Showing papers on "Gibbs–Duhem equation published in 2010"

Chemical and biochemical thermodynamics: from ATP hydrolysis to a general reassessment.

Abstract: The Legendre-transformed Gibbs energy change for a biochemical reaction, Delta(r)G', is shown to be equal to the nontransformed Gibbs energy change, Delta(r)G, of any single reaction involving selected chemical species of the biochemical system. These two Gibbs energies of reaction have hitherto been thought to have different values. The equality of the quantities means that a substantial part of biochemical and chemical thermodynamics, previously treated separately, can be treated within a unified thermodynamic framework. An important consequence of the equality of Delta(r)G and Delta(r)G' is that the Gibbs energy change of many enzyme reactions can be quantified without specifying which chemical species is the active substrate of the enzyme. Another consequence is that the transformed standard Gibbs energy change of a reaction, Delta(r)G'(0), can be calculated by a simple analytical expression, rather than the complex computational methods of the past. The equality of the quantities is restricted to Gibbs energy changes and does not apply to enthalpy or entropy changes.

Communication: Tracing phase boundaries via molecular simulation: An alternative to the Gibbs–Duhem integration method

Abstract: Precise simulation of phase transitions is crucial for colloid/protein crystallization for which fluid-fluid demixing may be metastable against solidification. In the Gibbs-Duhem integration method, the two coexisting phases are simulated separately, usually at constant-pressure, and the phase boundary is established iteratively via numerical integration of the Clapeyron equation. In this work, it is shown that the phase boundary can also be reproduced in a way that avoids integration of Clapeyron equations. The two phases are simulated independently via tempering techniques and the simulation data are analyzed according to histogram reweighting. The main output of this analysis is the density of states which is used to calculate the free energies of both phases and to determine phase coexistence. This procedure is used to obtain the phase diagram of a square-well model with interaction range 1.15σ, where σ is the particle diameter. The phase boundaries can be estimated with the minimum number of simulations. In particular, very few simulations are required for the solid phase since its properties vary little with temperature.

Advances in lattice Boltzmann modeling (LBM) to simulate two-phase dynamics

Abstract: In this paper, a new lattice Boltzmann model, called the artificial interface lattice Boltzmann model (AILB model), is proposed for the simulation of two-phase dynamics. The model is based on the principle of free energy minimization and invokes the Gibbs-Duhem equation in the formulation of non-ideal forcing function. Bulk regions of the two phases are governed by a non-ideal equation of state (for example, the van der Waals equation of state), whereas an artificial near-critical equation of state is applied in the interfacial region. The interfacial equation of state is described by a double well density dependence of the free energy. The continuity of chemical potential is enforced at the interface boundaries. Using the AILB model, large density and viscosity ratios of the two phases can be simulated. The model is able to quantitatively capture the coexistence curve for the van der Waals equation of state for different temperatures. Moreover, spatially varying viscosities can be simulated by choosing the relaxation time as a function of local density.

Thermodynamics and Chemistry: How Does a Theory Formulated without Reference to Matter Explain the Properties of Matter?

Abstract: Varieties of chemical and phase equilibria are controlled by the minimum Gibbs energy principle, according to which the Gibbs energy for a system will have the minimum value at any given temperature and pressure. It is understood that the minimum is with respect to all nonequilibrium states at the same temperature and pressure. The abstract relation between Gibbs energy and the equilibrium constant is deduced from fundamental laws of thermodynamics. However, actual use of this relation calls for the Gibbs energy as a function of concentrations of the chemicals. Since thermodynamics is formulated without any reference to materials, how does one get that relation? This article provides the answer, and in the process shows that application of theory to experiments requires several intermediate layers where theory and experiment commingle.

Information as a thermodynamic function of a living system

Abstract: It is suggested to introduce an information term into the Gibbs thermodynamic equation in the case of living systems. The possibility of describing the behavior of organisms by means of such an approach is shown.

Existence of Gibbs measure for a model of T-tessellations

Abstract: The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random T-tessellation, as defined by Kien Kieu et al., and of its Gibbsian modifications. The combinatorial bound is sharp, but likely pessimistic in typical cases.

Gibbs Free Energy and Chemical Equilibria

Abstract: I already said that it is important to understand and to know how to calculate and prepare different concentrations. Many chemical reactions – and all the biochemical reactions that run our bodies – take place in a solution. Now we are going to put together a formula for the Gibbs energy of a chemical in solution and a formula for calculating the Gibbs energy in a chemical reaction.

Chemical Reactions and Gibbs Free Energy

Abstract: We have shown that when two things are mixed together we can calculate the entropy of mixing. We can also calculate the concentration of this mixture, as we did in the previous three examples. A most complete description of the chemicals and their mixtures is by using Gibbs free energy (we say it is free because it does not contain any pV work, like when we are working with gases). Let us think for a moment of the following mixture: a solution of urea, O=C(NH2)2, in water, H2O. Water, a liquid, is present in larger quantity so we call it the solvent.