ABSTRACT LONG, YUN. Pressure Tensor of Adsorbate in ...

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very large bulk pressure is needed (e.g., ~ 4000 bar for mercury in a carbon pore) to push the adsorbate to intrude into the pore, and the adsorbate layer in the central region of the pore is equally or even more compressed (by the bulk pressure) than the contact layer, where the weaker attraction from the wall decreases the degree of the compression. (e) The normal pressure of the confined phase depends on its compression in the normal direction, and thus depends on the pore size, or more precisely, the match between the pore size and the adsorbate layer arrangement in the normal direction. As a result, the normal pressure exhibits an oscillation between positive and negative values with increasing pore size. (f) The normal pressure of adsorbate acting on the wall is also enhanced (by a factor of 10 3 ), but the value can be positive or negative depending on the pore size. This large normal pressure also causes deformation of the porous material: a positive normal pressure (strong repulsive force) expands the pore, while a negative normal pressure (strong attractive force) contracts the pore. (g) In the cylindrical and spherical pores (wetting system), the pressure enhancement effect is stronger than that in the slit pore of the same size. Because of the curvature of the walls, the attraction from the wall is enhanced due to more wall atoms interacting strongly with the adsorbate phase, and thus the adsorbate in the cylindrical and spherical pores are more compressed, which results in a larger tangential pressure at the contact layer. 162
(h) The roughness of the pore wall, in general, decreases the pressure enhancement effect (for the wetting system), because the roughness prevents the contact layer of adsorbate from arranging into a very close-packed structure due to the steric hindrance effect, which probably also produces roughness of the adsorbate layers and prevents the inner layer in contact with this “contact layer” from being closely packed. As a result, the tangential pressure at the contact layer of adsorbate confined in a pore with rough walls is not as large as that in a similar pore with smooth walls. (i) The pressure tensor (specifically, the tangential pressure component in a slit pore) calculated from the mechanical route by using the Irving-Kirkwood definition is different from that by using the Harasima definition, due to the different physical meanings of the two definitions. However, integral of the tangential pressure and its average over the pore width are the same for both definitions. (j) The pressure tensor components calculated from the mechanical route (with the Irving- Kirkwood choice of the integral contour) agree well with those calculated from the thermodynamic route (with the Irving-Kirkwood-like definition of local energy). (k) The pressure tensor components can be averaged in various ways, providing different information. The choice of the ways of averaging depends on the purpose and applications. The local pressures, although not experimentally measurable at present, are also interesting because they contain the information of maximum values and the 163
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ABSTRACT LONG, YUN. Pressure Tensor
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Pressure Tensor of Adsobate in Nano
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ACKNOWLEDGMENTS In the first place,
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TABLE OF CONTENTS LIST OF TABLES ..
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9.1 Introduction ..................
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LIST OF FIGURES Figure 2.1 Phase di
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Figure 6.9 The normal pressure and
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CHAPTER 1 Introduction and Backgrou
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enhancement of argon adsorbed in ca
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including ice VIII and ice IX, phas
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These experimental results are summ
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experiment, indicating that a phase
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(SAXS) measurements, Professor Kane
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y the microporous materials, curren
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tangential pressure of water was ~
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θ-directions P φφ = P θθ = P T
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ρ dPN ( ρ) Sphere: PT( ρ) = PN(
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α β pi pi J α ∂ α (,) r t =
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Figure 3.2 Schematic representation
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P 1 du( r ) r N ij ij 1 conf , IK (
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e ( α ) = ( α )/ ( α ) . where
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The physical meaning of the Dirac D
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It is instructive to expand the rig
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will lead to different tangential p
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It is more complex to get the ρ- a
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summation of the volume changes con
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V V PTϕ ( ρ) = f1( ρ) + 2 ρad(
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Figure 3.5 A plane at constant φ,
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Figure 3.6 The shaded annuluses of
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As for in the cylindrical pore, a n
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(3.4)), so it is not necessary to d
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pressure is calculated (see Sec. 5.
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microscopic property over all possi
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such as translational displacement,
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methane and ethane onto a microporo
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CHAPTER 5 Pressure Enhancement in S
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Table 5.1 The BFW parameters for ar
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We also developed a realistic pore
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component, etc.) are sampled every
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esults and one does not have to cho
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Figure 5.4 The normal pressures cal
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phase (at P bulk ~ 1 × 10 -4 bar).
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Figure 5.5 The density and pressure
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etween argon molecules within the l
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It is of interest to note that this
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Figure 5.8 The average in-pore dens
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BFW potential (Figure 5.1), that is
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closely packed in the direction par
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CHAPTER 6 Effects of the Wetting Pa
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(or simply the wetting parameter),
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Figure 6.3 Experimental contact ang
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T = T ( H , α ) for small adsorbat
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Figure 6.4 The capillary condensati
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6.5.2 Results and Discussion The in
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Moreover, the wetting parameter α
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section, except for a jump at capil
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α w = 0.1221, suggesting a highly
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ulk pressure (e.g., 1,010 bar compa
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We also study the effect of pore wi
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ole on the in-pore structure of the
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of the cylindrical pore cannot be c
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adsorbate molecule (a channel diame
Page 125 and 126: which is also found in the slit por
Page 127 and 128: Figure 7.2 The density and pressure
Page 129 and 130: Figure 7.3 The (a) tangential and (
Page 131 and 132: Figure 7.4 The density and pressure
Page 133 and 134: 7.3.3 Effects of Bulk Pressure for
Page 135 and 136: 7.4 Conclusions The pressure tensor
Page 137 and 138: dimensions of the simulation cell w
Page 139 and 140: pore is of finite length and the ad
Page 141 and 142: Figure 8.2 The normal pressures of
Page 143 and 144: 8.3.2 Modeling Details A simple car
Page 145 and 146: are cut off at 2 nm. As reported by
Page 147 and 148: Figure 8.4 The normal pressure of (
Page 149 and 150: 8.4 Argon Adsorbed in Cylindrical a
Page 151 and 152: spherical pores is due to additiona
Page 153 and 154: CHAPTER 9 Effects of Wall Roughness
Page 155 and 156: and u i is the potential energy of
Page 157 and 158: Figure 9.2 (a) The density and pres
Page 159 and 160: 9.3 Effects of Wall Roughness on Ad
Page 161 and 162: Figure 9.5 A functionalized graphen
Page 163 and 164: Figure 9.6 The adsorption isotherms
Page 165 and 166: splitting effect becomes smaller, b
Page 167 and 168: We studied the effect of bulk press
Page 169 and 170: ight after capillary condensation,
Page 171 and 172: Finally, we show in Figure 9.10 the
Page 173 and 174: peak value of the tangential pressu
Page 175: (a) The pressure of fluids confined
Page 179 and 180: mercury as fluids), where the addit
Page 181 and 182: REFERENCES [1] K.E. Gubbins, Y.C. L
Page 183 and 184: [21] H. Kanda, M. Miyahara, K. Higa
Page 185 and 186: [42] U. Raviv, P. Laurat, J. Klein,
Page 187 and 188: [64] J.R. Henderson, Potential-Dist
Page 189 and 190: [89] Q. Cai, A. Buts, N.A. Seaton,
Page 191 and 192: [113] T.M. Reed, K.E. Gubbins, Appl
Page 193 and 194: APPENDICES 179
Page 195 and 196: Recalling that [ e e e ] = δ e ,
Page 197 and 198: ∂ ∂ ∂Pρρ (1) e e e P e e e
Page 199 and 200: ∂ ∂z P Tz = 0 , (A.15) where P
Page 201 and 202: ∂ ∂ ∂ eρ = 0; eθ = 0; eϕ =
Page 203 and 204: Appendix B Volume Balance Examinati
Page 205 and 206: dV tk = + − 3 [(1 ξ ) 1] V tk,0
Page 207 and 208: dyh ρ + syh = 0 , (C.3) d ρ and s
Page 209 and 210: To simplify the answer, we calculat
Page 211 and 212: ln < e > P P P k T P k T −ΔU( ρ
Page 213 and 214: For the dipolar fluids (C 6 H 5 Br
Page 215 and 216: The parameters of various walls and
Page 217 and 218: c1 c2 c3 small change in the volume
Page 219 and 220: with Irving-Kirkwood definition P C
Page 221 and 222: ij Distance between particles i and
Page 223: divided in the ρ-direction σ Stre
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