scholarly journals GENERALIZED PARTITION FUNCTIONS, INTERPOLATING STATISTICS AND HIGHER VIRIAL COEFFICIENTS

1999 ◽  
Vol 14 (18) ◽  
pp. 1217-1226 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
Boundary Condition ◽  
Finite Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Generalized Partition

Starting from determinants at finite temperature obeying an intermediate boundary condition between the periodic (bosonic) and antiperiodic (fermionic) cases, we find results which can be mapped onto those obtained from anyons for the second virial coefficient. Using this approach, we calculate the corresponding higher virial coefficients and compare them with the results in the literature.

scholarly journals GENERALIZED PARTITION FUNCTIONS AND INTERPOLATING STATISTICS

1998 ◽  
Vol 13 (11) ◽  
pp. 843-852 ◽  
Author(s):  
P. F. BORGES ◽  
H. BOSCHI-FILHO ◽  
C. FARINA
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Limit ◽  
Partition Functions ◽  
High Temperature Limit ◽  
Full Temperature ◽  
Generalized Partition ◽  
Relativistic Particles

We show that the assumption of quasiperiodic boundary conditions (those that interpolate continuously periodic and antiperiodic conditions) in order to compute partition functions of relativistic particles in 2+1 space–time can be related with anyonic physics. In particular, in the low temperature limit, our result leads to the well-known second virial coefficient for anyons. Besides, we also obtain the high temperature limit as well as the full temperature dependence of this coefficient.

scholarly journals THE FOURTH VIRIAL COEFFICIENT OF ANYONS

1998 ◽  
Vol 13 (21) ◽  
pp. 3723-3747 ◽  
Author(s):  
ANDERS KRISTOFFERSEN ◽  
STEFAN MASHKEVICH ◽  
JAN MYRHEM ◽  
KÅRE OLAUSSEN
Keyword(s):  
Monte Carlo ◽  
Fourier Series ◽  
Monte Carlo Method ◽  
Path Integral ◽  
Virial Coefficient ◽  
Path Integrals ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Partition Functions ◽  
Two Dimensional

We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle θ. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagramatically in such a way that the connected diagrams give the cluster coefficients. This provides a general proof that all cluster and virial coefficients are finite. We give explicit polynomial approximations for all path integral contributions to all cluster coefficients, implying that only the second virial coefficient is statistics dependent, as is the case for two-dimensional exclusion statistics. The assumption leading to these approximations is that the tree diagrams dominate and factorize.

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
Keyword(s):  
Methyl Acetate ◽  
Virial Coefficient ◽  
Methyl Formate ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Ethyl Formate ◽  
Carbonyl Oxygen ◽  
Second Virial Coefficients ◽  
Theoretical Significance ◽  
Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

The second virial coefficients of mixed organic vapours

1952 ◽  
Vol 210 (1103) ◽  
pp. 557-564 ◽  
Keyword(s):  
Hydrogen Bonding ◽  
Binary Mixtures ◽  
Diethyl Ether ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Corresponding States ◽  
Linear Variation ◽  
Second Virial Coefficients

The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.

The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

Measurement of the temperature variation of virial coefficients. I. Application to the second virial coefficient of n-butane

1964 ◽  
Vol 17 (5) ◽  
pp. 501 ◽  
Author(s):  
GA Bottomley ◽  
TH Spurling
Keyword(s):  
Temperature Dependence ◽  
Temperature Variation ◽  
Virial Coefficient ◽  
Small Volume ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Absolute Pressure ◽  
Isothermal Expansion ◽  
Volume Increment

An unconventional apparatus, described in detail, determines, through a measured small volume increment, the temperature dependence of the second virial coefficient of a vapour without the necessity for isothermal expansion. Absolute pressure determinations are avoided by working differentially, vapour against nitrogen reference gas. Results for n-butane at 0-150� agree with established work.

scholarly journals Drug Design Outlook by Calculation of Second Virial Coefficient as a Nano Study

2017 ◽  
Vol 56 (2) ◽  
Author(s):  
M. Monajjemi ◽  
F. Naderi ◽  
F. Mollaamin ◽  
M. Khaleghian
Keyword(s):  
Potential Energy ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Basis Set ◽  
Intermolecular Potential ◽  
Energy Curve ◽  
Basis Set Superposition Error ◽  
Second Virial Coefficients ◽  
Calculated Potential Energy

Intermolecular potential energy surface for an interaction of drug with Na has been examined using HF level of theory with 6-31G* basis set. The name of drug is meso-tetrakis (p-sulphonatophenyl) porphyrin (here after abbreviated to TSPP) . The numbers of Na<sup>+</sup> have a significant effect on the calculated potential energy curve (including position, depth, and width of the potential well). Counterpoise (CP) correction has been used to show the extent of the basis set superposition error (BSSE) on the potential energy curves obtained for TSPPNa. The second virial coefficients are calculated by these data.

Pairwise additive third virial coefficients for multipolar molecules : Application to water vapour

1971 ◽  
Vol 24 (8) ◽  
pp. 1567 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Water Vapour ◽  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Axially Symmetric ◽  
Multidimensional Integration ◽  
Third Virial Coefficient ◽  
Qualitative Effect ◽  
Experimental Values

Pairwise additive third virial coefficients for axially symmetric multipolar molecules have been calculated using a non-product multidimensional integration formula. Results for the Stockmayer potential agree with the corrected results of Rowlinson. It is found that the inclusion of the dipole-quadrupole and quadrupole-quadrupole terms in the potential function has a marked qualitative effect on the shape of the C-T curve. Values of the third virial coefficient for water vapour calculated using a potential function derived from gaseous viscosity and second virial coefficient data are in good agreement with the experimental values.

Parameters of the Morse Potential from Second Virial Coefficients of Gases

1987 ◽  
Vol 42 (5) ◽  
pp. 447-450 ◽  
Author(s):  
Akira Matsumoto
Keyword(s):  
Temperature Dependence ◽  
Morse Potential ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Polyatomic Molecules ◽  
Inert Gases ◽  
Second Virial Coefficients ◽  
Analytic Expression

An analytic expression for the second virial coefficient in case of the Morse potential is derived. The parameters of the Morse potential are determined for eighteen species comprising inert gases, diatomic and polyatomic molecules, and mixtures of gases using experimental second virial coefficients. The calculated second virial coefficients based on the obtained Morse potential agree well with the empirical second virial coefficients and their temperature dependence.

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