J. Phys. Chem. B 2006, 110, 25901-25907
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Dispersion Stability of Colloids in Sub- and Supercritical Water Swapan K. Ghosh,*,† Rossitza G. Alargova,†,§ Shigeru Deguchi,† and Kaoru Tsujii‡ Extremobiosphere Research Center, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka 237-0061, Japan, and Nanotechnology Research Center, Research Institute for Electronic Science, Hokkaido UniVersity N21, W10 Kita-ku, Sapporo 001-0021, Japan ReceiVed: August 30, 2006; In Final Form: October 25, 2006
Dispersion stability of colloids has been investigated in sub- and supercritical water by measuring the hydrodynamic diffusion coefficients of the particles by means of dynamic light scattering. It is interestingly found that coagulation of the colloids in sub- and supercritical water is a universal phenomenon irrespective of the material of the colloids. Highly charged colloids were found to be more stable in water against high temperature. Numerical analysis reveals that the stability of the colloids at elevated temperature and pressure is primarily governed by the temperature dependence of the dielectric constant of the medium. The effect of the temperature dependence of the ion product of water (pKw) was found to be very little. Surface charge density and Stern potential may change with respect to temperature due to the readjustment of the ion concentration in the diffuse layer through the enhanced ion product and reduced dielectric constant of water. These are the secondary causes of the particle coagulations in sub- and supercritical water.
Introduction Colloids in the dispersion move randomly and continuously due to Brownian motion and under the influence of gravity. They frequently encounter each other and tend to aggregate. Therefore, most colloids are thermodynamically unstable in the dispersion; however, they remain dispersed for a long period of time provided that a sufficiently high kinetic potential barrier exists between the particles. Being a highly polar solvent, ambient fresh water is an excellent dispersion medium for many colloids including metals, minerals, and polymers. Dispersion stability of such colloids in water has been extensively investigated1-9 in terms of the electrolyte concentrations of the medium and the surface properties of the particles. As the temperature and pressure of water increase, physicochemical properties such as density (F), viscosity (η), dielectric constant (), ion product (pKw), and refractive index (n) change dramatically. For example, at the critical point, F, η, and decrease to 0.322 g cm-3,10 0.05 cp,11 and 5.7,12 respectively. Because of the large changes in the physicochemical properties, the dispersion stability of the colloids in water at high temperature and pressure is likely to change significantly. However, this is still unknown in the field of colloid and interface science. In recent years, a state of the art experimental system has been developed combining a dynamic light scattering (DLS) technique with a flow type high-temperature and high-pressure sample cell to investigate dispersion stability of colloids in suband supercritical water.13 Diffusion coefficients of polystyrene latex and colloidal gold have been successfully measured within a wide thermodynamic range from ambient temperature to near the critical point by this system.14 Very recently this system * Corresponding author. Telephone: +81-46-867-9704. Fax: +81-46867-9715. E-mail:
[email protected]. † Extremobiosphere Research Center. ‡ Nanotechnology Research Center. § Present Address: Vertex Pharmaceuticals Inc., 130 Waverly St., Cambridge, MA 02139.
was used to measure the viscosity of water at high temperatures and pressures.15 These initial experiments motivate us to conduct further detailed experimental and theoretical investigations of the colloidal stability in sub- and supercritical water. The stability of the colloids in a dispersion is determined by the forces acting between the surfaces of the colloids. These forces depend on the surface properties of the colloids and the physicochemical properties of the medium. In a sub- and supercritical condition, the medium is sometimes inhomogeneous16,17 and its properties are highly sensitive to temperature and pressure. Therefore, interparticle forces can be controlled by changing the temperature and the pressure. Temperature dependence of the dispersion stability of the colloids in suband supercritical water is fascinating, because it can be continuously controlled through the medium properties by changing only temperature and pressure without any additives. In this work, we have investigated the stability behavior of standard colloidal particles including metal, polymer, and inorganic materials in sub- and supercritical water, where the medium is inhomogeneous and the physicochemical properties are highly sensitive to temperature and pressure. We have examined the origin of particle aggregations in sub- and supercritical water by applying classical DLVO (DerjaguinLandau and Verwey-Overbeek) theory.3,5,7,8 Experimental Section A. Materials and Sample Preparations. Standard polystyrene latex (PSL) (10% solids, mean diameter 214 nm) and colloidal gold (CG) (mean diameter 66 nm) were purchased from Polysciences Inc. (Warrington, PA). Diamond nanoparticles (DP) (mean diameter 190 nm) were purchased from Maruto Co. Ltd. (Japan). PSL was used as purchased. CG and DP were dialyzed against water. Nanoparticles of C60 (mean diameter 126 nm) were prepared in our laboratory.18 We received powdered natural clay minerals (CL) from American Colloid Co. (Arlington Heights, IL). Dispersion of clay minerals (mean diameter 176 nm) was prepared by the method described
10.1021/jp0656328 CCC: $33.50 © 2006 American Chemical Society Published on Web 12/07/2006
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TABLE 1: Physical Quantities Used in the Numerical Calculationsa materials
dH/nm
ζ/mV
n1
1
A/10-20J
PSL DP C60 CG CL
107 95 63 33 88
-42.23 -26.23 -37.89 -46.28 -40.93
1.5574 2.41819 2.020 0.42719 1.5922
2.554 5.7019 4.021 ∞ 5.523
1.37 18.45 8.46 404 1.67
a Mean hydrodynamic radius, dH, is measured at T ) 25 °C and P ) 25 MPa. ζ is measured in pure water with pH 7 at T ) 25 °C. n1 and 1 are the refractive index and dielectric constant, respectively. Hamaker’s constant, A is calculated from eq 8 at T ) 25 °C and P ) 25 MPa. We used νe ) 2.65 × 1015 s-1 in the calculation.
in the Supporting Information. Samples were sufficiently diluted with deionized water produced by a Milli-Q system (Millipore, USA). The ζ potential of these samples was measured at 25 °C by an electrophoretic light scattering photometer (ELS-8000, Otsuka Electronics Co. Ltd, Japan) under atmospheric pressure (Table 1). B. Dynamic Light Scattering Measurements. Diffusion coefficients of dispersed colloids were measured by DLS using DLS-820 (Otsuka Electronics, Co. Ltd., Osaka, Japan) equipped with a He-Ne (10 mW, 632.8 nm) and a solid-state (50 mW, 532 nm) laser. The experimental set up allows DLS measurement at fixed 90° angle, within the temperature limit (450 °C), and the pressure limit (40 MPa). Structural design13 of the hightemperature and high-pressure sample cell and experimental details are described elsewhere.13,14 During the measurement, pressure and temperature were maintained with an accuracy of (0.1 MPa and (0.1 °C, respectively. DLS-820 works in a homodyne mode of operation, and the scattered light intensity autocorrelation function, g(2)(τ) is given by24
g(2)(τ) )
〈IS(t)IS(t + τ)〉 〈IS〉2
(1)
where Is is the intensity of the scattered light. The corresponding electric field autocorrelation function, g(1)(τ), is related to g(2)(τ) by24
g(2)(τ) ) 1 + |g(1)(τ)|2
(2)
For a dispersion of spherical particles with uniform size, g(1)(τ) is an exponential function of the diffusion coefficient of the particles and is expressed by24
g (τ) ) exp(-Dq τ) (1)
2
(3)
where q ) (4πn/λ0)sin(θ/2) is the scattering vector; n, λ0, and θ are the refractive index of the medium, the wavelength of the incident light, and the scattering angle, respectively. The hydrodynamic diameter (dH) of the particles can be calculated from the measured diffusion coefficients by the Einstein-Stokes relation
kBT D) 3πηdH
given in ref 25. When polydispersed spherical particles are measured, eq 3 becomes a multiexponential function and the cumulant method can be applied to determine the average particle size and polydispersity index from g(1)(τ).24,26 Results and Discussion A. Diffusion Coefficients of Colloids in High-Temperature and High-Pressure Water. The dispersion behaviors of PSL, CL, C60, CG, and DP in pure water have been investigated by measuring diffusion coefficients in the temperature range of 25382 °C at a constant pressure of 25 MPa, unless otherwise noted. Experimental results show that diffusion coefficients of the particles increase with increasing temperature in the lower temperature regime (Figure 1). The solid lines in Figure 1 are the theoretical curves calculated by the Einstein-Stokes relation (eq 4) assuming that the particle size is constant. The agreement between the experimental diffusion coefficients and the theoretical prediction (solid line) was excellent in the temperature range between ambient temperature and a certain high-temperature limit, Tcg. At temperatures T g Tcg, however, the diffusion coefficient deviates downward and decreases abruptly as time passes as described in Figure 1. Figure 2 shows the plot of dH determined from D by eq 4 against temperature. We observed that the size of the particles is almost constant up to Tcg, above which dH rapidly increases, suggesting that the particles aggregate at the temperatures T g Tcg. The characteristic temperature, Tcg, depends on the material, i.e., 301 °C for PSL, 225 °C for CL, 250 °C for C60, 346 °C for CG, and 201 °C for DP. The standard colloids, which remain dispersed in ambient pure water for a long period of time, coagulate rapidly at elevated temperatures by simple heating above Tcg. We define this characteristic temperature, Tcg, as the critical coagulation temperature. B. Mechanism of Colloid Aggregation in the Water at High Temperatures and Pressures. Interparticle Potential in the Dispersion Medium. The stability of a colloidal dispersion is governed by the forces acting between the surfaces of the colloid particles in the dispersion. A long-range van der Waals attractive force exists between the particles, which is balanced by the electrostatic repulsive force acting between the electric double layers around the particles. The theory of the colloid stability is popularly known as DLVO theory,1,2,4-6,8 which is expressed by
VD ) V A + V R
(5)
where VD is net DVLO potential, VA is the van der Waals attractive potential, and VR is the electrostatic repulsive potential due to the overlap of electrical double layers. For two identical spherical particles of radius r, having the Stern potential ψS, and separated by a distance H, VA and VR are expressed by5
(
[
VR ) 2π0rψ2Sln[1 + exp(-κH)] (4)
where D is the diffusion coefficient, kB is Boltzmann’s constant, T is the absolute temperature, and η is the viscosity of the medium. To measure the temperature and the pressure dependence of D and dH, one requires the temperature and pressure dependence of n and η. Appropriate values of n and η for each temperature and pressure were calculated according to the data
)]
x(x + 2) 1 A 1 + 2ln + VA ) 2 12 x(x + 2) (x + 1) (x + 1)2
(6) (7)
where A is Hamaker’s constant, x ) H/2r, is the dielectric constant of the medium, 0 is the permittivity of the vacuum, and κ is the Debye-Hu¨ckel parameter. For particles dispersed in a medium, A and κ are expressed by4
( )
3hνe (n2 - n21)2 - 1 2 3 A ) kBT + 2 2 3/2 4 + 1 16x2 (n + n1)
(8)
Colloid Dispersion Stability in Sub-/Supercritical Water
J. Phys. Chem. B, Vol. 110, No. 51, 2006 25903
Figure 1. Diffusion coefficient of colloids as a function of temperature at P ) 25 MPa. (a) PSL, (b) CL, (c) C60, (d) CG,14 and (e) DP. D decreases abruptly as time passes when the sample was kept at temperatures T g Tcg. Solid lines represent Einstein-Stokes relation (eq 4).
and
( ) e2
κ)
∑i cizi
0kBT
1/2
(9)
where 1 is the dielectric constant of the particles, h the Planck’s constant, νe the electronic absorption frequency, n the refractive index of the medium, n1 the refractive index of the particles, e the electronic charge, ci the concentration of ionic species i, and zi is its valence. Numerical Analysis. Temperature dependence of the DLVO potential is numerically calculated assuming that properties of the medium vary with temperature but that those of the particles (such as ψS, ζ, 1, and n1) are constant with temperature. Due to these assumptions, temperature dependence of the DLVO
potential is solely determined by the temperature dependence of ,25 n,25 and pKw,27 as described in Figure 3. Temperature Dependence of the Van der Waals potential. The temperature dependence of A and VA is calculated for the PSL, CL, C60, CG, and DP samples. Figure 4 shows A and VA for PSL at 25 MPa. Both A and |VA| increase slowly with increasing temperature. For example, A increases from 1.37 × 10-20 to 3.22 × 10-20 J when the temperature increases from 25 to 375 °C. Similar results were obtained for all the samples except for CG (Supporting Information). The numerical calculations demonstrate that VA becomes slightly more attractive at elevated temperatures. In this calculation, we assumed that 1 and n1 are invariant with respect to temperature. In reality, they might decrease slightly with respect to temperature resulting in an increase in |VA| at elevated temperatures. We estimate this error in VA owing
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Figure 2. Hydrodynamic diameter of PSL, CL, C60, CG, and DP as a function of temperature at 25 MPa. Lines are a guide to the eye.
Figure 4. (a) Temperature dependence of Hamaker’s constant calculated by eq 8 at 25 MPa. (b) van der Waals potential at temperatures 25, 50, 100, 150, 200, 250, 300, 350, and 375 °C at 25 MPa.
Figure 3. Temperature dependence of the physicochemical properties of water at 25 MPa. (a) and η.25 (b) pKw27 and n.25 To calculate pKw, density data was taken from ref 25.
to our assumption and find only small effects on the net DLVO potential. Temperature Dependence of the Electrostatic RepulsiVe Potential. VR depends on both the surface properties of the colloid particles and the physicochemical properties of the medium. Because the temperature dependence of the properties of the particles are assumed to be constant for this calculation, the temperature dependence of VR is determined only by the change of the properties of the medium. In the liquid continuum, water molecules easily ionize into H + and OH- ions. In pure water at 25 °C, pKw is 10-14 mol2/kg2, which changes27 with temperature as described in Figure 3b. To examine the influence of the temperature dependence of pKw on the stability of the colloids, we calculated the temperature dependence of κ-1 from eq 9 for both the constant ion product (10-14 mol2/kg2) and variable pKw(T). The results suggest that the temperature dependence of pKw affects κ-1 significantly, which indicates that the interparticle repulsion is screened out more strongly
Figure 5. Temperature dependence of κ-1 at 25 MPa for constant pKw () 10-14 mol2/kg2) and variable pKw(T).
due to the acceleration of the water dissociation (Figure 5). Therefore, the temperature dependence of pKw is incorporated in this calculation. VR is calculated for the PSL, CL, C60, CG, and DP samples at temperatures 25, 50, 100, 150, 200, 250, 300, 350, and 375 °C assuming that ψS ) ζ (25 °C). The calculated value of VR for PSL is plotted in Figure 6. The results clearly demonstrate that VR decreases dramatically with increasing temperature. Similar results were obtained for all the samples. Analysis shows that the decrease in VR with increasing temperature is mainly governed by the temperature dependence of , whereas the effect of the temperature dependence of pKw is found to be minor.
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Figure 8. Net DLVO potential barrier at maximum as a function of temperature.
Figure 6. VR for PSL at temperatures 25, 50, 100, 150, 200, 250, 300, and 350 °C for (a) constant pKw () 10-14mol2/kg2) and (b) variable pKw(T).
that the coagulation of the colloids in sub- and supercritical water is a universal phenomenon. C. Kinetic Stability of a Colloidal Dispersion. Kinetics of aggregation allows one to predict how fast particles coagulate in the dispersion. The rate at which the particles coagulate in the dispersion depends on (i) the collision frequency with which the particles encounter one another and (ii) the probability that their thermal energy is high enough to overcome the kinetic potential energy barrier. In the presence of a repulsive interparticle potential energy barrier, only a fraction of the encounters results in the permanent aggregations. Complete aggregation kinetics can be calculated if it is assumed that the rate constants are practically independent of particle size. The universal rate constant for diffusion-controlled aggregation of identical spherical particles is described as8
kr =
8kBT 3η
(10)
where kr is independent of the particle size. The collision frequency can be determined from eq 10, which is expressed by
fc ) krnc )
8kBT n 3η c
(11)
where nc is the number of the particles per unit volume. In order to stabilize a colloidal dispersion at temperature T during a period of time, τ1, we require that the probability of aggregation of two colliding particles overcoming their potential energy barrier (∆E) should be less than 1/fcτ1, i.e., Figure 7. Net DLVO potential between two polystyrene latices at 25 MPa.
Temperature Dependence of the Net DLVO Potential. The net DLVO potential, VD, is calculated for the PSL, CL, C60, CG, and DP samples at temperatures 25, 50, 100, 150, 200, 250, 300, 350 and 375 °C. VD for PSL is plotted in Figure 7. One can see that VD decreases very fast with increasing (i.e., VD at temperature. The DLVO potential barrier, Vmax D maximum), for PSL, CL, C60, and DP is plotted against temperature in Figure 8. We observed that it rapidly decreases with increasing temperature. For example, in the case of PSL, Vmax D decreases from 139- to 12kBT when temperature increases from 25 to 350 °C. This large decrease in Vmax at elevated D temperature results mainly from the temperature dependence of ; in contrast, the temperature dependence of pKw has a minor contribution. Both experiments and theoretical analysis suggest
Pf(T,τ1) ) exp(-∆E/kBT)
6 × 105 s). To estimate the interparticle potential barrier that is required to stabilize the dispersion over the experimental observation period, we calculated ∆ES for τ1 ) 300 s and τ1 ) 1800 s for nc ) 5.35 × 1014 m3 (concentration of the PSL sample). Figure 9 shows that a dilute aqueous colloidal dispersion should remain stable in the whole temperature range from ambient temperature to the supercritical fluid state provided that the kinetic potential barrier between the particles is higher than 7.0kBT. D. Critical Coagulation Temperature. Tcg is theoretically estimated from the correspondences between the stability criterion and the DLVO potential barrier (Figure 10a). Figure 10b shows the theoretical and the experimentally observed Tcg values. One can see that Tcg is higher for higher ζ potential. This suggests that highly charged colloids are more stable in water even at elevated temperature. Analysis shows that the experimental Tcg is always smaller than the theoretical Tcg (th). This discrepancy arises due to the fact that the net kinetic potential barrier (Vmax D ) is overestimated, because (a) the surface properties of the colloids in water were assumed to be invariant with respect to temperature and pressure and (b) the effect of the non-DLVO forces including hydration forces was neglected. Due to the limitation of experimental data and also the lack of appropriate theories, it is quite difficult to estimate these factors at present. Our theoretical interpretation is at the initial stage of the development at present and we plan to work on it by expanding our present model to account for as many effects as possible in near future. We predict that the counterion condensation onto the colloid surfaces may take place in high-temperature and high-pressure water due to the lowering of the dielectric constant and result in the decrease in surface potential. A decrease in the surface potential at high temperature and pressure would lower the net kinetic potential barrier and Tcg(th) as well. The temperature and pressure dependence of the short-range hydration force is not clear, and we estimate that its effect on the net kinetic potential barrier is negligible. Conclusions The dispersion stability of the standard colloids in water has been investigated as a function of temperature at 25 MPa by measuring the diffusion coefficients of the particles. We observed that the colloids, which are highly stable in ambient pure water, coagulate rapidly in hot and compressed water. The
Figure 10. (a) Correspondence between DLVO potential barrier (Vmax D ) and kinetic stability criterion. Tcg (th) is estimated from the intercept of the Vmax curve and the ∆Es curve (indicated by arrows). D (b) Tcg is plotted as a function of ζ measured at 25 °C at atmospheric pressure.
results indicate that the coagulation of the colloids in sub- and supercritical water is a universal phenomenon irrespective of the materials. We find that highly charged colloids are more stable in water against high temperature. The numerical analysis reveals that the interparticle electrostatic repulsive potential, which stabilizes the particles in the dispersion, dramatically decreases at high temperature and pressure because of the decrease in the dielectric constant of water. This is the primary cause of the coagulations of the colloids in sub- and supercritical water. We find that the enhanced dissociations of water molecules with increasing temperature screen out the electrostatic repulsion. But its effect on the stability of the colloids in the dispersion was found to be minor. Acknowledgment. The authors sincerely acknowledge the continuous support and encouragement of Koki Horikoshi (JAMSTEC). Authors also thank Sada-atsu Mukai (JAMSTEC) for discussions and helpful suggestions. This study is carried out as a part of the “Ground-Based Research Announcement for Space Utilization” promoted by the Japan Space Forum. Financial support from the Kao Foundation for Art and Sciences and the Sumitomo Foundation is acknowledged. Supporting Information Available: Preparation of the working dispersion of CL and van der Waals potential of CG. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Derijaguin, B. V. Theory of Stability of Colloids and Thin Films; Plenum Press: New York, 1989.
Colloid Dispersion Stability in Sub-/Supercritical Water (2) Verwey, E. J.; Overbeek, J. T. G. Theory of Stability of Lyophobic Colloids; Elsevier: Amsterdam, The Netherlands, 1948. (3) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, U.K., 1995; Vol. 1. (4) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991. (5) Shaw, D. J. Introduction to Colloid and Surface Chemistry, 4th ed.; Butterworth-Heinemann Ltd: Oxford, U.K., 1992. (6) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; John Wiley and Sons: New York, 1997. (7) Heimenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, 3rd ed.; Marcel Dekker: New York, 1997. (8) Evans, P. F.; Wennerstro¨m, H. The Colloidal Domain, 2nd ed.; Wiley-VCH: New York, 1999. (9) Benson, C.; Claxton, T. A. Phys. Chem. Solids 1964, 25, 367. (10) Levelt Sengers, J. M. H. In Supercritical Fluids Fundamentals and Applications; Kiran, E., Debenedetti, P. G., Peters, C. J., Eds., Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. (11) Somiya. S., Ed. Suinetsu Kagaku Handbook (Handbook of Hydrothermal Science) (In Japanese); Gihoudou: Tokyo, 1997. (12) Bennett, G. E.; Johnston, K. P. J. Phys. Chem. 1994, 98, 441. (13) Alargova, R. G.; Deguchi, S.; Tsujii, K. Colloids and Surf., A 2001, 183-185, 303. (14) Alargova, R. G.; Tsujii, K. Prog. Colloid Polym. Sci. 2004, 126, 134.
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