How the Overlapping Time Scales for Peptide Binding and Terrace Exposure Lead to Nonlinear Step Dynamics during Growth of Calcium Oxalate Monohydrate

Using in situ atomic force microscopy (AFM), we investigate the inhibition of calcium oxalate monohydrate (COM) step growth by aspartic acid-rich peptides and find that the magnitude of the effect depends on terrace lifetime. We then derive a time-dependent step-pinning model in which average impurity spacing depends on the terrace lifetime as given by the ratio of step spacing to step speed. We show that the measured variation in step speed is well lit by the model and allows us to extract the characteristic peptide adsorption time. The model also predicts that a crossover in the time scales for impurity adsorption and terrace exposure leads to bistable growth dynamics described mathematically by a catastrophe. We observe this behavior experimentally both through the sudden drop in step speed to zero upon decrease of supersaturation and through fluctuations in step speed between the two limiting values at the point where the catastrophe occurs. We discuss the model's general applicability to macromolecular modifiers and biomineral phases.