Solid-fluid phase transition

Runge, K. J. Chester, G. V., Solid-fluid phase transition of quantum hard spheres at finite temperature, Phys. Rev. B 1988, 38, 135-162... 

Computer simulations of molecular models by MC and MD techniques have revolutionized our understanding of the solid-fluid phase transition. 

Alder and Wainwright [5,6] published the first paper of a molecular dynamics simulation of a condensed phase fluid system and this paper began a trend that did have a strong impact on statistical mechanics. These authors tackled one of the open questions of the day, whether a solid-fluid phase transition existed in a system of hard spheres. This problem could not be solved by existing analytical methods and Alder and Wainwright s simulation demonstrated that such analytically intractable problems could be studied and solved by direct MD simulation of the equations of motion of a many-body system. Of course, the simulation was modest by today s standards and was carried out on systems containing 32 and 108 hard spheres. This research set the stage for the development of MD as a basic tool in statistical mechanics. 

Pure solid + fluid phase equilibrium calculations are challenging but can, in principle, be modeled if the triple point of the pure solid and the enthalpy of fusion are known, the physical state of the solid does not change with temperature and pressure, and a chemical potential model (or equivalent), with known coefficients, for solid constituents is available. These conditions are rarely met even for simple mixtures and it is difficult to generalize multiphase behavior prediction results involving even well-defined solids. The presence of polymorphs, solid-solid transitions, and solid compounds provide additional modeling challenges, for example, ice, gas hydrates, and solid hydrocarbons all have multiple forms. 

The Camahan-Starling equation of state (4.5.4) has been extended by Mansoori et al. [16] to binary mixtures of hard spheres having different diameters. Binary mixtures of hard spheres exhibit fluid-solid phase transitions at packing fractions somewhat larger than that for the pure substance that is, at T) > 0.5. The exact state for the transition depends on composition and on the relative sizes of the spheres. We expect the density of the transition to increase as the size disparity increases the limited computer simulation data available support this expectation [17]. Certain kinds of hard-sphere mixtures are the simplest substances to exhibit a fluid-fluid phase transition [17], but those phase transitions are more like liquid-liquid than vapor-liquid. Analytic representations of the Z(r ) for hard-sphere and other hard-body fluids have been critically reviewed by Boublik and Nezbeda [18]. 

The objective of statistical mechanics is generally to develop predictive tools for computation of properties and local structure of fluids, solids and phase transitions from the knowledge of the nature of molecules comprising the systems as well as intra and intermolecular interactions. 

Miyahara M., Kanda H., Shibao M. and Higashitani K., Solid-liquid phase transition of Lennard-Jones fluid in slit pores nnder tensile condition, J. Chem. Phys. 112 (2000) pp. 9909-9916. 

To our knowledge, these are the first measurements of a lipid bilayer linear elastic response, i.e. the basic macroscopic characteristic of a solid structure. It was found that the membrane effective stiffness decreases down to zero (within experimental error) at T, which is the indication of a continuous gel-fluid phase transition. 

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 CS pressures are close to the machine calculations in the fluid phase, and are bracketed by the pressures from the virial and compressibility equations using the PY approximation. Computer simulations show a fluid-solid phase transition tiiat is not reproduced by any of these equations of state. The theory has been extended to mixtures of hard spheres with additive diameters by Lebowitz [35], Lebowitz and Rowlinson [35], and Baxter [36]. 

Reiss H and Hammerich ADS 1986 Hard spheres scaled particle theory and exact relations on the existence and structure of the fluid/solid phase transition J. Phys. Chem. 90 6252... 

Although Eqs. (33), (34), and especially (35), are useful they have a problem. They all predict that the hard sphere system is a fluid until = 1. This is beyond close packing and quite impossible. In fact, hard spheres undergo a first order phase transition to a solid phase at around pd 0.9. This has been estabhshed by simulations [3-5]. To a point, the BGY approximation has the advantage here. As is seen in Fig. 1, the BGY equation does predict that dp dp)j = 0 at high densities. However, the location of the transition is quite wrong. Another problem with the PY theory is that it can lead to negative values of g(r). This is a result of the linearization of y(r) - 1 that... 

Membranes are composed of phospholipids and proteins. The fatty acid composition of the phospholipids in a membrane influences how it is affected by the cold. In general, as the temperature of a cell is lowered the lipids in the membrane bilayer undergo a phase transition from a liquid crystalline (fluid) state to a gel (more solid) state. The temperature at which this transition takes place is very narrow for phospholipids composed of a simple mixture of fatty acids, but is quite broad for the phospholipids in cellular membranes. It is usually implied from various methods... 

Deposition of adamantane from petroleum streams is associated with phase transitions resulting from changes in temperature, pressure, and/or composition of reservoir fluid. Generally, these phase transitions result in a solid phase from a gas or a liquid petroleum fluid. Deposition problems are particularly cumbersome when the fluid stream is dry (i.e., low LPG content in the stream). Phase segregation of solids takes place when the fluid is cooled and/or depressurized. In a wet reservoir fluid (i.e., high LPG content in the stream) the diamondoids partition into the LPG-rich phase and the gas phase. Deposition of diamondoids from a wet reservoir fluid is not as problematic as in the case of dry streams [74, 75]. 

With the critical exponent being positive, it follows that large shifts of the critical temperature are expected when the fluid is confined in a narrow space. Evans et al. computed the shift of the critical temperature for a liquid/vapor phase transition in a parallel-plates geometry [67]. They considered a maximum width of the slit of 20 times the range of the interaction potential between the fluid and the solid wall. For this case, a shift in critical temperature of 5% compared with the free-space phase transition was found. From theoretical considerations of critical phenomena... 

The study of how fluids interact with porous solids is itself an important area of research [6], The introduction of wall forces and the competition between fluid-fluid and fluid-wall forces, leads to interesting surface-driven phase changes, and the departure of the physical behavior of a fluid from the normal equation of state is often profound [6-9]. Studies of gas-liquid phase equilibria in restricted geometries provide information on finite-size effects and surface forces, as well as the thermodynamic behavior of constrained fluids (i.e., shifts in phase coexistence curves). Furthermore, improved understanding of changes in phase transitions and associated critical points in confined systems allow for material science studies of pore structure variables, such as pore size, surface area/chemistry and connectivity [6, 23-25],... 

Qads.(max) = 5.7 molecules by unit cell). Generally speaking, Qacis.(max) is closely related to the molecular size, as it is observed for the other molecular species. Secondly, as shown on Figure 5, sorption isotherm sub-step observation could be another signature of zeolite inner surface influence. Such isotherm sub-step reflects a phase transition existence between a fluid phase and a solid phase stabilized by the inner surface sorption sites. 

The initial hydration rate v and the equilibrium hydration amount were obtained as parameters reflecting the hydration behavior of LB films (see Figure 8). Temperature dependencies of the hydration behavior (v0and W ) of 10 layers of DMPE (Tc = 49 °C) LB films are shown in Figure 9. Large W and v0 values were observed only around the phase transition temperature (7C) of DMPE membranes. Thus, DMPE LB films were hydrated only near the Tc, but not in the solid state below the Tc and in the fluid state above the Tc. This indicates that the... 

The physical-chemical properties of a supercritical fluid are between those of liquids and gases supercritical fluids (SCFs) indicate the fluid state of a compound in pure substance or as the main component above its critical pressure (pc) and its critical temperature (Tc), but below the pressure for phase transition to the solid state, and in terms of SCF processing, a density close to or higher than its critical density. 

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