Abstract
The kinetics of crystallization of the R = 3 hydrate of zinc chloride, [Zn(OH2)6][ZnCl4], is measured by time-resolved synchrotron x-ray diffraction, time-resolved neutron diffraction, and by differential scanning calorimetry. It is shown that analysis of the rate data using the classic Kolmogorov, Johnson, Mehl, Avrami (KJMA) kinetic model affords radically different rate constants for equivalent reaction conditions. Reintroducing the amount of sample measured by each method into the kinetic model, using our recently developed modified-KJMA model (M-KJMA), it is shown that each of these diverse rate measurement techniques can give the intrinsic, material specific rate constant, the velocity of the phase boundary, vpb. These data are then compared to the velocity of the crystallization front directly measured optically. The time-resolved diffraction methods uniquely monitor the loss of the liquid reactant and formation of the crystalline product demonstrating that the crystallization of this hydrate phase proceeds through no intermediate phases. The temperature dependent vpb data are then well fit to transition zone theory to extract activation parameters. These demonstrate that the rate-limiting component to this crystallization reaction is the ordering of the waters (or protons) of hydration into restricted positions of the crystalline lattice resulting in large negative entropy of activation.
Highlights
Time-resolved diffraction provides a powerful tool with which to study the rate of condensed matter reactions such as phase transitions
We present the results of the crystallization rate measurements by bulk and individual crystallite Temperature- and Time-Resolved X-ray Diffraction (TtXRD), bulk Time-Resolved Neutron Diffraction (TtND), and differential scanning calorimetry (DSC)
We demonstrate the necessary corrections afforded by modified-KJMA model (M-KJMA) analysis to yield a comprehensive set of rate constants that are intrinsic to the sample and the conditions of the specific crystallization reaction
Summary
Time-resolved diffraction provides a powerful tool with which to study the rate of condensed matter reactions such as phase transitions. While time-resolved diffraction is an effective means to measure the rate of a transformation, it is necessary to apply some model to the rate data to extract kinetic, and subsequently mechanistic information about the transition of interest. (KJMA) model, Equation (1), is the most commonly utilized rate expression for kinetic analysis of condensed phase reactions. This expression assumes a phase boundary controlled process, with α(t) corresponding to the fraction of the sample transformed, kA the rate constant, t0 the time of the onset of nucleation, and the exponent n describing the dimensionality of the process. The KJMA expression provides excellent fits for diverse phase transition kinetic data, from which mechanistic detail is frequently inferred. As we recently summarized [2], and here provide another case study, the KJMA parameters are significantly affected by experimental factors that do not necessarily reflect the true reaction mechanism
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