Deposition of Rutile Titanium Dioxide Particles onto Oppositely

Dec 1, 1996 - School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 ... The rate of deposition of paint-grade rutile titanium dioxi...
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Langmuir 1997, 13, 14-22

Deposition of Rutile Titanium Dioxide Particles onto Oppositely Charged Surfaces: A Comparison of Stagnation Point Flow and Quiescent Conditions and the Formation of Two-Dimensional “Rafts” Nick Marston and Brian Vincent* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, U.K. Received January 22, 1996. In Final Form: October 1, 1996X The rate of deposition of paint-grade rutile titanium dioxide particles (∼0.3 µm diameter) onto model substrates, under a variety of conditions, has been monitored. The model substrates used were opticallyflat glass plates, whose surfaces were made cationic by reaction with (aminopropyl)trimethoxysilane, APTMS. A flow geometry was arranged such that the particles impinged, through a jet, normally onto the substrate. This creates a stagnation point region near the substrate surface, opposite the mouth of the jet. In this region, at relatively low mass transfer rates, it is supposed that particles reach the surface by a diffusion process. The deposition (rate) of the particles was monitored visually using both a microscope and also a CCD camera linked to an image-analysis system. This allowed the number of particles deposited per unit area to be monitored. Deposition rates, and maximum coverages, have been established at various particle concentrations and various background electrolyte (NaCl) concentrations. The results obtained agreed well with experiments in which APTMS-coated glass plates were simply immersed (“vertically”) in a suspension of titania particles, and particles were allowed to deposit under Brownian motion conditions. In the flow experiments, provided the NaCl concentration was below a critical value, the particles remained stable in dispersion and “isolated” on the substrate surface. However, over a certain salt concentration range, when the particles were precovered with an adsorbed layer of poly(vinyl alcohol), two-dimensional aggregation (“raft formation”) was observed on the substrate surface.

Introduction Deposition of colloidal particles onto solid surfaces is of great importance in a variety of processes. For example, it may be used to achieve (selective) separation of particles in mixed dispersions. This may be used either as a route to extract a valuable component or as a means of purification by removing obnoxious particulates.1 Particle deposition also plays an important part in the manufacture of paper,2 textile science, ceramics, surface and powder science, and coatings technology. Adventitious deposition also results in problems such as fouling of membranes, biological systems,3,4 and heat exchanger surfaces. Effective control of each of these various operations requires an understanding of the mechanisms, and the corresponding interparticle forces, that control particle adsorption. Several workers have studied deposition using stagnation point flow (SPF) methods. The flow regime prevailing in cells of this type has been extensively analyzed.5-7 Within the “stagnation point” regime, the particles are thought to undergo Brownian diffusion toward the collector surface. Dabros and van de Ven5 first employed a SPF cell to study the deposition of 0.5 µm polystyrene latex particles onto flat glass substrates. By optical observation the rate of particle deposition was monitored as a function of cell geometry. Optimum cell dimensions and dispersion flow rates were determined. * To whom correspondence should be addressed. X Abstract published in Advance ACS Abstracts, December 1, 1996. (1) Bernhardt, H.; Schell, H.; Luesse, B. Water Supply 1986, 4, 159. (2) Alince, B.; Robertson, A. A.; Inoue, M. J. Colloid Interface Sci. 1978, 65, 98. (3) Dazzo, F. B. In Adsorption of Microorganisms to Surfaces; Bitton, G., Marshall, K., Eds.; Wiley: New York, 1980. (4) Gibbons, R. J.; van Houte, J. Annu. Rev. Microbiol. 1975, 29, 19. (5) Dabros, T.; van de Ven, T. G. M. Colloid Polym. Sci. 1983, 261, 694. (6) Dabros, T.; van de Ven, T. G. M. J. Colloid Interface Sci. 1992, 149, 493. (7) Dabros, T.; van de Ven, T. G. M. Colloids Surf. 1993, 75, 95.

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Several workers have studied the closely-related process of heteroaggregation between particles of markedly different sizes.8-14 In most cases the extent of adsorption of the small particles on the larger ones was assessed by the use of centrifugation to remove the larger particles, allowing one to determine the concentration of unadsorbed small particles remaining in the supernatant. For example, Cheung8 studied the adsorption of 0.21 µm cationic latex particles onto 1.07 µm anionic polystyrene particles. High-affinity adsorption isotherms were found. The number of small particles adsorbed by each large particle was found to rise with electrolyte concentration. Vincent and Young9,10 reported results for similar systems, but with both sets of particles carrying a monolayer of physisorbed poly(vinyl alcohol) (PVA). Below a critical electrolyte concentration, high-affinity, irreversible particle adsorption isotherms were found. Above this critical concentration, low-affinity (“s-shaped”) reversible isotherms were found. These results were rationalized in terms of a balance between the attraction of small particles to the oppositely charged large particle and a lateral force between the adsorbed small particles. The lateral force may be attractive or repulsive, dependent upon the thickness of the adsorbed PVA layer and the electrolyte concentration. For low-affinity systems it was proposed that a net attraction between small particles at the surface leads to the observed formation of twodimensional, “raftlike” structures. Scanning electron microscopic (SEM) observations supported these results. (8) Cheung, W. K. Heterocoagulation of Cationic and Anionic Polystyrene Latices; Ph.D. Thesis, University of Bristol, 1979. (9) Vincent, B.; Young, C. A. Faraday Disc. Chem. Soc. 1978, 65, 296. (10) Vincent, B.; Young, C. A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 665. (11) Vincent, B.; Luckham, P. F. Colloids Surf. 1980, 1, 281. (12) Vincent, B.; Jafelicci, M.; Luckham, P. F.; Tadros, Th. F. J. Chem. Soc., Faraday Trans. 1 1980, 76, 674. (13) Vincent, B.; Luckham, P. F. Colloids Surf. 1983, 6, 83. (14) Vincent, B.; Thompson, D.; Harley, S. Colloids Surf. 1992, 62, 163.

© 1997 American Chemical Society

Formation of Two-Dimensional “Rafts”

More recently Vincent and Harley14 investigated heteroaggregate morphology as a function of the two particle sizes and electrolyte concentration, with and without adsorbed PVA, by the use of cryo-SEM. High- and lowaffinity adsorption isotherms were again obtained within the electrolyte concentration ranges previously identified by Vincent and Young,9,10 even though in this case twodimensional raftlike structures as such were not observed. In the work presented in this paper, the deposition of essentially spherical rutile titanium dioxide particles onto modified glass substrates of opposite charge has been studied. A SPF cell, based on the design of Dabros and van der Ven,5 has been employed. By a combination of bright-field incident light microscopy and image analysis, the kinetics of deposition and the maximum amount of TiO2 adsorbed on the substrate surface have been examined. An investigation into two-dimensional raft formation has also been made, when the particles carried preadsorbed layers of PVA.

Langmuir, Vol. 13, No. 1, 1997 15

Figure 1. Structure of the adsorbed layer of (aminopropyl)trimethoxysilane.

Experimental Section Materials. Rutile titanium dioxide particles (R-SM3) were used as supplied by Tioxide plc. and have a mean radius of 165 nm with a deviation about this mean size of 20%. The density of the particles was determined to be 4.08 g cm-3. The BET surface area of the particles was measured as 7.6 ( 0.6 m2 g-1 and the surface area available for adsorption as 6.0 ( 0.5 m2 g-1 by Methylene Blue adsorption. Poly(vinyl alcohol) (PVA), ex Nippon Gohsei, had a viscosityaverage relative molar mass of 22 000 and was 88% hydrolyzed poly(vinyl acetate). Adsorption isotherms of PVA onto the particles were established as follows: 0.05 g of solid rutile titanium dioxide R-SM 3 was equilibrated with 1 cm3 of PVA solution in the concentration range 200-1000 ppm in sealed tubes, which were rotated end-over-end for 24 h to achieve equilibrium. The rutile particles plus adsorbed PVA were removed by centrifugation. The supernatant was then diluted so as to ensure that the PVA concentration fell in the range 0-100 ppm, over which range the calibration graph (described below) was linear. The concentration of the PVA present in the supernatant was determined by the following technique. A solution of boric acid (3.96 g), iodine (0.153 g), and potassium iodide (0.3 g) in 100 cm3 of water was prepared. A 0.5 g portion of indicator solution was added to 1 g of diluted supernatant solution. In the presence of PVA a dark green complex precipitates, the PVA enclosing the iodine molecules in a helical structure.15 This complex exhibited an absorbance peak at a wavelength of 650 nm; the absorbance was measured using a Kontron “Uvikon 940” spectrophotometer. The concentration of PVA in the supernatant was then calculated by means of a calibration graph of absorbance versus PVA concentration. Electrophoresis measurements were made using a phase analysis light scattering (PALS) apparatus.16 The mobility, µ, values obtained were converted to zeta potentials, ζ, using the method of O’Brien and White.17 The substrates used for the deposition experiments were prepared as follows. Glass coverslips were coated with a layer of (3-aminopropyl)trimethoxysilane (APTMS) using the method described by Vandenberg et al.18 A 0.4% by weight solution of APTMS in toluene was freshly prepared before use and was stored in a sealed bottle. The coating procedure was as follows. The glass substrate (a microscope coverslip) was immersed in the solution for 24 h, after which the substrates were washed three times in an excess of ethanol and then thoroughly dried in air. (15) Pritchard, J. G. In Poly(vinyl alcohol)-Basic Properties and Uses; Polymer Monographs, Vol. 4; MacDonald Technical and Scientific: London, 1970. (16) Miller, J. The Determination of Very Small Electrophoretic Mobilities of Dispersions in Non-Polar Media Using Phase Analysis Light Scattering; Ph.D. Thesis, University of Bristol, 1990. (17) O’Brien, R. W.; White, L. R. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1607. (18) Vandenberg, E. T.; Bertilsson, L.; Liedberg, B.; Uvdal, K.; Erlandsson, R.; Elwing, H.; Lundstro¨m, I. J. Colloid Interface Sci. 1991, 147, 103.

Figure 2. Geometry of the stagnation point flow cell. This procedure is known to create a layer having the structure shown in Figure 1.18 The amine groups will inpart a net positive charge upon the substrate surface under conditions of low pH.19 Stagnation Point Flow Cell. Stagnation point flow (SPF) cells allow the study of deposition under conditions of constant diffusion boundary layer thickness. In addition they have the advantage that the collector surface is stationary. If a transparent collector is used, then deposition may be directly observed by use of an optical microscope. The deposition experiments carried out as part of this work have been performed using a stagnation point flow cell based upon the design, and theoretical analysis, of van de Ven et al.5 Further evaluation of this type of cell has been carried out by Adamzyck et al.20 The stagnation point flow cells used by previous authors have been mainly constructed of glass. A platinum foil, with a hole in it, was bonded to the top of the central column of the cell to form the second plate. The design of the stagnation point flow cell used in this work differs from previous designs in that it is constructed from machined brass. This was chosen as it offered superior dimensional uniformity and had the advantage of a movable second plate. To ensure that there was no contamination of the flowing suspensions by ion release, the cell was cleaned extensively between uses. Figure 2 shows the geometric arrangement of the cell. The radius of the inlet tube is denoted by R, the distance between the parallel plates by h, and the lower plate diameter by L. When fluid flows through the hole in the lower plate (PLATE II) a stagnation point is produced adjacent to the top plate (PLATE I) opposite the exit of the jet. Dabros and van de Ven5 contend that this cell design is superior to those using a submerged impinging jet (as described by Deshpande and Vaishnav21 ) since the presence of the second plane (PLATE II) eliminates the effect of hydrodynamic disturbances on flow conditions near to the stagnation point. This is especially convenient as this is the region of interest for the study of particle deposition. An optimized geometry has been developed by Dabros and van de Ven.5 The design of the cell used in this work was based upon their geometry. A detailed discussion of the flow within the cell will not be entered into here. A Seescan “Master” image analysis system (Cambridge, U.K.) was used to determine the exact dimensions of the flow cell. (19) Goodwin, J. W.; Harbron, R. S.; Reynolds, P. A. Colloid Polym. Sci. 1990, 268, 766. (20) Adamczyk, Z.; Czarnecki, J.; Siwek, B.; Zembala, M. J. Colloid Interface Sci. 1986, 110, 188. (21) Deshpande, M. D.; Vaishnau, R. N. J. Fluid Mech. 1982, 114, 213.

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Marston and Vincent dispersions of the titanium dioxide particles at the required particle concentration, NaCl concentration, and pH. At the end of the equilibration period the collectors were carefully removed and washed in a large excess of pure water. As far as could be ascertained, this “washing” did not lead to the removal of any adsorbed particles. The collectors were examined using a Nikon “Optiphot” transmitted light microscope, and the resulting images were captured by the image analyzer for subsequent analysis.

Results and Discussion

Figure 3. Complete apparatus. These were found to be exactly as specified in the optimized design of van de Ven et al.:5 the lower plate width, L, being 5 mm, the radius of the exit pipe, R, was found to be 1 mm. A depth micrometer was used to set (and check) the plate separation, h, at 1.72 mm. A 250 cm3 sample of rutile dispersion, at the required particle concentration, was prepared by diluting a stock solution of known solids concentration, using an aqueous NaCl solution at a given concentration. The pH of the dispersion was then adjusted (to 4.8, see later) by the addition of the minimum amount of ca. 0.1 mol dm-3 HCl solution. The cell was fed from a reservoir containing the colloidal dispersion, which was drawn through the cell, by syphoning, to an outlet reservoir. The dispersion was then recycled, using a peristaltic pump, to the inlet reservoir. The flow rate was set to 7.5 cm3 min-1. The flow cell was placed directly upon the stage of a Meiji RMM incident light microscope. A Sony CCD camera was fitted directly to the microscope, and the optics allowed simultaneous image capture and user observation, via the eye piece. A schematic diagram of the apparatus is shown in Figure 3. The flow intensity in the stagnation point flow cell is characterised in terms of a parameter R j ,5 which is related to the Reynolds number, Re, for the prevailing flow conditions. The dependence of the particle motion within the cell upon thermal (Brownian) and external forces (in this case the flow of the fluid) is characterized by the Peclet number, Pe, defined by

2R j va3 Pe ) 2 R D0 where v is the flow velocity, a is the particle radius, and D0 is the diffusion coefficient. If the Peclet number is much less than unity, then thermal, rather than hydrodynamic, forces predominate. The Reynolds number for the experimental flow conditions was calculated to be 44.7. From this the flow intensity, R j was determined to be 21.0. In turn the Peclet number was calculated to be 5.3 × 10-3. The value of the Peclet number implies that Brownian, rather than hydrodynamic forces, do indeed predominate in the cell in the region of the stagnation point. The experimental technique described above allowed the capture of gray shade video images into the silicon chip memory of the image analysis system. Each image was also recorded onto the instrument’s Winchester hard drive. All measurements were made for an area of 100 µm2 centered at the stagnation point. The first step in the analysis of the image was automated thresholding to separate objects from the background. An analysis was then performed of the total area of objects of interest, i.e. the total area of objects within the frame. From these data the coating density (the number of particles per unit area), Γ, could be calculated. One may also define the “coverage”, θ ) Γ/Γhcp, where Γhcp is the maximum number of particles that could be packed in an hexagonally close packed array on the substrate. Immersion Cell. In order to check that the hydrodynamic conditions prevailing near the stagnation point are indeed “Brownian”, a few experiments were carried out in which the APTMS-modified glass plates were simply immersed “vertically” in a series of (sealed) glass vials containing 25 cm3 sample

Deposition of “Bare” Titanium Dioxide Particles using the Stagnation Point Flow Cell. The deposition of the rutile particles from stable dispersions (i.e. at NaCl concentrations less than 10-3 mol dm-3) was studied under a variety of conditions. No deposition of rutile TiO2 was observed onto uncoated glass substrates. However, for all substrates bearing an adsorbed layer of APTMS, rapid deposition of particles was seen. Typical images obtained for this latter type of system are shown in Figure 4. It can be seen that the particles deposit individually, the coverage increasing with time. The corresponding Γ (and θ) versus time plot for this system is shown in Figure 5. The error bars are chosen to be representative of the distribution of Γ values obtained for a number of repeat experimental runs. It may be seen that Γ eventually reaches a “plateau” value (Γpl). Note that the corresponding θpl value is significantly less than 1, due to blocking of further adsorption, by particles already adsorbed. Dabros and van der Ven5 have shown that Γ(t) data of the type shown in Figure 5 can be fitted by an equation of the form

Γ ) Γpl - Γpl exp(-kdt)

(1)

where kd is the deposition rate constant. This equation may be derived from the following first-order rate equation for the deposition process11

dΓ ) kd*n(1 - θ*) dt

(2)

where n is the number of particles per unit volume in the dispersion (constant in the current experiment) and (1 θ*) is effectively a blocking factor due to previously adsorbed particles, where θ* ) Γ/Γpl ) θ/θpl. The experimental data shown in Figure 5 for Γ as a function of t, have been fitted using eq 2. The value for kd* and Γpl obtained from this are tabulated in Table 1 for different particle and electrolyte (NaCl) concentrations. Some main features emerge from the data given in Table 1. Firstly, in respect to the variation in NaCl concentration, kd* appears to be more or less independent of NaCl concentration. Other trends apparent from Table 1 are that Γpl increases somewhat with electrolyte concentration. Such a salt concentration effect has been observed in the small particle and larger particle adsorption studies referred to previously. Higher Γpl values at lower electrolyte concentrations arise from the decrease in the lateral repulsion between neighboring particles on the substrate. Monte Carlo, MC, simulations have been used before to model structure formation in dilute colloidal dispersions.22-25 Recently, Adamczyk et al. developed MC techniques to model localized, sequential adsorption of particles. The first, the random sequential adsorption (RSA) model,26,27 generated distributions of particles on (22) van Megen, W.; Snook, I. J. Colloid Interface Sci. 1975, 53, 172. (23) van Megen, W.; Snook, I. J. Chem. Soc., Faraday Trans. 2 1976, 76, 216. (24) van Megen, W.; Snook, I. J. Chem. Phys. 1977, 66, 813. (25) Jo¨nsson, B.; Svensson, B. Mol. Phys. 1983, 50, 489.

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Langmuir, Vol. 13, No. 1, 1997 17

Figure 4. Deposition from a stable dispersion (10-3 mol dm-3 NaCl: 1.2 × 1015 R-SM 3 particles cm-3) after (a) 600, (b) 1200, (c) 1800, and (d) 2400 s.

a surface by examining the two-dimensional electrostatic interaction (neglecting van der Waals forces) between newly adsorbing particle placed at a random position on the surface and those particles already adsorbed. The second, the sequential Brownian deposition (SBD) model,28,29 involved a calculation to assess the contributions from hydrodynamic, gravitational, dispersion, and colloidal forces acting upon the particle as it approached the surface and these forces determined the position in which the particle would adsorb. The simulated distributions from both models were found to be in good agreement with experimental results. In this work the particle adsorption model developed by Vincent and Harley30 (and used by Vincent and Waterson31 for mixed systems of particles) was adapted to model the sphere plate interactions examined. The new model was designed to not only predict the kinetics of deposition obtained by experiment but also to predict the geometric distribution of deposited particles upon the collector surface. The model employed a grid of size 200a × 200a (where a is the radius of the adsorbing particle) with periodic boundary conditions. Particles were brought toward the (26) Adamczyk, Z.; Zembala, M.; Siwek, B.; Warszynski, P. J. Colloid Interface Sci. 1990, 140, 123. (27) Adamczyk, Z.; Siwek, B.; Zembala, M. Colloids Surf., 1992, 62, 119. (28) Adamczyk, Z. Adv. Colloid Interface Sci. 1994, 48, 151. (29) Adamczyk, Z. Adv. Colloid Interface Sci. 1996, 63, 41. (30) S. Harley, Ph.D Thesis, University of Bristol, 1990. (31) J. Waterson, Ph.D Thesis, University of Bristol 1989.

grid at randomly chosen positions, with a flux determined from the experimental data, along a linear trajectory perpendicular to the surface. The interaction between the particle and the surface was calculated by a summation of a van der Waals interaction32 and an electrostatic contribution according to the constant potential model of Hogg, Healy, and Fuerstenau.33 The same approach was applied to determine the interaction potential of the particle with any preadsorbed particles in the vacinity. The total interaction energy was determined by addition of these contributions. If this potential energy of approach exceeded an arbitrary value (15 kT), then it was assumed that the particle would not adsorb at the surface. This value was chosen since it represented the point at which aggregation rates in the bulk typically become negligible. A data set consisting of the coordinates of the adsorbed particles and the times at which they arrived at the surface was generated. The data for θ as a function of time obtained from the model was found to be in good agreement with the experimental data for the electrolyte conditions studied (see Figure 6). The data from the model was relatively insensitve to the magnitude of the maximum surmountable potential barrier chosen. The distribution of particles upon the surface was also found to be comparable to the experimentally determined distributions as well as the distributions generated by the other models discussed here.26-29 (32) Hamaker, H. C. Physica, 1937, 4, 1058. (33) Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Trans. Faraday Soc. 1966, 62, 1638.

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Marston and Vincent Table 1. Values of Initial Particle Flux, kd*, and Plateau Coating Density, Γpl, for Bare Rutile TiO2 Particlesa NaCl concn/mol dm-3

kd* (×106)/s-1

Γpl (×10-12)/m-2

2.5 × 10-5 1 × 10-4 1 × 10-3

1.69 ( 0.10 1.60 ( 0.06 1.77 ( 0.11

2.3 ( 0.1 2.8 ( 0.3 3.8 ( 0.2

a

Number concentration, n ) 1.2 × 1015 m-3.

Figure 5. Γ versus t plots for “bare” rutile TiO2 in the presence of (a) 2.5 × 10-5, (b) 10-4, (c) 10-3 mol dm-3 NaCl. Data obtained from both flow experiments (O) and immersion experiments (0) are shown.

Deposition of “Bare” Titanium Dioxide Particles under Quiescent Conditions. An important objective of this project was to establish that the deposition data obtained from the stagnation point flow experiments, under the specific conditions chosen, correlated with results obtained for deposition resulting from direct diffusion of rutile TiO2 particles to a collector. Experiments were performed using dispersions with particle concentration of 1.2 × 1015 particles m-3; NaCl concentrations of 2.5 × 10-5, 10-4, and 10-3 mol dm-3 were

Figure 6. A comparison of the experimental data to that generated by the theoretical model in the presence of (a) 2.5 × 10-5, (b) 10-4, (c) 10-3 mol dm-3 NaCl.

examined. The images captured by the image analysis system were analyzed in the same way as for the stagnation point flow experiments. The data obtained from these immersion experiments are also presented in Figure 5 as squares with error bars. It is clear that the two sets of experiments tend to the same plateau value of particle coverage, at each of the

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Figure 7. Adsorption isotherm for PVA onto rutile R-SM 3.

electrolyte concentrations, although the kinetics of particle adsorption differ between the two types of experiment as expected. Deposition of PVA-Coated Particles under SPF Conditions. The adsorption for the PVA sample used onto the TiO2 particles is shown in Figure 7. These results are similar to those determined by other workers for the adsorption of PVA onto anionic and cationic latexes.34-36 A comparison of the stability of the PVA-coated and bare TiO2 particles in the presence of NaCl is shown in Figure 8. As may be seen, the PVA-coated TiO2 particles in 3.7 × 10-3 mol dm-3 NaCl are now effectively stable to aggregation over a 1 h period. Γ values as a function of time for the PVA-coated particles in 3.7 × 10-3 mol dm-3 NaCl solution are shown in Figure 9. The curve has the same general form as those previously presented. However, the plateau coating density for these polymer-coated particles is higher than the values obtained for bare particles at the same NaCl concentration. The Γ versus time curve has been fitted using eq 1. A one-parameter fit was employed to determine kd using the experimentally determined Γpl values. The data obtained are similar to those presented in Table 1. An interesting feature of the data is that the Γpl values for the PVA-coated particles are consistently ∼4 × 1012 particles/m2 over the NaCl range 2.5 × 10-5 to 3.7 × 10-3 mol dm-3. This is comparable to the value for the bare particles at 10-3 mol dm-3 NaCl. This suggests that the lateral repulsion between PVA-coated particles is significantly reduced compared to the bare particles, at low electrolyte concentrations. This is supported by the ζ potential data for the two sets of particles shown in Table 2. Figure 10 shows an example of deposition from the dispersion of the PVA-coated TiO2 in 3.7 × 10-3 mol dm-3 NaCl. The deposition of individual particles can be seen in the initial images, but a build up of two-dimensional aggregates is observed with time. In addition to following the deposition process using image analysis system, the coated collectors produced were also examined using scanning electron microscopy (SEM). The coated coverslips were removed from the flow cell and allowed to dry in air. No rearrangement of the surface particles was expected as the adsorption is irreversible, and the particles were known to be immobilized, even (34) Garvey, M. J.; Tadros, Th. F.; Vincent, B. J. Colloid Interface Sci. 1976, 55, 440. (35) Young, C. Heterointeractions in Mixed Sterically Stabilised Dispersions; PhD. Thesis, University of Bristol, 1978. (36) Harley, S. Aggregate Morphology in Mixed Colloidal Dispersions; Ph.D. Thesis, University of Bristol, 1990.

Figure 8. Stability of (a) bare rutile TiO2 (R-SM 3) NaCl; (b) PVA-coated rutile TiO2 (R-SM 3) in the presence of 10-4 (1), 10-3 (2), 3.7 × 10-3 (3), 6 × 10-3 (4), and 10-2 (5) mol dm-3.

Figure 9. Γ versus t plot for a dispersion containing: 3.7 × 10-3 mol dm-3 NaCl; 1.2 × 1015 R-SM3 particles m-3; and 500 ppm PVA.

when washed with concentrated electrolyte. The dried coverslips were then mounted onto SEM stubs and sputtercoated with a layer of gold. SEM examination of the samples revealed the presence of two-dimensional, raftlike structures. An example of the structure observed is shown in Figure 11. These had dimensions of the order of 10s of µm. In areas between these surface aggregates the coverage appeared to be low in comparison to the results obtained for more stable dispersions equilibrated for the same period of time. The presence of three-dimensional aggregates at the surface was also observed in dispersions of PVA-coated particles at 10-2 mol dm-3. However, by referring to the

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Marston and Vincent

Figure 10. Deposition from a R-SM 3 dispersion, in 3.7 × 10-3 mol dm-3 NaCl, with adsorbed PVA after (a) 240, (b) 1250, (c) 1850, and (d) 4500 s. Table 2. Mobility and ζ Potential Data for Rutile TiO2 (R-SM 3) Particles as a Function of NaCl Concentration at pH ) 4.8 bare TiO2

PVA-coated TiO2

NaCl concn/mol dm-3

mobility (×108)/m2 s-1 V-1

ζ potential/mV

mobility (×108)/m2 s-1 V-1

ζ potential/mV

2.5 × 1 × 10-4 1 × 10-3 3.7 × 10-3

-1.96 ( 0.12 -1.52 ( 0.07 -1.31 ( 0.05

-27 ( 5 -23 ( 2 -21 ( 1

-0.58 ( 0.05

-11 ( 1.0

-0.86 ( 0.07 -0.62 ( 0.05

-11 ( 1.1 -9 ( 1.5

10-5

stability plot (Figure 8), it can be seen that in these cases aggregates are already present in the dispersion prior to adsorption on the collector. Figure 12 shows the progress of deposition from this dispersion. The mode of deposition is clearly different from that presented in Figure 10. Electron microscope examination of coverslips from these unstable dispersions revealed a very different morphology for the deposited particles compared to the dispersions that exhibit surface aggregation. The structure of the aggregates was found to be far more “open”, and the average aggregate size was much smaller than those described previously. This result indicates that the raft formation is indeed not simply a deposition of aggregates already present in the bulk. The explanation of the raft formation, given by Vincent and Young,9 reflects weak lateral attraction between adsorbed particles on the surface. A colloidal dispersion will be thermodynamically stable to aggregation in the bulk if the free energy of flocculation, ∆Fflocc is positive.

∆Fflocc ) ∆Uflocc - T∆Sflocc

(3)

In this equation ∆Uflocc is the energy change and ∆Sflocc is the entropy change accompanying flocculation and T is the temperature. ∆Uflocc is negative and will depend upon the depth in the pair potential well for two interacting particles on close approach. The entropy term, ∆Sflocc, will also be negative for a flocculation process as the formation of aggregates will lead to an increase in the order of the system. Therefore, the sign of ∆Fflocc depends on the subtle balance of the ∆Uflocc and ∆Sflocc terms. |∆Sflocc| is smaller for flocculation in 2D than in 3D. Therefore the minimum value of ∆Uflocc required to achieve aggregation (limiting condition ∆Fflocc ) 0) on a surface is smaller than that in the bulk. Hence a dispersion which is stable in the bulk may show 2D flocculation on a surface. It is possible that this adsorption effect may be the result of a gradient coagulation due to the large liquid velocity gradient at the interface. However, it is thought that this is not the case as the “raft” formation appears to occur uniformly across the area examined and by a mechanism involving the approaching particles becoming attached

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Langmuir, Vol. 13, No. 1, 1997 21

has been calculated, and the results are shown in Figure 13. V (the total interaction energy) comprises three terms: VE (electrostatic), VA (van der Waals), and VS (steric). The various equations and parameters used for each of these terms can be found in the Appendix. At 2.5 × 10-5 mol dm-3 NaCl the dispersion is predicted to be stable as observed. At 3.7 × 10-3 mol dm-3 NaCl the V(h) curve has a minimum of ∼4 kT in depth. This value may be sufficient for 2D flocculation on a substrate. An analogy to this is the fact that 2D condensation of vapor molecules can occur on adsorption, while the vapor itself is stable (to 3D condensation). At very high electrolyte concentrations the VE contribution is effectively eliminated. This would predict Vmin for the PVA-coated particles to be ∼8 kT, which should be sufficient to see 3D flocculation. Conclusions

Figure 11. SEM micrograph of the surface aggregates formed.

preferentially adjacent to particles already adsorbed at the interface. The interparticle pair potential V as a function of separation (h) for two PVA-coated TiO2 particles at two NaCl concentrations, 2.5 × 10-5 and 3.7 × 10-3 mol dm-3,

A comparison has been made for the deposition of negative rutile TiO2 particles onto positively charged modified glass substrates, under SPF and quiescent conditions. For the system studied, good agreement was found for the plateau values of particle coverage obtained using both methods. The dependence of the plateau values for θ upon electrolyte concentration seems to be in good agreement with the predictions of theory. The modeling of the experimental data indicates that the magnitude of the composite interaction between the approaching particle and the surface and any preadsorbed particles is indeed the factor governing the degree of coverage achieved.

Figure 12. Deposition from an unstable dispersion (1 × 10-2 mol dm-3 NaCl; 1.2 × 109 R-SM 3 particles cm-3) after (a) 315, (b) 610, (c) 1500, and (d) 3660 s.

22

Langmuir, Vol. 13, No. 1, 1997

Marston and Vincent

valuable discussions. We would also like to thank the EPSRC and ICI Paints Division plc. (Slough, U.K.) for financial support of this work, and, in particular, Drs. David Taylor and Simon Emmett from ICI for valuable discussions. Appendix Contributions to V(h). For the van der Waals attraction between the particles, eq A1 was used

VA )

-Aa 12h

(A1)

where a is the particle radius and h is the interparticle distance. A is the Hamaker constant for rutile/water/ rutile, and was taken to be 15.6 kT after Buscall.37 The electrostatic interaction between the bare particles was calculated using the following equation:

VE ) 2π0aζ2 ln(1 + exp[-κh])

(A2)

In this equation ζ is the zeta potential of the particles, 0 is the permitivity of free space, and  is the dielectric constant of the medium. In the presence of adsorbed polymer, a simple treatment, suggested by Vincent,38 is to calculate VE for distances of separation h > 2δ, where δ is the thickness of the polymer layer. Equation A2 then becomes

VsE ) 2π0(a + δ)ξs ln(1 + exp[-κ(h - 2δ)]

Figure 13. Calculated interaction curves for PVA coated particles in a background electrolyte of (a) 2.5 × 10-5 and (b) 3.7 × 10-3 mol dm-3 NaCl.

The Γ versus t results have been fitted to a first-order rate equation. Values for the deposition rate constant (kd*) have been derived. The trends in the Γpl and kd* values, with electrolyte concentration, are similar to those reported previously by others.9-14 In addition, the conditions for two-dimensional raft formation on the substrate have been explored. Basically this occurs for sterically stabilized particles over a narrow range of electrolyte concentration where the depth of the potential energy minimum is of the order of a few kT. Acknowledgment. The authors would like to thank Dr. Dudley Thompson of this Department for many

(A3)

If h < 2δ, the expression for the electrostatic interaction energy is more complicated. However, under these conditions VE is usually much smaller than the interaction energy due to “steric” forces and therefore need not be considered in detail. For the purposes of these calculations a steric barrier in the from of a hard wall potential was imposed at h ) 2δ. For these calculations, values for the parameters used in these theoretical calculations either were taken from the literature or were determined experimentally. For the PVA-coated particles the thickness of the adsorbed PVA layer was taken to be 15 nm, as it could not be determined for the present system. This layer thickness was previously determined for a similar PVA layer adsorbed on polystyrene latex particles.34 LA960075+ (37) Buscall, R. Colloids Surf. 1993, 75, 269. (38) Vincent, B. Adv. Colloid Interface Sci. 1974, 4, 193.