scholarly journals Low melting temperature and liquid surface layering for pair potential models

2002 ◽  
Vol 117 (23) ◽  
pp. 10777-10788 ◽  
Author(s):  
E. Velasco ◽  
P. Tarazona ◽  
M. Reinaldo-Falagán ◽  
E. Chacón
Keyword(s):  
Melting Temperature ◽  
Liquid Surface ◽  
Pair Potential ◽  
Potential Models ◽  
Surface Layering

ON A MAPPING BETWEEN HARD-CORE POTENTIAL MODELS FOR NEMATOGENS AND CONTINUOUS ONES

1995 ◽  
Vol 09 (01) ◽  
pp. 85-102 ◽  
Author(s):  
S. ROMANO
Keyword(s):  
Field Theory ◽  
Nearest Neighbor ◽  
Pair Potential ◽  
Hard Core ◽  
Particle Orientation ◽  
Molecular Field ◽  
Formal Similarity ◽  
Potential Models ◽  
Core Potential ◽  
Molecular Field Theory

Hard-core nematogenic models can be studied using Onsager’s theory, and, on the other hand, continuous interaction potentials can be investigated using the molecular field approach pioneered by Maier and Saupe. Comparison between these treatments shows a certain formal similarity, reflecting their common variational root; on this basis, hard-core potential models can be mapped on separable continuous ones, via their excluded volume. As a specific example, we have, therefore, considered hard spherocylinders and hence the continuous potential model(s) [Formula: see text] here uj denotes the unit vector defining particle orientation, xj denotes the coordinate vector of its center of mass, and ∊ is a positive quantity setting temperature and energy scales(i.e. T*=kBT/∈). The |sin| function can be expanded in a series of Legendre polynomials of even order, with a dominant P2 term; particles’ centers of mass were associated with a simple-cubic lattice, the function ɸ(r) was truncated at nearest-neighbor separation, and values of the two parameters p and q were chosen so as to make contact with the Lebwohl-Lasher lattice model, i.e. [Formula: see text]. The resulting pair potential was studied by molecular field theory and by computer simulation; molecular field theory predicts a first-order transition at [Formula: see text], whereas the result obtained by simulation was [Formula: see text]; comparison with the Lebwohl-Lasher model shows that the higher-order interactions contained in the potential tend to increase the transition temperature towards its molecular field limit.

Predictions of Adsorption Enthalpy on Graphitic Surfaces Using Statistical Thermodynamics

2013 ◽  
Author(s):  
Aaron P. Wemhoff
Keyword(s):  
Solid Surface ◽  
Fluid Model ◽  
Pair Potential ◽  
Statistical Thermodynamic ◽  
Intermolecular Potentials ◽  
Adsorption Enthalpy ◽  
Potential Models ◽  
Lennard Jones ◽  
Fluid Interaction ◽  
Molecule Interaction

A method is proposed to estimate the enthalpy associated with the desorption of liquid molecules away from a solid surface as a function of temperature using a generic statistical thermodynamic formulation with known intermolecular potentials. This paper specifically focuses on coupling the well-known Redlich-Kwong fluid model with the interactive pair potential models between fluid molecules and a graphite surface. An example is applied where an approximate Lennard-Jones 6–12 intermolecular model dictates fluid-fluid molecule interaction, while the Steele potential is applied for the graphite-fluid interaction. Predictions suggest that the adsorption enthalpy of methanol on graphite is approximately 0.1 J/m2. A new metric is also established that suggests the qualitative magnitude of adsorption enthalpy for a variety of fluids, with alcohols and acetone appearing to be the most favorable.

Embedded-Atom and Related Methods for Modeling Metallic Systems

MRS Bulletin ◽  
1996 ◽  
Vol 21 (2) ◽  
pp. 24-28 ◽  
Author(s):  
Stephen M. Foiles
Keyword(s):  
Local Density ◽  
Pair Potential ◽  
Defect Structures ◽  
Generic Properties ◽  
Potential Models ◽  
Potential Term ◽  
Embedded Atom ◽  
Pair Potentials ◽  
Dependent Part ◽  
Metallic Systems

This article discusses simple but realistic models of the bonding in metallic systems. As is discussed in the introduction, such methods are valuable both to study complex systems that are intractable with more rigorous methods and to study generic properties that do not depend on the fine details of the energetics. In addition, simple models are useful for gaining a physical understanding of a system.As discussed in the article by Vitek, a great deal of progress in the understanding of defect structures has been gained by the use of constant-volume pair potentials, that is, pair-potential models that include a volume-dependent term. In this picture, the energy is assumed to have two parts, a large density-dependent but structure-independent part and a structure-dependent part that is represented by pair interactions. This view follows from a physical picture where the metal is viewed as a uniform electron gas and the interactions between the atoms are obtained by performing perturbation theory on this reference system. This approach has a serious limitation, though, in that it is restricted to situations where the system is essentially uniform such as when the bulk or defects do not introduce significant changes in the local density. This is true for two reasons. First, there is not a clear prescription for how the structure-independent part of the energy should be treated in an inhomogeneous region. This is a serious problem since a large part of the binding energy is included in this term. Second, the pair-potential term in this picture depends on the overall density. In the vicinity of a inhomogeneity such as a surface, there is no prescription for how the pair-potential term should vary.

Computer Simulation Study of Classical Spin Models in Two Dimensions with Long-Range Ferromagnetic Interactions Anisotropic in Spin Space

1998 ◽  
Vol 12 (18) ◽  
pp. 1871-1885 ◽  
Author(s):  
S. Romano ◽  
Valentin A. Zagrebnov
Keyword(s):  
Long Range ◽  
Pair Potential ◽  
Two Dimensions ◽  
Spin Space ◽  
Potential Models ◽  
Classical Spin ◽  
Site Cluster ◽  
Invariant Pair ◽  
Ferromagnetic Interactions ◽  
Ordering Transition

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k ∈ Z2}, and interacting via a translationally invariant pair potential, of the long-range ferromagnetic form, anisotropic in spin space [Formula: see text] here a ≥ 0, b ≥ 0, σ > 2, ∊ is a positive constant setting energy and temperature scales (i.e. T*=kBT/∊), xj denotes dimensionless coordinates of lattice sites, and uj,α cartesian spin components; our discussion has been specialized to the extreme, O(2)-symmetric, case 0=a < b. When 2 < σ < 4, the potential model can be proven to support an ordering transition taking place at finite temperature; on the other hand, when σ ≥ 4 a Berezinskiǐ–Kosterlitz–Thouless-like transition takes place. Two potential models defined by σ=3 and σ=4, respectively, have been characterized quantitatively by Monte Carlo simulation. For σ=3, comparison is also reported with other theoretical treatments, such as Molecular Field and Two Site Cluster approximations.

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