Isotropic soft interactions

First we introduce the isotropic interaction which results from the mixing of rods and solvents. The previous theory, without the mixing contribution to entropy, is only applicable to an athermal system. If there is a mixing entropy contribution, the free energy in Equation 2.39 is implemented by a term x4>ns, where x is the Flory-Huggins interaction parameter. Flory called the mixing term the isotropic soft interaction to distinguish it from the steric interaction of rods. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Later Flory further took the two soft interactions between the molecules into account. The anisotropic interaction is associated with molecular orientations while the isotropic one is irrelevant of the molecular orientation. In fact, the anisotropic interaction was the basis of another well-known theory in liquid crystals — Maier-Saupe theory (Maier Saupe, 1959). Flory successfully captured the essence of the theory. 

Figure 14 (a) Schematization of the isotropic nematic transition for molecularly dispersed polymers (b) closed supramolecular polymers (c) open (linear) supramolecular assemblies. Coupling of contact interactions ( ) with hard and soft interactions (—) causes growth simultaneous to orientation for case (c). (From A. Ciferri. Liq. Cryst 26 489, 1999. Copyright 1999 Taylor Francis.)... 

The growth of orientational correlations and the slow down of collective orientational dynamics were subsequently investigated using a soft potential [106]. Allen and Warren (AW) studied a system consisting of N = 8000 particles of ellipsoids of revolution, interacting with a version of the Gay-Beme potential, GB (3, 5, 1, 3), originally proposed by Berardi et al. [107]. AW computed the direct correlation function, c( 1, 2), in the isotropic phase near the I-N transition. The direct correlation function is defined through the Omstein-Zemike equation [108]... 

The chemical shielding, dipole-dipole, spin-spin indirect coupling or J-coupling, spin-rotation, and hyperfine couplings represent the major internal magnetic interactions. The quadrupolar interaction has an electrostatic character. All these interactions have a tensorial character, ie, are function on the ori-entation of the principal axes of the tensor relative to the direction of Bq. They are relevant for solid polymers below and around the glass transition temperatures. For polymer in solution or for soft polymers fast molecular motions average these anisotropic interactions to isotropic or residual values which can be zero. Detailed description of the properties of these spin interactions can be found in References 1-9. 

Competition between two different local particle arrangements, arising from either directional or core-softened isotropic forces, is usually deemed to be responsible for anomalous thermodynamic behavior. However, our results show that the same behaviors may also occur for isotropic interactions characterized by a repulsion that is only marginally softened and yields a single structure at a local level. Such potentials can be relevant in the realm of soft matter, where engineering interparticle forces is possible, and also for hard matter under extreme conditions, where pressure-triggered rearrangements of the crystal structure induce a partial... 

Aggregation in colloidal systems can be introduced by various mechanism. Attractive interactions between the colloids is the most prominent example. Another possibility is to confine the colloids in one phase of a phase separating mixture, e.g., in the isotropic phase of a liquid crystalline fluid that is undergoing the isotropic-to-nematic transition [52, 53]. This unusual soft solid consists of a foam hke structure, where the bubbles are filled with liquid crystal in the nematic phase and the colloids are confined in the walls separating the bubbles [54]. 

We describe two numerical procedures for creating isotropically compressed MS packings of frictionless particles at jamming onset (1) a Lubachevsky-Stillinger (LS) [18,19] method for hard particles and (2) a dissipative MD method for soft particles that interact via purely repulsive contact forces [13]. 

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