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Langmuir 1990,6, 296-302
Ordering of Latex Particles and Ionic Polymers in Solutions+ Norio Ise,’ Hideki Matsuoka, Kensaku Ito, Hiroshi Yoshida, and Junpei Yamanaka Department of Polymer Chemistry, Kyoto University, Kyoto 606, Japan Received February 6, 1989. I n Final Form: August 17, 1989 Experimental data that substantiate the intermacroion (or interparticle) attractive interaction were reviewed. In addition to the fact hitherto often emphasized by us that the observed spacing between solute species (2D,,,) is smaller than the average spacing (20,) at low solute concentrations, the tendency of the 20,, to decrease with decreasing dielectric constant of the solvent was pointed out to be consistent with the existence of an electrostatic attraction between latex particles: the 2Dexpshould increase if only the repulsion is in action. The insensitivity of the 20, e to temperature is suggested to be due to the intensification of the attraction caused by the corresponding change of the dielectric constant with temperature. The enhanced attraction counterbalancedthe thermal expansion, resulting in insensitivity; according to the repulsion-only assumption widely believed, the spacing should increase with the decrease in dielectric constant and with the rise in temperature, which is contrary to the observation. The single broad scattering peak often observed for ionic polymers and latices was accounted for in terms of the paracrystalline distortion, the limited size of the localized ordering, and the DebyeWaller effect without invoking the repulsive interaction between the solute species. The kinetics of the growth of the localized ordered structures of polymer latices was studied in dilute suspensions. The growth of the structure was found to obey the Ostwald ripening mechanism: larger structures grew at the expense of smaller ones, which demonstrates that the surface tension of the structure is important and hence the attractive interaction between latex particles. Consistent with this idea, larger structures were found to live longer than smaller ones.
Introduction In 1938, Langmuir stated in the abstract of his paper,’ “It is now shown that the Coulomb attraction between the micelles and the oppositely charged ions in the solution gives an excess of attractive force which must be balanced by the dispersive action of thermal agitation and another repulsive force. Thus there is no need to assume long range van der Waals forces.” He perspicuously claimed that the attraction must exist between the micelles and it is of electrostatic nature but not the van der Waals interaction. However, the current majority opinion seems to be that the colloidal phenomena can be described in terms of purely repulsive Coulombic interaction between similarly charged particles or in terms of the Coulomb repulsion combined with a van der Waals attractive interaction between them. A question arises: why has the electrostatic attractive interaction been overlooked? Figure 1 shows a “highly concentrated dispersed system”. Under such a condition, we feel only repulsive (hardsphere type) interaction with neighbors and cannot be aware of attractive interaction; the “rod-like biopolymers” in Figure 1could form an ordered arrangement as a result of the repulsive interaction. It is pointless, however, to ask whether and why the ordered arrangement is maintained under such a condition. If we choose such experimental conditions in the study of colloidal suspensions, the repulsive-only assumption would give a seemingly satisfactory description.2 However, this is only a Presented as a keynote lecture a t the symposium entitled “Ordered Particles and Polymer Colloids”, 196th National Meeting of the American Chemical Society, Los Angeles, Sept 25-30, 1988. (1) Langmuir, I. J . Chem. Phys. 1938,6, 873. (2) One of the beet examples is the Alder transition, in which the process was discussed at very high volume fractions of solute particles such as 70%. On the other hand, we are studying much lower fractions below lo%, mostly about 1%or so.
0743-7463/90/2406-0296$02.50/0
part of the truth, which was uncovered under an improperly chosen experimental condition. If we wish to disinter the true nature of the interparticle interaction in its totality, such an experimental condition symbolized in Figure 1 should not be used; instead, we have to select such a situation as shown in Figure 2. In such a case, the “solute particles” have the freedom to move around and can take seats that have not been occupied. If two “particles” sit next to each other under this boundary condition (in other words, if the “interparticle” distance is smaller than the statistical average distance), we may conclude that there exists an attractive interaction between the two particles. The attractive interaction can be detected only in a dilute suspension similar to Figure 2 but not in a concentrated one like Figure 1. Obviously, concentrated colloidal suspensions have attracted keen attention from many physical chemists and colloid scientists. Such systems are of interest for various reasons but are not appropriate for the discussion of interparticle interaction. For this and other reasons, we have been studying dilute solutions and suspensions of ionic polymers and polymer latices. We have been finding the electrostatic attraction between similarly charged ionic (macromolecular) species, which counterbalances the widely accepted electrostatic repulsion and thermal agitation. We note explicitly that we realized earlier the existence of the electrostatic (intermacroionic) interaction on the basis of the concentration dependence of solute activities of polyelectrolytes in solution^:^ the cube-root dependence of the mean activity coefficient of polyelectrolytes was taken as implying the “regular” distribution of macroions, which was due to attraction between the macroions through the intermediary of the counterions. Furthermore, the extremely rapid decrease of the single-ion activity of mac(3) For a review of the thermodynamic activity of polyelectrolytes, see for example: Ise, N. Adu. Polym. Sci. 1971, 7, 536.
0 1990 American Chemical Society
Ordering of Latex Particles and Ionic Polymers
Langmuir, Vol. 6, No.2, 1990 297 tions on ionic polymer latex suspensions? The earlier developments have already been reviewed? Herein we report several new lines of evidence, supporting the existence of the attractive interaction, which have not been paid due attention in its cross demand.
C&
Figure 2.
" I h l u t c ~dispwsed system". On lhi, right-hand siilc. fwe seats are availahle. Thus, if they like, -sdute particlrs' can sit in the free seats. Nonetheless, most 'solute particles" sit voluntarily on the left-hand side. This indicates that there exists some kind of attraction hetween the "solute particles". Of course, they cannot sit in the same place a t the same time because of the 'hard-sphere" type repulsive interaction working a t the short distance. The whole situation shown in this picture indicates that, in addition to the short-range repulsive interaction. there exists a medium-range attractive interaction, which cannot he detected or might be easily overlooked under the situation shown in Figure 1. The *solute particles" in Figure 2 are some of the graduate students who are contributing to the present work, to whom our sincere thanks are due.
roions with increasing polyelectrolyte concentration led one of the present authors (N.1.) to the conclusion that such an outstanding deviation from the Raoult law was due to the existence of the intermacroion attraction. These thermodynamic studies motivated the smallangle X-ray scattering (SAXS) experiments on polyelectrolyte solutions4 and subsequent microscopic investiga(4) Ise. N. et SI. J. Am. Chem. Soe. 1979. 101. 5836.
Discussion The Interparticle or Intennacroionic Spacing Was Smaller Than the Average lntermacroion Spacing. The SAXS study on dilute solutions of various synthetic and biological polyelectrolytes furnished a single broad peak when the solute concentration and molecular weight were sufficiently large. Accepting that the peak was due to the Bragg diffraction, the Bragg spacing was calculated from the peak position ( 2 0 4 : it was smaller than the average spacing (20,). for example, by a factor of 2 for fractionated polyacrylate or poly(styrenesulfonate), which have a very small polydispersity. The argument can be more straightforward for polymer latex particles than for ionic polymers, since the interparticle spacing can be directly determined from the micrographs showing the distribution of latex particles in suspensions. We note that the spacing experimentally found for both soluble ionic polymers and latex particles (designated also 20,, ) was smaller than the average statistical spacing ( 2 0 2 a t low concentrations. Furthermore, as will be mentioned below, ZD,,, has been determined for a large number of particles with the aid of the image data analyzer in our recent publication,7.' which supersedes our earlier measurements on several pairs of particles: in a sense that the computer-aided technique gets rid of subjective arbitrariness in judging the distinction of ordered and disordered particles and can provide statistically reliable results. An important factor, which cannot be overlooked for polymer latex particles of larger dimensions, is whether the inequality relation, 20, < ZOO,and hence the twostate structure, has been caused by the gravitational sedimentation of solute particles, particularly the polystyrene-based latex particles, whose specific gravity is about 1.05. In light water and for large particles, the sedimentation would cause higher concentrations a t the bottom part of the observation cell, which was accessible to the reversed type microscope mostly used in our experiments. Since the light water has a specific gravity smaller than that of the latex particles (1.05 for polystyrenebased latices), the sedimentation would take place if the thermal agitation is not effective. However, the role of the gravitational sedimentation, if any, would be unimportant for the following reasons, as far as the interparticle spacing is concerned. First, 20,- < 20, was observed also for linear ionic polymers, whose dimension is small enough to warrant a negligible role of the sedimentation in the gravitational field on the surface of the earth, where most of the experiments were carried out. Second, the same inequality relation was concluded even in the mixture of heavy and light waters, which were used for the purpose of density matching? Third, the inequality relation and the two-state structure were also observed in a vertical plane in the suspension volume far from the bottom of the observation ~e11.1~~ The inequality relation 20, < 2Do is thus real and reflects the inhomogeneity (wtich we called the two(5) I-, N. et SI.J . Chem. Phys. 1983, 78.536. ( 6 ) Ise, N. Angew. Chem. 1986,Z. 323. (71 Ito. K.:Nakamura. H.: Yoshids. H.: Ise. N.J . Am. Chom. Soc. 1988. JJ0.6955. (8) Ise, N. e t el. J . Am. Chem. SOC.1985. 107.8074.
(91 It". K.;Nakemura, H.;Ise, N. J . Chem. P h w . I986.85,6136.
Zse et al.
298 Langmuir, Vol. 6, No. 2, 1990 state structure") in the solute distribution in apparently homogeneous solutions or suspensions. We note in passing that the above relation was obtained in relatively low concentrations such as 1%; at higher concentrations, for example above lo%, 2D,,, must be equal to 2D,, if the dead space is taken into consideration. It is noted that 2D,,, is the distance between particles existing in the ordered structure whereas 2 4 is the average distance that is calculated from the solute concentration by assuming a uniform distribution. This fact must be correctly realized. If one can measure the distance between free particles in random distribution, they would show a broad spectrum; some of them would be smaller than the average value (20,) and some others would be larger, provided that the random distribution uniformly covers the entire solution. These comparisons are not intended in our argument. What we are comparing with 2 0 , in our discussion is the distance (2D,,,) between ordered (not free) particles in the question. When this distance is found to be smaller than 2D,, it can be a strong support for the existence of an attraction. In this case, the size of the populations is important. If we measure the distances between a very limited number of particles, the comparison between 2D,,, and 2 0 , would not be physically significant. In our recent publication^,'^'^-'^ 2D,,, has been determined with the aid of an image data analyzer: In ref 7, the centers of 100-1OOOparticles were fed into the computer to estimate 2D,,,. In ref 12, about 4000-5000 particles were treated to obtain the Fourier pattern, from which 2D,,, was derived. In ref 11, we estimated the interparticle spacing from the Fourier patterns, which were obtained from the micrographs showing 2500 particles. In the most recent analysis (ref 13), the spacings for 35 000 particles were determined to obtain the radial distribution function. These numbers are much larger than those adopted in reports of similar nature by others,14 and we believe that they are statistically large enough. We further note that the inequality relation was found for latex suspensions first by Kat0 et al.15 and recently by us11v16 by a light-scattering technique. This fact is important in that the light-scattering method provides information on the solute distribution inside the suspension (not near the container wall) and rules out the possibility that the inequality relation is due to some kind of distortion in the solute distribution associated with sedimentation or wall effect. 20- Found for Latex SuspensionsDecreased with Decreasing Dielectric Constant of Solvents. By use of the binary mixtures of organic solvents and water, the spacing was found to decrease as the dielectric constant ( E ) was lowered from about 80.' For example, 20,, was 1.1 X lo* m in water whereas it was 0.6 X lo4 m at a t value of 67, as is seen from Figure 3. In such a discussion, important is the net valency of the particles, which must be an important factor determining the interparticle distance. To examine how the net valency of the particles changes with t, conductivity measurements were carried out in one such dispersion medium (ethylene (IO) Iee, N. et al. J. Am. Chem. SOC. 1980,102,7901. (11) Ito, K.; Okumura, H.; Yoshida, H.; Ueno, Y.; Ise, N. Phys. Rev.
€3 1988,523, 10852.
(12) Ito, K.; Ise, N. J. Chem. Phys. 1987,86, 6502. (13) Yoshida, H.; Ito, K.; Ise, N. J. Am. Chem. Soc., in press. (14) Okubo, T. Acc. Chem. Res. 1988, 21, 281 and the work cited therein. (15) Kato, T.; Masuda, H.; Takahashi, A. Polym. Prepr. Jpn. 1982, 31, 2249. (16) Yoshida, H.;Ito, K.; Ise, N., publication in preparation.
E, a no
Dielectric constant
Figure 3. Interparticle distance observed in the ordered structure of a latex suspension in the binary mixtures of ethylene glycol (O), methanol (X), dimethylfomamide (A),and dimethyl sulfoxide ( 0 ) :latex diameter, 3.69 X 10" m; charge density, 7.2 X 10" C/cm2; latex concentration, 1.3% (20, = 1.27 X 10" m); room temperature. The dotted line is an eye guide. Reprinted with permission from ref 8. 0.6
0.4
0.2
I
I
1 1 l concn. 1 8 )
Figure 4. Fraction of free protons in ethylene glycol-water (1:1)mixture (filled circles) and in water (open circles)as a function of latex concentration at 25 O C : latex, N-200(diameter 0.2 X IO* m); charge density, 3.44 X lo4 C/cma. Equivalent conductivitiesof protons were 25 and 349.8 in these dispemion media, respectively. Equivalent conductivity of protons at 0.01 M in ethylene glycol-water was taken from Erdey-Gruz, T.; Majtheryi, L. Acta Chim. Hung. Tomus 1959,20, 175 and limiting equivalent conductivity in water from Owen, B. B.; Sweeton,F. H. J. Am. Chem. SOC.1941,63,2811. glycol/water)." Figure 4 shows the fraction of free protons (f) as a function of latex concentration in water ( E = 78.3) and in an ethylene glycol-water 1:l mixture (t = 37.7). The f value was conveniently estimated from the measured electric conductivity and the limiting equivalent conductivity of protons by assuming that the transport number of the latex particles is negligible. In the t range covered in Figure 3, it can be concluded from Figure 4 that the f value and hence the net valency of the particles are constant with varying c. Since the 2D,,, value (1.1 X lo4 m) in water was already smaller than 2 0 , (1.27 X 10* m), further decrease in 2Derp implies that the interparticle attraction was more strongly enhanced by a lowered dielectric constant than the repulsive interaction. It is to be noted that 2D,, decreased, even though the net valency of the particfes was constant. Once again we emphasize that, if the repulsiononly assumption is correct, or without the attraction, 2D,,, should stay constant with varying dielectric constant. This is, however, not the case. Thus the realistic (17) Yamanaka, J.; Ise, N. publication in preparation.
Ordering of Latex Particles and Ionic Polymers
Langmuir, Vol. 6, No. 2, 1990 299
Dielectric Constant 87.74
83.83
0
10
80.1
20
76.55
30
Temperature ( C
73.15
69.91
40
50
)
Figure 5. Temperature dependence of the interparticle distance in the ordered structure of a latex suspension: latex, the same as in Figure 3; latex concentration, 2.0%; solvent, light water. The data are from ref 8.
The observed decrease in 2DeXpwith varying temperature and dielectric constant also excludes the possible contribution of the sedimentation effect: although the experiments were done on a horizontal plane in the lower part of the suspension cell by using the reversed-type microscope, such dependences were observed. Our argumer? is clearer for the data in binary mixtures of water with dimethyl sulfoxide or ethylene glycol. These solvents have specific gravities of 1.101 and 1.109 at 20 "C, respectively. Thus in these solvents, the latex particles might be affected by buoyancy; in contrast to the light water medium, the concentration of latex particles at the bottom part of the cell must be lower so that the interparticle distance must be larger in these solvents than in water, if the widely believed claim that the sedimentation effect is a main source of the inequality relation is correct. Experimentally, the interparticle distance was smaller in these solvents, which indicates that the gravitational factor is not so important, as far as the spacing is concerned for latex particles under consideration.
The Single Broad Scattering Peak Can Be Attributed to Paracrystalline Distortion, Limited Size of the Ordered Structure,and the Debye-Waller Effect without Invoking the Repulsive Interaction between Macroions or Particles. The single broad peak in the
0.2
0
1
I
1
2
3
concn. ( 8 )
Figure 6. Fraction of free protons at three temperatures as determined from conductivitymeasurements: latex, N-200 (same as in Figure 4). The limiting equivalent conductivities of protons used in the calculation were 250.1,349.8,and 419.6 at 5, 25,and 40 O C , respectively (taken from Owen, B. B.; Sweeton, 1941,63, 2811). Open circles, 25 "C; F. H. J.Am. Chem. SOC. filled triangles, 40 O C ; open squares, 5 O C . explanation of the observed change of 2Dexpis to accept the Coulomb attraction, which is intensified with decreasing dielectric constant, diminishing the interparticle distance. 2DeXpValue Stayed Practically Constant with Chanpng Temperature. When the temperature is raised, the interparticle spacing must become larger as a result of thermal expansion. However, this is apparently not the case, as shown in Figure 5; experimentally the spacing measured was practically constant or decreased though slightly with increasing temperature according to the microscopic study.'*' This weak dependence was also observed in the light-scattering experiment.l"l8 As shown in Figure 6, the fraction of the free protons was concluded not to be strongly dependent on the temperature." Thus the observed temperature dependence of the spacing can be accounted to the predominant role of attraction over repulsion. The attraction must be intensified by a decrease in the dielectric constant with elevating temperature and counteracts the thermal expansion. If only the repulsion is important, as is widely believed, the spacing should increase with temperature as a result of simultaneous contributions of the thermal expansion and the intensified repu1~ion.l~ (18) Hirtl, W.; Versmold, H. J. Chem. Phys. 1984,81, 2507. (19) This statement requires a further comment. If the repulsiononly assumption is valid, 2D.., must increase with temperature at the same rate aa the linear thermal expansion of solvent (water). This is again, however, not the case experimentally.
scattering profiles of ionic polymers was often claimed not to be reminiscent of some kind of orderin of solute species. Recent calculation by Matsuoka et a l j for cubic lattice systems with paracrystalline distortion shows that the scattering intensity and the number of peaks decrease with increasing degree of paracrystalline distortion, decreasing crystal size, and increasing DebyeWaller effect. This is a statistical theory invoking no interaction between particles or macroions. Nonetheless, a satisfactory agreement with experimental curves was obtained. For sake of space, we refer the readers to the original paper2' for the details of the theory and to a recent review article2' by us for general discussion on the distortion of the ordered structures of ionic particles. In the present paper, only one example of the successful application of the theoretical calculation is reiterated. Figure 7 shows the structure factor, S(q), obtained by light-scattering experiments on a polymer latex suspension and the lattice factor, Z(q), calculated by the paracrystal theory. In this figure is shown the structure factor calculated by the RMSA (rescaled mean spherical approximation) method with the repulsion-only assumption. The agreement between the three factors is amazinglygood. This implies that, in contrast to the widely accepted claim, the ordered structure need not always be attributed to the repulsive interaction. Further comments should be made on the recent twodimensional Fourier transform study" of the micrographs (density functions) of latex distribution, which indicates that the single peak in the Fourier space may correspond to the two-state structure, where crystallike, localized ordered structures coexist with random particles. Furthermore, the interparticle distance obtained from the Fourier halo is in good agreement with that determined from the micrographs. O n the basis of this analysis, we positively claim that the single peak observed for ionic polymers by SAXS and small-angle neutron scattering (SANS) substantiates the formation of localized ordered structures that are fairly highly distorted and involve substantial lattice vibration. (20) Matauoka, H.; Tanaka, H.; Hashimoto, T.; Ise, N. Phys. Rev. B: Condens. Matter 1987,36, 1764. (21) Ise, N.; Matauoka, H.; Ito, K. Macromolecules 1989,22, 1.
Ise et al.
300 Langmuir, Vol. 6, No. 2, 1990 3 ,
I
I
1
graphs was stored in the image data analyzer. By use of the method described in a previous paperjl' this information (equivalent to the density function p(x)) was then Fourier-transformed into the amplitude of scattered radiation, A(b), following the basic relation A(b) =
t 0 0
0.5
1.0
1.5 (lo5 cm-l)
2.0
2.5
Figure 7. Structure factor, S(q), determined by the lightscattering measurements (filled circles); the lattice factor, Z(q),calculated by the paracrystal theory (curve);and the structure factor, calculated by the RMSA method with the repulsiononly assumption (cross): latex diameter, 0.09 x lo4 m; latex concentration, 0.05%. The calculation by the paracrystal theory was for an fcc structure with interparticle spacing of 0.98 X IO4 m and a distortion factor of 0.17. The light scattering was performed by HBrtl, W.; Versmold, H.; Witti%,U. Ber. BunsenGes. Phys. Chem. 1984,81, 1063. Reprinted from ref 20 with permission. Copyright 1987, the American Physical Society.
Growth of the Localized Structure F Q ~ ~ Othe WOstS wald Ripening Mechanism, and Larger Structures Live Longer Than Smaller Ones. By using phase contrast micrographs, Luck22first noticed that the size (actual area) of localized ordered structures in latex suspensions changed with time. The essential aspect was that the larger structures grew at the expense of the smaller ones. Since a detailed description of the experimental data was not available in Luck's paper and more quantitative analysis appeared necessary, we started to analyze the growth rate and lifetime of the ordered structures in latex suspensions by taking advantage of modern video imagery.23 The growth of the ordered structure in latex suspensions was studied as follows. First, after careful purification procedures fully described in our recent paper,' the particles were allowed to form ordered structures in the observation cell. Then sodium chloride was added to this suspension to a final overall concentration of 1.0 x lo4 M. The ordered structure was naturally destroyed. Then, the NaCl concentration was decreased by the addition of highly purified ion-exchange resin particles. The process of deionization was followed by measuring the electric conductance. The conductance decreased with time until 2 h after the onset of the deionization and, thereafter, was constant. According to a control experiment performed under the same experimental condition without latex particles, the concentration of sodium chloride was 5.8 X lo4 M at 24 h, which was low enough for the ordering to proceed according to our previous measurement.' Our previous s t u d 9 indicated that the interparticle distance in the ordered structure did not show a salt concentration de endence within the experimental error below 1.71 X 10- M. Thus the change of the states of the ordering with time after 24 h was concluded not to be due to the progress of deionization. The micrographs showing the particle distribution were taken at a fixed position in the suspensions and at various stages of ordering, which are shown in Figure 8a. The information of the coordinates of particle centers in the micro-
B
(22) Luck, W. P. Physik. El. 1967,23, 304. (23) Ito, K.; Okumura, H.; Yoshida, H.; Ise, N. Phys. Rev. B: Condens. Matter, submitted.
J p(x) exp[-2db.x)]
du
(1)
where b and x are the Fourier space vector and real space vector, respectively. The Fourier patterns obtained are given in Figure 8b. Table I summarizes the change in the scattering profiles with time. Remarkably, the 2D,, did not change with time between 24 and 96 h. FurtKermore, as mentioned above, the salt concentration in this period has no practical influence on the 2D,,,. Therefore, the value of 1.3 X lo4 m was judged to be a reliable parameter in the structure formation. By using a computer device, we proceeded to pick up three particles (from the micrographs) that form a regular trianglez4with a side of 1.3 X lo4 (1 f 0.15) m. The triangles thus found are drawn by computer graphics and are shown in Figure 8c. It is to be noted that the 2D,,, value used in the graphics (1.3 X 10+ m) was smaller than 2D, found for the concentration adopted in the experiments (1.7 X lo4 m). I t is noteworthy that the ordering proceeded with such a lattice constant (2D,,,) shorter than the average distance (2D,), even at a n early stage of crystallization. Such a situation is conceivable only when there exists an attractive interaction between particles, though similarly charged. If only the repulsive interaction is in action, the crystallization should take place with a lattice constant equal to 20,. Table I1 shows the figures for the growth of the localized ordering. The total number of the particles increased slightly from 24 to 48 h after the onset of deionization. This is attributed to the rather small depth of the focus plane of the microscope. The particles are seen in the ordered structures since the "lattice" plane happens to be parallel to the focus plane, irrespective of the contribution of the wall. However, the free particles show Brownian motion not only in the planes but also in threedimensional directions. Thus, as the crystallization proceeds, we have more and more particles in the focus plane. Between 24 and 48 h, the number of units (triangles) was almost constant, while the number of clusters (aggregates of the triangles) decreased rapidly. This implies that, as time passes, the cluster size becomes larger. Correspondingly, the average number of bonds (B,) of particles increased from 3.32 to 3.94, while the maximum bond number is 6 for the particles at the center of the regular hexagonal arrangements and the minimum bond number is 2 for particles forming the triangle. Interestingly, during this period the Fourier pattern was hardly changed, and it was rather difficult to differentiate the extent of the crystallization, whereas the number of clusters decreased substantially in the corresponding period as seen in Table 11. The histogram in Figure 9 shows the relative frequency of particles of various bond numbers (or numbers of nearest neighbors). The number of particles having two neighbors decreased with time whereas that having six neighbors increased. This indicates that larger structures grew at the expense of smaller ones. This is exactly what Luck observed earlier. W. Ostwald found (24) The reason why the triangle. was chosen as a unit of the structures is that the micrographs usually showed 111 planes of a face-centered cubic lattice, which corresponds to regular hexagonal arrangements consisting of six regular triangles.
Ordering of Latex Particles and Ionic Polymers
Langmuir. Vol. 6, No.2,1990 301 I-b
I-C
I' :
11-a
11-b
I
P I S
"111 " ~ $ " ' O
I,
11-c
'"
: II
111-b
"1.1
111-2 7.
: II
"111 1 1 1 1 7 . 1 1
(I
(1.11
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Figure 8. Micrographs showmi: p a r t i c l e distribution ! a ) , t h e c ~ ~ r w s ~ ~ w ~Fourier d i n i : patterns (h!, and t h e computer graphics illustrating the structure units (triangles! (c! a1 6 h (I), 3fi h ( I l l . '42 h 1111) a n d 7 2 h (IV) after the deionization started. Table 1. Time Changes of Fourier Pattern and Interparticle Spacing (2D,.,). time, h 2D,.,, 10" m 2D-FT patterns 1 no halo no halo 1.4 halo 1.3 halo 1.3 halo 1.3 spots 1.3 spots Latex, N3Ml (diameter. 0.32 X IOd m; charge density, 1.8 X 10- C/cm2); latex concentration. 0.5% ( 2 4 = 1.7 X IO" m).
2 24 36 48 12 96
the same trend in the crystallization process of mercury oxide.2" The present situation can be understood if we accept the presence of an attractive interaction between (25) Ostwald. W.2.Z. Phya. Chem. 1900.34,495
Table 11. Growth of the Localized Ordered Structure. time, h particles treated no. of units no. of cluster B , R 24 48
I2
16 755 I8 036 18 560
14 440 14 584 25 525
1116 474 100
3.32 3.94 4.83
.,The same experimental condition as in Table 1. *Average number of bonds. similarly charged latex particles. This interaction causes surface tension, which is the motive force for reducing the total surface area in the system by increasing the number of larger structures or decreasing the number of smaller ones. Without the attraction, the surface tension is not conceivable. The above description might give an impression that, once formed, the larger ordered structures are stable and simply grow further. This is not true. They have defi-
302 Langmuir, Vol. 6, No. 2, 1990
Ise et al.
Concluding Remarks
2
3
4
5
6
number of nearest neighbors
Figure 9. Histogram showing the distribution of the number of nearest neighbors. Table 111. Distribution of Life Span of Core Particles. time, 1/30 s
X
1 2 3 4 5
percentage 24 h
48 h
69.3
58.0 13.9 8.3 8.3 5.2
20.0 6.7
2.7 1.3
6 7 8
2.4 1.0
9 10
0.7 1.4
0.7
See the text for the definition of the core particles.
nite lifetimes, at least under the present experimental conditions.26 In order to discuss the lifetime problem, we studied how long so-called core particles can survive. By core particles, we mean particles having six bonds. We counted by naked eye the number of bonds each core particle had in 10 consecutive video frames, i.e., for 1/3 s. The period in which they maintained six bonds was defined as the lifetime. Table 111summarizes the results of the counting at 24 and 36 h after the deionizationstarted. About 69% of the core particles lost at least one bond in 1/30s at 24 h, and the longest life span was 5/30 s. At 48 h, 58% stopped to be core particles, and 1.4% of the core particles lived longer than 1/3 s.~’ Since the average number of elementary units per cluster is about 12 and 30 (Table 11)at 24 and 48 h, respectively, the ordered structures can be said to live longer with their increase in size. This seems to be quite reasonable, since larger structures are more strongly stabilized by a smaller contribution of surface tension than smaller structures. Here again the important role of the attraction would be a necessary conclusion. (26) Ito, K.;Okumura, H.; Yoshida, H.; Ise, N. J. Am. Chem. SOC. 1989,111,2347. (27) Rigorously speaking, the term ‘life span” discussed in the text is not correct. What we measured was the upper limit of the l i e span, since we have no information on the period shorter than 1/30 s.
We have reviewed some experimental lines of evidence, which substantiate the presence of an interparticle attraction. In addition to the factors previously discussed, we have presented some recent kinetic data on the order formation. By usingvideo imagery and an image data analyzer, we showed that the growth of the ordered structure obeys the Ostwald ripening. We also measured the life span of the localized ordering. Larger ordered structures live longer. These kinetic facts clearly indicate the role of the surface tension of the ordered structure. Surface tension is possible only when attractive interaction exists between constituent particles. Thus the new kinetic data also confirm our constant claim on the essential role of the attractive interaction in colloidal systems. No mention was made on the nature of the attractive interaction in the present paper. We have already discussed this problem? In short, it is of an electrostatic nature in light of the salt concentration dependences of the interparticle distance and the easiness of the formation of the ordered structure. The new kinetic data disc w e d above were not in contradiction to this conclusion. We further note that the medium-range electrostatic attraction (in addition to the widely accepted shortrange repulsive interaction) was theoretically discussed and Lozadaby several authom such as C a s s ~ u .(It ~ ~would be interesting to draw attention to Suzuki’s recent work:’ in which he found that “effective attractive interaction” due to the boundary effect plays an essential role even in the Alder transition.) Essentially, the attraction we are discussing is brought about by the counterions in between similarly charged macroions or colloidal particles in a similar way to hydrogen bonding created between negative ions such as F- mediated by proton. This is in line with Langmuir’s summary, which was referred to at the very beginning of the present article.32
Acknowledgment. This work was made possible by valuable efforts rendered in the past by our co-workers. Their names are cited in the references. The most generous financial support from the Ministry of Education, Culture and Science is gratefully acknowledged (Grantsin-aid for Specially Promoted Research, 59065004 and 63060OO3). (28) Sogami, I. Phys. Lett. 1983, AM, 199. Sogami, I.; b e , N. J . Chem. Phys. 1984,81,6320. (29) Sogami, I. Ordering and Organization in Ionic Solutions, Ise, N.,Sogami, I., Eds.;World Scientific: Singapore, 1988, p 624. (30) Lozada-Cassou, M.; Dim-Herrera, E. ref 29, p 555. (31) Suzuki. M. J. Phvs. SOC.Jm..in Dress. For a convenient review of the’theoreticd treatmint of thii author, see ref 29, p 635. (32) Recently, Overbeek claimed that Sogami’e theory (ref 28) contains errors and, when the errors are corrected, the attraction predicted by the theory disappears (ref 33). Although a rebuttal will be made separately on the basis of a more general point of view, we simply point out here that Overbeek misused the Gibbs-Duhem equation. Actually the integrand of his equation (15) cannot be zero, opposite to his claim, since the contribution of macroions has not been taken into account in the equation. This implies either that some basic imperfections are involved in the argument of Overbeek or that the Gibba-Duhem equation is not valid for colloidal systems, while the second w e is definitely inconceivable. (33) Overbeek, J. Th. G. J . Chem. Phys. 1987,87,4406.
