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Gibbs phase transitions

Panagiotopoulos A Z 1995 Gibbs ensemble techniques Observation, Prediction and Simuiation of Phase Transitions in Oompiex Fiuids ed M Baus, L F Rull and J-P Ryckaert, vol 460 NATO ASi Series O (Dordrecht Kluwer) pp 463-501... [Pg.2285]

Figure 4.3 Behavior of thermodynamic variables at T for an idealized phase transition (a) Gibbs free energy and (b) entropy and volume. Figure 4.3 Behavior of thermodynamic variables at T for an idealized phase transition (a) Gibbs free energy and (b) entropy and volume.
Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... [Pg.87]

In this section we review several studies of phase transitions in adsorbed layers. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo, Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. Phase diagrams of fluids with internal quantum states are analyzed. Adsorbed layers of H2 molecules at a full monolayer coverage in the /3 X /3 structure have a higher transition temperature to the disordered phase compared to the system with the heavier D2 molecules this effect is... [Pg.97]

Fig. 16. Gibbs energy-temperature diagram if FCC and ECC are present in the system. Ai-isotropic (undeformed) melt, A2-deformed melt (nematic phase) points 1 and 4 - melting temperatures of FCC and ECC under unconstrained conditions (transition into isotropic melt) points V and 2 -melting temperatures of FCC and ECC under isometric conditions (transition into nematic phase), point 3 - melting temperature of nematic phase (transition into isotropic melt but not completely randomized)... Fig. 16. Gibbs energy-temperature diagram if FCC and ECC are present in the system. Ai-isotropic (undeformed) melt, A2-deformed melt (nematic phase) points 1 and 4 - melting temperatures of FCC and ECC under unconstrained conditions (transition into isotropic melt) points V and 2 -melting temperatures of FCC and ECC under isometric conditions (transition into nematic phase), point 3 - melting temperature of nematic phase (transition into isotropic melt but not completely randomized)...
We will be looking at first-order phase transitions in a mixture so that the Clapeyron equation, as well as the Gibbs phase rule, apply. We will describe mostly binary systems so that C = 2 and the phase rule becomes... [Pg.405]

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... [Pg.125]

Smit et al. [19] used the partition function given by (10.4) and a free energy minimization procedure to show that, for a system with a first-order phase transition, the two regions in a Gibbs ensemble simulation are expected to reach the correct equilibrium densities. [Pg.358]

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... [Pg.65]

During each phase transition of the type illustrated here, both of the intensive parameters P and T remain constant. Because of the difference in density however, when a certain mass of liquid is converted into vapour, the total volume (extensive parameter) expands. From the Gibbs-Duhem equation (8.8) for one mole of each pure phase,... [Pg.500]

Figure 9 Minima in the Gibbs potential in the vicinity of a co-existence curve curve and the critical point for a phase transition in a one-component system. Figure 9 Minima in the Gibbs potential in the vicinity of a co-existence curve curve and the critical point for a phase transition in a one-component system.
The Landau theory predicts the symmetry conditions necessary for a transition to be thermodynamically of second order. The order parameter must in this case vary continuously from 0 to 1. The presence of odd-order coefficients in the expansion gives rise to two values of the transitional Gibbs energy that satisfy the equilibrium conditions. This is not consistent with a continuous change in r and thus corresponds to first-order phase transitions. For this reason all odd-order coefficients must be zero. Furthermore, the sign of b must change from positive to negative at the transition temperature. It is customary to express the temperature dependence of b as a linear function of temperature ... [Pg.49]

It is easily shown that a first-order phase transition is obtained for cases were d < 0, whereas behaviour at the borderline between first- and second-order transitions, tricritical behaviour, is obtained for d = 0. In the latter case the transitional Gibbs energy is... [Pg.50]

Figure 5.2 Graph of molar Gibbs function Gm as a function of temperature. Inset, at temperatures below r(meit) the phase transition from liquid to solid involves a negative change in Gibbs function, so it is spontaneous... Figure 5.2 Graph of molar Gibbs function Gm as a function of temperature. Inset, at temperatures below r(meit) the phase transition from liquid to solid involves a negative change in Gibbs function, so it is spontaneous...
Second-order phase transitions are those for which the second derivatives of the chemical potential and of Gibbs free energy exhibit discontinuous changes at the transition temperature. During second-order transitions (at constant pressure), there is no latent heat of the phase change, but there is a discontinuity in heat capacity (i.e., heat capacity is different in the two... [Pg.64]

However, a more realistic model for the phase transition between baryonic and quark phase inside the star is the Glendenning construction [16], which determines the range of baryon density where both phases coexist. The essential point of this procedure is that both the hadron and the quark phase are allowed to be separately charged, still preserving the total charge neutrality. This implies that neutron star matter can be treated as a two-component system, and therefore can be parametrized by two chemical potentials like electron and baryon chemical potentials [if. and iin. The pressure is the same in the two phases to ensure mechanical stability, while the chemical potentials of the different species are related to each other satisfying chemical and beta stability. The Gibbs condition for mechanical and chemical equilibrium at zero temperature between both phases reads... [Pg.129]

As mentioned earlier, the Gibbs energy of adsorption can be analyzed using one of two independent electrical variables potential or charge density. The problem was discussed by Parsons and others, but it was not unequivocally solved because both variables are interconnected. Recent studies of the phase transition occurring at charged interfaces, performed at a controlled potential, show that if the potential is... [Pg.46]

The X transition in liquid helium shown in Figures 11.5 and 11.6 is a second-order transition. Most phase transitions that follow the Clapeyron equation exhibit a nonzero value of A5m and AYmi that is, they show a discontinuity in 5 and Fm. the first derivatives of the Gibbs free energy Gm- Thus, they are caHA A first-order transitions. In contrast, the X transition shows a zero value of A5m and AVm and exhibits discontinuities in the second derivatives of Gm, such as the heat capacity Cpm-... [Pg.273]

The excess thermodynamic properties correlated with phase transitions are conveniently described in terms of a macroscopic order parameter Q. Formal relations between Q and the excess thermodynamic properties associated with a transition are conveniently derived by expanding the Gibbs free energy of transition in terms of a Landau potential ... [Pg.109]

Salje (1985) interpreted overlapping (displacive plus Al-Si substitutional) phase transitions in albite in the light of Landau theory (see section 2.8.1), assigning two distinct order parameters Q n and to displacive and substitutional disorder and expanding the excess Gibbs free energy of transition in the appropriate Landau form ... [Pg.356]


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See also in sourсe #XX -- [ Pg.310 ]

See also in sourсe #XX -- [ Pg.310 ]




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