Radial growth rate of near-critical crystal nuclei in poly(l-lactic acid) (PLLA) in Tammann's two-stage development method

The specific features of crystal nucleation widely determine the morphology of the evolving crystalline material. Crystal nucleation is, as a rule, not accessible by direct observation of the nuclei, which develop with time. This limitation is caused by the small size (nanometer scale) of the critical nuclei and the stochastic nature of their formation. We describe an experimental approach to the determination of specific features of the cluster size distribution employing fast scanning calorimetry at scanning rates up to 10 000 K s^-1. The surviving cluster fraction is determined by selectively melting/dissolving clusters smaller than the critical size corresponding to the highest temperature of a short spike positioned between the nucleation and the development stage in Tammann's two-stage method. This approach allows for estimating the time evolution of the radius of the largest detectable clusters in the distribution. Knowing this radius as a function of nucleation time allows for determining a radial growth rate. In the example of poly(l-lactic acid) (PLLA), the order of magnitude estimate of radial growth rates of clusters of about 2-5 nm yields values between 10^-5 and 10^-3 nm s^-1. The radial growth rate of micrometer-sized spherulites is available from optical microscopy. The corresponding values are about three orders of magnitude higher than the values for the nanometer-sized clusters. This difference is explainable by stochastic effects, transient features, and the size dependence of the growth processes on the nanometer scale. The experimental and (order of magnitude) classical nucleation theory estimates agree well.