J. Phys. Chem. 1990, 94, 1962-1966
1962
no photocurrent and attributed this inactivity to the "displacement from the lattice" of Cd2+by Fe3+ or Cu2+. The present results clearly show photoactivity, and we suggest that the null result of White and Bard3 was due to the dark decomposition reaction of Fe3+ with CdS (eq 3) which caused complete reduction to Fe2+ in their cell prior to illumination. Their concentrations of Fe3+ and CdS were such that R = 30, and their CdS particle size was -0.1 pm. Note that our sample with R = 25 and I-pm particle size converted 36% of Fe3+to Fe2+via the dark reaction; therefore their particles with about 100 times the surface area should have readily reduced all of the Fe3+ before the critical Soadlayer thickness of about 5 monolayers was formed. The Fe3+ photoreduction rate constant obtained in this study of CdS (-0.5 min-I) is about 2 orders of magnitude faster than those obtained in similar experiments4 with TiO, (-0.004 min-I for anatase and -0.002 min-' for rutile). The CdS photoelectrochemical cell of Bard and White3 yielded a photocurrent rate constant of -0.5 min-l as estimated from their Figure 1 for MV2+ acceptor in solution. In earlier studies of Ti02suspensions under similar conditions, much smaller photocurrent rate constants could be deduced for both Fe3+ and MV2+ additions. In particular, for Fe3+,a photocurrent rate constant of -0.005 min-] can be estimated from Figure 7 of ref 5. The near quantitative agreement of the rate constants estimated from experiments in photoelectrochemical cells with our Mossbauer-determined rate constants is probably fortuitous, but the agreement in relative changes between CdS and Ti02suggests that inherent material properties are controlling the observed rate constants in both types of measurements. For example, the larger band gap of TiO, (3.0 eV) versus CdS (2.4 eV) will directly reduce the effective pseudo-first-order rate constant since a smaller fraction of the incident photons can create electron-hole pairs; however, this cannot explain the factor of 100 difference in rate constants. The much larger electron mobility in CdS (340 cm2/(V.s)18) than in TiO, ( 5 2 cm2/(V-s)19)may also be important. Another possibility is
-
that the very strong tendency for photocorrosion in CdS may enhance the photoreduction since the surface reaction in eq 4 may be very fast and hence effectively reduce the electron-hole recombination rate. Conclusions The kinetics of the photoreduction of Fe3+ by aqueous dispersions of CdS particles have been studied in a direct manner with 57FeMossbauer spectroscopy. Rate constants are observed that depend on the optical density of the dispersions in an expected fashion. The rate constant observed for the condition of maximum optical density is about 2 orders of magnitude faster than that for similar dispersions of TiO,, and a very high overall quantum efficiency near 50% is estimated for Fe3+to Fe2+conversion. This behavior can be attributed to either the intrinsically better semiconductor properties of CdS and/or the very high efficiency for photocorrosion of the CdS. A dark decomposition reaction occurs on the surface of the CdS particles such that a percentage of Fe3+ is reduced to Fe*+. Although this dark reaction stops before reduction of all the Fe3+, photoreduction will again commence upon illumination. This behavior can be explained by suggesting a dark reaction that occurs until a protective layer of elemental sulfur about 5 monolayers thick is formed. Further, upon illumination, this protective sulfur layer is "cleaned" by a series of reactions that convert the sulfur to sulfate or sulfite. These species then dissolve and allow photoreduction and photocorrosion to continue until either all the Fe3+ ions are reduced or all the CdS is decomposed. Indirect evidence of such reactions is obtained from the quantitative conversion of Fe3+ to Fe2+ relative to the amount of CdS in the dispersion.
Acknowledgment. This work was supported by the US.Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences. Registry No. Fe3+,20074-52-6;Fe2+, 15438-3 1-0; CdS, 1306-23-6; FeCI,, 7705-08-0; S, 7704-34-9.
( 1 7 ) Ward, M. D.; White, J. R.; Bard, A. J. J . Am. Chem. Sot. 1983, 105, 21.
( 1 8) Sze, S. M. Physics of Semiconductor Deuices; Wiley: New York, 1981; p 849.
(19) Jarzebski, Z. M. Oxide Semiconductors; Pergamon: New York, 1983; p 216. (20) Nozik, A. J.; Kaplan, M. J . Chem. Phys. 1968, 49, 4141.
Extraordlnary Viscosity Behavior of Binary Mixtures of Highly Deionized Colloids Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto 606, Japan (Received: May 22, 1989; In Final Form: September 11, 1989)
The viscosities of binary mixtures of different sizes of colloidal silica (diameter 8-45 nm) and monodisperse polystyrene spheres (diameter 85-109 nm) are measured in deionized aqueous suspensions. The specific viscosities (v,) of mixtures in the "gaslike" distributions change linearly with the mixing ratio ( x ) . vsp of "liquidlike" mixtures shows a negative deviation from linearity in the qSp-xcurves. This is explained reasonably by the decrease of void space and the increase in mean intersphere distance. Significant positive deviation is observed for mixed suspensions of "crystallike" structures. The sheared flow of binary mixtures forming alloy and superlattice structures is very difficult compared with that of the crystallike structures (face-centered cubic or My-centered cubic lattices) of constituent spheres. These results are consistent with the significant role played by electrical double layers under the influence of purely electrostatic intersphere repulsion in the effective hard-sphere model.
Introduction A study on the formation of ordered structure of monodisperse colloidal spheres in deionized aqueous suspension is helpful in understanding fundamental properties of solid crystals and also electrostatic interactions of macroionic systems. The ordered formation has been ascribed to expanded Debye screening length and electrostatic repulsion between spheres.'-17 ( I ) Luck, W.; Klier, M.; Wesslau, H. Ber. Bunsen-Ges. Phys. Chem. 1963, 67, 1 5 . 8 4 .
0022-3654/90/2094- 1962$02.50/0
In a previous paper,18this author discussed in detail the gaslike, liquidlike, and crystallike distributions of polystyrene spheres at ~~
~~
~~~~
(2) Stone-Masui, J.; Watillon, A. J . Colloid Interface Sci. 1968, 28, 187. (3) Vanderhoff, W.; van de Hul, H. J.; Tausk, R. J. M.; Overbeek, J. Th. G. In Clean Surfaces: Their Preparation and Characterization for Interfacial Studies; Goldfinger, G., Ed.; Dekker: New York, 1970. (4) Hiltner, P. A.; Papir, Y. S.; Krieger, I. M . J . Phys. Chem. 1971, 7 5 , 12, 1881. ( 5 ) Kme, A.; Ozaki, M.; Takano, K.; Kobayashi, Y.; Hachisu, S. J . Colloid Interface Sci. 1973, 44, 330.
0 1990 American Chemical Society
Binary Mixtures of Highly Deionized Colloids
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1963
sedimentation equilibrium and compared them with those of TABLE I: Properties of Colloidal Spheres Used homogeneous suspensions. Two-dimensional radial distribution charge density, functions corresponding to the real distributions of spheres were pC/cm2 obtained for the three phases. The spheres in crystallike structures strongly weakly moved around their equilibrium positions and were distributed sphere diameter, nm acidic acidic regularly along the cover glass far apart from each other. These Ludox-SM 8 f 1 (12 f 1)‘ 0.59 were typical features of the crystallike distribution, though some 0.54 1.9 Ludox- A M 13.5 f 1 defects and dislocation could also be seen. It should be noted that 0.33 Ludox-TM 25 f 2 ordered lattices were observed over the whole surface of the cover Snowtex-S 8 f l 0.32 5.6 glass and that regions of order and disorder did not coexist; Le., 0.68 Snowtex-2OL 45 5 5 two-state structures proposed by IseI9 were not obtained. The DlC25 85 f 6 1.5 1.o observation of two-state structures is not based on sound experDlC27 91 f 6 2.0 1.4 iments, and the intersphere attraction hypothesis deduced from 2.1 0.7 1 DlB76 109 f 3 LSN 109 f 5 3.3 2.8 the two-state structures is in error and should be discarded. The two-dimensional radial distribution function, g(r), for the crysa Determined by Dr. H. Matsuoka from small-angle X-ray scattering tallike distribution showed a long-range periodic distribution. The measurements. magnitude of the first peak was close to six as for hexagonally packed spheres. Quite recently, this author showed that the dependence when charge densities and monodispersities of spheres crystallike to liquidlike transition of colloidal systems occurs very were different.24 sharply, accompanied by typical patterns of transmitted-light Formation of alloy structures in binary mixtures of monodisspectra corresponding to each structureS2O perse polystyrene spheres has been studied by Hachisu et al.25-27 Spheres in the liquidlike distribution, which were observed The superlattice structures observed hitherto are AIBz, NaZnI3, microscopically, moved vigorously and comparatively freely, but CaCu5, MgCu2, and AB4 types. These alloy structures have been the distances between nearest neighbors seemed similar. The analyzed successfully by using the effective hard-sphere model. difference between crystallike and liquidlike structures was quite The structure type was determined mainly by the ratio of the distinct under microscopic observation. The liquidlike pattern effective diameters, including the Debye screening length, of the of g(r) showed the first and second broad peaks; g(r) values of constituent spheres. This author observed two-dimensional the first peak were close to two. Note that those liquidlike patterns structures of the binary mixtures of different sizes in sedimentation are very similar to the radial distribution functions for a typical equilibrium by using a metallurgical microscope.% Various kinds liquid. of alloy structure were observed. Furthermore, intersphere disIn the gaslike state, the spheres moved vigorously in Brownian tances between largelarge, largesmall, and smallsmall spheres motion and changed their positions over long distances. The agreed well with the effective sizes of spheres which include the gaslike distribution functions showed no peaks, and g(r) remained Debye screening length. Quite recently, this author studied alloy unity above a certain distance. structures by the reflection spectrum method at sedimentation Recently, this author measured the viscosities of colloidal e q ~ i l i b r i u m . ~Substituted ~ solid solution (sss) like structures, and spheres in deionized aqueous suspensions with the use of an superlattices of the MgCu, type, NaZn,, type, etc., formed in the Ostwald-type viscometer and a rotational v i s c ~ m e t e r . ~Ex~ - ~ ~ mixtures. traordinary viscosity behavior was observed: (1) The reduced The following sections discuss in detail the viscosity behavior viscosity (specific viscosity, qsp,divided by concentration, c) of of binary mixtures in gaslike, liquidlike, and crystallike structures. liquidlike suspensions was much higher than would be expected Depending on the structure, binary mixtures of different sizes of by Einstein’s equation and decreased sharply with increasing colloidal spheres showed characteristic behavior in plots of specific concentration.21q22 (2) A sharp peak in qsp/cvs c curves showing viscosity against mixing ratio; i.e., linear dependence, negative the transition between liquidlike and crystallike structures was deviation, and positive deviation from the linear dependence were observed for deionized spheres.21,22(3) The sharp increase in shear obtained for gaslike, liquidlike, and crystallike structures, restress with increasing shear rate (q) was observed for the crystallike spectively. structures, from which the elastic modulus was evaluated.23 (4) Experimental Section The log q values for the crystallike suspensions decreased linearly as log q increased.23 The log q vs log q plots for the liquidlike Materials. Colloidal silica spheres, Ludox-SM, Ludox-AM, suspensions showed non-Newtonian flows; q increased as q deand Ludox-TM were kindly donated by Du Pont, Japan (Tokyo). Colloidal silica spheres of Snowtex-S and Snowtex-20L were gifts creased, and then 7 reached a constant value. The gaslike suspensions showed Newtonian flow with constant viscosity irrefrom Nissan Chemical Industries (Tokyo). DlC25, DlC27, and spective of q values. (5) qsp/cshowed quite different concentration D 1B76 were monodisperse polystyrene spheres purchased from Dow Chemical Co. Monodisperse polystyrene spheres of LSN were prepared by Dr. M. Sugimura. Emulsifier-free radical copolymerization of styrene, styrenesulfonate, and a small amount (6) Crandall, R. S.; Williams, R. Science 1977, 198, 293. of vinylnaphthalene was carried out at 70 OC with 2,2’-azobis(7) Schaefer, D. W. J . Chem. Phys. 1977, 66, 3980. (8) Mitaku, S.; Otsuki, T.; Okano, K. Jpn. J . Appl. Phys. 1978, 17, 305, (2-methylpropionitrile) (AIBN) as an initiator. The diameters 627. and other characteristics of spheres used in this work are listed (9) Clark, N. A.; Hurd, A. J.; Ackerson, B. J. Nafure (London) 1979,281, in Table I. The values for diameters and their dispersions were 6, 57. measured by the manufacturers using an electron microscope. (10) Goodwin, J. W.; Ottewill, R. H.; Parentich, A. J . Phys. Chem. 1980, 84, 12, 1580. Strongly acidic (sulfate ions) and weakly acidic (carboxylic acid) (11) Lindsay, H. M.; Chaikin, P. M. J . Chem. Phys. 1982, 76, 3774. groups coexisted for all these spheres. The charge densities of (12) Hansen, J. P.; Haytor, J. B. Mol. Phys. 1982, 46, 651. the spheres for these groups were determined by conductometric (1 3) Tomita, M.; Takano, K.; van de Ven, T. G. M. J. Colloid Interface titration with a Wayne-Kerr autobalance precision bridge, Model Sci. 1983, 92, 367. (14) Pieranski, P. Confemp. Phys. 1983, 24, 25. B331, Mark I1 (Bognor Regis, Sussex). These spheres were (15) Hartl, W.; Versmold, H. J . Chem. Phys. 1984, 81, 2507. carefully purified several times by using an ultrafiltration cell (16) Okubo, T. Acc. Chem. Res. 1988, 21, 281. (17) Ottewill, R. H. Langmuir 1989, 5, 4. (18) Okubo, T. J . Chem. Phys. 1989, 90, 2408. (19) he, N. Angew. Chem., Znt. Ed. Engl. 1986, 25, 323. (20) Okubo, T. J . Chem. SOC.,Faraday Trans.,submitted for publication. (21) Okubo, T. J. Chem. Phys. 1987, 87, 6733. (22) Okubo, T. Nafurwissenschaffen 1988, 75, 91. (23) Okubo, T. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 504.
(24) (25) (26) (27) (28) (29)
Okubo, T. Polym. Bull. 1988, 20, 269. Hachisu, S.; Yoshimura, S. Nafure (London) 1980, 283, 188. Yoshimura, S.; Hachisu, S. Prog. Colloid Polym. Sci. 1983,68, 59. Yoshimura, S.;Hachisu, S. J. Phys. ( h s Ulis, Fr.) 1985, 46, C3-115. Okubo, T. J . Chem. Phys. 1987.87, 5528. Okubo, T. J . Chem. Phys., submitted for publication.
1964
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 I
Okubo interaction parameter. For example, the vsp values for Ludox-SM (+ol = 0.0248) and Ludox-AM ( 4 1 = ~ ~0.0269) suspensions are 0.062 (= 2.5 X 0.0248) and 0.067 (= 2.5 X 0.0269) from eq 2, respectively, while the observed values, 0.169 and 0.145, are 2-3-fold larger. Qualitatively, the high viscosity of deionized colloidal suspensions is explained by enlarged effective volume of spheres, including the electrical double layers, and the enlarged effective volume fraction ( + e f f ) of spheres.
I
a
9 'A
~ s pN
kl+eff
(3)
Thickness of the double layers is approximated by the Debye screening length, D,,and eq 4 holds 0057-
O0 L
05
Ludox-SM
X
__
1:
(4)
where do is the physical diameter of the spheres. The Debye length is calculated from
1
D, = (4rBn)-'I2
Ludox-AM
Here, B is the Bjerrum length (0.719 nm at 25 OC in H 2 0 ) given by e2/ekT,where e is the electronic charge and e is the dielectric ~) constant of the solvent. n is the number concentration ( ~ m - of the diffusible cations and anions in suspension given by
Figure 1. Plots of qsp and pH against x for Ludox-SM (1) and LudoxAM (2) mixtures at 25 OC. 0 (q,), 0 (pH): bo,= 0.0248, $02 = 0.0269; A (qrp), A (pH):60, = 0.0248, 602 = 0.0108.
(Model 202, membrane: Diaflo XM300, Amicon Co.). Then they were treated on a mixed bed of cation- and anion-exchange resins (Bio-Rad, AG501-X8(D), 20-50 mesh) for at least 10 days. The resulting suspension was believed to contain only the macroions and their counterions (protons). Water used for the purification and for solution preparations was deionized by using cation- and anion-exchange resins (Puric R, Type G10, Organo Co. (Tokyo)) and purified further by a Milli-Q reagent grade water system (Millipore Co., Bedford, MA). Viscosity Measurements. An Ostwald-type viscometer was used at 25 f 0.05 OC. The diameter of the capillary tube was 0.62 mm. The shear rate for water near the glass wall of the capillary tube was 310 s-l. The viscometer was cleaned by a chromic acid mixture followed by rinsing thoroughly with pure water. Experimental errors in the specific viscosity were estimated to be within f3%. Potentiometric titration was measured on a Horiba pH meter (Type F8L, Kyoto).
Results and Discussion Binary Mixtures in Gaslike Structures. Figure 1 shows the specific viscosity, vsp ( v / q o- 1, 7, and vo: viscosities of the suspension and the solvent), of the mixtures of Ludox-SM (component 1) and Ludox-AM (component 2) and their pH values. The mixing ratio, x, is the suspension volume fraction of the component 2 given by x = u2/(u,
+ u2)
(1)
where 0, and ut are the volumes of the initial suspensions of components 1 and 2, respectively, and the sum u , u2 was taken to be 15 mL. The initial concentrations of suspensions of components 1 and 2 are given by do, and cjO2by volume fraction of spheres. The straight broken lines in the figure connect the vsp values of suspensions containing pure components 1 and 2. Clearly, a linear relationship was obtained for observed viscosities at various x values. This linear relationship suggests that (1) the spheres, Ludox-SM, and Ludox-AM are distributed at random in the mixtures and (2) the distribution is gaslike, but the spheres still interact strongly due to electrostatic repulsion. As was clarified in previous p a p e r ~ , ~ lthe - * ~absolute values of qspfor suspensions of pure Ludox-SM (x = 0) and Ludox-AM (x = 1 ) were fairly large compared with values given by Einstein's equation. According to most previous work on specific viscosity of colloidal spheres in aqueous electrolyte, the following equation may apply:
+
Here $C is the concentration of the colloids by volume fraction. k , is the Einstein coefficient, 2.5. k , denotes the electrostatic
n = n,
+ n, + no
(5)
(6)
where n, is the concentration of diffusible counterions, n, the concentration of ions from added electrolyte, and no the concentration of hydrogen and hydroxide ions from dissociation of water. n, was taken to be 2 X lo-' (M) X X NA ( ~ m - in ~ )this work, where NA is Avogadro's number. The fraction of free counterions (0)of spheres is less than unity and decreases sharply with increasing sphere charge number.3w32 As is clear in eq 5 , the Debye length increases as n decreases, and D,for the completely deionized suspension is significantly large, on the order of micrometers. The value of 0 for Ludox-AM was estimated to be 0.85.32 n, and D, for the Ludox-AM suspension at 4 = 0.0269 were estimated as 6.7 x 10-4 (MI x 10-3 x N A ( ~ m - and ~ ) 18 nm, respectively. Thus, the values of denand q were found to be 1.33 and 3.32 from eqs 4 and 3, respectively. course, the +eff value calculated, which is larger than unity, is not physically realistic. However, the increase in defffor a deionized suspension can be explained well qualitatively. It should be noted that Debye lengths observed from viscosity measurements of Snowtex-S suspensions were always smaller than the calculated ones by a factor of = 10. This difference is ascribed to the strong distortion of the electrical double layers from sphericity under the shearing flow of a capillary tube of the viscometer. The axes of the Debye cloud of the double layers in directions normal to the flow will be shortened and elongated in the flow direction. Envelopes of the double layers are very fragile and are compressed or distorted by external f o r ~ e . ~ ~ - ~ ~ Qualitatively, the large specific viscosity obtained in deionized suspensions implies that the electrostatic repulsive interaction is significant and the electrical double layers around the spheres are very thick. Thus, according to the effective hard-sphere model, the translation of spheres should be retarded beyond the theoretical values expected from Einstein theory and crystallographic size of spheres. Note that the possibility of flow effects due to interaction of the double layer on the spheres with the double layer at the surface of the capillary glass is neglected. When both kinds of spheres are very small, their concentrations are low and/or the solution contains added electrolyte; the linear
8f
(30) Alexander, S.;Chaikin, P. M.; Grant, P.; Morales, G. J.; Pincus, P.; Hone, D . J . Chem. Phys. 1984, 80, 5776. (31) Okubo, T. Eer. Bunsen-Ges. Phys. Chem. 1987, 91, 1064. (32) Okubo, T. J . Colloid Interface Sci. 1988, 125, 380. (33) Tomita, M.; van de Ven, T. G. M. J . Colloid Interface Sci. 1984, 99, 374. (34) Lindsay, M.; Chaikin, P. J . Phys. (Les Ulis,Fr.) 1985, 46, C3-269. (35) Jorand, M.; Koch, A. J.; Rothen, F. J . Phys. ( t e s Ulis, Fr.) 1986, 47, 217 (36) Ackerson, B. J.; Haytor, J. B.; Clark, N. A.; Cotter, L. J . Chem. Phys. 1986, 84. 2344.
Binary Mixtures of Highly Deionized Colloids 0 5-
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1965
5p6
I
,' I
0.15c
I
,/ jj//' /'
04, 0 0
0
I 0.1
1
I
r
I
P
F
1
,/'
P O
a
0
. * *~
0
0.05t
0
-3
I
2-0
-~d2
0.1
0
05
Ludox-SM
x
1 Ludox-T M
Figure 2. Plots of qsp and pH against x for Ludox-SM (1) and LudoxTM (2) mixtures at 25 OC. 0 (qsp), 0 (pH): $01 = 0.0248, $02 = 0.0309 A (qsp), A (pH): $01 = 0.0248, $02 = 0.0154.
0
A
,
1k
0
05
1
Snowtex-S
X
Snowtex-20L
Figure 4. Plots of qsp and pH against x for Snowtex-S (1) and Snowtex-20L (2) mixtures at 25 " C . 0 (qsp), @ (pH): $o, = 0.0257, bo2=
0.00232. 2 01
i
I
i6
13
A A
A'3
I
I 0-
0
05
12 1
Ludox-SM
X
Snowtex-20L
Figure 3. Plots of qsp and pH against x for Ludox-SM ( I ) and Snowtex-2OL (2) mixtures at 25 OC. 0 (qsp), 0 (pH): $ol = 0.0248, OOz = 0.00696; A (qsp), A (pH): $01 = 0.0248, $02 = 0.002 32.
2-0
0 0.5 1 DlC27 X DlC25 Figure 5. Plots of qapand pH against x for D1C27 (1) and DlC25 (2) mixtures at 25 OC. 0 (qsp), 0 (pH): dol = 0.007 56, $02 = 0.007 53; A (qSp), A (pH): $01 = 0.003 78, $02 = 0.003 77; 0 (qsp), (pH): $01 =
0.001 89, $02 = 0.001 88.
relationship in specific viscosity-mixing ratio curves has been obtained in our experiments, though further graphs illustrating this are omitted. It must be mentioned here that gaslike structures always lead to a linear relationship between viscosity and mixing ratio. However, the linear relationship does not always imply the gaslike nature of the mixtures. Binary Mixtures in Liquidlike Structures. When sphere sizes are large and total concentrations are comparatively high, the plots of qsp against x deviate downward convexly from linear as shown in Figures 2-4. Figure 2 shows the vSpof Ludox-SM and Ludox-TM mixtures. The broken lines show the linear relationship. The negative deviation of specific viscosities from linear was obvious for all the mixtures shown in Figures 2-4. In liquidlike distributions the effective volume fractions of enlarged spheres with thick double layers are very high. In concentrated suspensions of bimodal colloidal spheres, negative deviations have been rep ~ r t e d . ~ ' -Evenson3' ~~ suggested that a suspension with bimodal (37) Evenson, G. F. Rheology of Disperse Systems; Mill, C. C., Ed.; Pergamon Press: London, 1959; p 61. (38) Parkinson, C.; Matsumoto, S.; Sherman, P J . Colloid Interface Sci. 1970, 33, 150.
size distribution can be regarded as a system in which the larger spheres are suspended in a continuous phase, formed by a suspension of smaller spheres in the fluid medium. In many cases the specific viscosities showed pronounced minima when the smaller spheres constituted ca. 25% of the total sphere volume c o n ~ e n t r a t i o n .Qualitatively, ~~ decrease in the void (dead) space and then increase in mean intersphere distance are the main cause for negative deviation. For the highly deionized bimodal suspensions studied in this work, the thickness of the electrical double layers changes very sensitively with the concentration of free H+ ion in the suspensions. Thus, the surface charge densities of the spheres influence the effective sizes of spheres greatly. For example, when a small amount of suspension, which contains a large amount of H+ ion, is mixed with a suspension of low H+ concentration, the Debye screening length decreases sharply. Figures 3 and 4 demonstrate this situation; Le., pH values of the Snowtex-2OL suspension decreased sharply on addition of a small amount of Ludox-SM (39) Chong, J. S.; Christiansen, E. B.; Baer, A. D. J . Appl. Polym. Sci. 1971, 15, 2007.
1966
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 20
Okubo
l6
a
P
l
01-
I Q
A
,I'
,'
n
,
I 0 5-
,
,A'
Q'
,
-~3
'
A
I
I
12
0 0 D1876
05 X
1
DlC25
00 LSN
2
05 X
1 LUdox-TM
Figure 6. Plots of qs, and pH against x for DlB76 (1) and DlC25 (2) mixtures at 25 "c. 0 (vrp),0 (pH): dol = 0.0170, @02 = 0.007 53; A (vSp),A ( p H ) : $0, = 0.008 49, $02 = 0.007 53.
Figure 7. Plots of qspand pH against x for LSN (1) and Ludox-TM (2) mixtures at 25 OC. 0 (qsp), 0 (pH): @ol = 0.0234, bO2= 0.0309; A (qsp), A (pH): $01 = 0.0141, @02 = 0.0309; 0 (qsp), (pH): $01 = 0.0234, $02 = 0.0309. [NaCI] = 6.67 X M.
(or Snowtex-S), which contained a large amount of H + ion, and specific viscosity dropped substantially. It is very difficult to discuss the magnitude of the negative deviations quantitatively, because many factors influence binary mixtures of deionized colloids. However, significant deviation of the specific viscosity from the linear relationship itself clearly indicates that the binary mixtures are liquidlike. Binary Mixtures in Crystallike Structures. Open symbols in Figure 5 show the specific viscosities of DlC27 DIC25 mixtures at three different total volume fractions, Le., 0.007 55, 0.003 78, and 0.001 89. Concentrations for the transition between crystallike and liquidlike structures are ca. 0.005 and ca. 0.006 by volume fraction for D1C27 and DlC25 spheres in deionized aqueous suspensions, respectively.20 Interestingly, the specific viscosities of the mixtures of DlC27 (40 = 0.00756) and DlC25 (40 = 0.007 53) showed an extraordinary x dependence as is clearly shown by open circles in Figure 5: there are two maxima and one minimum! The maxima and minima shown in Figures 5-7 were checked at least three times, and reproducibility was high. All of the independent suspensions of DlC25 or DlC27 spheres and their mixtures shown by open circles displayed strong iridescence. Furthermore, crystallites were observed in all suspensions except that at x = 0.5, in which iridescent color only was recognized. A previous report on the reflection spectrum measurements of D1C25 and D1C27 mixtures clearly showed that the sss-like alloy structures formed in all the mixtures of D1C25 (40 = 0.0181) and DlC27 (& = 0.0184) at x = 0.25, 0.5, and 0.75.29 The positive deviations of v,, from linear and the existence of two maxima are caused by formation of sss-like alloy structures in the suspensions. The reason why viscosities of the alloy structures are higher than those of crystallike structures of constituent suspensions is given as follows; slipping planes for sheared flow may be much more easily and widely formed for the bodycentered cubic (bcc) or face-centered cubic (fcc) lattices, which are the structures for the D1C25 or DlC27 suspensions. The sss-like alloy structures are more compact (voids are narrower) than the fcc or bcc lattices. Thus, it is plausible that crystallike alloy structures are more stable against shearing flow. Negative deviation of vsp or the existence of a minimum at x = 0.5 is
reasonably explained by the fact that the mixtures around x = 0.5 were not crystallike but liquidlike! Note that the suspensions around x = 0.5 showed iridescent color but did not show any crystallites. This supports the liquidlike nature of the suspension. Open triangles in Figure 5 show the viscometric data for liquidlike suspensions. Negative deviation from linear was not observed. This, however, is due to the fact that experimental errors were larger than the magnitudes of the negative deviations. When total volume fractions are as low as the levels of gaslike structures as shown by open squares, the linear relationship between vrpand x holds nicely. Note here that the pH values did not show any characteristic changes as x changed. The q,,-x profiles of the binary mixtures of DlB76 (do = 0.00849) and DlC25 (40= 0.007 53) shown in Figure 6 were quite similar to those of DlC25 + DlC27 systems given in Figure 5; Le., two maxima and a minimum were observed, consistent with the fact that all suspensions examined are crystallike except those around x = 0.5 (open triangles). When the concentration of DIB76 was doubled, positive deviation of the qspvalues from the linear relationship was quite substantial! When D1C25 (r+$o = 0.0181) and D1B76 (do= 0.0232) were mixed, the sphere distribution was a eutectic mixture of sss-type lattices and the MgCu2-type super lattice^.^^ Now, let us discuss the rheological properties of mixtures of liquidlike and crystallike suspensions. The results are shown by open circles in Figure 7 for suspensions of LSN spheres (crystallike) and Ludox-TM spheres (liquidlike). A clear-cut maximum from the positive deviation appeared at small x . The suspensions at large x are liquidlike. When a small amount of sodium chloride was added to the suspension, the qlsqvaluesdecreased significantly and the linear relationship was obtained as shown by open squares in the figure. This indicates that the suspensions are now gaslike.
+
Acknowledgment. The author thanks Dr. T. Matsumoto very much for his valuable suggestions during this work. Nissan Chemicals Co. and Du Pont, Japan, are acknowledged for supplying the colloidal silica samples. The author is grateful to the Japanese Ministry of Education, Science, and Culture for support of this work.
