Soft-sphere potential

Step 3a Adjust potential energy functions to yield a soft sphere potential by halving the atomic radii from their actual size and by using no rotational barriers. 

As a simple model for binary fluids, we consider in our MD simulation soft-sphere mixtures composed of Ni atoms of mass mi and diameter ai and atoms of mass m2 and dieimeter <72 in a volume V for a 3-d system or in an area S for a 2-d system the atoms interact through the purely repulsive soft-sphere potentials ... 

Excluded Volume Effects. These could be effective hard sphere potentials representing the finite size of the particles. Such potentials are important for the crystallization transition the left side of Figme 3.4 is an example. For ligated nanoparticles, the finite size is likely better represented by a soft sphere potential, the softness due to the steric interactions of the ligands (see below). 

Oligschleger and Schober also investigated the intermittent diffusion processes in supercooled liquids. They generated a glass using a modified soft-sphere potential. 

Figure 11 Some potential energy versus distance curves (a) hard-spheres potential, (b) soft-spheres potential, (c) Sutherland potential, (d) square-well potential (e) Kreglewski potential, (f) bireciprocal potential...

Note that, for = 0, the potential given above does not reduce to the Lennard-Jones (12-6) function, because the soft Lennard-Jones repulsive branch is replaced by a hard-sphere potential, located at r = cr. The results for the nonassociating Lennard-Jones fluid can be found in Ref. 159. 

Soft Spheres Fragility Invariance on The Repulsive Potential Softness. 

Block copolymer micelles with their solvent swollen corona are a typical example of soft spheres having a soft repulsive potential [61]. The potential has been derived by Witten und Pincus for star polymers [62] and is of form u(r) ln(r). It only logarithmically depends on the distance r and is therefore much softer compared to common r x-potentials such as the Lennard-Jones potential (x=12). The potential is given by... 

We would like to mention that RHNC is able to reproduce qualitatively accurate bridge functions inside the core, especially when a reference system (RS) of soft spheres is utilized rather than the conventional hard-sphere fluid. However, the prescription used to determine the RS requires a priori knowledge of both the RS and the system under investigation. This feature restricts the applicability of RHNC to sytems for which the EOS is available. The optimization of the RS proposed by Lado does not have such a drawback, but requires intensive computation since the optimization has to be performed at each state point. Furthermore, it was shown [85] that for the LJ potential, there exists a region around the critical point where the RHNC [54] has no solution. 

As in the case of two interacting soft plates, when the thicknesses of the surface charge layers on soft spheres 1 and 2 are very large compared with the Debye length 1/k, the potential deep inside the surface charge layer is practically equal to the Donnan potential (Eqs. (15.51) and (15.52)), independent of the particle separation H. In contrast to the usual electrostatic interaction models assuming constant surface potential or constant surface... 

Further studies by electron microscopy on some of the samples exhibiting the Pm3n cubic phase show the existence of grain bormdaries and stacking faults [118]. These are all consistent with the presence of quasi-spherical assemblies or more precisely to polyhedral-like micelles, and moreover suggest that the supramolecular spheres are deformable, interacting with one another through a relatively soft pair potential [119]. The majority of such quasi-spherical assemblies are thus distorted into an oblate shape. 

In the present work we study binary soft-sphere mixtures with a core-size ratio mass ratio m2/m = 2.0 and an equimolar concentration (ij = 0.5) for both 3-d and 2-d systems. Using a constant-temperature MD technique and the peiodic boundary conditions, we have carried out MD simulations for the models. The pair potential, Eq. (1), was cut off over the distance rlnumber density wm kept constant, i.e. n" = 0.8 the temperature was varied to achieve a desired Teff. The microscopic time scale was chosen to... 

Several models have been developed to describe these phenomena quantitatively, the main difference being the interaction potential between the particles. There are two major approaches the hard sphere and the soft sphere. The hard sphere assumes that the only interaction between particles is a strong repulsion at the point of contact. The soft sphere is more realistic and assumes a potential with a barrier and a primary minimum like in DLVO theory (Figure 11.8). 

The first attempt to evaluate the viscosities of a liquid crystal model system by computer simulation was made by Baalss and Hess [31]. They mapped a perfectly ordered liquid crystal onto a soft sphere fluid in order to simplify the interaction potential and thereby make the simulations faster. The three Mies-owicz were evaluated by using the SLLOD equations of motion. Even though the model system was very idealised, the relative magnitudes of the various viscosities were fairly similar to experimental measurements of real systems. 

The model system we consider here is 300 soft sphere particles interacting via a purely repulsive potential of the form ... 

A potential limction consists of one or more parameter sets that fit the equation and atom types to experimental data. Each of these functions usually contains a small number of adjustable parameters that can be used to optimize the simulations. There are live main potential functions the hard sphere (HS) potential, the soft sphere (SS) potential, Sutherland (S) potential, the Lennard-Jones potential, and the Buckingham (B) potential (2). This section provides a brief review of the most frequently used potential function [Lennard-Jones (LJ) potential] and its application for molecular modeling. 

---