Local equilibrium of the Gibbs interface in two-phase systems

We analyze the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface. This insight strengthens the foundations of the local equilibrium assumption for interfaces and can be used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge-invariant properties. Using the principle of gauge invariance, we show that the validity of Clapeyron equations can be extended to nonequilibrium interfaces, and an additional jump condition for the momentum density is recognized to be of the Clapeyron type. © 2012 Europhysics Letters Association.

Studies on the adsorption equilibrium and kinetics of pentachlorophenol on suspended particulate matter of Donghu Lake water

In this paper, the adsorption equilibrium and kinetic behaviors of pentachlorophenol (PCP) on suspended particulate matter (SPM) in Donghu Lake water were investigated. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and their constants were evaluated. The results indicated that the adsorption of PCP on Donghu Lake SPM followed the Freundlich isotherm. Furthermore, the first order Lagergren rate equation and the pseudo-second order rate equation were used to describe the kinetic behaviors of PCP adsorption on Donghu Lake SPM, the rate constants were determined, and the kinetic process of the adsorption of PCP on Donghu Lake SPM followed the second order kinetic model.

Analysis of steric mass-action model for protein adsorption equilibrium onto porous anion-exchange adsorbent

The ion-exchange equilibrium of bovine serum albumin (BSA) to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments at pH values ranging from 5.26 to 7.6 and ionic strengths from 10 to 117.1 mmol/l. Using the unadjustable adsorption equilibrium parameters obtained from batch experiments, the applicability of the steric mass-action (SMA) model was analyzed for describing protein ion-exchange equilibrium in different buffer systems. The parametric sensitivity analysis was performed by perturbing each of the model parameters, while holding the rest constant. The simulation results showed that, at high salt concentrations or low pHs close to the isoelectric point of the protein, the precision of the model prediction decreased. Parametric sensitivity analysis showed that the characteristic charge and protein steric factor had the largest effects on ion-exchange equilibrium, while the effect of equilibrium constant was about 70%-95% smaller than those of characteristic charge and steric factor under all conditions investigated. The SMA model with the relationship between the adjusted characteristic charge and the salt concentration can well predict the protein adsorption isotherms in a wide pH range from 5.84 to 7.6. It is considered that the SMA model could be further improved by taking into account the effect of salt concentration on the intermolecular interactions of proteins. (c) 2006 Elsevier Ltd. All rights reserved.

A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Application of the compatibility relationship(1) in seeking a functional relationship among species' equilibrium quantities in complex systems

A new algorithm, representing an important advance in determination of the functional relationship, is first reported here. The algorithm is very useful and convenient for analyzing the incorporation of impurities. To show how the algorithm works, two early and well-known vapor phase epitaxy (VPE) experiments-Ashen's (Ashen, D. J.; Dean, P. J.; Hurle, D. T. J.; Mullin, J. B.; Royle, A.; White, A. M. Gallium Arsenide and Related Compounds, Institute of Physics Conference Series 24, 1974; Institute of Physics: London, 1975; p 229.), involving the doping of silicon and DiLorenzo's (DiLorenzo, J. V. J. Cryst. Growth 1972, 17, 189.), involving the mole fraction effect-are calculated to find the functional relationship between the Si contamination and the partial pressure of HCl. The calculated curves agree with the experimental results. A conclusion that the calculated values are greater than the true values has been drawn.

Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of a dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasilocal gravitational energy found recently for f(R) gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the Friedmann-Robertson-Walker spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for f(R) gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.