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Helmholtz Free Energy (helmholtz + free_energy)
Selected AbstractsThermodynamic study of capillary pressure curves based on free energy minimizationGEOFLUIDS (ELECTRONIC), Issue 3 2001Y. Deng Abstract This paper presents a new method for pore level network simulation of the distribution of two immiscible phases in a permeable medium. The method requires that the Helmholtz free energy of the system , the medium and the two phases contained within the pore space , be a minimum at all saturation states. We describe the method here and show some typical results from a computer algorithm that implements it. The results include (i) an explanation of the ,scanning' behaviour of capillary pressure curves based wholly on the free energy minimization, (ii) predictions of capillary pressure at arbitrary wetting states, including negative capillary pressures, and (iii) illustrations of how the minimized free energy changes along the scanning curves. The method also predicts the known dependency of the capillary pressure on the pore size distribution and interfacial tension. The current work is restricted to two-dimensional networks, but the free energy minimization appears to be generalizable to three dimensions and to more than two fluid phases. Moreover, functions generated through the minimization, specifically contact areas between the medium surface and the phases, appear to have applications predicting other multiphase petrophysical properties. [source] Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape-memory alloysINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Youngjean Jung Abstract This work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension,torsion, as well as for a simplified model of a biomedical stent. Copyright © 2004 John Wiley & Sons, Ltd. [source] The Planck,Benzinger thermal work function in the condensation of water vaporINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2006Paul W. Chun Abstract Based on the Planck,Benzinger thermal work function using Chun's method, the innate temperature-invariant enthalpy at 0 K, ,H0(T0), for the condensation of water vapor as well as the dimer, trimer, tetramer, and pentamer form in the vapor phase, was determined to be 0.447 kcal mol,1 for vapor, 1.127 for the dimer, 0.555 for the trimer, 0.236 for the tetramer, and 0.079 kcal mol,1 for the pentamer using ,G(T) data reported by Kell et al. in 1968 and Kell and McLaurin in 1969. These results suggest that the predominant dimeric form is the most stable of these n -mers. Using Nemethy and Scheraga's 1962 data for the Helmholtz free energy of liquid water, the value of ,H0(T0) was determined to be 1.21 kcal mol,1. This is very close to the value for the energy of the hydrogen bond EH of 1.32 kcal mol,1 reported by Nemethy and Scheraga, using statistical thermodynamics. It seems clear that very little energy is required for interconversion between the hypothetical supercooled water vapor and glassy water at 0 K. A hypothetical supercooled water vapor at 0 K is apparently almost as highly associated as glassy water at that temperature, suggesting a dynamic equilibrium between vapor and liquid. This water vapor condensation is highly similar in its thermodynamic behavior to that of sequence-specific pairwise (dipeptide) hydrophobic interaction, except that the negative Gibbs free energy change minimum at ,Ts,, the thermal setpoint for vapor condensation, where T,S = 0, occurs at a considerably lower temperature, 270 K (below 0°C) compared with ,350 K. The temperature of condensation ,Tcond, at which ,G(T) = 0, where water vapor begins to condense, was found to be 383 K. In the case of a sequence-specific pairwise hydrophobic interaction, the melting temperature, ,Tm,, where ,G(Tm) = 0 was found to be 460 K. Only between two temperature limits, ,Th, = 99 K and ,Tcond, = 383 K, where ,G(Tcond) = 0, is the net chemical driving force favorable for polymorphism of glassy water and hypothetical supercooled water vapor. Analysis of the water vapor condensation process based on the Planck,Benzinger thermal work function confirms that a thermodynamic molecular switch occurs at 10 K, wherein a change of sign in [,Cp(T)]cond leads to a true negative minimum in the Gibbs free energy of vapor condensation, and hence a maximum in the related equilibrium constant, Kcond. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Application of entropy calculations to the determination of transition temperature in zirconiumPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 8 2005Pornjuk Srepusharawoot Abstract The Helmholtz free energy is determined in order to calculate the bcc,hcp phase transition temperature in zirconium. The molecular dynamics method is employed to calculate the vibrational entropy which comprises both the harmonic and anharmonic vibrational entropy. Electronic effects are estimated and taken into account. The anharmonic vibrational entropy is determined from the anharmonic free energy and the electronic entropy is calculated via the electronic density of states. By considering the Helmholtz free energy, the bcc,hcp transition temperature from our simulations is 1047 ± 210 K compared to 1135 K from experimental results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Theory and Numerics of Rate-Dependent Incremental Variational Formulations in FerroelectricityPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Daniele Rosato This paper is concerned with macroscopic continuous and discrete variational formulations for domain switching effects at small strains, which occur in ferroelectric ceramics. The developed new three,dimensional model is thermodynamically,consistent and determined by two scalar,valued functions: the energy storage function (Helmholtz free energy) and the dissipation function, which is in particular rate,dependent. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. The rate,dependent character of the dissipation function allows us also to reproduce the experimentally observed rate dependency of the above mentioned hysteresis phenomena. An important aspect is the numerical implementation of the coupled problem. The discretization of the two,field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of a benchmark problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||