From Rate Measurements to Mechanistic Data for Condensed Matter Reactions: A Case Study Using the Crystallization of [Zn(OH2)6][ZnCl4]

Abstract

Abstract:The kinetics of crystallization of the R = 3 hydrate of zinc chloride, [Zn(OH 2 ) 6 ][ZnCl 4 ], 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, v pb . 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 v pb 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.

LaMer's 1950 model of particle formation: a review and critical analysis of its classical nucleation and fluctuation theory basis, of competing models and mechanisms for phase-changes and particle formation, and then of its application to silver halide, semiconductor, metal, and metal-oxide nanoparticles

“…Most recently in 2017, a modified-KJMA (M-KJMA) 49 was proposed to ''ensure rate constants are intrinsic to the sample and reaction conditions, not the specific technique of measurement.'' 49 The assumptions behind and issues with these models are discussed elsewhere 50,51 and need not be rehashed here, save to emphasize four key points: 50,51 (i) all the models in Table 1 assume instantaneous/burst nucleation no matter if they are postulated to occur instantaneously at t = 0 or for example at some later, predetermined time, t = t 0 (known as ''sporadic'' as opposed to ''instantaneous'' nucleation in the Avrami-model literature [42][43][44][45][46][47]49 ); (ii) hence these mathematical Kolmogorov (1937), Johnson and Mehl (1939) (''KJMA''), 45,46 Erofe'ev (1946) 47 ) [a = extent (fraction) of reaction; k = a rate parameter; n = the ''Avrami exponent''] 1950 LaMer 1 Stat. mech; CNT (for S n sol formation)…”

“…[x = nucleus radius; ss = supersaturation; D = diffusion coefficient; r = (bulk) S n density; h = sphere radius] Word version: burst nucleation from supersaturated solution, then diffusion-controlled growth 2017 Martin (M-KJMA) 49 Mathematical; semi-empirical models say nothing about nucleation; instead, are really growth models post some presumed, undetailed nucleation events of unknown kinetics and unknown molecularity; (iii) the Avrami exponent, n, is a convolution of the dimension in space that the growth takes place in plus a parameter related to the assumed time dependence of the nucleation function. [42][43][44][45][46][47]49 Hence and unfortunately, the Avrami exponent parameter, n, has been destined to failure despite 480 years of literature trying to deconvolute and interpret nucleation and growth convoluted from the start into the single Avrami parameter, n. Additionally, (iv) the one k in the Avrami model is not a rate constant, as it is not defined by a balanced equation as rate constants must be.…”

Transition Zone Theory Compared to Standard Models: Reexamining the Theory of Crystal Growth from Melts

“…In our previous reports, we demonstrated that the TZT c accurately describes the temperature-dependent growth rates of diverse systems ranging from the strong SiO 2 to the fragile ortho -terphenyl (OTP). ,,, However, in none of those reports was the TZT c model directly compared to fits of data to standard models. Although it is never possible to prove a mechanistic model correct, some degree of validation is afforded to models that best fit experimental data with the fewest number of fitting parameters and for which the parameters have chemical/physical meaning, as opposed to empirical fitting parameters.…”

“… a Both Wagstaff data sets (refs and ) were used for the analysis reported here to mirror the standard model analysis in ref . Our previous TZT c analysis of SiO 2 crystallization (ref ) did not utilize data from ref because that report indicates significant oxygen deficiency of the system. b For comparison to the data analyzed in ref , growth-rate data from ref series-1 was used.…”

Combinatorial appraisal of transition states for in situ pair distribution function analysis

“…The analysis of structural transitions using diffraction or PDFs typically involves fitting data throughout the transition region with a linear combination of distinct phase models (Caliandro & Belviso, 2014;Schmidt et al, 2014;Chapman et al, 2015;Hillis et al, 2016). If there are any multi-phase regions, this linear combination approach approximates the relative volume fraction of the phases as a function of some transition coordinate (time, temperature, pressure etc.).…”