Langmuir 1994,10,8-16
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Ralph K. Iler Award Uniform Inorganic Colloid Dispersions. Achievements and Challenges? Egon Matijevi6 Center for Advanced Materials Processing, Clarkson University, Potsdam, New York 13699-5814 Received May 19,1993. In Final Form: July 22,199P This review deals with the preparation, properties, and interactions of well-defined colloids of simple and composite nature. The formation of such dispersions by precipitation from homogeneous solutions is described and some problemsrelated to the mechanismsof the formationand growth of "monodispersed" particles are cited. A few examples of the use of uniform dispersions in the evaluation of their properties as a functionof particle size and shapeare offered,with specific referenceto optical and magneticphenomena. Finally, some experimental results in (hetero)coagulationand particle adhesion processes are described, as obtained with well-defined colloids, in order to evaluate the theories of interactions in systemsconsisting of dissimilar particles.
Introduction The fascination with the so-called monodispersed colloids dates back to more than a century, when Faraday described his gold sols, the brilliant colors of which were found to depend on the particle size.' Originally,uniform dispersed matter attracted the interest of scientists essentially for academic reasons; i.e. to quantitatively interpret physical properties or surface interactions as a function of the morphology, size, and other characteristics of such systems. Presently, the importance of well-defined fine particles has been recognized in numerous applications, as in ceramics, catalysis, pigments, recording materials, medical diagnostics, and many others. These dispersions are also used in the attempts to elucidate some of the vexing problems of colloid and surface science, such as heterocoagulation,particle adhesion, corrosion, to name a few. Recently, significant progress has been made in the preparation of a large number of inorganic colloids consisting of particles of different chemical composition, shape, and modal size, especially by precipitation. Still a number of questions need yet to be satisfactorily answered, including those of chemical and physical mechanisms of their formation and growth, as well as of particle morphology. The reason for so many essential unknowns is easily understood, if one recognizes the complexity of processes involved in the formation of these materials and in their interactions. As an example one may cite the work of Iler in whose honor has this award been established. His classic text of more than 800 pages deals with one inorganicmaterial only, i.e. silica!2 Needless to say, another even larger volume could be written on iron oxides or some other family of compounds. This review illustrates certain aspects of the preparation and properties of monodispersed colloids and offers t Supported by the NSF Grant CHE9108420.
* Based on the lecture presented at the 205th National Meeting
of the American Chemical Society in Denver, CO, on the occasion of the author receiving the ACS Ralph K. Iler Award.
e~Abstract published in Advance ACS Abstracts, December 1, 1993. (1) Faraday, M. Philos. Trans. R. Soc. London, Ser. A 1857,147,145. (2) Iler, Ralph K. The Chemistry of Silica; Wiley-Interscience: New York, 1979.
0743-7463/94/2410-08$04.50/0
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Figure 1. Transmission electron micrograph (TEM)of silica particles prepared by aging at 40 "C for 1 h a solution containing 0.25 mol dm-3 tetraethyl orthosilicate (TEOS), 0.90 mol dm4 NH3,8.0 mol dm-3 HzO, and 383 cm3 ethanol."
examples of (hetero)coagulation and particle adhesion studies with such materials. A number of questions, some of which quite challenging, are indicated. Obviously, the first prerequisite to resolve these elusive problems is the availability of well-defined dispersions.
Synthesis of Monodispersed Colloids While the term "monodispersed" is commonly used, it is understood that it describes systems (solid, liquid, or bubbles) of narrow size distributions. This review deals mostly with uniform inorganic fine particles prepared by precipitation from homogeneous solutions. 0 1994 American Chemical Society
Langmuir, Vol. 10, No. 1, 1994 9
UniformInorganic Colloid Dispersions A. Particlesof Simple Composition. The principles involved in the precipitation of well-defined colloidal particles have been described in a number of review article^,^^ which also show that it is now possible to obtain uniform metal (hydrous)oxides, halides, sulfides,selenides, phosphates, carbonates, etc. in different morphologies. Only a few examplesare shownhere to illustrate the variety of the available powders. It is appropriate that the first electron micrograph represents monodispersed silica, prepared by a procedure originally developed by Stober et al.l0 and later modified," which demonstrates the exceptional uniformity in the size of these spherical particles. Figure 2a displays lead sulfide12 and Figure 2b is the electron micrograph of cobalt phosphate.l3 A particle of copper(1) oxide of unique shape is shown in Figure 3.14 These examples are chosen to illustrate the diversity of materials both in terms of chemical composition and morphology. There are two essential aspects of the formation of these particles that need to be addressed in principle; they refer to (a) the chemical processes leading to their precipitation and (b) the mechanismsof particle nucleation and growth. With respect to chemical aspects of precipitation, it is obvious that the composition of all solute species must be elucidated in order to establish which of these act as precursors to the solid-phase separation. This task may be difficult, especially when dealing with higher charged metal ions, which tend to form polymeric and polynuclear complexes, often in metastable form. Yet, these solutes significantly affect the precipitation process. It is also understood that each system would differ, resulting in a variety of precipitates in terms of their chemical,structural, and morphological characteristics. The applicability of the generally accepted principles, regarding the particle nucleation and growth processes that should lead to "monodispersed" colloids, first expounded by LaMer,lSJ6 have now been seriously questioned. The proposed concept that a short nucleation burst, followed by diffusional growth is required for the precipitation of uniform dispersed matter, has been shown to apply to a limited number of cases, and often only to the initial stages of the process. Instead, more recently, much evidence has been provided showing that the mechanism involves first the generation of tiny solid precursors, which subsequently aggregate into uniform larger particles. This sequence of events is equally applicable to spherical as well as to other shapes, as illustrated in Figure 4.17J8 In both examples the subunits are clearly discernible, although at lower magnification these particles appear perfectly smooth. It is interesting to note that the aggregation mechanism was also claimed in the formation of silica particles (3) MatijeviC, E. Chem. Mater. 1993,5,412. (4) Livage, J.; Harry,M,; Sanchez, C. Prog. Solid State Chem. 1988, 8,259. (5) Sugimoto, T. Adu. Colloid Interface Sci. 1987,28,65. (6) Haruta, M.; Delmon, B. J. Chim. Phys. 1986,83,859. (7) Matijevit, E. Langmuir 1986,2, 12. (8) MatijeviC, E. Annu. Rev. Mater. Sci. 1985, 15,485. (9) Overbeek, J. Th. G. Adu. Colloid Interface Sci. 1982, 15,251. (10) Stijber, W.; Fink, A.; Bohn,E. J. Colloid Interface Sci. 1968,26, 62. (11) HSU,W. P.; Yu, R.; MatijeviC, E. J. Colloid Interface Sci. 1993, 156,56.
(12) Murphy-Wilhelmy, D.; MatijeviC, E. Colloids Surf. 1985, IS, 1. (13) Ishikawa,T.; Matijevit, E. J. Colloid Interface Sci. 1988,123,122. (14) Keklikian-Durand,L.; MatijeviC, E. Unpublished results. (15) LaMer, V. K. Znd. Eng. Chem. 1952,44,1269. (16) LaMer, V. K.; Dinegar, R. J . Am. Chem. SOC.1950,72,4847. (17) OcaiTa, M.; MatijeviC, E. J. Mater. Res. 1990,5, 1083. (18) Hsu, W. P.; Riinnquist, L.; Matijevit, E. Langmuir 1988, 4, 31.
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Figure2. (a) Scanningelectronmicrograph(SEM) of lead sulfide particles obtained by the addition of 0.50 cm3 of a 5 X le2mol dm3 thioacetamide solution to 20 cm3 of a lead sulfide sol with subsequent aging at 20 "C for 20 min.12 The longest bar is 10 pm. (b) SEM of cobalt phosphate particles obtained by aging at 80 "C for 3 h a solution 5.0 X 103 mol dm3 in COSOI,5.0 X 10-3 mol dm3 in NaH2PO4,l.Omol dm3 in urea, and 1.0 X le2 mol dm3 in sodium dodecyl sulfate.13 The longer bar is 1 pm.
prepared by the hydrolysis of tetraethyl orthosilicate (TEOS), illustrated in Figure l.19 However, in a recent extensive study:() it was indicated that the aggregation observed by electron microscopy was an artifact. Instead, it was demonstrated that these silica particles grow by the incorporation of hydrolyzed monomers. While the aggregation mechanism has been established in many cases,a quantitative explanation for the formation of monodispersed larger particles, by interaction of a huge number of tiny subunits, is still not available. An even more difficult,but essential challengethat needs attention refers to the morphology of precipitated solids.2l In some cases the shape of the particjes is related to their chemical 'composition, yet in many other instances the solids of the same compound appear in different geometries, even when the changein the experimentalconditions (19) Bogush, G. H.;Zukogki IV,C. F. J. Colloid Interface Sci. 1991, 142, 1. (20) Van Blaaderen,A.; Van Geest,J.; Vrij, A. J. Colloid Interface Sci. 1992, 154,481. (21)Matijevit, E. Control of Powder Morphology. In Chemical Processing of Advanced Materials; Hench, L. H., Weat, J. K., Eds.; Wiley: New York, 1992; p 513.
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Figure 3. SEM of a copper(1) oxide particle obtained by aging at 100 "Cfor 1 h a solution 0.05 mol dm-3 in CuC12,0.2mol dm-3 in EDTA,and 1.7 mol dm-3 in NaOH.14 The longer bar is 1 pm.
is rather small. While cubic, tetrahedral, etc. solids are expected to be crystalline, spherical particles have appeared either amorphous or they showed X-ray characteristics of known minerals. In the latter case the above mentioned aggregation mechanism was found responsible for their formation. It should be noted that particles of well-defined geometric shape are not necessarily single crystals; many are also internally composite. The difference in the morphology of particles of the same chemical composition is also related to the natures of the precursor subunits, as recently clearlydemonstrated on the example of colloidal hematite.22 At present, it is possible to rationalize the formation of particles of given shapes once these have been pre~ared,~~923 but no fundamental principles have been established that would make it possible to predict their habitus based on certain experimental conditions, especially when solids appear in rather unique forms as illustrated in Figure 3. Since an increased number of well-defined dispersions is being produced by carefully controlled processes, some generalities in terms of morphologies may be developed, once both the chemical and growth mechanisms are elucidated for families of related compounds. B. Composite Particles. Properties of powders can be modified either by producing solidsof internally mixed composition or by coating cores with shells of a different compound. Uniform particles have been achieved in both kinds of systems. a. Particles of Internally Mixed Composition. In this class of materials one can deal with solids of fixed or variable composition. In the latter case coprecipitation from solutions containing more than one kind of reactant can yield spheres of narrow size distribution^.^^,^^ When compounds contain more than one metal, two aspects of these systems need special attention. The first refers to the relationship between the molar ratio of the constituent metal species in the original solution to that in the precipitated particles, while the second relates to their internal homogeneity. It has been shown that the distribution of constituents in compositespheres varies from the center to the periphery, which means that the rate of (22) Bailey, J. K.; Brinker, C. J.; Mecartney,M. L. J. Colloid Interface Sci. 1993, 157, 1. (23) Sapieszko, R. S.; Patel, R. C.; Matijevit, E. J . Phys. Chem. 1977, 81, 1061. (24) Ribot, F.; Kratohvil, S.; MatijeviC, E. J. Mater. Res. 1989,4,1123. (25) Hsu,W. P.; Wang, G.; Matijevit, E. Colloids Surf. 1991,61,255.
. Figure 4. (a) TEM of tin(IV) oxide particles obtained by aging at 100 "C for 2 h a solution 1.5 X 103 mol dm-3 in SnC4 and 1.5 X 10-l mol dm-5in HCl.16 (b) TEM of a cerium(n7)oxide particle obtained by aging at 90 "Cfor 12 h a solution 1.5 X le2mol dm4 mol dm-3 in H804,and 1.6 X le1 in (NH&Ce(NO& 6.4 X le2 mol dm3 in Na2S01.l~
precipitation of individual components changes with the particle growth. Figure 5 demonstrates such a case on the example of mixed cadmium/nickel phosphates.26 Furthermore, the surface properties can be completely dominated by one of the compounds, although the other one may actually be present in excess. Again, once several such systems have been investigated in depth, it should be possible to generalize some of these phenomena by taking into consideration the complex composition of the solutes, the relative solubilities of the components, the rates of their precipitation, and other parameters. b. Coated Particles. It has been shown that uniform coatings can be achieved on a variety of particles, in different combinations, i.e. inorganic cores with inorganic or organic shells, and vice versa.273o Figure 6 illustrates hematite covered with silica and a polymer latex with yttrium basic carbonate. (26) QuiMn, J.; MatijeviC, E. Colloids Surf., in press. (27) Ohmori, M.; Matijevib,E. J. Colloid Interface Sci. 1992,150,594. (28) Garg, A.; MatijeviC, E. J. Colloid Interface Sci. 1988, 126, 243. (29) Kratohvil, S.; MatijeviC, E. Adu. Ceramic Mater 1987,2, 798. (30) Kawahashi, N.; MatijeviC, E. J . Colloid Interface Sci. 1990,138, 534.
Langmuir, Vol. 10, No. 1, 1994 11
UniformInorganic Colloid Dispersions
a
o'"'"'''""''""""''' 90 180 270 360 t/min
450
Figure 5. Overall composition of internally mixed nickel and cadmium phosphate solid particlea, [Cd]/ [Nil, precipitated in solutionsof initial molar ratios [Cd2+l/[Ni2+]= 2.0,1.0, and 0.5, respectively, as a function of the aging time at 80 OC.=
b
a
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Figure 7. (a) TEM of iron particles coated with silica by f i t preparing hematite particles coated with silica as illustrated in Figure 6a. The dried coated particles were then reduced with hydrogen at 450 "C for 3 h.31 (b) TEM of hollow yttria particles obtained by calciningparticles shown in Figure 6b at 600 "C for 3L.32
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0.2p m
Figure 6. (a) TEM of hematite (a-Fe2O3)particles coated with silicabyagingat40"Cfor 18hadispersionof73mgdm3hematite particles in 2-propanol,containing 0.45 mol dm-3NH3,3.05 mol dm-3 H20, and 4 X 10-3 mol dm-3 TEOS.n. (b) TEM of polystyrenelatex particles coated with yttrium basic carbonate shellsby aging at 90 "C for 2 h a dispersion of 100 mg dm-3latex, 5 X 10-3mol dm4 Y(NO&, 1.8 mol dma urea, and 1.2 wt 96 poly(vinylpyrro1idone) (PW).
The shells can be formed either by a direct surface reaction, such as by polymerization of hydrolyzed species,
or by precipitation of the coating material in the form of tiny particles in the presence of the suspended cores. In the latter case, the so generated finely dispersed matter may heterocoagulate under appropriate conditions with the preformed particles to produce surface layers, the thickness of which can be varied by the adjustment of the experimental parameters. Again, it is not always possible to a priori assume which of the two mechanisms will prevail in a given system. There are some interesting additional products which have been made possible with the availability of coated particles. Figure 7a is the electron micrograph of pure iron encased in silica, prepared by reduction of particles shown in Figure 6a with hydrogen.31 Since this process is carried out at an elevated temperature, the originally gas permeable silica layer becomes sintered and, therefore, it protects the metal core. As a consequenceof this process, magnetic properties of the powder are also changed. Figure 7b is of hollow yttria spheres obtained by burning off the polymer core of the coated latex particles shown in Figure 6b.32 ~
~
~-
(31) Ohmori,M.; Matijevit, E. J. Colloid Interface Sci. 1993,160,288. (32) Kawahashi, N.;Matijevit, E. J. Colloid Interface Sci. 1991,143, 103.
12 Langmuir, Val. 10, No. 1, 1994
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Figure 8. Particle extinction cross section per unit area, Q, calculated for spheres of different diameters, which have the refractive index of hematite dispersed in water, as a function of the wavelengths and particle diameters (calculated by Dr. N. Ryde in the author's laboratory).
Characterization of Monodispersed Colloids One significant advantage of uniform particles is the possibility to investigate the effects of their size and shape on different properties of dispersed matter. In this review examples will be given, related to some optical and magnetic characteristics of colloids. A. Optical Properties. It has been well-known that the color purity and saturation of pigments depend not only on chemical composition but also on their particle size. Optical properties of spherical particles are fully understood and can be quantified once their refractive index and diameter are given.33 To illustrate this effect, Figure 8 shows the calculated scattering efficiency, Q, of spheres which have the refractive index of hematite (aFen031 dispersed in water as a function of the wavelength and of their size. Obviously, the spectra are exceedingly sensitive to even a small change in the particle diameter. Based on this example, it is easily concluded that for the quantification and reproducibility of pigment properties, it is essential to have the colored matter as uniform as possible. Since most pigments cannot be prepared as well-defined dispersions, it is more convenient to design such materials by combining dyes with perfectly uniform spherical cores of known size and refractive index. Using dyes of different color in known concentrations can yield pigments of precise optical characteristic^.^^^^^ For this purpose colloidalsilica is particularly convenient as carrier, due to its sphericity, uniformity, and low refractive index, as illustrated in Figure 9. The optical properties of such pigments can be varied with the nature and the concentration of the dye, which may be incorporated either by coprecipitation or by adsorption, as well as with the particle size of silica (or any other spherical core of a known refractive index). Figure 10 shows reflectance spectra of powders consisting of amino-modified silica particles coupled with different dyes.35 The pigments can be further modified by coating the cores with a shell of a different chemical composition in varying thicknesses. Sincethe optics of particles consisting of concentric spheres is fully under~tood,~S it is again possible to design dispersions for specific uses, such as whiteners. Figure 11 illustrates a coated model particle (33) Kerker, M. The Scattering of Light and Other Electromagnetic Radiation; Academic Press: New York, 1969. (34) Hsu, W . P.; Yu, R.; MatijeviE, E. Dyes Pigm. 1992, 19, 179. (35) Giesche, H.; MatijeviC, E. Dyes Pigm. 1991, 12, 323.
1 mn Figure 9. TEM of dye-incorporatedparticles in silica: (a) and (b) Methylene Blue and Azure A, respectively, introduced by coprecipitation; (c) and (d) Ethyl Violet and Thioflavine T, respectively, by adsorption on silica surface. In all cases the dye concentration was 1.0 x 1V mol dm-3."
A/nm Figure 10. Reflectancespectra determined with 1mg of pigment
powders per cm2 for samples of amino-modified silica particles (a), and those coupled with different dyes: (b) Flavazin L, (c) C.l.Acid Red 183, (d) Violamin R, (e and 0 C.l.Acid Blue 45.96
and Figure 12 gives the calculations of the scattering coefficients of silica cores covered with different layers of titania, as a function of the optical size, and compares the so obtained values with those of pure titania, all in a cellulose matrix.11 The effects both of the size and of the shell on the optical properties of this system are quite obvious. Figure 13shows the reflectances of the so coated particles to be comparable or better than those obtained with a commercial titania whitener.ll B. MagneticProperties. Magnetic properties of fine particles are also a function of their size and shape, in
Uniform Inorganic Colloid Dispersions
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1.0 u m SiOl wt.% Coating
.-. 50 ....... 4030 --.I-
-- 20 -
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CELLULOSE, nM = 1.45 F i g u e 11. Schematic diagram of a concentric sphere consisting of a silica core and titania shell in a cellulose matrix." TITANIA COATED SILICA
w
SiO, ( u m )
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WAVELENGTH ( nm) Figure 13. Reflectance spectra (a) of the same silica particles (1 pm in diameter) coated with different amounts of titania and (b)of silica particlea of different sizescoated with the same percent amount (40%)of titania. Heavy solid line is for a commercial titania sample (RLPS)."
a
x
d
20
16 0
2
4
6
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OPTICAL SIZE ( Z I T ~ / X ) Figure 12. Scatteringcoefficient, QEA, as a function of the optical size, 2 d A (r = particle radius, X = wavelength of the light), of titania (heavy line) and of silica particles coated with different thicknesses (B/r)of titania,all incorporated in acellulosematrix.ll addition to the chemical composition and structure. These dependencies can now be investigated by using chemically the same materials, but of different physical characteristics. One such study is illustrated here on the example of the relationship of the Morin temperature, TM,to the particle size of Bulk a-Fe203 possesses the corundum-type crystal structure with an antiferromagnetic spin ordering. This material exhibits a first-order magnetic transition at 263 K (which is known as the Morin temperature). A series of dispersions of uniform spherical hematite particles of different modal diameters (ranging from 0.07 to 0.62 pm) were prepared and annealed to eliminate the strain. Thus, the true Morin temperature (TM")values could be evaluated, depending on the size only. Figure 14 shows the measured Morin temperatures, T#, as a function of the applied magnetic field, while ~ Figure 15 displays the dependence of TM"( T Mextrapolated to H = 0) on the inverse diameter ( l l d ) . The extrapolation to d = gives T M O = 264 K, which is in excellent agreement with the literature value of 263 K for hematite in bulk, while for small particles (80A) TM" coincides with the onset of ~uperparamagnetism.3~ Another consequence of magnetic properties of small hematite particles is illustrated on the example of the electric conductivity of such colloidal systems. Figure 16 shows that the conductance of aqueous dispersions of (36) Amin, N.;Arajs, 5.; Matijevib, E. Phys. Status Solidi A 1987,104, K65. (37) Amin, N.;Arajs, S.Phys. Reu. B 1987, 35, 4810.
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a
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0
T,(K)
Figure 14. Morin temperature, T#, as a functionof the applied magnetic field H for spherical hematite particles of different diameters: (1)0.07,(2) 0.10,(3) 0.13, (4)0.17,(5)0.33, and (6) 0.62 fim.s7
spindle-type a-FezO3 particles changes with the strength of the superimposed magnetic field.38 This effect is observed with both a perpendicular and a parallel field, relative to the direction of the conductivity measurements, and its magnitude depends on the particle size and anisometry. The change was explained by the orientation of the particles and was accounted for by using an equation similar to that derived for the transient electric or magnetic birefringence, i.e. AK = K ( l - 3 / p coth p + 3/p2)
(1) where AKis the change in the conductivity,K is a constant, the value of which is dependent on the shape of the particles (38) Ozaki,M.;Nakata, N.; Matijevib,E. J.Colloidlnterface Sci. 1989, 131, 233.
MatijeuiE
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Scaled Particle Size
Figure 17. Regions of applicability,in terms of particle size and surfacepotential,of different theoretical treatmentsof thedoublelayer interactions (refs 43-46).
l/d (l06ni1)
Figure 15. Morin temperature, T M O , as a functionof the inverse diameter, lld, of hematite particles listed in Figure 14.37
-3
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500
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1500
MAGNETIC FIELD STRENGTH /Oe Figure 16. Change in the conductivity of an aqueous dispersion of spindle-type hematite particles (0.46 pm long with an axial ratio of 4.4) under the applied magnetic field perpendicular (0) and parallel (0)at pH -3.7. The solid line is calculated by means of eq 1 using the best values for M and K.% as well as on the other parameters, and p = M H / k T in which H is the magnetic field strength and M the magnetic moment. Transient magnetically induced birefrigence technique was used for the rapid measurement of the particle size distribution of sub-micrometer anisometric iron oxides.39 The ordering of hematite particles into chains has also been observed and explained by the effect of geomagnetic field on such dispersion^.^^*^^ The direction of such linear aggregates could be altered or the aligned particles could be redispersed by appropriate superposition of a magnetic field. The calculations showed that these effects were due to a pronounced secondary minimum caused by magnetic interactions as illustrated later on in Figure 22, which also strongly depended-on the particle ~ i z e . ~ 1 Interactions of Unlike Colloidal Particles The stability of dispersions of unlike particles is of great interest, both academic and practical, but the interpretation of interactions in such systems is considerably more (39) James, R. 0. Colloids Surf. 1987,27, 133. (40) Ozaki, M.: Suzuki, H.: Takahashi. K.: MatiieviE, . E. J. Colloid Interface Sci. 1986, 113, 76. (41) Ozaki, M.; Egami, T.; Sugiyama, N.; Matijevib, E. J. Colloid Interface Sci. 1988, 126, 212.
difficult than for those of identical particles. Thus, it is of no surprise that much effort has been devoted to the problems of heterosystems, frequently with controversial theoretical explanations. The present state of affairs in this area has been recently reviewed, and the ranges of validity of different modifications and approximations of the theories for interactions of dissimilar spherical double layers have been estimated. Figure 17 summarizes the results in terms of the particle sizes and Essentially, the same theoretical treatments can be extended to particle adhesion (depositionand detachment) phenomena. In any attempt to test the theories of heterocoagulation (or particle adhesion), it is essential to carry out carefully designed experiments with uniform spherical particles. Here a few examples of studies of colloid stability and of particle adhesion will be described. a. (Hetero)coagulation. The stability coefficients were determined for a number of dispersions, consisting of uniform spherical particles, by careful measurements of the rates of aggregation, as a function of different parameters including particle surface potentials and size, electrolyte content, etc. As an example, data for homocoagulation of colloidal hematite in solutions of different ionic strengths are plotted in Figure 1847and compared with values based on the Hogg, Healy, and Fuerstenau (HHF)&and the Overbeep expressions. Obviously, there is a significant difference between the experimentally determined and theoretically calculated stability coefficients. Analogous discrepancies were observed with a number of other systems, consisting either of one kind or of a mixture of dissimilar particle^.^*^^ A comprehensive analysis was carried out to establish the causes of such serious disagreements. The values of different parameters were varied in order to see if the theoretical curves could match the experimental results, but all these attempts failed. However, it was established that the assumption of the discreteness of charges on particle surfaces, rather than the normally accepted smooth distribution, could bring the measured and calculated stability ratios into concordance, as illustrated on the example of polystyrene (42) Kihira, H.; MatijeviE, E. Adu. Colloid Interface Sci. 1992,42,1. (43) Devereux, 0. F.; deBruyn, P. L. Interactions of Plane Parallel Double Layers; MIT Press: Cambridge, MA, 1963. (44) Hogg,R.;Healy, T. W.; Fuerstenau,D. W. J. Chem.Soc., Faraday Tram 1 1966,62, 1638. (45) Oshima, H.; Chan, D. Y. C.; Healy, T. W.; White,L. R. J. Colloid Interface Sci. 1983, 92, 232. (46) Overbeek, J. Th. G. Colloids Surf. 1990,51, 61. (47) Kihira, H.; Ryde, N.; Matijevib, E. Colloida Surf. 1992,64,317. (48) Kihira,H.; Ryde, N.; MatijeviE,E. J. Chem. Soc.,Faraday Trans. 1 1992,88, 2379. (49) Kihira, H.;Matijevib, E. Langmuir 1992,8, 2856.
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Langmuir, Vol. 10, No. 1, 1994 15 1 .o
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Hematite on glass
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Figure 18. Stability coefficients, W , for homocoagulation (0) of spherical hematite particles (r = 33 nm) and for their multilayer adhesion on glass beads ( 0 )as a function of the ionic strength. The calculatedfunctionsusing the Overbeek&and Hogg, Healy, and Fuerstenau (HHF)' expressions are given by the solid and broken lines, respectively.
I ' -3
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log(l/mol M a ) Figure L9. Experimentally determined stability ratios, W (O), for an aqueous solution of uniform spheres of polystyrene latex of 66 nm radius at pH: 5.7 as a function of the ionic strength, Z (KNG). Curve a is calculated using the Overbeek expression,a while curves W are obtained by assuming increasing surface charge segregation.@
latex in Figure 19.48 The theoretical curve a is based on the smoothed-out charge, whereas curves b-d are calculated assuming increasing degree of the discreteness of charge. The open circles represent the experimental results which are fitted well with the curve corresponding to -30% segregated charge. b. Particle Adhesion. Figure 18 also shows that similar discrepanciesbetween the theory and experiments were found in the kinetios of the deposition on glass of the same spherical hematite particles, as used in the coagulation. This result is not unexpected since particle adhesion on solid substrates represents a special case of the heterocoagulation process. Indeed, studies of the attachment and removal of particles can yield valuable information on double layer interactions between different solids. A convenient system for such investigations consists of a column packed with relatively large beads (50-100 pm) through which are passed uniform spherical particles (
