Terms Of Chemical Potential Research Articles

Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics

Advances in the fields of catalysis and electrochemical energy conversion often involve nanoparticles, which can have kinetics surprisingly different from the bulk material. Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create variations that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend not only on the order parameter but also on its gradients at phase boundaries. Reaction-driven phase transformations are common in electrochemistry, when charge transfer is accompanied by ion intercalation or deposition in a solid phase. Examples abound in Li-ion, metal-air, and lead-acid batteries, as well as metal electrodeposition-dissolution. Despite complex thermodynamics, however, the standard kinetic model is the Butler-Volmer equation, based on a dilute solution approximation. The Marcus theory of charge transfer likewise considers isolated reactants and neglects elastic stress, configurational entropy, and other nonidealities in condensed phases. The limitations of existing theories recently became apparent for the Li-ion battery material LixFePO4 (LFP). It has a strong tendency to separate into Li-rich and Li-poor solid phases, which scientists believe limits its performance. Chemists first modeled phase separation in LFP as an isotropic "shrinking core" within each particle, but experiments later revealed striped phase boundaries on the active crystal facet. This raised the question: What is the reaction rate at a surface undergoing a phase transformation? Meanwhile, dramatic rate enhancement was attained with LFP nanoparticles, and classical battery models could not predict the roles of phase separation and surface modification. In this Account, I present a general theory of chemical kinetics, developed over the past 7 years, which is capable of answering these questions. The reaction rate is a nonlinear function of the thermodynamic driving force, the free energy of reaction, expressed in terms of variational chemical potentials. The theory unifies and extends the Cahn-Hilliard and Allen-Cahn equations through a master equation for nonequilibrium chemical thermodynamics. For electrochemistry, I have also generalized both Marcus and Butler-Volmer kinetics for concentrated solutions and ionic solids. This new theory provides a quantitative description of LFP phase behavior. Concentration gradients and elastic coherency strain enhance the intercalation rate. At low currents, the charge-transfer rate is focused on exposed phase boundaries, which propagate as "intercalation waves", nucleated by surface wetting. Unexpectedly, homogeneous reactions are favored above a critical current and below a critical size, which helps to explain the rate capability of LFP nanoparticles. Contrary to other mechanisms, elevated temperatures and currents may enhance battery performance and lifetime by suppressing phase separation. The theory has also been extended to porous electrodes and could be used for battery engineering with multiphase active materials. More broadly, the theory describes nonequilibrium chemical systems at mesoscopic length and time scales, beyond the reach of molecular simulations and bulk continuum models. The reaction rate is consistently defined for inhomogeneous, nonequilibrium states, for example, with phase separation, large electric fields, or mechanical stresses. This research is also potentially applicable to fluid extraction from nanoporous solids, pattern formation in electrophoretic deposition, and electrochemical dynamics in biological cells.

Cahn-Hilliard Reaction Model for Isotropic Li-ion Battery Particles

ABSTRACTUsing the recently developed Cahn-Hilliard reaction (CHR) theory, we present a simple mathematical model of the transition from solid-solution radial diffusion to two-phase shrinking-core dynamics during ion intercalation in a spherical solid particle. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary under all conditions, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of the diffusional chemical potential in the CHR theory. We also consider the effect of surface wetting or de-wetting by intercalated ions, which can lead to shrinking core phenomena with three distinct phase regions. The basic physics are illustrated by different cases, including a simple model of lithium iron phosphate (neglecting crystal anisotropy and coherency strain).

Thermodynamics of continuous media with electromagnetic fields

The thermodynamics of an electrically charged, multicomponent continuous medium with electromagnetic fields is analysed in the non-relativistic limit. Applying locally the first and second law of thermodynamics and Maxwell’s equations for a linear theory of electromagnetism, three equations characterising the continuous medium are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. For a local thermodynamic equilibrium, explicit expressions for the temperature and the chemical potentials in terms of the electromagnetic fields are obtained. The linear phenomenological relations describe novel effects of non-uniform electromagnetic fields on the transport equations and account also for magnetoresistance and optical tweezers.

Stability of colour-flavour locked quark matter with three massive quark flavours

We investigate the role of the dynamical masses of up, down, and strange quarks on the stability of electrically and colour neutral Colour-Flavour Locked (CFL) quark matter in chemical equilibrium. We derive a condition for the stability of such matter in terms of the chemical potentials of quarks and electrons, the quark masses, as well as the pairing gap. The free energy density of CFL quark matter is analyzed for a broad range of dynamical quark masses. A comparison with ordinary (non-CFL) quark matter shows that low strange quark masses favor colour superconductivity. Stability of the CFL phase can also be achieved, however, for larger values of the quark chemical potential and larger values of the dynamical strange quark mass, provided the differences between the quark masses are not too big.

QCD phase diagram with two-flavor lattice fermion formulations

We propose a new framework for investigating two-flavor lattice QCD with finite temperature and density. We consider the Karsten-Wilczek fermion formulation, in which a species-dependent imaginary chemical potential term can reduce the number of species to two without losing chiral symmetry. This lattice discretization is useful for study on finite-$(T,\ensuremath{\mu})$ QCD since its discrete symmetries are appropriate for the case. To show its applicability, we study strong-coupling lattice QCD with temperature and chemical potential. We derive the effective potential of the scalar meson field and obtain a critical line of the chiral phase transition, which is qualitatively consistent with the phenomenologically expected phase diagram. We also discuss that $O(1/a)$ renormalization of imaginary chemical potential can be controlled by adjusting a parameter of a dimension-3 counterterm.

Phase structure for lattice fermions with flavored chemical potential terms

We discuss the chiral phase diagram in the parameter space of lattice QCD with minimal-doubling fermions, which can be seen as lattice fermions with flavored chemical potential terms. We study strong-coupling lattice QCD with the Karsten-Wilczek formulation, which has one relevant parameter $\mu_{3}$ as well as gauge coupling and a mass parameter. We find a nontrivial chiral phase structure with a second-order phase transition between chiral symmetric and broken phases. To capture the whole structure of the phase diagram, we study the related lattice Gross-Neveu model. The result indicates that the chiral phase transition also exists in the weak-coupling region. From these results we speculate on the $\mu_{3}$-$g^{2}$ chiral phase diagram in lattice QCD with minimal-doubling fermions, and discuss their application to numerical simulations.

Spin Resistivity in Magnetic Materials

We show in this paper recent results on the spin resistivity in magnetically ordered materials obtained by Monte Carlo simulations. We discuss its behavior as a function of temperature in various types of crystal: ferromagnetic, antiferromagnetic, and frustrated spin systems. In the model used for simulations, we take into account the interaction between itinerant spins and that between lattice spins and itinerant spins. We also include a chemical potential term, as well as an electric eld. We study in particular the behavior of the spin resistivity at and near the magnetic phase transition where the e ect of the magnetic ordering is strongest. In ferromagnetic crystals, the spin resistivity shows a sharp peak very similar to the magnetic susceptibility. This can be understood if one relates the spin resistivity to the spin spin correlation as suggested in a number of theories. The dependence of the shape of the peak on physical parameters such as carrier concentration, magnetic eld strength, relaxation time etc. is discussed. In antiferromagnets, the peak is not so pronounced and in some cases it is absent. Its direct relationship to the spin spin correlation is not obvious. As for frustrated spin systems with strong rst-order transition, the spin resistivity shows a discontinuity at the phase transition. To show the e ciency of the simulation method, we compare our results with recent experimental data performed on semiconducting MnTe of NiAs structure. We observe a very good agreement with experiments on the spin resistivity in the whole range of temperature.

GMCT : A Monte Carlo simulation package for macromolecular receptors

Generalized Monte Carlo titration (GMCT) is a versatile suite of computer programs for the efficient simulation of complex macromolecular receptor systems as for example proteins. The computational model of the system is based on a microstate description of the receptor and an average description of its surroundings in terms of chemical potentials. The receptor can be modeled in great detail including conformational flexibility and many binding sites with multiple different forms that can bind different ligand types. Membrane embedded systems can be modeled including electrochemical potential gradients. Overall properties of the receptor as well as properties of individual sites can be studied with a variety of different Monte Carlo (MC) simulation methods. Metropolis MC, Wang-Landau MC and efficient free energy calculation methods are included. GMCT is distributed as free open source software at www.bisb.uni-bayreuth.de under the terms of the GNU Affero General Public License.

Description of hot and dense hadron-gas properties in a new excluded-volume model

A new equation of state for a hot and dense hadron gas (HG) is obtained where the finite hard-core size of baryons has been incorporated in a thermodynamically consistent formulation of excluded volume correction. Our model differs from other existing approaches on the following points. We assign a hard-core volume only to each baryon and mesons though possess a small volume but they can fuse and interpenetrate into one another. Use of the full quantum statistics is made in obtaining the grand canonical partition function where excluded-volume correction has been incorporated by explicitly integrating over volume. We thus find that the new model works even for the cases of extreme temperatures and/or densities where most of other approaches fail. The model does not violate causality even at extreme densities. The temperature and density dependence of various thermodynamical quantities, e.g. pressure, baryon density, entropy and energy density compare well with the results of other microscopic HG models. After suitable parametrization of the centre-of-mass energy in terms of temperature and baryon chemical potential, we explore some new freeze-out criteria which exhibit full independence of the collision energy and of the structures of the colliding nuclei. We further demonstrate the suitability of our model in explaining various experimental results of the multiplicity-ratios of various particles and their antiparticles. Finally, we use our excluded-volume model to obtain the transport behaviour of the hot and/or dense HG such as shear viscosity to entropy ratio, speed of sound etc. and compare the results with earlier calculations.

Solvent effects in ionic liquids: empirical linear energy–density relationships

Multiparameter linear energy-density relationships to model solvent effects in room temperature ionic liquids (RTILs) are introduced and tested. The model incorporates two solvent dependent and two specific solute-solvent parameters represented by a set of electronic indexes derived from the conceptual density functional theory. The specific solute-solvent interactions are described in terms of the electronic chemical potential for proton migration between the anion or cation and the transition state structure of a specific reaction. These indexes provide a quantitative estimation of the hydrogen bond (HB) acceptor basicity and the hydrogen bond donor acidity of the ionic solvent, respectively. A sound quantitative scale of HB strength is thereby obtained. The solvent dependent contributions are described by the global electrophilicity of the cation and nucleophilicity of the anion forming the ionic liquid. The model is illustrated for the kinetics of cycloaddition of cyclopentadiene towards acrolein. In general, cation HB acidity outweighs the remaining parameters for this reaction.

DFT study of 1,3-dipolar cycloaddition of azomethine imines with electron deficient dipolarophiles acrylonitrile, methylpropenoate, and dimethylmaleate

The 1,3-dipolar cycloaddition reactions of azomethine imines with some electron deficient dipolarophiles viz. acrylonitrile, methylpropenoate, and dimethylmaleate leading predominantly to 4-substituted pyrazolidines have been computationally studied which could be useful for the stereoselective synthesis of C-nucleosides. The mechanism of regioselectivity, chemoselectivity and diastereofacial selectivity were studied through the evaluation of activation parameters and philicity indices on the assumption of a concerted mechanism. The reactions were followed by performing transition state optimization, calculation of Intrinsic Reaction Coordinate and activation energies. The regioselectivity and reactivity were amply predicted by employing local and global electrophilicity and nucleophilicity indices. The reactions were considered to be nonpolar or at the most weakly polar on the basis of charge transfer calculated in the transition states. In the present cases, no facial selectivity could be observed due to energetic identity of the different enantiomeric transition states. A rationalization of the trends in regio- and chemoselectivity were also attempted in terms of chemical potential, hardness, global electrophilicity differences, local electrophilicity, local nucleophilicity, Pauling’s bond order and Wiberg bond indices in the transition state. Theoretical evaluation of rate constants for elementary reaction steps employing the transition state theory is very much useful for getting quantitative idea about the kinetic rates associated with those steps. Calculation of rate constants were performed with the Eyring’s TST rate equation and using total partition functions of the concerned species at different temperatures. The activation energy was recomputed for consistency from the slope of the plot of 1000/ T vs. −log ( k). All the computed results were derived from density functional calculations at the B3LYP/6-31G(d) level of theory. Considering the fact that the reactions are practically carried out in solutions, some calculations were performed in solvents of different polarity to examine its influence on the activation barrier or the reaction rate.

Notes on chiral hydrodynamics within the effective theory approach

We address the issue of evaluating chiral effects (such as the newly discovered chiral separation) in hydrodynamic approximation. The main tool we use is effective theory which defines interaction in terms of chemical potentials $\mu,\mu_5$. In the lowest order in $\mu,\mu_5$ we reproduce recent results based on thermodynamic considerations. In higher orders the results depend on details of infrared cutoff. Another point of our interest is an alternative way of the anomaly matching through introduction of effective scalar fields arising in the hydrodynamic approximation.

Hawking radiation of charged rotating particle in Kerr-Newman spacetime

We extend the method that Banerjee and Majhi studied Hawking radiation. Under the condition that the total energy, total charge and total angular momentum of spacetime are conservative, we discuss Hawking radiation of the charged rotating particle by the new defined Tortoise coordinate transformation. Taking the radiation particle reaction to the spacetime into consideration, we obtain the black hole radiation spectrum that satisfies the unitary principle of quantum mechanics. And it is shown that the contribution from ingoing wave is equal to the one from outgoing wave in the radiation spectrum chemical potential term caused by the charged rotating particle. It makes people have a new understanding to physical mechanism of Hawking radiation of the black hole.

On the Motive Power of Chemical Transformations in Open Systems

The classical basic concepts of cyclic processes and the efficiency of heat engines are used here to conjecture about the laws of thermodynamics for open systems that can exchange matter with a surrounding environment. An ideal chemomechanical elastic bar is envisioned that changes its stiffness while undergoing a chemical transformation which is, in turn, influenced by the axial strain of the bar. Stable equilibrium states are identified as minimizers of the total energy, which is assumed to be nonconvex in type. If the bar is loaded and then alternatively placed in environments at chemical potentials either μ i or μ s >μ i , a reversible cycle analogous to the classical Carnot cycle may be traced. In this case, the environmental “chemical potential” plays the role of the temperature and the “chemical work” the role of heat. For the system, the main form of interaction with the exterior, other than mechanical work, is the exchange of mass of a component at different environmental chemical potentials. It is then possible to obtain an elementary theory of chemical engines in which efficiency estimates (in terms of environmental chemical potentials) and related pertinent issues can be discussed. This model may serve as a basis for analyzing coupled chemo-mechanical processes occurring in materials such as ionized gels for possible applications as actuators, and to interpret complex phenomena in biological systems, such as the chemical kinetics of smooth muscles.

Compositional dependent thin film stress states

This paper addresses in situ stress evolution of two-component FexPt1−x, where x spanned 0 to 1, alloy thin films. The stresses of the high-temperature, quenched-in, solid solution phase was determined by in situ wafer curvature measurements during ambient temperature growth. The measured stresses were shown to be compositional dependent and spanned both compressive and tensile stress states. Under specific growth conditions, a “zero-stress” state could be achieved. The alloy stress states did not show any significant stress recovery upon ceasing the deposition, i.e. the stress state during growth was retained in the film. X-ray diffraction, transmission electron microscopy, and atom probe tomography were used to characterize the microstructures of each thin film. The evolution of the stress state with composition is described in terms of a chemical potential term for preferential segregation of one species in the alloy to the grain boundaries.

Hawking Radiation of Charged Particles in Reissner–Nordström Black Hole

We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the charged black hole by a new Tortoise coordinate transformation. Taking the reaction of the radiation of the particle to the spacetime into consideration, we not only derive the radiation spectrum that satisfies the unitary principle in quantum mechanics but also show that the contribution of ingoing particles is equal to the one of outgoing particles on the similar chemical potential term in radiation spectrum caused by charged particles.

Calculating the chemical potential of components of a binary solution in a plane-parallel pore

The chemical potential of components of a binary solution is calculated using the expansion of the external field potential in a Taylor series. An expansion of the chemical potential in terms of concentration-concentration direct correlation functions of all orders is obtained. For a plane-parallel pore with an exponential near-wall potential, a solution to the obtained differential equation is constructed in the smooth-inhomogeneity approximation.

Suspension flow modelling in particle migration and microfiltration

We review existing mixture models for shear-induced migration (SIM) in flowing viscous, concentrated particle suspensions via an analysis of the models from the perspective of a two-fluid formulation. Our analysis shows that particle suspensions in strong non-linear shear fields are a prime example of a driven soft matter system. The driving forces for particle migration can be expressed in terms of non-equilibrium osmotic pressure and chemical potential. Using the linear scaling of the effective temperature with the shear stress, we show that the osmotic pressure and shear-induced diffusion coefficients can be written in identical equations. This is similar to the equations for Brownian motion - with the temperature replaced by the effective temperature. As a guiding application we have taken crossflow microfiltration, where the driving is very strong and there is formation of a jammed state, cake layer, coexisting with the fluid state. The question whether the SIM mixture models holds for this aplication is investigated. Another questions is how SIM models can be extended for bidisperse suspensions, which is relevant for microfiltration applications involving particle fractionation. Analysis of existing closures of SIM mixture models from the two-fluid perspective learns us that the theory seems to be extendable towards bidisperse suspensions by means of the effective medium theory.

A coarse-grained density functional theory, chemical potential equalization and electric response in molecular systems

A simple coarse grained description of the electron density changes in molecular systems due to change in external potential, which may include the effect of external electric fields in addition to the potential due to the nuclei, has been proposed in terms of the induced atom–atom charges and atomic dipoles. The density functional perturbation theory has been used for deriving the expressions for the interaction energy and the effective chemical potentials in terms of these coarse grained variables. A route to the calculation of these quantities and hence the dipole polarizability of the molecular system is provided. The proposed approach would also be useful for obtaining polarizable charge based force field for intermolecular interaction in computer simulation.

Transport through mixed proton, oxygen ion and electron (hole) conductors: Goldman–Hodgkin–Katz-type equation

Many high temperature oxides and low temperature polymeric materials transport protons, oxygen ions, and electrons or holes. These materials are candidates as membranes for fuel cells and electrolyzers. This manuscript examines non-equilibrium steady state transport through such membranes under the assumption of local equilibrium. A simple equivalent circuit analysis is given for transport through mixed proton, oxygen ion, and electron (hole) conducting membranes. The cell potential can be described in terms of transport parameters of charged species (H + , O 2− and e or h) and internal EMFs given in terms of chemical potentials of neutral species ( μ H 2 , μ O 2 ). The resulting equation for cell potential is similar to the Goldman–Hodgkin–Katz (GHK) equation used in cell physiology. Transport through a fuel cell based on such materials is examined. Effects of electrolyte/electrode interfaces are explicitly included in the analysis. Fluxes of H 2 and O 2 through the membrane are evaluated at open circuit and under load. They obey Onsager reciprocity relations, inclusive of interface effects. The analysis also shows that the chemical potentials of H 2 and O 2 and electric potential, φ , exhibit abrupt changes across interfaces.