A one-sided diffusion-limited model for dendritic growth in two dimensions is simulated numerically by means of a Green’s function in quasistationary approximation. Anisotropy in the surface tension is found necessary for dendritic growth. Scaling behavior of the growth rate and tip radius is found as function of the undercooling and anisotropy, in agreement with recent results for needle crystals. The sidebranches scale with the stability length. The numerical procedure is described in some detail.

Dendritic growth of crystals in two dimensions is analyzed by a Green’s-function method. A one-sided diffusional model is treated in quasistationary approximation. Anisotropy is found necessary for dendritic growth. We find scaling with anisotropy to be in agreement with recent results for needle crystals in the symmetric model. For fixed anisotropy the growth rate is proportional to the square of the Peclet number. The side-branch pattern is in qualitative agreement with experiments in three dimensions for different anisotropies.

Micelles formed by (ethylene oxide) (propylene oxide) (ethylene oxide) triblock copolymers (Pluronic F127 and L64) in aqueous solutions have been visualised by cryogenic transmission electron microscopy (cryo-TEM). The resolution achieved allows detailed inspection of the individual micelles, their size, shape, core-shell structure as well as long-range order. The dependence of the microstructure on the concentration of the solution as well as on the type (block sizes) of the Pluronic polymer are reported and demonstrate the sensitivity of the method to these parameters.

After reviewing the present status of research on the crystallization of flexible polymers some new perspectives in the field, as arising from ongoing research, will be presented. First, a brief resumé is given of the experimental material on chain-folded crystallization (here to be termed ‘main stream’) on polyethylene as the model substance. This is followed by a brief account on extended chain type crystallization as realizable, in the case of polyethylene, under hydrostatic pressure through the intervention of a mobile phase (here termed ‘speciality stream’). This is followed by a review of theoretical attempts to account for the experimental facts with special emphasis on open-ended issues and on connections with the main body of theories on crystal growth outside the polymer field. The new perspectives are aimed at linking the two streams, chain-folded and chain-extended, through a scheme based on new experimental recognitions on polyethylene but with potential relevance to all crystal growth, in fact phase transitions. It relies on crystal size as a variable, leading to the realistic possibility that phase stabilities can invert with size, i.e. a phase which is metastable for infinite size can become stable when the phase is sufficiently small. When this condition is applied to crystal growth it follows that a crystal in such a situation will appear and grow in a phase that is different from that in its state of ultimate stability. These general thermodynamic considerations can be linked to kinetic criteria accounting, amongst others, for the frequently observed dominance of metastable phases, thus providing a combined thermodynamics- and kinetics-based justification to Ostwald's rule of stages. In the case of polymers such transient phases can have greatly enhanced influence owing to the associated high chain mobility. The latter enables thickening growth through the agency of sliding diffusion, which can then create altogether new possibilities in the field of polymer crystallization.