Coupling between Molecular Mobility and Kinetics of Crystal Growth in a Hydrogen-Bonded Liquid

Our aim here is to gain new insight into the nature of the crystalline phase formed in supercooled glycerol near the glass transition temperature and to establish the interrelationship between the kinetics of crystal growth and fundamental dynamic properties. The liquid’s dynamics and the crystalline development in glycerol, a hydrogen-bonded liquid, is studied by means of dielectric spectroscopy. We monitored the kinetics of crystallization by isothermal treatment at temperatures between 220 and 240 K (Tg = 185 K). Given the thermal protocol employed, we stimulated the growth of the crystalline phase from preexisting nuclei, in such a way that the observed kinetics is dominated by the crystal growth step. Our experimental results are discussed in terms of the classical theory of crystallization which predicts a significant correlation between the liquid’s diffusion and the crystal growth rate. The coupling between dynamic properties, such as dielectric α relaxation time, viscosity, and self-diffusion coefficient, and the characteristic crystal growth time is analyzed. We find that the crystal growth time scales with the glycerol’s self-diffusion coefficient as τcryst ∝ D−0.85, confirming that the liquid’s dynamics is the principal factor governing the crystal growth in glycerol above but close Tg. ■ INTRODUCTION Supercooled liquids, that is, liquids below their melting temperature Tm, have higher values of free energy with respect to the crystalline state. This excess of free energy drives the transformation of liquids into crystals through a first-order phase transition. Crystallization is a complex phenomenon, in which, apart from this thermodynamic driving force, several factors are simultaneously involved. Molecular mobility of the mother phase, surface tension of the liquid/crystal interface, intermolecular attractions, purity of the sample and its interactions with the environment, among others, are known to govern the crystallization tendency of supercooled liquids. Indeed, it is well established that the liquid’s dynamics plays a major role in the crystalline development, although the exact nature of this interrelationship is still a matter of debate. Moreover, contrary to the general impression, the study of crystallization may be seen as an indirect strategy for learning more about the relaxation dynamics of supercooled liquids. Seeking a better understanding of the structure−dynamics correlations during crystallization, here we report on the crystal growth behavior of the associated liquid glycerol. Glycerol is a model in numerous studies from the glass-forming-system community, and it has also attracted the attention of groups interested in exploring its crystallization behavior. The present report provides new information about the kinetics of crystal growth above but close to the glass transition temperature, Tg, as explored by dielectric relaxation spectroscopy. We followed the thermal protocol proposed by Möbius and co-workers, who considered the possibility that a glacial phase could be formed near Tg. 12 Our hypothesis is that the transformation of liquid glycerol into a metastable glacial phase (presumably formed by nanocrystals dispersed in a liquid matrix) would lead to the presence of an active dielectric relaxation due to the incomplete molecular ordering. We repeated our experiments several times and, with the exception of one case, we found no evidence of formation of a glacial or partially disordered crystal phase. The characteristic crystallization time at different temperatures was estimated through the so-called Avrami equation using the method proposed by Avramov and colleagues. The Avramov approach also provided us information about the dimensionality and morphology of the growing crystals. We complemented these results by applying the Maxwell−Wagner model for heterogeneous systems to our dielectric data as it has been recently proposed in a real-time crystallization study. Finally, we investigate the coupling between the characteristic time of crystal growth and the dielectric α relaxation time and, since we discuss our results under the framework of the classical theory, we also correlate our data with the liquid’s selfdiffusion coefficient. Our results indicate that the main factor governing the crystallization tendency in supercooled glycerol near Tg is the molecular mobility, at least for the thermal protocol we employed. ■ EXPERIMENTAL SECTION We used dry samples of glycerol purchased from Sigma-Aldrich (CH2OH−CHOH−CH2OH, >99.5% purity). Without additional Received: April 4, 2017 Revised: August 1, 2017 Published: August 3, 2017 Article pubs.acs.org/crystal © 2017 American Chemical Society 4628 DOI: 10.1021/acs.cgd.7b00484 Cryst. Growth Des. 2017, 17, 4628−4636 purification, fresh samples were used for every experiment and were handled under nitrogen atmosphere inside a glovebag. We explored the phase transformation of the supercooled liquid by means of dielectric spectroscopy. With this purpose, we filled a twoplate capacitor (electrodes made of brass) with 20 mm diameter and a gap of 0.25 mm controlled by a Kapton polyimide spacer. Once the capacitor was filled with the liquid material, it was transferred to the measuring cryostat and collection of the sample capacitance as a function of frequency was carried out. For a detailed description of the dielectric setup and cryostat, we refer the reader to the following publications. From the raw data, the complex dielectric permittivity of the sample ε*(ω) = ε′(ω) − iε′′(ω) is easily calculated by dividing the complex capacitance of the capacitor filled with the sample by the empty one. The procedure we used to induce the solidification of glycerol consisted of the thermal protocol depicted in Figure 1. We cooled down the liquid sample from 300 to 190 K at a cooling rate of approximately 5 K/h. Then, an isothermal annealing, approximately 5 K above Tg, at 190 K during 19 h was followed by a second isothermal treatment at the corresponding crystal growth temperature. ■ RESULTS AND DATA ANALYSIS We have recently discussed the effect of annealing at 190 K on the dielectric signal in detail. We observed a direct dependence of this annealing on the kinetics of crystal growth at higher temperatures, demonstrating the effectiveness of such annealing near the glass transition to induce the crystal nucleation. In this paper we go a step further and we explore the temperature dependence of the crystal growth kinetics. As an example, Figure 2 shows the temporal evolution of the complex dielectric permittivity of glycerol in the course of crystal growth at 220 K. As the molecules abandon the liquid phase and attach to the surface of the growing crystalline lattice, the amplitude (dielectric strength) of the α relaxation progressively decreases. Assuming that dipole−dipole correlations do not undergo significant modifications during the crystallization process, the observed reduction in intensity of the dielectric relaxation curve can be related to an increase of crystallinity. As the crystallization proceeds, there is a concomitant reduction in density of relaxing entities which, in accordance to the theory of dielectric relaxation, must be reflected in a reduction of the dielectric strength (Δε) as indicated by ε Δ ∝ μ N k T 2 d