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 c...
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| Format: | Article |
| Language: | en_US |
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American Chemical Society (ACS)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90946 |
| _version_ | 1826188387351003136 |
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| author | Bazant, Martin Z. |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Bazant, Martin Z. |
| author_sort | Bazant, Martin Z. |
| collection | MIT |
| description | 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 Li[subscript x]FePO[subscript 4] (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 hermodynamics. 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. |
| first_indexed | 2024-09-23T07:58:51Z |
| format | Article |
| id | mit-1721.1/90946 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:58:51Z |
| publishDate | 2014 |
| publisher | American Chemical Society (ACS) |
| record_format | dspace |
| spelling | mit-1721.1/909462022-09-23T10:01:25Z Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics Bazant, Martin Z. Massachusetts Institute of Technology. Department of Chemical Engineering Massachusetts Institute of Technology. Department of Mathematics Bazant, Martin Z. 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 Li[subscript x]FePO[subscript 4] (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 hermodynamics. 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. National Science Foundation (U.S.) (Contract DMS-0842504) National Science Foundation (U.S.) (Contract DMS-0948071) MIT Energy Initiative 2014-10-15T16:56:18Z 2014 2014-10-15T16:56:18Z 2013-04 Article http://purl.org/eprint/type/JournalArticle 0001-4842 1520-4898 http://hdl.handle.net/1721.1/90946 Bazant, Martin Z. "Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics." Acc. Chem. Res., 2013, 46 (5), pp 1144–1160. en_US http://dx.doi.org/10.1021/ar300145c Accounts of Chemical Research Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Chemical Society (ACS) arXiv |
| spellingShingle | Bazant, Martin Z. Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title | Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title_full | Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title_fullStr | Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title_full_unstemmed | Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title_short | Theory of Chemical Kinetics and Charge Transfer based on Nonequilibrium Thermodynamics |
| title_sort | theory of chemical kinetics and charge transfer based on nonequilibrium thermodynamics |
| url | http://hdl.handle.net/1721.1/90946 |
| work_keys_str_mv | AT bazantmartinz theoryofchemicalkineticsandchargetransferbasedonnonequilibriumthermodynamics |