TY - JOUR
TI - Molecular Principle of Corresponding States for Viscosity and Thermal Conductivity of Fluid Mixtures
AU - Mo, K. C.
AU - Gubbins, K. E.
T2 - Chemical Engineering Communications
AB - Abstract Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (ε) and molecular masses; it is more sensitive to the size difference of the molecular components, however. For cryogenic liquid mixtures composed of simple liquids good results are obtained using two-parameter corresponding states for the reference fluid. For polyatomic fluids it is necessary to use a three-parameter corresponding states approach for the pure fluids. A method of introducing a third parameter, while retaining the simplicity of having only two independent variables, is used for such fluids. Good results are obtained for a variety of binary mixtures. The method is of particular value for multicomponent fluids. Thus, without fitting any parameters from ternary data the theory predicts viscosities for the system carbon tetrachloride/n-hexane/benzene over the full composition range with a standard deviation of only 1.69%.
DA - 1974/1//
PY - 1974/1//
DO - 10.1080/00986447408960438
VL - 1
IS - 6
SP - 281-290
SN - 0098-6445 1563-5201
UR - http://dx.doi.org/10.1080/00986447408960438
ER -
TY - JOUR
TI - Perturbation theory for molecular fluids using a nonspherical reference potential
AU - Mo, K.C.
AU - Gubbins, K.E.
T2 - Chemical Physics Letters
AB - A new perturbation expansion is proposed for fluids composed of nonspherical molecules. The reference fluid is one of rigid but nonspherical molecules, and the expansion procedure is similar to that used by Weeks, Chandler and Andersen for monatomic fluids. Calculated internal energies are compared with Monte Carlo results for liquids with dipolar, quadrupolar, and anisotropic overlap forces. The range of validity of the first-order theory appears to be considerably greater than that for the corresponding approximation in the Pople expansion.
DA - 1974/7//
PY - 1974/7//
DO - 10.1016/0009-2614(74)80465-3
VL - 27
IS - 1
SP - 144-148
J2 - Chemical Physics Letters
LA - en
OP -
SN - 0009-2614
UR - http://dx.doi.org/10.1016/0009-2614(74)80465-3
DB - Crossref
ER -
TY - JOUR
TI - Isothermal compressibility and partial molal volume for polyatomic liquids
AU - Gubbins, K. E.
AU - O'Connell, J. P.
T2 - The Journal of Chemical Physics
AB - For dense polyatomic liquids (ρ > 2ρc), the anisotropic part of the intermolecular forces has remarkably little influence on the isothermal compressibility or on the partial molal volume for the case of mixtures; this is also the case for dilute gases at high reduced temperatures. Such behavior is shown to be predicted by a perturbation treatment in which these properties for the polyatomic fluid are expanded about the corresponding values for a fluid with isotropic intermolecular forces. For dense liquids (or dilute, high temperature gases), the perturbation terms in such series usually become negligible compared to the zeroth order term. This leads to corresponding states relationships for these properties, which have the same functional form as for fluids composed of simple isotropic molecules, such as argon. This prediction is confirmed by a comparison of isothermal compressibilities for polyatomic liquids with the values for argon at the corresponding state condition.
DA - 1974/5//
PY - 1974/5//
DO - 10.1063/1.1681558
VL - 60
IS - 9
SP - 3449-3453
J2 - The Journal of Chemical Physics
LA - en
OP -
SN - 0021-9606 1089-7690
UR - http://dx.doi.org/10.1063/1.1681558
DB - Crossref
ER -
TY - JOUR
TI - Monte Carlo calculations of the mean squared force in molecular liquids
AU - Gray, C.G.
AU - Wang, S.S.
AU - Gubbins, K.E.
T2 - Chemical Physics Letters
AB - Abstract The mean squared intermolecular force ( F 2 1 ) on a molecule in a diatomic liquid has been evaluated by a Monte Carlo calculation at reduced density p * = 0.8 and reduced temperature 7 * = 0.72. The isotropic intermolecular potential is of Lennard-Jones form; anisotropic multipolar and overlap potentials of various strengths are used. For the largest strengths studied, the anisotropic contribution to ( F 2 1 ) is about 50–60% of the isotropic one.
DA - 1974/6//
PY - 1974/6//
DO - 10.1016/0009-2614(74)80428-8
VL - 26
IS - 4
SP - 610-612
J2 - Chemical Physics Letters
LA - en
OP -
SN - 0009-2614
UR - http://dx.doi.org/10.1016/0009-2614(74)80428-8
DB - Crossref
ER -
TY - JOUR
TI - The mean squared torque in pure and mixed dense fluids
AU - Twu, C.H.
AU - Gray, C.G.
AU - Gubbins, K.E.
T2 - Molecular Physics
AB - The mean squared torque on a molecule can be obtained from infra-red or Raman band moments, and provides a direct measure of the strength of the anisotropic intermolecular forces. The expression for the mean squared torque on a molecule of species α in a fluid mixture is given in terms of the intermolecular potential and the angular pair correlation functions. This relation is made tractable by introducing a perturbation expansion in powers of the anisotropic potential strength for the angular pair correlation functions. Monte Carlo calculations of the mean squared torque are presented for a liquid of linear molecules having dipolar, quadrupolar and anisotropic overlap interactions. Comparison of the perturbation expansion to second order with these ‘exact’ results shows good agreement for μ*=μ/(εσ3)1/2 and Q*=Q/(εσ5)1/2 values less than about 0·5, and for values of the dimensionless overlap constant |δ| less than about 0·2. Finally, experimental values of the mean squared torque for both pure and mixed liquids are compared to the Monte Carlo and to the perturbation theory results.
DA - 1974/6//
PY - 1974/6//
DO - 10.1080/00268977400101331
VL - 27
IS - 6
SP - 1601-1612
J2 - Molecular Physics
LA - en
OP -
SN - 0026-8976 1362-3028
UR - http://dx.doi.org/10.1080/00268977400101331
DB - Crossref
ER -
TY - JOUR
TI - The radial distribution function in fluid mixtures: Conformal solution theory and molecular dynamics results
AU - Mo, K.C.
AU - Gubbins, K.E.
AU - Jacucci, G.
AU - McDonald, I. R.
T2 - Molecular Physics
AB - The conformal solution approach is used to relate the distribution functions g αβ(r) for a fluid mixture to those of a pure fluid, g x(r). The procedure is to expand g αβ(r) about the corresponding function for an ideal solution, using σ αβ 3 and εαβσαβ 3 as expansion parameters; the expansion of the function y αβ(r) is also considered. Molecular dynamics results are reported for the tg αβ for argon-krypton liquid mixtures using the Lennard-Jones (12, 6) potential. These results are used to test the conformal solution expansions to first order; the g αβ expansion is found to be superior to that for y αβ for most r values of interest. The second order term in the conformal solution expansion for the Helmholtz free energy is also calculated for argon-krypton mixtures, and found to be about 10 per cent of the value of A E given by the van der Waals 1 theory.
DA - 1974/5//
PY - 1974/5//
DO - 10.1080/00268977400101041
VL - 27
IS - 5
SP - 1173-1183
J2 - Molecular Physics
LA - en
OP -
SN - 0026-8976 1362-3028
UR - http://dx.doi.org/10.1080/00268977400101041
DB - Crossref
ER -
TY - JOUR
TI - Perturbation theory for equilibrium properties of molecular fluids
AU - Ananth, M.S.
AU - Gubbins, K.E.
AU - Gray, C.G.
T2 - Molecular Physics
AB - Perturbation theory for the angular pair correlation function g(r12 ω 1 ω 2), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties. Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states. Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections. Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties. The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressibility, in agreement with the first-order theory. Molecular anisotropy has a relatively small effect on the configurational energy and on the Helmholtz free energy, but the effect is large for pressure and specific heat. The pressure is more sensitive to short-range anisotropic forces than the other properties, whereas the specific heat is particularly sensitive to the long-range anisotropic forces. Mean squared torques (derived from infra-red and Raman band moments) are very sensitive to the strengths of the anisotropic forces, and are more sensitive to higher terms in the multipole series than are the other properties. The structure factors for oxygen and nitrogen are found to be little affected by the anisotropic forces.
DA - 1974/10//
PY - 1974/10//
DO - 10.1080/00268977400102331
VL - 28
IS - 4
SP - 1005-1030
J2 - Molecular Physics
LA - en
OP -
SN - 0026-8976 1362-3028
UR - http://dx.doi.org/10.1080/00268977400102331
DB - Crossref
ER -
TY - JOUR
TI - Monte Carlo study of the angular pair correlation function in a liquid with quadrupolar forces
AU - Wang, S.S.
AU - Egelstaff, P.A.
AU - Gray, C.G.
AU - Gubbins, K.E.
T2 - Chemical Physics Letters
AB - The angular pair correlation function g(R12 ω1 ω2), giving the probability that two molecules have orientations ω1 and ω2 and are at vector separation R12, has been studied by the Monte Carlo method for a dense liquid. The intermolecular potential model studied consisted of a Lennard-Joes (12,6) potential plus quadrupole—quadrupole interaction. The results are used to test several approximation methods for determining g(R12ω1ω2). While none of these methods works for the largest quadrupole moment tested (Q* = 1), the perturbation methods give good results for smaller moments.
DA - 1974/2//
PY - 1974/2//
DO - 10.1016/0009-2614(74)85301-7
VL - 24
IS - 3
SP - 453-456
J2 - Chemical Physics Letters
LA - en
OP -
SN - 0009-2614
UR - http://dx.doi.org/10.1016/0009-2614(74)85301-7
DB - Crossref
ER -
TY - JOUR
TI - A lattice model of gas-gas equilibria in binary mixtures
AU - Bartis, J.T.
AU - Hall, C.K.
T2 - Physica
AB - A two-component decorated lattice model is introduced to study critical phenomena and phase equilibrium in binary fluids. For certain ranges of interaction parameters, the model demonstrates gas-gas equilibria of the first and second types. Since no assumption of analyticity is made, the model yields non-classical critical behavior. In particular, at the critical double point (the coalescence of two critical points), the exponent β which, before the coalescence, describes the shape of the isothermal coexistence curves in the pressure-mole fraction plane, is changed to 2β. It is shown that this renormalization of β is in agreement with the phenomenological theory of Griffiths and Wheeler.
DA - 1974/11//
PY - 1974/11//
DO - 10.1016/0031-8914(74)90305-x
VL - 78
IS - 1
SP - 1-21
J2 - Physica
LA - en
OP -
SN - 0031-8914
UR - http://dx.doi.org/10.1016/0031-8914(74)90305-x
DB - Crossref
ER -