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Thermodynamically consistent derivation of chemical potential of a battery solid particle from the regular solution theory applied to LiFePO₄.

ABSTRACT: The chemical potential of lithium in Li_xFePO₄ active cathode nanoparticles and the surface free energy between Li_xFePO₄ and electrolyte were determined with the novel thermodynamically consistent application of the regular solution theory. Innovative consideration of crystal anisotropy accounts for the consistent determination of the dependency of the chemical potential on the mechanistically derived enthalpy of mixing and the phase boundary gradient penalty. This enabled the analytic, thermodynamically consistent determination of the phase boundary thickness between LiFe_PO₄ and FePO₄, which is in good agreement with experimental observations. The obtained explicit functional dependency of the surface free energy on the lithium concentration enables adequate simulation of the initiation of the phase transition from FePO₄ to LiFePO₄ at the surface of active cathode particles. To validate the plausibility of the newly developed approaches, lithium intercalation into the Li_xFePO₄ nanoparticles from electrolyte was modeled by solving the Cahn-Hilliard equation in a quasi-two-dimensional domain.

SUBMITTER: Zelic K

PROVIDER: S-EPMC6375981 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature

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Publications

Thermodynamically consistent derivation of chemical potential of a battery solid particle from the regular solution theory applied to LiFePO4.

Zelič Klemen K Katrašnik Tomaž T

Scientific reports 20190214 1

The chemical potential of lithium in LixFePO4 active cathode nanoparticles and the surface free energy between LixFePO4 and electrolyte were determined with the novel thermodynamically consistent application of the regular solution theory. Innovative consideration of crystal anisotropy accounts for the consistent determination of the dependency of the chemical potential on the mechanistically derived enthalpy of mixing and the phase boundary gradient p ...[more]

PMID: 30765797

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Project description:BackgroundThe dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function.ResultsWe introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database.ConclusionsTCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.

Project description:BackgroundEstimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.ResultsWe introduce a Bayesian analysis approach for computing thermodynamically consistent estimates of the rate constants of a closed biochemical reaction system with known stoichiometry given experimental data. Our method employs an appropriately designed prior probability density function that effectively integrates fundamental biophysical and thermodynamic knowledge into the inference problem. Moreover, it takes into account experimental strategies for collecting informative observations of molecular concentrations through perturbations. The proposed method employs a maximization-expectation-maximization algorithm that provides thermodynamically feasible estimates of the rate constant values and computes appropriate measures of estimation accuracy. We demonstrate various aspects of the proposed method on synthetic data obtained by simulating a subset of a well-known model of the EGF/ERK signaling pathway, and examine its robustness under conditions that violate key assumptions. Software, coded in MATLAB®, which implements all Bayesian analysis techniques discussed in this paper, is available free of charge at http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.html.ConclusionsOur approach provides an attractive statistical methodology for estimating thermodynamically feasible values for the rate constants of a biochemical reaction system from noisy time series observations of molecular concentrations obtained through perturbations. The proposed technique is theoretically sound and computationally feasible, but restricted to quantitative data obtained from closed biochemical reaction systems. This necessitates development of similar techniques for estimating the rate constants of open biochemical reaction systems, which are more realistic models of cellular function.

Dataset Information

Thermodynamically consistent derivation of chemical potential of a battery solid particle from the regular solution theory applied to LiFePO₄.

Publications

Thermodynamically consistent derivation of chemical potential of a battery solid particle from the regular solution theory applied to LiFePO<sub>4</sub>.

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