Density component, computer-simulated

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present hr the interatomic potential (e.g. atoms interacting tlirough a Leimard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of tire critical isothemr in the P - Vplane. 

The wall-PRISM theory has also been implemented for binary polymer blends. For blends of stiff and flexible chains the theory predicts that the stiffer chains are found preferentially in the immediate vicinity of the surface [60]. This prediction is in agreement with computer simulations for the same system [59,60]. For blends of linear and star polymers [101] the theory predicts that the linear polymers are in excess in the immediate vicinity of the surface, but the star polymers are in excess at other distances. Therefore, if one looks at the integral of the difference between the density profiles of the two components, the star polymers segregate to the surface in an integrated sense, from purely entropic effects. 

Our findings for rs and th may be compared with results of computer simulations for water. Values between 1 and 2 ps are stated for the average lifetime of a hydrogen bond by different authors (121-123), in satisfactory agreement with our experimental values. It is also interesting to compare with the frequency shift correlation function of the vibrational modes of water obtained from MD computations (124). Recently a slower component of this function with an exponential time constant of 0.8 ps was predicted for HDO in D20 at 300 K and a density of 1.1 g/cm3 (pressure %2 kbar). The existence of the slow component is a necessary prerequisite for the observation of spectral holes and the spectral relaxation time rs reported here. The faster component of the frequency shift correlation function with rc = 50 fs (124) represents rapid fluctuations that contribute to the spectral bandwidths of the spectral species and of the spectral holes. 

These dynamic features in the trans-bUayer direction can be averaged for the collective behavior of many lipid molecules and plotted as the averaged electron density profiles of various Upid groups and segments. In computer simulations, the electron density profile can be calculated on the basis of the atomic number and the so-called partial charges for aU heavy atoms (i.e., G, O, N, and P). The summation of all components gives the total electron density profile, which is typically what is measured experimentally by X-ray diffraction. Figure 3.6 shows an example of an... 

Computer simulation has been used to obtain sudi local thermodynamic functions as the energy density, < (z), the transverse component of Irving and Kirkwood s definition of the pressure tensor.s" Pr(z), and hence the height of the related surface of tension in a planar interface.s° The essential arbitrariness of these calculations has been discussed in 4.3 and 4.10. 

Molecular level computer simulations based on molecular dynamics and Monte Carlo methods have become widely used techniques in the study and modeling of aqueous systems. These simulations of water involve a few hundred to a few thousand water molecules at liquid density. Because one can form statistical mechanical averages with arbitrary precision from the generated coordinates, it is possible to calculate an exact answer. The value of a given simulation depends on the potential functions contained in the Hamiltonian for the model. The potential describing the interaction between water molecules is thus an essential component of all molecular level models of aqueous systems. 

From such spectroscopic studies it is also possible to infer the thermodynamic state dependence of the local density enhancement effects. For example, Carlier and Randolph examined the bulk-density dependence of the effective local-solvent-density, Pc, around di-tert-butyl nitroxide radicals in SC ethane via the spectroscopic method of electron paramagnetic resonance (EPR). These authors observed a maximum in local density enhancement (pc/p). Figure 6, to occur at p (l/2)pc consistent with the predictions of Chialvo and Cummings for the direct component of the density enhancement. While such spectroscopic studies are very suggestive, they do not actually allow for direct observation of local density enhancements. As a result, these methods can provide only cumulative, effective values of the local density enhancement and little information about the spatial distribution of these density effects. It is here that computer simulation and other computational techniques can contribute significantly to our understanding of SCF solvation. 

The effect of a structured surface on the crystallization of hard-sphere colloids has been extensively studied in experiments [87, 88, 89, 90], These experiments indicate that crystallization on a template is induced at densities below freezing. This finding is supported by computer simulations of hard spheres in contact with a patterned substrate, by Heni and Lowen [91], These simulations indicate that surface freezing already sets in 29% below the coexistence pressure. Furthermore the effect of a surface on crystallization has also been studied in mixtures of binary hard-spheres [92, 93] and colloid-polymer mixtures [94, 95, 96], In both systems surface crystallization was found to take place before bulk fluid-solid coexistence. In the systems studied in Refs. [92, 93, 94, 95, 96], depletion forces favor the accumulation of the larger component on the wall, and this should facilitate surface crystallization [97]. 

Different theories have been proposed to explain hydrophobic attraction. Like on hydrophilic surfaces, the structure of water at hydrophobic surface is different from the bulk structure. Computer simulations [1211, 1212], sum-frequency vibrational spectroscopy [1163], X-ray [1078, 1213, 1214], and neutron reflectivity [1076, 1077] show a layer of up to 1 nm with a reduced density and an increased order. When two hydrophobic surfaces approach each other at some point, the surface layers overlap and lead to an attractive force [1212,1215,1216]. This force is, however, short ranged and can certainly not explain the long-range component. 

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