6906
J. Phys. Chem. B 2008, 112, 6906–6913
Effect of Pressure on Colloidal Behavior in Hydrothermal Water Swapan K. Ghosh*,† 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: NoVember 21, 2007; ReVised Manuscript ReceiVed: March 4, 2008
The pressure dependence of the colloidal phenomena of nanoparticles in hydrothermal water was investigated by both experiment and theory. Dynamic light scattering experiments show that diamond nanoparticles, which are highly stable in ambient water, easily aggregate in high-temperature and high-pressure water. Although the stability of nanoparticles in ambient pure water does not depend on pressure, it is interestingly found that at constant temperature particles aggregate faster in the hydrothermal regime when the pressure is higher. A theoretical interpretation is proposed to predict the stability of colloids in water as a function of temperature and pressure. Numerical analysis shows that the repulsive interparticle potential barrier, which stabilizes particles in the dispersion, decreases dramatically in high-temperature and high-pressure water. The decrease in the potential barrier arises from the temperature and the pressure dependencies of the dielectric constant (ε) and the ion product (pKw) of water. Numerical analysis shows that the pressure dependence of ε is negligible in the temperature range of 20-300 °C, whereas the pressure dependence of pKw is significant at temperatures of T > 150 °C. The theory reveals that the pressure dependence of the rate of size increment in the hydrothermal regime results from the pressure dependence of pKw. An increase in pressure in the hydrothermal water enhances the ionization of water molecules which reduces the surface potential of the particles. This effect lowers the interparticle repulsive potential barrier, which accelerates aggregation of the particles. Introduction Fine particles of colloidal size (1 nm to 1 µm) remain dispersed in fresh water for a long period of time. They move around in the dispersion due to random Brownian motion and frequently encounter each other. The combined effects of the encounters and van der Waals attraction lead to the formation of aggregates. Thus, a colloidal dispersion is thermodynamically unstable. The stability of the colloids in the dispersion is often attained kinetically by the electrostatic repulsion between the charged surfaces of the particles. Particles acquire such surface charges by ionization (or dissociation) of the surface groups and/or by adsorption of the ions from the solution onto the surface.1 The mechanism of the surface charging depends on the physicochemical properties of the solvent in which the particles are dispersed. The stability of the colloids in a dispersion is governed both by the properties of the solvent and the properties of the surfaces of the particles. The stability of the colloids in ambient water has been extensively studied by changing the properties of water and the properties of the surfaces of the particles by adding various additives.2–8 Although the stability of the colloids in ambient water is well-known, the stability of the colloids in high-temperature and high-pressure water is almost unknown. The physicochemical properties of water change significantly with respect to temperature (T) and pressure (P). The dielectric constant (ε), for example, decreases from 78 to 10 when the temperature is increased from 25 to 374 °C (at 25 * Corresponding author’s present address: Molecular and Information Life Science Unit, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama, 351-0198 Japan. Tel: +81-48467-9403. Fax: +81-48-467-4667. E-mail:
[email protected]. † Japan Agency for Marine-Earth Science and Technology. ‡ Hokkaido University.
MPa). The viscosity (η) and the ion product of water (pKw) also change dramatically with respect to T and P. Due to the decrease in the dielectric constant with increasing temperature, surface charging of the particles in water at high temperature becomes difficult. The changes in the properties of water with respect to temperature and pressure alter the surface properties of the particles, which affect particle-particle interactions. Therefore, the stability of the particles in pure water can be varied continuously just by heating without any additives. High-temperature and high-pressure water including supercritical water has emerged as an environmentally benign reaction medium for various chemical processes.9–11 In recent years, hydrothermal water has been used as a novel solvent for the synthesis of nanoparticles12–17 and as a solvent for the crystallization of water-insoluble polymers.18 Besides these recent trends, colloidal behavior in high-temperature and high-pressure water has enormous importance in the geothermal process in the Earth’s subsurface.19,20 It is considered that the fine particles of metals or metallic sulfides are transported from distant places to the locations where they are found today by high-temperature and high-pressure colloidal dispersions,19 which are emitted from deep-sea hydrothermal vents. Despite its importance in various fields, the present understanding of the colloidal phenomenon in high-temperature and high-pressure liquid is very limited because of the insufficient experimental evidence and lack of theoretical studies. In recent years, we have investigated colloidal behavior in high-temperature and high-pressure water,21–23 ethanol,24 and methanol. The aggregation of colloids in sub- and supercritical water was found to be a universal phenomenon.23 Most colloids such as polystyrene latex (PSL), colloidal gold (CG), diamond nanoparticles (DNP), and C60 aggregate in water within the
10.1021/jp711084y CCC: $40.75 2008 American Chemical Society Published on Web 05/15/2008
Colloidal Behavior in Hydrothermal Water temperature range of 201-346 °C at 25 MPa. Particles aggregate in high-temperature and high-pressure water because the repulsive interparticle potential barrier decreases rapidly when temperature is increased. The decrease in the repulsive interparticle potential with increasing temperature was attributed to the decrease in the dielectric constant of water with increasing temperature.23 Within the temperature range (201-346 °C) at which most colloids aggregate, the dielectric constant of water varies between 35 and 15. This is comparable with the dielectric constants of various organic solvents including methanol (32.61), ethanol (24.31), and propanol (20.21). Despite the low dielectric constants of the solvents, colloids including PSL, CG, C60, and silica nanoparticles remain stable in ambient ethanol and methanol for a long period of time. More interestingly, it was observed that PSL,25 CG,25 and silica nanoparticles24 remain stable in high-temperature and high-pressure ethanol, which is almost nonpolar with a dielectric constant of less than 8. These experimental facts strongly support the idea that, in addition to the dielectric constant, there must be other parameters that play key roles in controlling the stability of the particles in hightemperature and high-pressure water. Recently, we proposed a theoretical interpretation to explain colloidal behavior in high-temperature and high-pressure water.23 The theory was incomplete, because it did not account for the changes in the surface properties of the particles. Due to this shortcoming, the observed critical coagulation temperature, Tcg, and the predicted critical coagulation temperature, Tcg (th), showed disagreement. To elucidate the mechanism of colloidal stability in hightemperature water, one must examine the effect of pressure, which is still unknown. In this study, the effect of pressure on the stability of colloids is investigated by both experiment and theory. Here, we propose a complete theoretical interpretation that incorporates the temperature and the pressure dependencies of both the properties of water and the properties of particle surfaces. Experimental Section A. Materials and Sample Preparations. An aqueous dispersion of diamond nanoparticles (DNP) was purchased from Maruto Co., Ltd., Japan. The original sample was dialyzed for 21 days to remove ionic impurities.The size of the particles was measured by dynamic light scattering (DLS) at ambient temperature. The mean diameter of the particles was found to be 180 nm with a polydispersity of about 11%. Standard polystyrene latex (PSL) (mean diameter 214 nm) was purchased from Polysciences, Inc. (Warrington, PA, U.S.A.) and was used as purchased. The working solutions were prepared by diluting the original suspensions with deionized water produced by the Milli-Q system (Millipore, U.S.A.). B. DLS Experiments. The hydrodynamic diffusion coefficient (D) of the particles was measured by DLS using a DLS-820 (Otsuka Electronics, Co., Ltd., Osaka, Japan) instrument equipped with He-Ne (10 mW, 632.8 nm) and solidstate (50 mW, 532 nm) lasers. The scattered light was detected by a photomultiplier at a fixed 90° angle. The temperature and the pressure of the sample were controlled in a flow-type sample cell, which was connected to a sample injector (HPLC pump), a pressure gauge, an injection valve, and a back-pressure regulator. The structural design of the sample cell and further details of the experimental procedure may be found elsewhere.21,22 Prior to the measurement, the entire flow system was carefully washed by deionized water and filled with the sample solution.
J. Phys. Chem. B, Vol. 112, No. 23, 2008 6907 The pressure was then increased up to the desired limit, and the flow of the dispersion into the cell was terminated. The sample cell was then heated to the desired temperature. After equilibration of the sample cell at the desired temperature and pressure, the scattered intensity of DLS was measured. Measurement was started 10 min after the desired pressure and temperature were reached. At optimum condition, the present experimental setup allows DLS measurements with a temperature limit of 450 °C and a pressure limit of 40 MPa. New (fresh) sample was used for each measurement. In this study, the diffusion coefficient of the particles was measured within the temperature range of 20-300 °C. During the measurement T and P were controlled with the accuracy of (0.2 °C and (0.1 MPa, respectively. DLS-820 works in the homodyne mode of operation where the scattered light intensity autocorrelation function g(2)(τ) is expressed by26
g(2)(τ) )
〈IS(t)IS(t + τ)〉 〈IS 〉2
(1)
Here, Is is the intensity of the scattered light. The corresponding electric field autocorrelation function, g(1)(τ) is related to g(2)(τ) by
g(2)(τ) ) 1 + |g(1)(τ)|2
(2) g(1)(τ)
For a dispersion of spherical particles with uniform size, is an exponential function of the diffusion coefficient (D) of the particles and is expressed by
g(1)(τ) ) exp(-Dq2τ)
(3)
where q ) (4πn/λ0) sin(θ/2) is the scattering vector and τ, n, λ0, and θ are the correlation time, refractive index of the medium, wavelength of the incident light, and the scattering angle, respectively. The hydrodynamic diameter (dH) of the particles can be calculated from the observed D by the Einstein-Stokes relation
D)
kBT 3πηdH
(4)
where kB is the Boltzmann constant, T is 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 dependencies of n and η. Appropriate values of n and η for each temperature and pressure were calculated according to the data given in ref 27. 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).26,28 C. ζ-Potential Measurement. The ζ-potential of the particles was measured in water at 25 °C by an electrophoretic light scattering photometer (ELS-8000, Otsuka Electronics Co., Ltd., Osaka, Japan) under atmospheric pressure (Table 1). Results and Discussion A. Temperature and Pressure Dependence of the Diffusion Coefficient and the Hydrodynamic Diameter. The dispersion behavior of DNP in pure water has been investigated by measuring the diffusion coefficients of the particles in the temperature range of 20-300 °C at 10 and 25 MPa. Figure 1 shows that D value increases with increasing T value. The broken line (10 MPa) and the solid line (25 MPa) in Figure 1 are the theoretical predictions calculated by the Einstein-Stokes
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TABLE 1: Physical Quantities Used in the Numerical Calculationsa materials
r/nm
ζ/V
n1
ε1
A/10-20 J
diamond
90
-0.042
2.41829
5.7029
18.45
Mean hydrodynamic radius r is measured at 25 °C. ζ, n1, and ε1 are the ζ-potential, refractive index, and dielectric constant of diamond, respectively. Hamaker’s constant A is calculated from eq 8 at T ) 25 °C and P ) 25 MPa. We used Ve ) 2.65 × 1015 s-1 in the calculation. a
Figure 3. Mean hydrodynamic diameter of DNP, dH, as a function of time, t, spent by the particles at 300 °C under pressures of 10 MPa (open circles) and 25 MPa (solid circles), respectively. The solid lines are the linear fits to the observed data.
Figure 1. Hydrodynamic diffusion coefficient of DNP in water as a function of temperature at 10 MPa (open circles) and 25 MPa (solid triangles). The broken line and the solid line represent the Einstein-Stokes (ES) relationship (eq 4) for 10 and 25 MPa, respectively.
Figure 2. Mean hydrodynamic diameter of DNP, dH, as a function of T at 10 MPa (open circles) and 25 MPa (solid triangles), respectively. dH is calculated from observed D by eq 4 using appropriate values of η at each temperature.
relation (eq 4) assuming that the particle size remains unchanged with respect to temperature. The agreement between the observed D value and the theoretical prediction is excellent in the temperature range of 20-200 °C. However, the observed D value deviates downward from the theoretical prediction at T g 200 °C. Figure 2 shows corresponding hydrodynamic diameter, dH, which is calculated from the observed D by eq 4. Results show that size of the particles remains almost unchanged within the temperature range, 20-200 °C for both 10 and 25 MPa. Results also show that size of the particles increases in the temperature range, T g 200 °C. Critical coagulation temperature, Tcg, was estimated from the experimental result which is ∼200 °C. The results demonstrate that although diamond nanoparticles remain stable in ambient water for a long period of time (>1.3 × 106 s), they aggregate in hydrothermal water in the temperature range of T g 200 °C, within minutes. The pressure dependence of D was not observed in the pressure range of 10-25 MPa and in the temperature range of 20-200 °C. The
Figure 4. Mean hydrodynamic diameter of PSL, dH, as a function of time, t, spent by the particles at 300 °C under pressures of (a) 15 MPa and (b) 25 MPa. Different symbols indicate measurements at different time. The lines are the linear fits to the experimental data.
cause is perhaps that we investigated D only at the initial stage (only a few minutes) of the aggregation process, where the pressure effect on D is negligible or undetectable. The effect of pressure on the stability of nanoparticles in hightemperature and high-pressure water was investigated further by measuring D with respect to heating time t at a constant pressure and a constant temperature. The corresponding dH value was determined from the observed D value by eq 4. The pressure dependencies of the mean hydrodynamic diameter of DNP and PSL at 300 °C are shown in Figures 3 and 4, respectively. The lines are the linear fits to the experimental data. The slope of the linear fit to the experimental data provides the rate of increment of the size of the particles (ddH/dt), which is summarized in Table 2. Experiments suggest that in the hydrothermal water, particles aggregate faster when the pressure is higher.
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TABLE 2: Rate of Increment of the Size (ddH/dt) of Diamond Nanoparticles (DNP) and Polystyrene Latex (PSL) in Water (at 300 °C)a materials
T/°C
P/MPa
ddH/dt
DNP
300
10 25
2.5 3.6
PSL
300
15 25
1.7 (mean) 5.5 (mean)
a Rates determined from the linear fits of the experimental data described in Figures 3 and 4.
In the later sections, the stability of particles in water is discussed by applying the DLVO theory in which the temperature and the pressure dependence of the physicochemical properties of water and the properties of the surfaces of the particles are taken into consideration. B. DLVO Potential in the Aqueous Dispersion. Stability of the colloids in the dispersion is determined by the forces acting between the surfaces of the particles. The net interparticle potential in a medium with low electrolyte concentration is often accounted for by the DLVO theory,2–5,7,8 which is expressed by
VD ) VA + VR
(5)
where VD is net DVLO potential, VA is van der Waals attractive potential, and VR is the electrostatic repulsive potential. For two identical spherical particles of radius r, having Stern potential ψS, and separated by a distance H, VA and VR are expressed by5
VA ) -
[
(
1 x(x + 2) A 1 + 2 ln + 12 x(x + 2) (x + 1)2 (x + 1)2
)]
Figure 5. Temperature dependence of the properties of water: (a) η27 and (b) ε27 at 10, 25, 50, and 75 MPa.
(6)
and
VR ) 2πεε0rψS2 ln[1 + exp(-κH)]
(7)
where A is Hamaker’s constant, x ) H/2r, ε is the dielectric constant of the medium, ε0 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 by1
( )
ε - ε1 2 3hνe (n2 - n21)2 3 A ) kBT + 2 3⁄2 2 4 ε + ε1 16√2 (n + n1) and
κ)
(
e2
)
∑ i cizi2 1⁄2
εε0kBT
(8)
(9)
where ε1 is the dielectric constant of the particles, h is Planck’s constant, Ve is the electronic absorption frequency, n1 is the refractive index of the particles, e is the electronic charge, ci is the concentration of ionic species i, and zi is the valence. The extent of the electrostatic repulsion (VR) is characterized by κ, which is determined by only the properties (such as the dielectric constant and the ion concentration) of the medium. VA and VR depend on the properties of the medium and the properties of the particles. The temperature and the pressure dependence of the net potential barrier VD may be numerically calculated by eq 5 by accounting for the temperature and the pressure dependence of the parameters. C. Temperature and Pressure Dependence of the Physicochemical Properties of Water. Physical and chemical properties of water change dramatically with respect to tem-
Figure 6. Temperature dependence of pKw at 10, 25, 50, and 75 MPa. pKw is calculated by the formulation given in ref 30, for which the density data was calculated according to the formulation in ref 27.
perature and pressure. Figure 5 shows that both η and ε decrease significantly with increasing temperature. There is very little pressure dependence of η and ε within the temperature range of 20-300 °C; however, dependence is strong at temperatures above 300 °C. In the liquid continuum, water molecules easily ionize into hydronium (H3O+) and hydroxide (OH-) ions. In pure ambient water, pKw is 10-14 mol2/kg2. The temperature and pressure dependence of pKw is shown in Figure 6. pKw increases very fast with increasing temperature within the temperature range of 20-200 °C. pKw also depends on pressure; however, the pressure dependence is different at different temperatures. Although there is very little pressure dependence of pKw within the temperature range of 20-150 °C, it is very strong at temperatures above 150 °C (Figure 6). The temperature and the pressure dependence of κ-1 is calculated by eq 9, which is described in Figure 7. The temperature dependence of κ indicates that the interparticle repulsion is screened out significantly in the hydrothermal water within the temperature
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Figure 7. Temperature dependence of κ-1 in pure water at 10, 25, 50, and 75 MPa. κ-1 is calculated by eq 9.
range of 200-300 °C. This occurs because pKw is enhanced in this temperature regime due to the acceleration of the ionization of water molecules. D. Temperature and Pressure Dependence of the Surface Potential. The temperature and the pressure dependencies of the properties of water are expected to modify the surface properties of the particles. Since the Coulomb attraction is inversely proportional to the dielectric constant of the medium, the electrostatic force that binds a cation to an anion on the surface of a particle is stronger for lower ε value. Because of the low dielectric constant, the surface charging of the particles in high-temperature water becomes difficult, which alters the surface potential of the particles. Here, we examine the temperature and the pressure dependencies of the Stern potential in a pure aqueous dispersion. In the Stern model, for the electrical double layer to be neutral overall, the surface charge density Qs must be equal to the total summed charges in the diffuse layer, i.e., ∞
Qs ) -
∫ F(x) dx
(10)
0
where Qs and F are surface charge density and net volume charge density in the diffuse layer. Solution of eq 10 is expressed by4
Qs )
(
2κε0εkBT zeψs sin h ze 2kBT
)
(11)
While an exact solution of ψs is very difficult to determine from eq 11, a special case is considered for simplicity. For low surface potential, if |zeψs| , kBT, eq 11 provides a very convenient solution, which is
ψs = -
Qs ε0εκ
(12)
Equation 12 is an approximate formulation; however, for the present purpose this approximation is good enough to understand the behavior of ψs with respect to temperature and pressure in the hydrothermal water. To clarify the temperature and the pressure dependencies of ψs, one must use the temperature and the pressure dependencies of ε, κ, and Qs in eq 12. The temperature and the pressure dependencies of ε and κ are described in Figures 5b and 7. The negative charges on the surface of the diamond powder may originate from the adsorption of some dispersing agent(s) added by the manufacturer, although unfortunately no information on the dispersing agent was given from the manufacturer.
Figure 8. Temperature dependence of ψs in pure water at 10, 25, 50, and 75 MPa, respectively. ψs is calculated by eq 12 for Qs ) 30 µC · m-2. The temperature dependencies of ε and κ used in this calculation are shown in Figures 5b and 7, respectively.
Due to technical difficulties, at present, it is impossible to measure the temperature and the pressure dependence of surface charges. In this study we have assumed that Qs remain unchanged with respect to temperature and pressure. The temperature and the pressure dependencies of ψs are calculated by eq 12 assuming that Qs remains unchanged with respect to temperature and pressure. For the calculation, Qs is adjusted to be 30 µC · m-2 to adjust ψs = ζ ) -0.042 V. Figure 8 describes the temperature dependence of ψs at 10, 25, 50, and 75 MPa. With increasing temperature, ψs decreases very fast in the temperature range of 20-100 °C and reaches the minimum at around 200 °C. Numerical results clearly show that at a given temperature |ψs| decreases when pressure is increased. The temperature and the pressure dependence of ψs is highly sensitive to κ, which strongly depends on pKw. E. Numerical Analysis. The net DLVO potential VD is calculated considering that both the properties of water and the properties of the particles vary with respect to temperature and pressure. Parameters used in the calculation are described in Table 1 and Figures 5–8. The temperature dependence of VD is shown in Figure 9 for 10, 25, 50, and 75 MPa. Corresponding potential barrier at maximum, VDmax, is shown in Figure 10. Results demonstrate that an increase in temperature reduces Vmax D dramatically. For example, when the temperature is increased from 25 to 250 °C, VDmax decreases from 103 kBT to ∼3.5 kBT at 10 MPa; and 77 kBT to ∼1.5kBT at 75 MPa, respectively. VDmax, which reaches the minimum at around 250 °C, varies significantly with respect to pressure in the hydrothermal regime. The pressure dependence of VDmax in the hydrothermal water may arise due to the contributions from both VA and VR. Numerical results show that the pressure dependence of VA in the temperature regime of 20-300 °C is negligible. Thus, the pressure dependence of VDmax in the temperature regime of 20-300 °C is attributed to the pressure dependence of VR. The repulsive electrostatic potential VR is proportional to ψs2 and ε. Equation 12 shows that ψs is a function of ε and κ. In pure water, κ strongly depends on pKw. Therefore, VR is determined by ε and pKw. Hence, it may be tentatively concluded that the pressure dependence of VDmax is determined by the pressure dependence of ε and pKw. To find a realistic explanation of the experimental results, the temperature regime of 20-300 °C, in which most nanoparticles aggregate in water,23 is carefully examined. The pressure dependence of ε in the temperature range of 20-300 °C is practically negligible (Figure 5). The pressure dependence of pKw in the temperature range of 20-100 °C is also negligible (Figure 6), whereas the pressure dependence of pKw is signifi-
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J. Phys. Chem. B, Vol. 112, No. 23, 2008 6911
Figure 10. Temperature dependence of DLVO potential barrier at maximum, VDmax, at 10, 25, 50, and 75 MPa. VDmax is extracted from Figure 9.
pressure accelerates the aggregation of particles, which enhances the rate of aggregation. F. Kinetic Stability of Colloids in the Dispersion. The aggregation rate of the particles in a dispersion depends on (i) the collision frequency with which the particles encounter each other 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 barrier, only a fraction of the collisions results in the permanent aggregations. The 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 expressed by8
kr =
8kBT 3η
(13)
kr is independent of the particle size. Hence, the collision frequency with which the particles encounter one another can be expressed by
fc ) krnc )
8kBT n 3η c
(14)
where nc is the number of the particles per unit volume. In order to stabilize particles in the dispersion at a given temperature T for a period of time τ1, one requires that the probability of the permanent aggregation of two colliding particles overcoming their kinetic potential energy barrier (∆E) should be less than 1/(fcτ1), i.e.,
Pf(T, τ1) ) exp(- ∆E/kBT)
6 × 105 s). In fact, the aggregation of particles starts much earlier than actually observed during the experiment. ∆ES is calculated for τ1 ) 300 s and nc ) 5.35 × 1014/m3. Figure 11 shows the temperature dependence of ∆E. The pressure dependence of ∆ES is negligible in the temperature range of 20-300 °C. According to the kinetic stability theory, nanoparticles are expected to remain stable in water, within the temperature range of 20-300 °C, provided that the interparticle repulsive potential barrier is ∼4kBT or higher. The theoretical critical coagulation temperature, Tcg (th), can be predicted from the correspondence between VDmax and ∆ES (Figure 12). For diamond nanoparticles dispersed in pure water, Tcg (th) is 196 °C for 10 MPa; and 184 °C for 25 MPa. This is very close to the experimentally observed Tcg, which is 200 °C. G. Effect of Hydration Forces. The hydration force is a short-range force, which might be oscillatory, repulsive, or attractive and decays roughly exponentially with a characteristic decay length of 0.1-0.3 nm.31,32 Although the hydration force does not depend on ionic strength and the composition of the dispersion medium,31 it is an important factor for a highly electrolyte system in which the kinetic potential barrier is located at very short distance from the surface of the particle. It is expected that the ranges of the hydration forces might decrease with increasing temperature and pressure due to the fact that at high-temperature and high-pressure conditions the number of hydrogen bonds decreases and the water structure becomes more
The dispersion stability of nanoparticles in hydrothermal water is investigated by both experiment and theory. Dynamic light scattering experiments show that diamond nanoparticles and polystyrene latexes remain stable in high-pressure (25 MPa) water within the temperature ranges of 20-200 and 20-300 °C, respectively. At temperatures above these limits, particles easily aggregate in water. Pressure dependence of the rate of increment of the particle size in the hydrothermal regime demonstrates that a lower applied pressure suppresses aggregation process and makes the dispersion more stable. A theoretical interpretation is presented to predict the stability of the particles in water as a function of temperature and pressure. Analysis shows that the repulsive interparticle potential barrier, which stabilize particles in the dispersion, decreases dramatically in hydrothermal water due to the temperature and pressure dependencies of the dielectric constant (ε) and the ion product (pKw) of water. It is found that the pressure dependence of ε on the stability of the particles is negligible in the temperature range of 20-300 °C, whereas the pressure dependence of pKw on the stability of the particles is significant at temperatures of T > 150 °C. Analysis suggests that the pressure dependence of the stability of the particles in hydrothermal water results from the pressure dependence of pKw. A higher applied pressure in the hydrothermal regime enhances the ionization of water molecules which causes a decrease of the surface potential of the particles. This effect reduces the interparticle repulsive potential barrier and enhances the aggregation of particles. Acknowledgment. The authors sincerely acknowledge the continuous support and encouragement of Professor Koki Horikoshi (JAMSTEC) during this project. The authors are grateful to Dr. Shigeru Deguchi (JAMSTEC) for his valuable comments. The authors are thankful to Dr. Rossitza G. Alargova (Vertex Pharmaceuticals Inc.) and Dr. Sada-atsu Mukai (Kyushu University) for their helpful discussions and suggestions.
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