Equilibrium bond orientational ordering

Figure 3 shows an ordering map for this Lennard-Jones system, with the translational order t (of Eq. [2]) plotted against the bond-orientational order Qs (of Eq. [5]). It can be observed that the data, collected over a wide range of temperatures and densities, collapse onto two distinct equilibrium branches... 

Fig. 9. Two-parameter ordering phase diagram for a system of 500 identical hard spheres (Truskett et ai, 2000 Torquato et ai, 2000). Shown are the coordinates in structural order parameter space (r, ) for the equilibrium fluid (dot-dashed), the equilibrium FCC crystal (dashed), and a set of glasses (circles) produced with varying compression rates. Here, r is the translational order parameter from (26) and is the bond-orientational order parameter Q( from (25) normalized by its value in the perfect FCC crystal ( = Each circle...

The melting, or dissolution, of long chain molecules at high dilution is a natural consequence of phase equilibrium. The dissolution process results in the separation of the solute molecules and is usually accompanied by a change in the molecular conformation of the chain from an ordered structure to a statistical coil. However, it is also possible for the individual polymer molecules to maintain the conformation in solution that is typical of the crystalline state. This is particularly true if the steric requirements that favor the perpetuation of a preferred bond orientation or the ordered crystalline structure can be maintained by intramolecular bonding, such as hydrogen bonds. Further alterations in the thermodynamic environment can cause a structural transformation in the individual molecules. Each molecule is then... 

Methane, CH4, has an equilibrium nuclear conformation with four bonds oriented symmetrically, with all bond angles equal to 109.5 . In order to create LCAOMOs that contain only two atomic orbitals and point in these directions, we create a third set of hybrid orbitals, the 2sp hybrid orbitals ... 

This bimodal dynamics of hydration water is intriguing. A model based on dynamic equilibrium between quasi-bound and free water molecules on the surface of biomolecules (or self-assembly) predicts that the orientational relaxation at a macromolecular surface should indeed be biexponential, with a fast time component (few ps) nearly equal to that of the free water while the long time component is equal to the inverse of the rate of bound to free transition [4], In order to gain an in depth understanding of hydration dynamics, we have carried out detailed atomistic molecular dynamics (MD) simulation studies of water dynamics at the surface of an anionic micelle of cesium perfluorooctanoate (CsPFO), a cationic micelle of cetyl trimethy-lainmonium bromide (CTAB), and also at the surface of a small protein (enterotoxin) using classical, non-polarizable force fields. In particular we have studied the hydrogen bond lifetime dynamics, rotational and dielectric relaxation, translational diffusion and vibrational dynamics of the surface water molecules. In this article we discuss the water dynamics at the surface of CsPFO and of enterotoxin. 

The order of magnitude of such a dipole will be equal to the product of the charge on an electron (1.6 x 10 19 C) and a typical bond length (10 10 m) giving a value of 10" 29 Cm. The old electrostatic Debye unit of molecular dipoles was in fact equivalent to 3.335 x 10 30 Cm. Orientation of such molecular dipoles will clearly produce an extra contribution to the molar polarisation in addition to dipoles induced by the applied field, and it is not unreasonable to expect that the equilibrium degree of orientation in a given field will depend on temperature. 

The crystal structure of human albumin located Cysteine-34 at the turn between helices h2 and h3 with the side chain sulfhydryl group oriented toward the protein interior, consistent with EPR studies suggesting that it is 950 pm below the surface. Sadler has demonstrated by H NMR studies that the cys-34 residue must move outward from the crevice created by the helices before it can react to form disulfide bonds or bind to Et3PAu+ derived from auranofin. These structural observations are consistent with the kinetic mechanism for the reactions of albumin with auranofin and its triisopropylphosphine analogue, which revealed a slow crevice opening reaction in equilibrium between open and closed forms of albumin. The kinetic model accounts for a process that is first order in protein when the auranofin is present in excess. 

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