Kinetics of Crystal Nucleation

In order to obtain data at lower temperature, specifically designed nudeation experiments were recently performed by fast scanning chip calorimetry in a wide temperature range between 40 and 110 °C [51, 52]. The PLA melt was rapidly cooled to the analysis temperature and then annealed for different periods of time to permit nuclei formation. The number of formed crystal nuclei was then probed by measurement of the crystallization rate at 120 °C, which accelerates according to the progress of earlier nuclei formation at the annealing temperature. 

Regarding the pathway of nudeation on the crystallization rate, it has been shown for PLA with 4.25% D-unit content that isothermal cold-crystallization is faster than melt-crystallization at identical temperature [53]. The half-time 

Effective routes for acceleration of the inherent slow crystaUization rate of PL A are the increase of the nudeation density by addition of heterogeneous nucle-ators and the increase of the chain mobility by addition of plasticizers [14, 57]. Chemical nudeation agents such as organic salts of sodium, which successfully were employed to accelerate the crystallization of poly(ethylene terephthalate) or polycarbonate, failed in the specific case of PLA [14, 57, 58]. Physical nudeation agents, in contrast, have been shown to be effective to enhance the crystallization of PLA. Among these, talc has been proven superior, most effective, and cost 

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Turnbull, D., and R.L. Cormia, Kinetics of Crystal Nucleation in Some Alkane Liquids, J. Chem. Phys. 34 820-831 (1961). 

An alternative possibility arises from considerations related to the development of crystalline structure in polyethylene [22], The main feature of this structure is the periodic folding of the polymer chains in the crystal. Theoretically this is explained within the context of the kinetics of crystal nucleation and growth from solution. According to Cormia, Price, and Turnbull [22], the fold-surface energy in polyethylene crystals is comparable to the end-interfacial energy of rodshaped nuclei. These surface free energies are of the order of 10 to... 

Androsch, R. and Di Lorenzo, M.L. (2013) Kinetics of crystal nucleation of poly(L-lactic acid). Polymer, 54, 6882-6885. 

The example indicates that, due to the transient chain deformation between the initial affine and the steady state mode, we expect transient effects in free energy and, in consequence, in the kinetics of crystal nucleation also at fixed deformation rates applied to the system. With a time-dependent deformation rates, ej(t), the transient effects are more complex. But they are tractable in terms of the present model where a numerical solution of (4.11) is needed for specified time dependent elongation rates. 

Supersaturation is an important parameter which drives crystallization and influences the kinetics of crystal nucleation and growth, and thus determines the outcome of crystallization. The degree of supersaturation can be defined as... 

Hancock B, Shamblin S, Zografl G (1995) Molecular mobflity of amorphous pharmaceutical solids below their glass transition temperatures. Pharm Res 12(6) 799-806 James PF (1985) Kinetics of crystal nucleation in silicate glasses. J Non-Crystalline Solids 73(1-3) 517-540... 

James RE, "Kinetics of Crystal Nucleation in Silicate Glasses," /. Non-Cryst. Solids, 73, 517-40 (1985). 

The influence of the solvent is also crucial in crystallization from solution, the most common crystallization technique in practice, but, as discussed in Section 13.10, there are practically no instances in the literature where this problem has appropriately been dealt with using dynamic simulation on realistic systems - not just the Lennard-Jones fluid. It is probably appropriate to say that if real progress in predicting the appearance of crystal polymorphs is desired, the current effort in improving intermolecular potentials and search algorithms for comparing static, final crystal structures should be redirected to the study of pre-crystallization states, and to the improvement of dynamic methods for the simulation of the kinetics of crystal nucleation and growth. 

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

Tavare, N.S. and Garside, J., 1986. Simultaneous estimation of crystal nucleation and growth kinetics from batch experiments. Chemical Engineering Research and Design, 64, 109. 

Before discussing the effect of short-chain branching on the kinetics of crystallization process, it is necessary to revisit the theory of secondary nucleation and the concept of regimes as given by Lauritzen and Hoffmann... 

Kinetics of Secondary Nucleation of Alumina Triliydrate in a Batch Crystallizer... 

In semi-crystalline polymers the interaction of the matrix and the tiller changes both the structure and the crystallinity of the interphase. The changes induced by the interaction in bulk properties are reflected by increased nucleation or by the formation of a transcrystalline layer on the surface of anisotropic particles [48]. The structure of the interphase, however, differs drastically from that of the matrix polymer [49,50]. Because of the preferred adsorption of large molecules, the dimensions of crystalline units can change, and usually decrease. Preferential adsorption of large molecules has also been proved by GPC measurements after separation of adsorbed and non-attached molecules of the matrix [49,50]. Decreased mobility of the chains affects also the kinetics of crystallization. Kinetic hindrance leads to the development of small, imperfect crystallites, forming a crystalline phase of low heat of fusion [51]. 

Any possible way to modify the final <001> / size ratio appeared to require that growth of crystals be conducted in an optimum range of supersaturation (corresponding to a concentration of aluminium between 2 and 4 mmol/1) without modification of the initial conditions, which determine the number of crystals nucleated. The practical way in which we realized this objective was the use of an initial synthesis medium containing only the aluminium present in the structure directing mixture. Once the nucleation occurred, an aluminate solution was injected in the autoclave in order to maintain the aluminium concentration at the desired level. The expected increase in growth surface was calculated using the above kinetic equations, and the flow rate of the injected solution was continuously adjusted in order to balance the incorporation of nutrient by the crystals. 

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