Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL)

The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer.

Comparison of Different Approaches to the Determination of the Work of Critical Cluster Formation

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation-Gibbs' method, the van der Waals-Cahn and Hilliard, and a newly developed modified Gibbs' approach-is given. As a model system for comparison, regular solutions are chosen. In addition to the work of critical cluster formation, the composition of the critical clusters, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is found, in particular, that, for regular solutions, Tolman's equation cannot serve as a first approximation for the description of the curvature dependence of the surface tension even for large cluster sizes and an alternative formula is developed. It is shown that the latter two mentioned methods of determination of the work of critical cluster formation (the van der Waals-Cahn and Hilliard and the modified Gibbs' approach) lead-at least for the model system considered-to qualitatively and partly quantitatively equivalent results. Nevertheless, differences remain which may lead to quantitative deviations when applied to the determination of the steady-state nucleation rates. The possible origin of such deviations is discussed and some further directions of analysis are anticipated. Copyright 2000 Academic Press.

Kinetics of Nucleation at Increasing Supersaturation

The kinetics of homogeneous nucleation-growth processes under increasing supersaturation is investigated. The increase of the supersaturation is hereby caused by an appropriate variation of external parameters such as pressure and temperature. Analytic expressions are formulated for the dependence of the number of supercritical clusters both on the rate of change of the supersaturation and on time. In generalization of previous studies, both thermal and athermal nucleation are taken into consideration. It turns out that in dependence on the rate of change of the external parameters, either thermal (for moderate rates) or athermal (for higher rates) nucleation, dominates the process. It is shown further that, in the range where thermal nucleation dominates, the onset of nucleation-growth processes, i.e., the minimum value of the supersaturation required for intensive nucleation, depends weakly (logarithmically) on the rate of increase of the supersaturation. Criteria are formulated under which conditions the commonly employed assumption-independence of the nucleation-growth process on the way the initial unstable state is established-is applicable. As shown, quite generally these criteria are not fulfilled. In a further step of the analysis, simultaneously to external variations of the thermodynamic parameters, internally generated changes of the state of the system (depletion effects) are accounted for. For segregation processes in solutions (bubble formation), which are analyzed here as an example, such effects result from a decrease of the supersaturation due to the consumption of solute particles by the clusters of the newly formed phase. Basic characteristics of the nucleation-growth process, such as the maximum number of clusters formed in the system, are determined in dependence on both externally (rate of change of the external parameters) and internally (depletion effects) induced changes of the thermodynamic state of the system. It is shown, in particular, that the interplay of both factors is, in general, of comparable importance for the outcome of the nucleation-growth process. Copyright 1999 Academic Press.