Capillarity effects on crystallization kinetics: Insulin

During layerwise growth of crystals, capillarity governs the generation of new crystal layers. Theory predicts that the line tension of the layer edge determines, via the characteristic two-dimensional capillary length L _c, the rates of generation and initial growth of the new layers. To test the correlation between L_c and the rate of layer generation, we used in situ Tapping Mode Atomic Force Microscopy (TM-AFM) to study the generation and spreading of layers during crystallization of rhombohedral, R3, porcine insulin. We show that crystallization of this insulin form is uniquely suitable for such an investigation due to the linear kinetics of step growth it exhibits. This linear kinetics reflects the abundance of the incorporation sites along the rough steps, the lack of long-range step-step interactions, and the transport control of the growth kinetics. The kinetic coefficients are 7 × 10^-3 and 4 × 10^-2 cm s^-1, respectively, in the absence and presence of the cosolvent acetone-somewhat high for proteins and comparable to values for inorganic systems. We show that (i) the relevant capillary length, the size of a critical quadrangular 2D nucleus L_c, is the main scaling factor for the density of growth steps, while (ii) all steps longer than L_c grow with a rate determined only by the supersaturation and independent of their length. We explain the divergence of (ii) from theoretical predictions with the high supersaturations typical of the growth of this protein system.