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

More documents

Recommendations

Info

hand side in Eqn. (3.9) can be expressed in a more explicit form by considering the relationship between force and momentum: α ∂ N N ∂ N p i δ( r− ri) =− U( r ω ) + V( r ) δ( − i) α α r r , (3.10) ∂r ∂r i i i i where U and V are the internal potential energy and external force field, respectively. After mathematical manipulations (and considering that Newton’s third law requires that −∇ i iU vanishes) for Eqn. (3.10), and we obtain: α ∂ N N ∂ N p i δ( r− ri) =− U( r ω ) + V( r ) ( i) α α δ r−r ∂r ∂r ∂ N N ∂ N =− U( r ω ) δ( r−ri) − V( ) δ( − i) α r r r α ∂r ∂r i i i i i i N N ∂U( r ω ) ∂v( r) =− [ δ( r−ri) −δ( r−r0 )] −ρad( r, t) α α ∂r ∂r i i N N ∂U( r ω ) ∂ β β ∂v =− − dl δ( −l ) −ρad ( , t) α β C0i i ∂r ∂r r () r r α ∂r i N N ∂ ∂U( r ω ) β β ∂v( ) = dl r ( l ) ad ( , t) β δ ρ α − − r C α ∂ 0i i ∂r r r i ∂r i i , (3.11) where C 0i is an arbitrary contour from the center of mass position of particle i, to an arbitrary point r 0 in the fluid. By substituting Eqn. (3.11) into Eqn. (3.9), we get 20
α β pi pi J α ∂ α (,) r t =− ( i) pi ( i) β δ r− r + δ r−r ∂r i mi i . (3.12) N N ∂ ∂U( r ω ) β ∂v( r) = − ρad (,) tkT B + dlδ( −l) −ρad (,) t β r α r C α ∂ 0i i ∂r r r i ∂r If we define v() J α ∂ αβ ∂ r (,) r t = σ (,) r t −ρad (,) r t β α ∂r ∂r , (3.13) ∂ αβ αβ ∂v() r = σkin (,) t + σconf (,) t −ρad (,) t β α ∂r r r r ∂r and considering the relationship between the stress tensor and pressure tensor (Eqn. (3.8)), we get the expressions for the kinetic and configurational contributions and the total pressure tensor from the mechanical route [63]: N N ∂U ( r ω ) Pr () = ρad () rkT B 1− dl δ( −l) ∂ r , (3.14) r C0i i i P = ρ () r kT1, (3.15) kin ad B P conf N N ∂U ( r ω ) =− dl δ ( −l) ∂ r . (3.16) r C0i i i In the case that the spherical particles interact in a purely pair-wise fashion, the configurational contribution can be simplified as: P conf N 1 du( rij ) =− δ ( r ) d 2 dr − , (3.17) Cij i≠ j ij 21
Page 1 and 2: ABSTRACT LONG, YUN. Pressure Tensor
Page 3 and 4: Pressure Tensor of Adsobate in Nano
Page 5 and 6: ACKNOWLEDGMENTS In the first place,
Page 7 and 8: TABLE OF CONTENTS LIST OF TABLES ..
Page 9 and 10: 9.1 Introduction ..................
Page 11 and 12: LIST OF FIGURES Figure 2.1 Phase di
Page 13 and 14: Figure 6.9 The normal pressure and
Page 15 and 16: CHAPTER 1 Introduction and Backgrou
Page 17 and 18: enhancement of argon adsorbed in ca
Page 19 and 20: including ice VIII and ice IX, phas
Page 21 and 22: These experimental results are summ
Page 23 and 24: experiment, indicating that a phase
Page 25 and 26: (SAXS) measurements, Professor Kane
Page 27 and 28: y the microporous materials, curren
Page 29 and 30: tangential pressure of water was ~
Page 31 and 32: θ-directions P φφ = P θθ = P T
Page 33: ρ dPN ( ρ) Sphere: PT( ρ) = PN(
Page 37 and 38: Figure 3.2 Schematic representation
Page 39 and 40: P 1 du( r ) r N ij ij 1 conf , IK (
Page 41 and 42: e ( α ) = ( α )/ ( α ) . where
Page 43 and 44: The physical meaning of the Dirac D
Page 45 and 46: It is instructive to expand the rig
Page 47 and 48: will lead to different tangential p
Page 49 and 50: It is more complex to get the ρ- a
Page 51 and 52: summation of the volume changes con
Page 53 and 54: V V PTϕ ( ρ) = f1( ρ) + 2 ρad(
Page 55 and 56: Figure 3.5 A plane at constant φ,
Page 57 and 58: Figure 3.6 The shaded annuluses of
Page 59 and 60: As for in the cylindrical pore, a n
Page 61 and 62: (3.4)), so it is not necessary to d
Page 63 and 64: pressure is calculated (see Sec. 5.
Page 65 and 66: microscopic property over all possi
Page 67 and 68: such as translational displacement,
Page 69 and 70: methane and ethane onto a microporo
Page 71 and 72: CHAPTER 5 Pressure Enhancement in S
Page 73 and 74: Table 5.1 The BFW parameters for ar
Page 75 and 76: We also developed a realistic pore
Page 77 and 78: component, etc.) are sampled every
Page 79 and 80: esults and one does not have to cho
Page 81 and 82: Figure 5.4 The normal pressures cal
Page 83 and 84: phase (at P bulk ~ 1 × 10 -4 bar).
Page 85 and 86:
Figure 5.5 The density and pressure
Page 87 and 88:
etween argon molecules within the l
Page 89 and 90:
It is of interest to note that this
Page 91 and 92:
Figure 5.8 The average in-pore dens
Page 93 and 94:
BFW potential (Figure 5.1), that is
Page 95 and 96:
closely packed in the direction par
Page 97 and 98:
CHAPTER 6 Effects of the Wetting Pa
Page 99 and 100:
(or simply the wetting parameter),
Page 101 and 102:
Figure 6.3 Experimental contact ang
Page 103 and 104:
T = T ( H , α ) for small adsorbat
Page 105 and 106:
Figure 6.4 The capillary condensati
Page 107 and 108:
6.5.2 Results and Discussion The in
Page 109 and 110:
Moreover, the wetting parameter α
Page 111 and 112:
section, except for a jump at capil
Page 113 and 114:
α w = 0.1221, suggesting a highly
Page 115 and 116:
ulk pressure (e.g., 1,010 bar compa
Page 117 and 118:
We also study the effect of pore wi
Page 119 and 120:
ole on the in-pore structure of the
Page 121 and 122:
of the cylindrical pore cannot be c
Page 123 and 124:
adsorbate molecule (a channel diame
Page 125 and 126:
which is also found in the slit por
Page 127 and 128:
Page 129 and 130:
Figure 7.3 The (a) tangential and (
Page 131 and 132:
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 and 176:
(a) The pressure of fluids confined
Page 177 and 178:
(h) The roughness of the pore wall,
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
show all

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

Create successful ePaper yourself

Delete template?

Save as template?