Heat capacity extrema: Solution of the Ornstein–Zernike equation in the Percus–Yevick approximation for the truncated Lennard‐Jones fluid

1994 ◽  
Vol 100 (4) ◽  
pp. 3094-3106 ◽  
Author(s):  
Ben C. Freasier ◽  
Richard J. Bearman
Keyword(s):  
Author(s):  
Toshihiro Kaneko ◽  
Kenji Yasuoka ◽  
Ayori Mitsutake ◽  
Xiao Cheng Zeng

Multicanonical molecular dynamics simulations are applied, for the first time, to study the liquid-solid and solid-solid transitions in Lennard-Jones (LJ) clusters. The transition temperatures are estimated based on the peak position in the heat capacity versus temperature curve. For LJ31, LJ58 and LJ98, our results on the solid-solid transition temperature are in good agreement with previous ones. For LJ309, the predicted liquid-solid transition temperature is also in agreement with previous result.


2007 ◽  
Vol 447 (4-6) ◽  
pp. 236-240 ◽  
Author(s):  
V.G. Baidakov ◽  
S.P. Protsenko ◽  
Z.R. Kozlova

1966 ◽  
Vol 44 (22) ◽  
pp. 2651-2656 ◽  
Author(s):  
Isamu Nagata

The Kihara potential has been applied to the Lennard-Jones and Devonshire cell theory in place of the Lennard-Jones potential. The expressions for the internal energy, heat capacity, and entropy, as well as the compressibility, are given in excess over those of a perfect gas. A comparison between experimental data and the present theory is made.


2005 ◽  
Vol 60 (1-2) ◽  
pp. 23-28
Author(s):  
Akira Matsumoto

The thermodynamic quantities of Lennard-Jones gases, evaluated till the fourth virial coefficient, are investigated for an isobaric process. A partition function in the T-P grand canonical ensemble Y(T,P,N) may be defined by the Laplace transform of the partition function Z(T,V,N) in the canonical ensemble. The Gibbs free energy is related with Y(T,P,N) by the Legendre transformation G(T,P,N) = −kT logY(T,P,N). The volume, enthalpy, entropy, and heat capacity are analytically expressed as functions of the intensive variables temperature and pressure. Some critical thermodynamic quantities for Xe are calculated and drawn. At the critical point the heat capacity diverges to infinity, while the Gibbs free energy, volume, enthalpy, and entropy are continuous. This suggests that a second-order phase transition may occur at the critical point.


2021 ◽  
Author(s):  
Simon Stephan ◽  
Monika Thol ◽  
Jadran Vrabec ◽  
Hans Hasse

Literature data on the thermophysical properties of the Lennard-Jones fluid, which were sampled with molecular dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data were complemented by simulation data from the present work that were taken in regions in which previously only sparse data were available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility β, thermal pressure coefficient γ, internal energy u, isochoric heat capacity cv, isobaric heat capacity cp, Grüneisen parameter Γ, Joule–Thomson coefficient μJT, speed of sound w, Helmholtz energy a, and chemical potential) were considered, as well as data on the vapor–liquid equilibrium (for given T: vapor pressure ps, saturated liquid and vapor densities ρ′ and ρ″, respectively, enthalpy of vaporization Δhv, and as well as surface tension γ). The entire set of available data, which contains about 35 000 data points, was digitalized and included in a database, which is made available in the Supporting Information of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated pointwise using data from their respective vicinity and equations of state. Approximately 10% of all homogeneous bulk data were discarded as outliers. The vapor–liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius–Clapeyron equation, and by an outlier test. Seven particularly reliable vapor–liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporization—excluding the region close to the critical point.


2021 ◽  
Author(s):  
Martin P. Lautenschläger ◽  
Hans Hasse

Transport properties of fluids can be determined efficiently from non-equilibrium molecular dynamics simulations using the two-gradient method which was introduced recently. It is shown here that also thermal and caloric properties of fluids can be determined accurately and efficiently along with the transport properties using this method. In a single run, all these properties are obtained for a series of state points at different temperatures and constant pressure. The truncated and shifted Lennard-Jones (LJTS) fluid is studied here as a test case. Data are reported for about 700 state points in the range of (T = [0:7; 8:5] and ? = [0:2; 1:0]). Besides data on the thermal conductivity, shear viscosity, and selfdiffusion the following thermal and caloric properties were measured: pressure p, internal energy u, enthalpy h, isobaric heat capacity cp and thermal expansion coefficient ?p. The results of the thermal and caloric properties agree very well with those from an accurate equation of state from the literature. Also the shear rate dependence of these properties can be studied easily with the two-gradient method. Keywords: local equilibrium; Lennard-Jones fluid; isobaric heat capacity; thermal expansion coefficient


Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 459
Author(s):  
Rifat Mahmud ◽  
A.K.M. Monjur Morshed ◽  
Titan C. Paul

Size and thermal effect on molar heat capacity of liquid at constant volume (Cv) on a nanometer scale have been investigated by controlling the temperature and density of the liquid domain using equilibrium molecular dynamics (EMD) simulations. Lennard-Jones (LJ) type molecular model with confinement gap thickness (h) 0.585 nm to 27.8 nm has been used with the temperature (T) ranging from 100 K to 140 K. The simulation results revealed that the heat capacity of the nanoconfined liquid surpasses that of the bulk liquid within a defined interval of gap thickness; that the temperature at which maximum heat capacity occurs for a nanoconfined liquid vary with gap thickness following a power law, TCv,max = 193.4 × (h/a)−0.3431, ‘a’ being the lattice constant of Argon (solid) at 300 K; and that for a specified gap thickness and temperature, the confined liquid can exhibit a heat capacity that can be more than twice the heat capacity of the bulk liquid. The increase in heat capacity is underpinned by an increase in non-configurational (phonon and anharmonic modes of vibration) and configurational (non-uniform density distribution, enhanced thermal resistance, guided molecular mobility, etc.) contributions.


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