Soft-core models

Hiwatari Y. The applicability of the soft core model of fluids to dynamical properties of simple liquids, Progr. Theor. Phys. 53, 915-28 (1975). 

The soft-core model may be more convenient in molecular dynamics simulation, since a continuously differentiable potential is available to calculate the force. In the case of a hardcore potential, collision times of all atom pairs have to be monitored and used to control the time step. 

Tanemura, M., Hiwatari, Y., Matsuda, H., Ogawa, T., Ogita, N., md Ueda, A. (1977) Geometrical Analysis of Crystallization of the Soft-Core Model, Prog. Theor. Phys., Vol. 58, pp.1079-1095. 

A novel feature of this particular model relates to the terminus of the LDL-HDL coexistence line. The introduction of the orientational degrees of freedom through the x variables leads to a richer phase diagram. The presence of an extra component, the orientation, in accordance with Gibbs phase rule [42], gives rise to a critical line ending the coexistence between the two phases in place of the critical point presented by the isotropic soft-core models. 

Taking this value for CmocL in account reduces the difference with the standard model somewhat. The actual value of the modulus then can reasonably well be described by the affine network model for the LJ system. Including Cmod = 1.5 one gets G% 0.027. Using p = 0.37cr (the density of the elastically active part) one gets within the affine model an effective strand length of Neff 13-14, while the cluster analysis yields Ng/f 11. The soft core model is somewhere in between the affine and the phantom model. 

From Field-Theoretic Fiamiltonians to Particie-Based Modeis Soft-Core Models 211... 

From Field-Theoretic Hamiltonians to Particle-Based Models Soft-Core Models... 

Multicomponent melts that are commonly found in such varied situations as material fabrification, reinforcement, blending, and so on are discussed in the chapter by Muller ( Computational Approaches for Structure Formation in Multi-component Polymer Melts ). Only equilibrium properties are discussed along with computational approaches for coarse-grained models in the mean field approximation. Both hard-core and soft-core models are used to cover a multitude of scales of length, time, and energy. Attention is also paid to methods that go beyond the mean field approximation. 

Instead of the hard-sphere model, the Lennard-Jones (LJ) interaction pair potential can be used to describe soft-core repulsion and dispersion forces. The LJ interaction potential is... 

More realistic treatment of the electrostatic interactions of the solvent can be made. The dipolar hard-sphere model is a simple representation of the polar nature of the solvent and has been adopted in studies of bulk electrolyte and electrolyte interfaces [35-39], Recently, it was found that this model gives rise to phase behavior that does not exist in experiments [40,41] and that the Stockmeyer potential [41,42] with soft cores should be better to avoid artifacts. Representation of higher-order multipoles are given in several popular models of water, namely, the simple point charge (SPC) model [43] and its extension (SPC/E) [44], the transferable interaction potential (T1PS)[45], and other central force models [46-48], Models have also been proposed to treat the polarizability of water [49],... 

More refined continuum models—for example, the well-known Fumi-Tosi potential with a soft core and a term for attractive van der Waals interactions [172]—have received little attention in phase equilibrium calculations [51]. Refined potentials are, however, vital when specific ion-ion or ion-solvent interactions in electrolyte solutions affect the phase stability. One can retain the continuum picture in these cases by using modified solvent-averaged potentials—for example, the so-called Friedman-Gumey potentials [81, 168, 173]. Specific interactions are then represented by additional terms in (pap(r) that modify the ion distribution in the desired way. Finally, there are models that account for the discrete molecular nature of the solvent—for example, by modeling the solvent as dipolar hard spheres [174, 175]. 

Taylor, R. D., Jewsbury, P. J., and Essex, J. W. (2003) FDS flexible ligand and receptor docking with a continuum solvent model and soft-core energy function. J. Comput. Chem. 24, 1637-1656. 

DPMs can also be used to understand the influence of particle properties on fluidization behavior. It has been demonstrated that ideal particles with restitution coefficient of unity and zero coefficient of friction, lead to entirely different fluidization behavior than that observed with non-ideal particles. Simulation results of gas-solid flow in a riser reactor reported by Hoomans (2000) for ideal and nonideal particles are shown in Fig. 12.8. The well-known core-annulus flow structure can be observed only in the simulation with non-ideal particles. These comments are also applicable to simulations of bubbling beds. With ideal collision parameters, bubbling was not observed, contrary to the experimental evidence. Simulations with soft-sphere models with ideal particles also indicate that no bubbling is observed for fluidization of ideal particles (Hoomans, 2000). Apart from the particle characteristics, particle size distribution may also affect simulation results. For example, results of bubble formation simulations of Hoomans (2000) indicate that accounting... 

The results of these calculations for this rather simple system indicate that our proposed technique produces the sought for effects, i.e., an effective interaction of simple form that yields a reasonable numerical result in a tractable model space. The need to treat co as a variable parameter, in order to obtain the same result as an exact calculation for He using the same potential, indicates the known deficiencies in our calculations, such as the use of the Reid-soft core potential, instead of one of the more attractive meson-exchange potentials, and the lack of a self-consistent basis space. 

The mean spherieal approximation (MSA) theory for fluids originated as the extension to eontinuum fluids of the spherical model for lattice gases. In praetice it is usually applied to potentials with spherical hard cores, although extensions to soft core and non-spherical core potentials have been discussed. 

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