As-produced carbon nanotubes come in bundles that must be exfoliated for practical applications in nanocomposites. Sonication not only causes the exfoliation of nanotube bundles but also unwanted scission. An understanding of how precisely sonication induces the scission and exfoliation of nanotubes will help maximising the degree of exfoliation while minimising scission. We present a theoretical study of the mechanics of carbon nanotube scission under sonicaton, based on the accepted view that it is caused by strong gradients in the fluid velocity near a transiently collapsing bubble. We calculate the length-dependent scission rate by taking the actual movement of the nanotube during the collapse of a bubble into account, allowing for the prediction of the temporal evolution of the length distribution of the nanotubes. We show that the dependence of the scission rate on the sonication settings and the nanotube properties results in non-universal, experiment-dependent scission kinetics potentially explaining the variety in experimentally observed scission kinetics. The non-universality arises from the dependence of the maximum strain rate of the fluid experienced by a nanotube on its length. The maximum strain rate that a nanotube experiences increases with decreasing distance to the bubble. As short nanotubes are dragged along more easily by the fluid flow they experience a higher maximum strain rate than longer nanotubes. This dependence of the maximum strain rate on nanotube length affects the scaling of tensile strength with terminal length. We find that the terminal length scales with tensile strength to the power of 1/1.16 instead of with an exponent of 1/2 as found when nanotube motion is neglected. Finally, we show that the mechanism we propose responsible for scission can also explain the exfoliation of carbon nanotube bundles.

The phase behaviour of small globular proteins is often modeled by approximating them as spherical particles with fixed internal structure. However, changes in the local environment of a protein can lead to changes in its conformation rendering this approximation invalid. We present a simple two-state model in which protein conformation is not conserved and where the high-energy, non-native state is stabilised by pair-wise attractive interactions. The resulting phase behaviour is remarkably complex, non-universal and exhibits re-entrance. The model calculations show a demarcation between a regime where conformational transitioning is largely enslaved by phase separation and one where this is not the case. In the latter regime, which is characterised by a large free energy difference between the native and the non-native state, we deduce that the kinetics of the phase transition strongly depend on the average conformation of the proteins prior to their condensation. For condensation to occur in this regime within a dispersion of native proteins, nucleation of a cluster of proteins in the non-native state is required. We argue that our theory supports the distinction between common phase separation and the nucleated assembly of non-native supramolecular aggregates in protein dispersions.

The coupling between protein conformation, molecular volume, and solution phase behaviour is studied theoretically for a two-state, coarse-grained protein model in which protein molecules can reversibly switch between a native and a non-native excited state. In the model, native and non-native conformers are represented by perfect spheres with different hard-core diameters. We presume the larger, non-native species to attract each other through some unspecified potential. We find that at low concentrations the native state is stabilised energetically and that at high concentrations the native state is again stabilised but this time by self-crowding, i.e., a lack of free volume. These two regimes are separated by two first-order transitions from a region where the non-native conformational state is prevalent, stabilised by attractive interactions between the proteins. The calculated phase diagram is very sensitive to even quite small differences in particle volumes and has unusual features, including the loss of a critical point if the size difference is sufficiently large. C 2015 AIP Publishing LLC. [http://dx