Transition Zone Theory: a New Theory to Explain the Mechanisms of Crystallization, Viscous Relaxation and Glass Transition

Crystal growth and viscous relaxation are known to be activated processes, albeit inadequately described by transition state theories. A new theory, transition zone theory (TZT), for crystallization, and also for the related but distinct process of liquid relaxation, has been developed by extending the Eyring transition state theory and the Kauzmann configurational entropy concepts to address the condensed phase activated processes, in which entropic and enthalpic activation probabilities scale with the cooperativity of the reactant, and the attempt frequency pre-factor (kBT/h) is scaled by a characteristic phonon wavelength equal to twice the lattice constant for crystal growth, and the density of the liquid and the sound velocity in the liquid for viscous relaxation. TZT accurately describes the temperature dependent crystal growth rates and viscosity of diverse materials over the entire temperature ranges Tg to Tm and Tg to T c, respectively, and affords detailed mechanistic understanding of condensed matter reactions like is afforded to molecular chemistry by the Eyring equation.;Previous group members have encountered the problem of the crystallization rate constants being experimental-technique dependent with the traditional Kolmogorov-Johnson and Mehl-Avrami (KJMA) model, and solved it by reintroducing the sample sizes and geometries into the KJMA model. Subsequently, melt and cold crystallization of the model system, halozeotype CZX-1, were investigated experimentally, with the latter normally exhibit more crystallites in the sample and faster crystallization rates than the former when bulk samples are evaluated. With the in-group developed software, the growth rates of individual crystallites in polycrystalline samples were obtained, which subsequently leads to an initial nucleation normalization constant introduced into the modified KJMA model to obtain material-specific crystallization kinetics for polycrystalline growth. With that, TZT for crystallization has demonstrated that melt and cold crystallization likely share the same mechanism, which has enabled investigation of crystallization kinetics over a broader temperature range by both melt and cold crystallization.;With the material-specific crystallization kinetics and a comprehensive theory for crystallization established, the kinetic isotope effect on crystallization of CZX-1 with differently isotopically substituted templates was studied to investigate the influence of the templating cation on the crystallization process, and to further articulate details of chemical processes involved in crystallization. By comparing the enthalpy and entropy of activation of crystallization obtained by TZT for differently isotopically substituted templates, both the hydrogen bonding and the template reorientational effects on crystallization were observed.;TZT demonstrates that the entropy of activation for crystallization and relaxation exhibit inverse temperature dependency such that there is a temperature at which their free energies of activation are equivalent. Below this temperature, TZT suggests that there is a greater probability of crystallization than of relaxation, yet under these conditions, crystallization can only propagate over the length scale that atoms and molecules rearrange cooperatively during relaxation. In the non-relaxed, quenched system, such crystal-type organization occurring over only a few tens of nanometers makes the barrier to bulk liquid relaxation insurmountable. Herein crystallization and viscosity data of fourteen diverse systems are evaluated by this theory demonstrating that the crystallization-relaxation free energy equivalence point defines the glass transition temperature.