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The article explains the size dependent nucleation mechanism, which is involved in the solid state polymorph transformations in teraphthalic acid. The mechanism is shown to continuously change with the size of the system.

We develop a theory to account for variable coverage of trace additives that lower the interfacial free energy for nucleation. The free energy landscape is based on classical nucleation theory and a statistical mechanical model for Langmuir adsorption. Dynamics are modeled by diffusion-controlled attachment and detachment of solutes and adsorbing additives. We compare the mechanism and kinetics from a mean-field model, a projection of the dynamics and free energy surface onto nucleus size, and a full two-dimensional calculation using Kramers-Langer-Berezhkovskii-Szabo theory. The fluctuating coverage model predicts rates more accurately than mean-field models of the same process primarily because it more accurately estimates the potential of mean force along the size coordinate. [ABSTRACT FROM AUTHOR]

We examine the capabilities and foundations of three landmark rate theories: harmonic transition state theory, classical nucleation theory, and the Marcus theory of electron transfer. Each of the three classic rate theories is widely used to predict rates and trends. They are also used "in reverse" to interpret experimental data with no computation at all. Their common foundations include a quasi-equilibrium assumption and dimensionality reduction to a physically meaningful, one-dimensional, and broadly applicable reaction coordinate. Many applications lie beyond the scope of the classic theories, so rare events research has pursued trajectory-based methods that efficiently predict accurate rate constants even when the reaction coordinate and mechanistic details are unknown. Trajectory based rare events methods achieved these ambitious goals, but (by construction) they provide rates rather than mechanistic understanding. We briefly discuss recent efforts to identify reaction coordinates, including methods which provide abstract statistically defined coordinates and those which identify physical collective variables. Finally, we note some natural synergies between existing simulation methods which might help discover simple and powerful quasi-equilibrium theories for the many applications that fall beyond the scope of the classic rate theories.

The reaction mechanism for nitrous oxide decomposition has been studied on hydrated and dehydrated mononuclear iron sites in Fe-ZSM-5 using density functional theory. In total, 46 different surface species with different spin states (spin multiplicity M(S) = 4 or 6) and 63 elementary reactions were considered. Heats of adsorption, activation barriers, reaction rates, and minimum energy pathways were determined. The approximate minimum energy pathways and transition states were calculated using the "growing string method" and a modified "dimer method". Spin surface crossing (e.g., O(2) desorption) was considered. The minimum potential energy structure on the seam of two potential energy surfaces was determined with a multiplier penalty function algorithm by Powell and approximate rates of spin surface crossings were calculated. It was found that nitrous oxide decomposition is first order with respect to nitrous oxide concentration and zero order with respect to oxygen concentration. Water impurities in the gas stream have a strong inhibiting effect. In the concentration range of 1-100 ppb, the presence of water vapor influences the surface composition and the apparent rate coefficient. This is especially relevant in the temperature range of 600-700 K where most experimental kinetic studies are performed. Apparent activation barriers determined over this temperature range vary from 28.4 (1 ppb H(2)O) to 54.8 kcal/mol (100 ppb H(2)O). These results give an explanation why different research groups and different catalyst pretreatments often result in very different activation barriers and preexponential factors. Altogether perfect agreement with experimental results could be achieved.