Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation

Kofke, David A.

doi:10.1080/00268979300100881

Cited by 339 publications

(222 citation statements)

References 8 publications

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“…Therefore the determination of the phase diagram reduces to the calculation of the coexistence curves. We use a combination of Helmholtz free energy calculations [7] and the so-called Kofke integration method [8] to trace out the coexistence curves. In this method Helmholtz free energy calculations are used to obtain phase coexistence points from which Kofke integration can be started to trace the rest of the coexistence curves.…”

Section: Model and Methodsmentioning

confidence: 99%

Phase diagrams of hard-core repulsive Yukawa particles

Hynninen

Dijkstra²

2003

Phys. Rev. E

152

229

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Using computer simulations we study the phase behaviour of hard spheres with repulsive Yukawa interactions and with the repulsion set to zero at distances larger than a density-dependent cut-off distance. Earlier studies based on experiments and computer simulations in colloidal suspensions have shown that the effective colloid-colloid pair interaction that takes into account many-body effects resembles closely this truncated Yukawa potential. We present a phase diagram for the truncated Yukawa system by combining Helmholtz free energy calculations and the Kofke integration method. Compared to the non-truncated Yukawa system we observe (i) a radical reduction of the stability of the body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the face centred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly any shift of the (FCC) melting line when compared with the (BCC) melting line for the full Yukawa potential for sufficiently high salt concentrations, i.e. truncation of the potential does not affect the location of the solid-fluid line but replaces only the BCC phase with the FCC at the melting line. We compare our results with earlier results on the truncated Yukawa potential and with results from simulations where the full many-body Poisson-Boltzmann problem is solved.

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Section: Model and Methodsmentioning

confidence: 99%

Phase diagrams of hard-core repulsive Yukawa particles

Hynninen

Dijkstra²

2003

Phys. Rev. E

152

229

View full text Add to dashboard Cite

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“…One necessary (but not sufficient) condition to have both upper and lower critical points is (26) to satisfy conditions (19) and (27) to satisfy (18). The second condition would require that the minimum of the mapping curve is lower than the critical temperature of the original system without solvent ( fig.…”

Section: Closed Loop Phase Diagrammentioning

confidence: 99%

“…To determine the solid-liquid coexistence curve we use Gibbs-Duhem integration proposed by Kofke [26,27]. This method is based on the integration of the Clausius-Clapeyron equation:…”

Section: Modification Of the Clausius-clapeyron Equation In The Presementioning

confidence: 99%

Role of solvent for globular proteins in solution

Shiryayev

Pagan

Gunton

et al. 2005

The Journal of Chemical Physics

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The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In particular we find for appropriate choices of parameters upper critical points, lower critical points and even closed loops with both upper and lower critical points, similar to one found before [1]. In the general case of systems whose interactions are not attractive square wells, this mapping procedure can be a first approximation to understand the phase diagram in the presence of solvent. We also present simulation results for both the square well model and a modified Lennard-Jones model.

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“…However, brute force computational power is not the only key to the success of simulation studies; much credit is due to the development of simulation techniques for the determination of phase equilibria. These techniques are the Gibbs ensemble Monte Carlo 19 and the NPTϩtest particle methods, 20 which are very useful in determining the vaporliquid equilibria, the Gibbs-Duhem integration method, 21,22 which becomes an invaluable tool when determining fluidsolid equilibria, the Rahman-Parrinello technique, essential in the study of solid phases, 23,24 and Einstein-crystal calculations, which provide the free energies of solid phases. 25 A general approach to the determination of global phase diagrams by computer simulation would entail:…”

Section: Introductionmentioning

confidence: 99%

The phase diagram of the two center Lennard-Jones model as obtained from computer simulation and Wertheim’s thermodynamic perturbation theory

Vega

McBride

Miguel

et al. 2003

The Journal of Chemical Physics

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The global phase diagram ͑i.e., vapor-liquid and fluid-solid equilibrium͒ of two-center Lennard-Jones ͑2CLJ͒ model molecules of bond length Lϭ has been determined by computer simulation. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. In the case of the solid phase, two close-packed solid structures are considered: In the first structure, the molecules are located in layers and all molecular axes point in the same direction; and in the second structure, the atoms form a close-packed arrangement but the molecular axes of the diatomic molecules have random orientations. It is shown that at the vapor-liquid-solid triple-point temperature, the orientationally disordered solid is the stable structure for the solid phase of this model. The vapor-liquid-disordered solid triple-point temperature of the 2CLJ model, with bond length Lϭ , is located at T*ϭ0.650(4). This is very close to the triple-point temperature of the Lennard-Jones monomer system (T*ϭ0.687). At very low temperatures, the ordered solid is the stable phase. The vapor-ordered solid-disordered solid triple point is situated at T*ϭ0.282. The simulation data are compared to Wertheim's first-order thermodynamic perturbation theory ͑TPT1͒ for the fluid and solid phases. It is found that Wertheim's TPT1 not only provides an accurate description of the equation of state in both the fluid and solid phases, but also provides accurate values of the free energies. The prediction of Wertheim's TPT1 for the global phase diagram of the 2CLJ model shows excellent agreement with the simulation results, illustrating the possibility of using Wertheim's perturbation theory to determine not only the vapor-liquid equilibria but also the global phase diagram of simple chain model molecules.

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Gibbs-Duhem integration: a new method for direct evaluation of phase coexistence by molecular simulation

Cited by 339 publications

References 8 publications

Phase diagrams of hard-core repulsive Yukawa particles

Phase diagrams of hard-core repulsive Yukawa particles

Role of solvent for globular proteins in solution

The phase diagram of the two center Lennard-Jones model as obtained from computer simulation and Wertheim’s thermodynamic perturbation theory

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