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1. Modeling Current-Potential Responses of Homogeneous-Heterogeneous Photocathodes

   Wadsworth, B. L.; Beiler, A. M; Khusnutdinova, D.; Moore, G. F. (April 2019, Abstract of Papers, Materials and Research Society Spring Meeting and Exhibit)

   Chemical modification of semiconductor surfaces with molecular electrocatalysts provides a strategy for developing integrated homogeneous-heterogeneous materials capable of converting sunlight to fuels and other value-added products, but their development is hampered by an incomplete understanding of the factors limiting their performance. Although kinetic models have been separately developed to describe photoelectrochemical or homogeneous electrocatalytic reactions, related modeling for molecular-modified hybrid photoelectrodes has not been as extensively elaborated. This presentation addresses the interplay between light absorption, charge transfer, and catalytic activity during photoelectrosynthetic transformations at a molecular-modified semiconductor surface. The analysis provides opportunities to better understand the principles governing these hierarchal constructs and develop improved photocatalytic assemblies. 

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2. Analysis of multi-electron, multi-step homogeneous catalysis by rotating disc electrode voltammetry: theory, application, and obstacles

   https://doi.org/10.1039/C9AN02192B  

   Lee, Katherine J.; Gruninger, Cole T.; Lodaya, Kunal M.; Qadeer, Saad; Griffith, Boyce E.; Dempsey, Jillian L. (February 2020, The Analyst)

   Rotating disc electrode (RDE) voltammetry has been widely adopted for the study of heterogenized molecular electrocatalysts for multi-step fuel-forming reactions but this tool has never been comprehensively applied to their homogeneous analogues. Here, the utility and limitations of RDE techniques for mechanistic and kinetic analysis of homogeneous molecular catalysts that mediate multi-electron, multi-substrate redox transformations are explored. Using the ECEC′ reaction mechanism as a case study, two theoretical models are derived based on the Nernst diffusion layer model and the Hale transformation. Current–potential curves generated by these computational strategies are compared under a variety of limiting conditions to identify conditions under which the more minimalist Nernst Diffusion Layer approach can be applied. Based on this theoretical treatment, strategies for extracting kinetic information from the plateau current and the foot of the catalytic wave are derived. RDEV is applied to a cobaloxime hydrogen evolution reaction (HER) catalyst under non-aqueous conditions in order to experimentally validate this theoretical framework and explore the feasibility of RDE as a tool for studying homogeneous catalysts. Crucially, analysis of the foot-of-the-wave via this theoretical framework provides rate constants for elementary reaction steps that agree with those extracted from stationary voltammetric methods, supporting the application of RDE to study homogeneous fuel-forming catalysts. Finally, obstacles encountered during the kinetic analysis of cobaloxime, along with the voltammetric signatures used to diagnose this reactivity, are discussed with the goal of guiding groups working to improve RDE set-ups and help researchers avoid misinterpretation of RDE data. 

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3. Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting

   https://doi.org/10.1353/ajm.2025.a966292  

   Ampatzoglou, Ioakeim; Collot, Charles; Germain, Pierre (August 2025, American Journal of Mathematics)

   Abstract: We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier; the space-homogeneous case is a simple variant. We determine nonlinearities for which the kinetic description holds, or might fail, up to an arbitrarily small polynomial loss of the kinetic time scale. More precisely, we focus on the convergence of the Dyson series, which is an expansion of the solution in terms of the random data. 

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4. Modulating Phase Behavior in Fatty Acid-Modified Elastin-like Polypeptides (FAMEs): Insights into the Impact of Lipid Length on Thermodynamics and Kinetics of Phase Separation

   https://doi.org/10.1021/jacs.3c12791  

   Zhang, Zhe; Lynch, Christopher J; Huo, Ying; Chakraborty, Somya; Cremer, Paul S; Mozhdehi, Davoud (February 2024, Journal of the American Chemical Society)

   Although post-translational lipidation is prevalent in eukaryotes, its impact on the liquid–liquid phase separation of disordered proteins is still poorly understood. Here, we examined the thermodynamic phase boundaries and kinetics of aqueous two-phase system (ATPS) formation for a library of elastin-like polypeptides modified with saturated fatty acids of different chain lengths. By systematically altering the physicochemical properties of the attached lipids, we were able to correlate the molecular properties of lipids to changes in the thermodynamic phase boundaries and the kinetic stability of droplets formed by these proteins. We discovered that increasing the chain length lowers the phase separation temperature in a sigmoidal manner due to alterations in the unfavorable interactions between protein and water and changes in the entropy of phase separation. Our kinetic studies unveiled remarkable sensitivity to lipid length, which we propose is due to the temperature-dependent interactions between lipids and the protein. Strikingly, we found that the addition of just a single methylene group is sufficient to allow tuning of these interactions as a function of temperature, with proteins modified with C7–C9 lipids exhibiting non-Arrhenius dependence in their phase separation, a behavior that is absent for both shorter and longer fatty acids. This work advances our theoretical understanding of protein–lipid interactions and opens avenues for the rational design of lipidated proteins in biomedical paradigms, where precise control over the phase separation is pivotal. 

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5. Pauli potential formalism at finite temperature

   https://doi.org/10.1103/cx82-lgn4  

   Goshadze, R_M N; Karasiev, Valentin V; Hilleke, Katerina P; Hu, S X (June 2025, Physical Review B)

   At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OF-DFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero-T to finite-T . We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero-T counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential. 

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