthy.~~-~g Most important is that the void structure remains for surprisingly long periods and that the void is three-dimensional.8 Recently Murray and her co-worker reported a similar kind of void structure for latex systems.20 Because their voids were formed simply because the space was too small to accommodate the latex particles, their void formation has nothing to do with interparticle interaction and does not correspond to the physical reality. In our case, the particles had freedom to form 3D-ordered structures and to move three-dimensionally, and nevertheless the voids containing practically no particles inside were created. There must be physical factor(s)behind the phenomenon. Since the void structure had been found exclusively by the metallurgical microscope, one has to consider an effect inherent to this method, (14) Einstein, A. Ann. Phys. (Leiprig) 1905, 17, 549. (15) Cornel1,R.M.; Goodwin,J. W.; Ottewill, R. H.J. Colloid Interface Sci. 1979, 71, 254. (16) Iee, N.; et al. J . Am. Chem. SOC.1985, 107, 8074. (17) Ise, N.; Ito, K.;Yoshida, H. Polym. Prepr. (Am. Chem. SOC.,Diu. Polym. Chem.) 1992,33, 769. (18) Ise, N. Proceedings of the 19th Yamada Conferenceon Ordering
and Organization in Ionic Solutiorw; Ise, N., Sogami, I., Ed.; World Scientific: Singapore, 1988; p 624.
(19) Keeavamoorthy,R.;Rajalakshmi,M.;Rao,C.B.J.Phys.: Condens.
Matter 1989, 1, 7149.(20) Van Winkel, D. H.; Murray, C. A. J. Chem. Phys. 1988,89,3885.
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for example, a wall effect. For polystyrene-based latex particles in water, the turbidity of the dispersions allows us to observe particles near the cover glass, at most 10pm and usually 1or 2 pm away from the glass wall. Although particles directly attached to the wall can be differentiated from other particles quite easily because the former does not show the vibrational motion discussed above, it is true that the wall effect is still a factor to be negated in our argument. If this were really a factor causing an artifact, the void structure should not be observed far inside of the dispersions. However, as is clear from Figure 6, a confocal laser scanning microscope, which enables us to observe the inside structure, recently revealed that the void size became larger with increasingdistance (up to 30pm) from the wall. Thus the wall effect may be ruled out, since it should become weaker with increasing distance. Although quite surprising, the presence of the void structure could be inferred from previous experiments; the interparticle distance determined on micrographs (20,,,) was smaller than the average spacing calculated from the initial latex concentration DO).'^ The inequality relation was first experimentally noted by Daly and Hasting.2l Probably because of its highly surprising nature, they attributed the inequality relation to evaporation of solvent, which must cause concentration of the dispersions and hence an apparently smaller interparticle distance. Since our dispersion cell was designed to prevent or minimize solvent evaporation, this factor can be excluded from further consideration, particularly at room temperature. Accepting that the inequality relation is a physical reality, we claim that the ordered structure, in which was measured, is not space-filling, but localized. Actually, such a localized structure could be photographed, as was shown in Figure 5. If all particles were assumed to be in the ordered structure and if 2Dexp is half of 200,the sum of the volumes of all localized structures must be l/g of the totaldispersionvolume: seveneighths of the dispersion volume cannot contain particles. Such a mass balance consideration provides of course an overestimated void volume, since Brownian particles can also exist in the dispersions, but it tells us that the presence of the void structure is not at all inconceivable. c. Kinetics of Crystal Growth The Fourier Transformation of Microscopic Information and the Ostwald Ripening Mechanism. As mentioned above, ordered structures were found to coexist with disordered (Brownian) particles. Furthermore Ito et al. showed that the size and shape of the structure changed with time.7 Thus, it was thought interesting to follow the kinetics of the growth of the ordered structure. To study the two-dimensional (2D) aspect in a relatively short time span, Ito et al. adopted the following procedure:22723Latex dispersions were purified and particles were allowed to form an ordered structure (in the dispersion cell for microscopic observation),which was confirmed by microscopy. Then a small amount of salt was added and the ordered structure was destroyed. Thereafter, purified ion-exchange resin was added to remove the added salt. The ordered structures were re-formed with time. The time evolution of the structures was photographed by a video camera at a fixed position in the dispersion cell. The micrographs were treated by an image data analyzer and coordinates of the centers of particles were obtained. Then by using the following very basic principle of the scattering (21) Daly, J. G.; Hasting, R. J. Phys. Chem. 1981,85,294. J.Am.Chem.Soc. 1989, (22) Ito,K.;Okumura,H.;Yoshida,H.;Ise,N. 111, 2347. (23) Ito, K.;Okumura, H.; Yoahida, H.; Ise, N. Phys. Rev. B 1990,41, 5403.
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Figure 6. Void structures observed on horizontal focus planes between 6 and 60 pm from the top of a latex dispersion by a confocal ’ in a D20-H20 mixture. laser scanning microscope: latex, NlOOO (diameter, 0.96 pm; charge density, 12.4 pC/cm2);concentration, 2.0 % The scale shown at the right bottom of the pictures is 50 pm. The six micrographs were taken at distances of 6,10,20,30,40, and 60 pm, respectively, from the glass-dispersion interface at the top of the dispersion. The pictures were taken without changing the position of the microscope and that of the dispersion. This means that the ‘black areas” seen represent the cross sections of 3D void structures. Note that the largest black area shown became larger with increasing depth between 6 and 20 p m (the largest distance was about 150 pm) and then became smaller. A t 60 pm, the black area is no longer seen, implying that the void is almost 60 pm long. The bright area is seen a t 60 pm in the same location as the black areas a t other depths, indicating that stronger light could reach because of lack of particles in the void.
phenomenon A(b) =
p(r) exp[-2ri(b*r)] dr
(1)
where r and b are the real space vector and reciprocal space vector, respectively, the amplitude of scattered radiation A(b)was computedfrom the particlecoordinates, (densityfunctionin real space,p(r)).24 Ito et al. confirmed (24) Ito, K.;Ise, N.J. Chem. Phys. 1987,86,6502.
that uhighly”ordered arrangementsof latex particlesgave spots in the Fourier space whereas neither spots nor halos were obtained for completely random arrangements. When ordered structures coexistedwith random particles, in other words, when the two-state structure was maintained, intermediate situations were obtained in the satbring profile. The interparticledistance,D e x p , found from the Fourier patterns agreed with that directly measured on the micrographs, as it should. To follow the time evolution of the ordered structure by
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Langmuir, Vol. 9, No. 2, 1993 399 b. 2hr 10min
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c. 2hrs 40min
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Figure7. Structure growth of latex particles: latex, N400;latex concentration, 2 % ,room temperature: (a) micrographs showing digitized particles and the unit of the ordered structure at 1h (i), 2 h (ii), and 2 h 45 min (iii) after the onset of crystallization; (b) corresponding Fourier patterns. The study was carried out as follows. First the ordering of latices in dispersion was confirmed by the ultramicroscope. Then, NaCl was added to the dispersion to a concentration of M, which destroyed the ordering. The crystallizationwas allowed to take place by putting highly purifiedion-exchange resin beads into the dispersion,which removed the added simple salt ions. The degree of purification was checked by conductivity measurements. The micrographs were taken at a fixed position of the dispersions at various times and digitized by the image data analyzer. The coordinates of the particles (density function) were 2D Fourier-transformed to obtain the amplitude of the scattered radiation. From the Fourier patterns, the interparticle distance 2Dexp was determined and found not to change with time. By using the 2DeXpvalue thus found, three particles forming a regular triangle with a side of 2Dexp (1i 0.15) were searched by a computer from the digitized micrographs,connected by the straight lines and shown in Figure 7a.
computer processing, the elementary unit of ordered structures was defined as a regular triangle with a side equal to 2Dexpwith a 15% latitude. This choice is reasonable since regular hexagons having six regular triangles were often observed and allowance had to be made for the lattice vibration and distortion. Thus, three particles apart from each other with a distance, 2of,(1 f 0.15), were searched and connected by straight lines. Figure 7 presents how the ordered structure grew with time. The number of the structureunits, namely triangles, increased with time, and the 2D Fourier images changed from halo(s)to spots. Amazingly, the interparticledistance from the images (u>,,,) hardly changed with time, reflecting the fundamental nature of this quantity.
1
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Figure 8. W)-radial distribution function g(r) determined by directly measuring the interparticle distance on the particle distribution images at (a) 20 min, (b) 130 min, (c) 160 min, and (d) 180min after deionizationwas started: latex, N300 (diameter, 0.32 pm; charge density, 1.3 pC/cm2); [latex], 1.0%; 25 "C. By use of a work station, Sun 4 (Sun Microsystems, Inc., Mountain View, CA), 4000-1oooO particles were treated. Reprinted with permission from ref 25. Copyright 1991 Royal Society of Chemistry.
Another way to examine the process of crystal growth is to determine the radial distribution function g(r). In a recent work by Yoshida et al.,25 the (2D) g ( r ) was determined directly from the coordinate information of the particle distribution. This procedure is straightforward, compared to the conventionalone employed in real atomic and molecular systems in which g(r) is determined from the scattering information. Figure 8 gives the g ( r ) at four different stages of crystallization of polystyrenebased latex particles in a D~O-HBO mixture. The number of nearest-neighboring particles, n, was conveniently computed from g(r) by
n = Npc Z ~ r g ( rdr)
(2)
where Npis the average number density of the particles and rl and r2 are the zero cross positions of the first peak of k(r) - 1I, in other words, g(r1) = g(r2) = 1. The g(r) at 20 min displayed a typical situation to be expected for noninteractingsystems. With the elapse of time, g ( r ) started showing peak(@as anticipated. After the very early stage of crystallization,as s h o p in Figure 9, the n increased up to about 4, where n was temporarily saturated. Then, the quick increase of n to about 5.5 followed and the ordered structure was almost complete. The n value smaller than 6, which is expected for the complete (2D) hexagonalpacking, might be due mainly to lattice defects and vibration present in the ordered structure. The time necessary for the Fourier patterns to become spots was dependent on latex concentration and temperature: for one sample, N300, it was 4 h 50 min, 3 h, and 1h 20 min for 0.5 % , 1% ,and 2% ,respectively, at room temperature. At 1%of another sample, SS-104 (diameter, 0.36 pm; charge density, 1.4 pC/cm2),it was 1 h 30 min, 4 h, 6 h 30 min, and 14 h at 10 "C, 20 "C, 30 "C, and 40 "C, respectively. Similar results were obtained in a H20-DzO mixture (specific gravity, 1.05); no significant differencefrom the results in H20 was noticed in either the 2D crystallization (25) Yoshida, H.;Ita,K.;Ise, N.J. Chem. SOC.,Faraday Trans. 1991, 87,371.
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Figure 9. Time evolutionof the number of nearest-neighboring particlesduring crystallization in a D20-H20mixture. The filled symbolsrepresentthe almost complete ordered structure. Latex, N300 (the same as in Figure 5); 25 “C; [latex]: circles, 0.5%; triangle, 1.0 % ; square, 2.0 % Reprinted with permission from ref 25. Copyright 1991 Royal Society of Chemistry.
.
48 hrs
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Figure 10. Time change of the structure size. Reprinted with permission from ref 23. Copyright 1990 American Physical Society.
time or the interparticledistancein the time span covered, ruling out any possibility that the observed crystallization of latex particles (specific gravity, 1.047) was due to gravitational sedimentation of the particles in the dispersions. Figure 10 shows the relative frequency of ordered structures of various sizes at three different times. The size here is discussed in terms of the number of nearest neighbors; the particles forming the triangle have two neighbors while particles at the center of the hexagons have six. The frequency of particles with two neighbors clearly decreased in the course of crystallization whereas that for six neighbors increased. This implies that large structures grow at the expense of small ones. This is qualitatively the Matthew effect or the Ostwald ripening effect.26 The effect can be easily understood if one pays attention to the thermodynamic requirement that the unfavorable surface energy forces the total system to shift to a lower free energy state by losing a large number of small ordered structures and by creating a small number (26) Oetwald, Wil. 2.Phys. Chem. (Leipzig) 1900,34,495.
of large structures. Intrinsically, the surface energy is brought about by a net attractive interaction between particlesso that the observed Ostwald ripening mechanism substantiates the existence of a (long-range) attraction between colloidal particles through the intermediary of counterions. (See ref 3 for details.) Ito et al. also determined the lifetime of the structure.22 The time span in which the particles maintained six neighbors was defined as the lifetime. The number of particles having six neighbors was counted for l / 3 s. In H20 at a latex concentrationof 0.5 % at 25 “C(latex,N300), about 69 % of the particleslost at least one neighbor in l / ~ s at 24 h after the onset of crystallization and the longest life span was ‘/6 s. At 48 h, 58% of the particles also lost one neighbor in l/30 sec. However, 11% of the particles lived longer than l/10 s at 24 h, whereas they amounted to 28% at 48 h and the longest life span was longer than l/3 sec. In other words, the structures disappeared before s at 24 h, while some of the structures at 48 h did not disappear but grew further. Since the structure size at 48 h was larger than that at 24 h, the above observation indicatesthat large structures live longer than small ones. This is reasonablein light of the fact that larger structures have lower energy (and hence lower enthalpy)than smaller structures, again indicating the contribution of the attractive interaction. Ostwald ripening may not be direct evidence for the existence of an attractive interaction. When the surface energy is determined from the enthalpy and entropy, a similar phenomenon could certainly take place even for hard-sphere systems, which can be described in terms of the pure repulsion (withoutattraction),if entropy increases for some reason when particles are transferred into an ordered structure from a disordered state. However, in the lack of “direct”(experimental) supports showing such an entropic increase,it is our strong belief that one should stick to an orthodox standpoint that surface is created by an attractive interaction between particles. The term “direct”means that these supportsmust be potentialformindependent experimental findings, not theoretical constructs derived on the repulsion-only assumption. A remark is necessary on the difference between the analysisbased on the opticaltransform method2’and that based on the Fourier transformation of the microscopic data. The recent development of a computer technique allows us to easilyproduce opticaldiffractionmasks, which can be optically Fourier-transformed to diffraction patterns. This optical transform method is certainly helpful in interpreting diffraction patterns of real atomic and molecular systems. Though powerful, the diffraction masks are artificially constructed and suitably scaled pictorial patterns, which are not exactly the same as the atomic and molecular distribution in real space. The patterns may agree only qualitatively or at most semiquantitatively with the real distribution. On the other hand, the “diffraction mask” in the study by Ito et al., mentioned above, was obtained by microscopic investigation: It is literallyreal-space information, in the sense that it is not artificial but exactly represents the true particle distribution in real space. Paying due attention to the facts that the particle distribution is twodimensionaland the number of particlesin the visual field is very limited,we still believe that the informationderived from the analysis by It0 et al. is more persuasive and realistic than that from the optical transform method. d. Structure of Liquids. On the basis of scattering (27) Lipaon, H. S. Optical Transform;Academic Prm: New York, 1973.
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which clearly shows an ordered structure in a “sea” of disordered particles. Figure l l b was obtained by 2D Fourier transformation of Figure lla. Figure l l c is the radial distribution function g(r) evaluated by direct measurements of interparticle distances. The g(r) was further transformed into the structure factor S(q) by the relationship
J
S(@ - 1= (N/ V) I&)
- 11[(sin ( ~ r ) ) / (47rr2) ~ r l dr (3) where q is the scattering vector, r the distance,and (N/ V)
data, only a short-range (about 5 molecular diameters) order is believed to exist in liquids.28 It is true that their structurefactor,S(q),has a limitednumber of rather broad peaks, but the following study of latex dispersions by Yoshida et al.29indicates that the above interpretation should be modified. Rather small, fluorescent latex particles (MC-6) were studied by a fluorescence microscope. Dynamic light scattering (DLS) was concurrently performed by a HeNe laser (632.8nm) to obtain directlyS(q)of the dispersion. In Figure l l a are given the distribution of the particles,
the number of particles per unit volume. The S(q) thus obtained was compared with the structure factor determined by the DLS experiments in Figure lld. It is reminded that colloidal crystals are apt to form crystal imperfection because of the very low elastic moduli, so that higher order scattering peaks become indiscernible and only one or two peaks remain, as is seen from Figure lld. The good agreement between the S(q) derived from the microscopy and the observed one demonstrates the reliabilities and consistency of the microscopicinformation in real space and the DLS results in the Fourier space. Most important is that the S(q ) havingtwo broad peaks corresponds to a real-space structure comprising randomly distributed particles and a localized ordered array. Usually, there is believed to be no correlation between molecules in high density liquids, when they are apart from each other by a distance of 5 molecular diameters.28 In simple ionic solutions such as nickel chloridesolutions,the radial distributionscalculatedfrom scattering data were claimed to be “broad and structureless”,3O so that terminology such as “quasi-lattice”was recommended to be dropped. On the basis of the realspace information on latex distributions, however, we believethat this terminology need not be abandoned.The judgment of solute distributions based on the shape and number of peaks of the structure factor, or the radial distribution function, should not be given too much emphasis. The two-state structure demonstrated in Figure l l a is definitely inconceivable, and even more so to those who take for granted the homogeneity in atomic or molecular distribution in apparently homogeneous dilute systems. Thus, the structure has been said to be an artifact due to polydisperse samples, glass-dispersion interface (wall) effect, unclean cell vessels, multiple scattering df light, and so Although we cannot agree with these comments, we have no intention to refute these claims here, although our countercommenton the wall effectwill be given in section 4a. We would like to point out that the structure factor (in Figure lld), which was characterized by one or two broad peaks and is usually attributed to liquid structure containing no long-range order, was calculated on the basis of the fundamental relationship between the density function and the amplitude of scattered radiation from a structure comprisingrandomly distributedparticles and a localized ordered array,whether the experiment was properly carried out or not. In other words, the “liquidlike”structure factor could be obtained even if the two-state structure-type diffraction mask is artificially drawn without experiments and is Fourier transformed. Thus, the so-called“liquidlike”structure factor does not imply lack of a long-range order. The scatteringprofiles depend on the lattice vibrations (DebyeWaller effect), the distortion of the second kind
(28) See for example, Marcus, Y. Introduction to Liquid State Chemistry; John Wiley New York, 1977; Chapter 2. (29) Yoshida, H.; Ito,K.; Ise, N. J. Am. Chem. SOC.1990, 112, 592.
(30) Enderby, J. E.; et al. J. Phys. Chem. 1987,91,5851. (31) Okubo, T.J. Chem. Phys. 1987,86,5182; Acc. Chem. Res. 1988, 21, 281.
u..., .... .... 1
0.0 0.0
.... 1.0
1
I
....
I
2.0
.... .... 3.0 4.0 I
I
r (1o - m) ~
q (107m-1)
Figure 11. Structure of a latex dispersion containing free particles and localized ordered structures: latex, MC-6, a fluorescent poly(methy1 methacrylate) latex (with a maximum absorption at 458 nm): diameter, 0.14 pm; charge density, 0.76 pC/cm2;latex concentration, 0.15%;temperature, 25 “C;fluorescentdye, Coumarin6. (a)Computer-treatedmicrograph. Since it is almost impossible on still pictures like the present one to distinguish the particles in the ordered structure from those in coexisting disordered regions, the ordered structure is conveniently surrounded by a closed curve and pointed to by an arrow. In reality, the motion of the ordered particles is discernible from that of the free particles. (See Figure 5.) (b) The Fourier pattern obtained from Figure l l a . (c) Radial distribution function g(r) determinedby directly measuring the interparticle distances for 35 OOO particles. (d) The interference functionDdD,Rdetermined by the dynamic light scattering experiment at 632.8 nm (open circles) and the structure factor S(q) (curve) derived from the g(r) of Figure l l c .
402 Langmuir, Vol. 9, No.2,1993
Doeho et al.
Table I. Rate Constants of Binary Collision between Cationic and Anionic Particles As Determined by Microscopic Observation. anionic latex
diameter
SS-40
0.3 0.37 0.13 0.3
G5301 SS-30 N-300
Ocm)
charge density (rClcm2) 11 10 7.6 1.3
kr (109/~s) 3.0 1.9 1.0 0.62
0 At 25 "C in water. Cationic latex: MATA-2 (copolymerof (3((methacry1oxy)amino)propyl)trimethyla"onium chloride and styrene) with a diameter of 0.3 pm and a charge density of 4.0 pC/cm2. The observation was made at a latex concentration of 0.FW.
(theparacrystalline distortion), and the size of the ordered structure. Matsuoka et al. calculated three-dimensional paracrystalline lattice f a ~ t o r P and 1 ~ ~showed that when the paracrystalline distortion and lattice vibrations become stronger,and when the ordered structurebecomes smaller, the scattering peak intensity is lowered and higher order peaks become indiscernible,while the peak position itself is not strongly affected. Thus it would be inappropriate to rule out the existence of the two-state structure, even when only a single broad peak is observed it might allude to large, highly distorted structuresor small, less distorted structures. e. Collision Theory: Direct Examination of the Smoluchowski Theory on Binary Collision. We anticipate that the collision theory in chemical kinetics is correct. However, it would be of interest if the collision theory could be directly examined. In this area again the polymer latex particles are quite useful. Kitano et al.34 took advantage of the modern video imagery to carry out time-resolved population analyses of monomeric and dimeric particles to examine the Smoluchowski equation.36~36 An aqueous suspension of anionic latex particles was mixed with a suspension of cationic particles in a thermostated observation cell on an ultramicroscope with a latex concentration of about 0.0676,the collision process was recorded by a videotape recorder, and the information was transferred onto a video disk. By replaying the disk, the percentages of dimeric particles in the suspension mixture were evaluated by using an image data analyzer. Table I shows the rate constant (kf)for the binary collisions of a cationic particle with four anionic particles of different charge densities. The theoretical rate constant, ktheo, can be estimated by the Smoluchowski equati0n,3~?% which reads ~ N A (+D&A) R A B / ~ ~ (4) whereNA is the Avogadro number,D the diffusion constant of the respective reactanta A and B, and R- the distance of closest approach. For the binary collisions between MATA-2 and G-5301, kth- was found to be 7.5 X lo9M-I 8-I at 25 O C in water. Amazingly kf is of the same order of magnitude 88 ktheo, even though the analytical valences of the latices were quite high (7.2 X 104 and 2.7 X 106 strong ionic groups per particle for MATA-2 and G-5301, respectively),while the theory deals with noninteracting particles. Most of the electric charges of the latex particles were probably neutralized by counterion association, as was shown in a most straightforward way by transference ktheo = ~
(32) Matsuoka, H.; Tanakn, H.; Hashimoto, T.; Ise, N. Phys. Reo. B 1987,36, 1754. (33) Matauoka,H.;Tanaka,H.;Iizuka,N.; Hashimoto,T.;Ise, N. Phys. Reo. E 1990, 41, 3854. (34) Kitano, H.; Iwai, S.; Ise, N. J. Am. Chem. SOC.1987, 109, 1867. (35) von Smoluchowski, M. Phys. 2. 1916, 27, 585. (36) von Smoluchowski, M. 2.Phys. Chem. 1917,92, 129.
experiments;37 in other words the net valence was much smaller than the analytical valence (probably about only 8% of it). AB mentioned in section 2b, the diffusion behavior of the free particles may be approximatelydescribed by the Einstein theory of Brownian motion. The collision measurementswere carried out at latex concentrations of about 0.06% or below, where the Einstein theory was found to be satisfactory. SinceEinstein-Stokes behavior is assumed in the Smoluchowski theory,the observed discrepancies for the rate constant should be accounted for in terms of factor(s) peculiar to the Smoluchowski theory. The binary collision between similarly charged latices was also studied recently by Ono et al.= The rate constant found was 2.0 X log M-I s-l in water at 1.0 M NaCl and 25 "C,which is to be compared with the theoretical value of 7.4 X logM-I s-'. The observed value was again smaller than the theoretical value. A similarly large discrepancy was found for the collision in a watel-glycerol mixture, which was used (for density matching) to prevent sedimentation of the latex. Since the salt concentration was high, we expected almost complete shielding of the electric charges and a better agreement between the Smoluchowski theory and the experiments. That the observed value was still much smaller than the theoretical one even in the present case seems to indicate that the electric charge effect is not a primary factor causing the failure of the Smoluchowski theory. From the preceding discussion,the hydrodynamic effect of the solvent was suspected to be a cause of the discrepancy. Solvent molecules around particles must be removed when particles are moving. When the particle diffusion is concerned, the removal appears not to require a large energy. However, in the case of particle collision, the solvent has to be pushed away through a relatively small channel between two colliding particles. Thus, the hydrodynamic effect would be more influential in the collision phenomena than in the diffusion process. This explains why the Smoluchowski equation showed disagreementwith the experimentswhile the Einstein theory was experimentally supported. 3. Kossel Line Analysis on Lattice Systems and
Crystal Growth over a Long Time Span The lattice systems of colloidal crystals can be studied most precisely by the Kossel image analysis,4v5namely the diffraction images from lattice planes of colloid crystals illuminated by divergent beams produced through random scattering of incident laser beams at a pointlike disorder inside the dispersions. By photographing the intrinsic Kossel diffraction images for over several hundred days, Yoshiyama and Sogami followed the process of 3D crystallization in latex dispersions in rectangular quartz cuvettes.39 The analysis of about loo0 photographic records of diffraction images for dispersionsat particle concentrations of 0.1-10% showed that the ordering proceeded through the following intermediate proceeses: two-dimensional hexagonal close-packed (2Dhcp) structure random layer structure layer structure with one sliding degree of freedom stacking disorder structure stacking disorder with multivariant periodicity face-centered-cubic (fcc) structure with (111)twin normal fee-structge bodycentered-cubic (bcc) structure with (112) or (112) twin normal bcc structure. The several early stages proceeded
-
+
--
-
+
--
(37) Ito, K.; Ise, N.; Okubo, T. J. Chem. Phys. 1986,82, 6732. (38) Kitano, H.; Ono, T.; Ito, K.; Ise, N. Langmuir 1992,8,999. (39) Sogami, I. S.; Yoshiyama, T. Phase Transitions 1990,21, 171.
Langmuir, Vol. 9, No. 2,1993 403
Polymer Latex Dispersions
._
Figure 12. Kossel images observedby Ar laser beams for a 0.58 95 dispersion of latex N100 latex diameter, 0.12 pm; chargedensity, 4.3 pC/cm2. (a, top) Pattern with a 6-fold symmetry recorded 1344 h after the onset of crystallization proves the appearance of an fcc twin structure with a twin plane (111). (b, bottom) Pattern with a %fold symmetryphotographed at 1896h indicates a normal fcc structure. Reprinted with permission from ref 39. Copyright 1990 Gordon & Breach, Inc., London.
Figure 13. Kossel images observed for a 0.49% dispersion of latex SS-32: latex diameter, 0.16 pm; charge density, 4.2 pC/cm2. (a, top) Recorded at 1848 h after the onset of crystallization. This shopls the appearance of a bcc twin structure with a twin plane (112). (b, bottom) Pattern with 2-fold symmetry photographed at 2496 h showing a normal bcc structure. Reprinted with permission from ref 39. Copyright 1990 Gordon & Breach, Inc., London.
rather rapidly and were characterizedby strong anisotropy originatingin the wall effect of the cuvette,which initiated the formation of a 2D hcp arrangement. The thermal agitation and interparticle interaction gradually rectified the anisotropy and advanced the latex dispersions to the later stages of the cubic structures. While the crystallization eventually terminated with the fcc symmetry in concentrated dispersions (>3 95 ), bcc structures were dominant in dilute dispersions (
