Unified comprehension of the kinetics of isothermal ceramic processes under field-free and resonant wave-field conditions

Abstract

This paper proposes a unified comprehension of the isothermal ceramic process kinetics stemming from mesoscopic irreversible thermodynamics. Accordingly, a unified process kinetic equation (UPKE) is derived, which predicts that the global isothermal process rate of any ceramic process is, in general, nonlinearly related both to its activation energy and its affinity. Nevertheless, for a low-affinity ceramic process conducted either in a field-free or resonant wave-field condition, its global isothermal rate, according to the proposed UPKE, is approximately linearly related to its affinity in the spirit of Fick's diffusion law. Therefore, the rate enhancement of a low-affinity process occurring in any resonant wave-field may be caused either by a reduction in activation energy, as in microwave-enhanced sintering, or by activation energy reduction along with an affinity augmentation, as in microwaveassisted glass-crystallization. Conversely, for a high-affinity ceramic process, e.g., a chemical reaction, the 'degenerate' UPKE predicts that its kinetics is exclusively dictated by the activation energy in the spirit of Arrhenius's rate law. Hence, isothermal rate enhancements of chemical reactions in ceramic processing under resonant wave-field conditions are believed to predominantly result from a field-induced reduction in activation energy.

Applying a unified process kinetic equation to advanced materials process analysis: Characterization of the kinetics of isothermal microwave‐assisted chemical syntheses

“…Accordingly, a unified process kinetic equation (UPKE) was derived. Rationale and predictions of this equation not only are highly compatible and consistent with findings inferred by classical kinetic theories of mass transport 32,33 and mass action, 29,31 its applications may also provide a unified comprehension and approach in characterizing isothermal kinetics of most materials processes, either diffusion‐ or reaction‐controlled 26–28 …”

“…Unified comprehension on isothermal materials process‐kinetics stemming from a mesoscopic irreversible thermodynamic model was recently proposed 26–28 . This model envisions that kinetically, any materials process should obey Onsager's phenomenological rate law; while energetically, matter transformation or transport occurring during the process should proceed along an activated, Prigogine‐type internal coordinate 29–31 .…”

“…Within the proposed mesoscopic irreversible thermodynamic framework, the steady‐state rate of any activated materials process occurring inside a nonequilibrium condensed system, which converts an ideal reacting mixture 31,34,35 at its initial α‐state into a product at the final β‐state, may be approximately expressed as 26–28 where ρ : global steady‐state process‐rate (mol m −2 s −1 ), R : gas constant (8.314 J mol −1 K −1 ), T : thermodynamic temperature (K), Щ : molar mobility of the reacting species (m mol s −1 N −1 ), c α : concentration of the ideal reacting mixture at the initial α‐state (mol m −3 ), δ : length of the mesoscopic process path between the initial α‐state and the final β‐state (m), Æ : activation enthalpy for the isothermal, isobaric materials process (J mol −1 ), with its magnitude greater than RT – the thermal energy provided by the surroundings, A ≡ −Δ r μ = [ μ (α)− μ (β)]: affinity (J mol −1 ), that is, difference between the totaled chemical potentials, μ , at the initial reactant‐state, α, and final product‐state, β, of the isothermal process, k a ≡ { RTЩδ −1 } × {exp[− Æ /( RT )]} = { R K } × {exp[− Æ /( RT )]}: a highly temperature‐dependent kinetic factor of the process, containing an activation enthalpy exponential term, {exp[− Æ /( RT )]}, and a pre‐exponential frequency coefficient, R K ≡ { RTЩδ −1 }, Φ IT ≡ {1−exp[− A /( RT )]}: general driving force of any isothermal materials process—a nonlinear function of the affinity, A , of the process.…”

“…Irreversible thermodynamics applies the first principles and methods of thermodynamics to describe energetics and kinetics of transformation/transport processes in systems that are not in overall equilibrium; yet, its formalism is independent of any specific kinetic theory or model. In accordance with irreversible thermodynamics and resonant electromagnetics, this author then derived and published a unified process kinetic equation (UPKE) for isothermal materials processes conducted under field‐free, conventional heating and resonant wave‐field heating conditions 26–28 . The UPKE, derived from a mesoscopic irreversible thermodynamic model accounting for NTME, has been successfully applied to characterize kinetics of both low and high‐affinity ceramic processes in the presence or absence of a resonant wave‐field 26–28 …”

“…In accordance with irreversible thermodynamics and resonant electromagnetics, this author then derived and published a unified process kinetic equation (UPKE) for isothermal materials processes conducted under field‐free, conventional heating and resonant wave‐field heating conditions 26–28 . The UPKE, derived from a mesoscopic irreversible thermodynamic model accounting for NTME, has been successfully applied to characterize kinetics of both low and high‐affinity ceramic processes in the presence or absence of a resonant wave‐field 26–28 …”