Rigorous Models for Vapor Diffusion in Polymers with Immobilization and Chemical Potential Gradients
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Engineering topics
Foley, Brandon L.
Publications and source records attributed to Foley, Brandon L..
A chemo-mechanical model for describing sorption hysteresis in a glassy polyurethane
Abstract Hysteretic sorption and desorption of water is observed from 0 to 95% relative humidity and 298–333 K on a glassy polyurethane foam. It is postulated that sorption-induced swelling of the glassy polyurethane increases the concentration of accessible hydrogen-bonding adsorption sites for water. The accessibility of sites is kinetically controlled due to the restricted thermal motions of chains in the glassy polymer, causing a difference in accessible site concentrations during sorption and desorption. This discrepancy leads to hysteresis in the sorbed concentrations of water. A coupled chemo-mechanical model relating volumetric strain, adsorption site concentration, and sorbed water concentration is employed to describe water sorption hysteresis in the glassy polyurethane. This model not only describes the final mass uptake for each relative humidity step, but also captures the dynamics of water uptake, which exhibit diffusion and relaxation rate-controlled regimes.
36 MATERIALS SCIENCE↗
Thermodynamically consistent forward and reverse degrees of rate control in reversible reactions
The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per k B T decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the apparent initial states and the apparent transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step at equilibrium. Here, this apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, $\bar{σ}$ The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.
42 ENGINEERING↗
Degree of rate control and De Donder relations – An interpretation based on transition state theory
We describe sensitivities of elementary steps as salient parameters in determining the rate determining character of elementary steps within a reaction network and develop a formalism wherein the overall composite reaction is described by an apparent rate-determining step that is a sensitivity-weighted average of the elementary steps that comprise the reaction. Reaction parameters—apparent reaction orders, apparent enthalpy and entropy of activation—of the composite reaction network are determined within the framework we develop by application of transition state theory to the apparent rate-determining step. From this formalism we develop methods for determination of surface coverages by measuring only reaction orders, novel methods for discrimination between proposed mechanisms, a proof that the kinetic degrees of rate control sum to unity, and a proof for the relationship between fractional coverages and thermodynamic degrees of rate control. Two complementary formalisms for identifying rate-limiting transition states are broadly employed in chemical kinetics—De Donder relations based on measuring the thermodynamic driving forces of elementary steps during reaction and degrees of rate control based on knowledge of the kinetics of elementary reaction steps. Here, the formalism developed herein unifies these two strategies to elucidate in the most general case a relationship between the thermodynamic driving forces of elementary steps captured by the reversibilities and the kinetic and thermodynamic degrees of rate control.
42 ENGINEERING↗
Degrees of Rate Control at Non(pseudo)steady-State Conditions
The degrees of rate control enable identification of rate-controlling transition states and species during (pseudo-)steady-state reaction. We demonstrate a method for identifying rate-controlling transition states and species at non-(pseudo-)steady-state conditions through modification of the definitions for degrees of rate control and sensitivities by superimposing the condition that time constants of the analytical rate function are kept constant when taking the partial derivatives of rate with respect to the rate constants/free energies. In conclusion, the utility of transient degrees of rate control is demonstrated for catalytic reaction networks to rationalize features of the transient rate including extrema and discontinuities.
42 ENGINEERING↗