Computer simulations of freezing

Figure 8 An example of the decreasing heat requirement during primary drying at a chamber pressure of 0.15 torr. 5% mannitol maintained at -20°C during primary drying. Results obtained by computer simulation of freeze drying (see Ref. 3). Heavy curve Shelf Fluid. Light curve Shelf surface. Lightweight dashed curve Product Bottom. Heavy dashed curve Sublimation.

MJ Pikal. Use of laboratory data in freeze drying process design Heat and mass transfer coefficients and the computer simulation of freeze drying. J Parenter Sci Tech-nol 39 115-138, 1985. 

Hydrate nucleation is the process during which small clusters of water and gas (hydrate nuclei) grow and disperse in an attempt to achieve critical size for continued growth. The nucleation step is a microscopic phenomenon involving tens to thousands of molecules (Mullin, 1993, p. 173) and is difficult to observe experimentally. Current hypotheses for hydrate nucleation are based upon the better-known phenomena of water freezing, the dissolution of hydrocarbons in water, and computer simulations of both phenomena. Evidence from experiments shows that nucleation is a statistically probable (not deterministically certain see Section 3.1.3) process. 

Thanks to advancement of the computer technology computer simulations of processes related to water freezing are becoming feasible. The greatest advantage of the calculations is that they can provide insight to the structure and dynamics of the system at an atomic level, with resolution often inaccessible to experimental techniques. 

A computer simulation of the surface of the amorphous Si02 has been reported in Ref. [16]. It was accomplished in two steps. First, the bulk amorphous atomic structure was simulated by the usual MD melt-quench technique described above. Then a free surface was created by removing the periodic boundary condition in one dimension (Z) and freezing the bottom layer of atoms. After that the system was annealed at 1000 K and then cooled gradually to 300 K. 

A second important example of an entropic phase transition is the freezing transition of hard spheres. The first direct evidence for this transition came from the computer simulations of Wood and Jacobson, and Alder and Wainwright [5]. Initially, these results were received with a lot of scepticism (see, e.g. Ref. [6]) however, in... 

Ref. [32] includes results from computer simulations of a system composed of spherical particles interacting via a discontinuous potential that includes a hard core, a repulsive square part, and an attractive square well. This model system, with appropriate parameterization, presents a LLCP that is metastable with respect to freezing. The system also shows kt and Cp maximum lines, however, no density anomaly is observed. 

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]. 

Computer Simulations of the Melting and Freezing of Simple Systems Using an Array Processor... 

This functional form is derived from exact results in the dilute vapor and hydrodynamic solvent limits. The coefficients A, B, C and D used in modeling high density fluids are determined uniquely from the equation of state of the corresponding hard sphere reference system (33,34)- This hard sphere fluid chemical potential model has been shown to accurately reproduce computer simulation results for both homonuclear and heteronuclear hard sphere diatomics in hard sphere fluids up to the freezing point density (35) ... 

The minimum information covers chemical formula, molecular weight, normal boiling point, freezing point, liquid density, water solubility and critical properties. Additional properties are enthalpies of phase transitions, heat capacity of ideal gas, heat capacity of liquid, viscosity and thermal conductivity of liquid. Computer simulation can estimate missing values. The use of graphs and tables of properties offers a wider view and is strongly recommended. 

The evidence from the analytical model described above that there may be unequal melting and freezing temperatures for finite clusters, has led to a renewed interest in examining in detail the melting portion of the caloric curves of small clusters. In this section we review the early computer simulation work on phase changes in small clusters. We proceed to discuss recent detailed constant energy simulations and their relation to the conclusions of the analytical model proposed for the transition. 

Though the above argument can leave no doubt that in the jellium model there will be a localized assembly of electrons, i.e. a Wigner crystal, in the extremely low density limit, the actual analytic calculation of when the electron liquid, at absolute zero of temperature, freezes as the density is lowered has proved very delicate [20]. Eventually, this matter was settled using quantum Monte Carlo computer simulation by Ceperley and Alder [38], They found in this way that the crystallization first occurred at rs = 100. Herman and March [39] subsequently pointed out that, for the Wigner crystal phase, the theoretical expression [40,41]... 

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