The Gibbs's definition of phase assumes completely homogeneous composition, with fluctuations bringing about local variations of less than a few percent. We apply light scattering, atomic force microscopy and other techniques to demonstrate that solutions of even a single protein of moderate concentration do not comply with this definition. In such solutions clusters of sizes from several tens to several hundred nanometers exist and have limited lifetimes. These clusters have a higher free energy than the protein solution, and their lifetime is determined by the barrier for their decay. The clusters determine the viscous and visco-elastic behavior of the solution and are an essential part of potential condensation and aggregation pathways. Cluster theories developed for colloid systems appear inapplicable to proteins due to the high level of implied Coulombic repulsion. A microscopic theory, which should account for stabilizing and destabilizing factors involving protein molecules and solvent inside the clusters, is still to be developed.
The triangular tessellation and the Fibonacci spiral patterns of definite chirality can be reproduced through stress manipulation on the Ag core/ SiO_2 shell microstructures. These results will be very helpful for the design and fabrication of patterned structures on curved surfaces that can find useful applications in photonics and foldable electronics. Furthermore, these results obtained in a purely inorganic material system hint at the role of stress in influencing the plant patterns. We speculate that the prerequisite for the occurrence of Fibonacci spiral patterns as stressed buckling modes be the availability of a conical support. The robust adherence of the stressed patterns to the geometry of the supports sheds some light on the mechanical rationale underlying the formation of particular plant patterns. Of course, a comprehensive model for the formation of plant patterns should incorporate as well the biochemical and genetic processes that alter growth at deeper levels.
Atomic force microscopy enables in-situ observations of mineral growth on a nanoscale. The direct observation at molecular resolution of mineral surfaces during growth from solutions can contribute to our knowledge of mineral growth processes. Crystallographic information obtained from observations as well as measurements of growth rates give valuable evidence for crystal growth mechanisms, either confirming existing models or suggesting alternatives. The morphology of a growing crystal is determined by the rate of growth of different crystallographic faces. However, growth modifications can be seen in the presence of changing solution concentration as well as impurity molecules. Anisotropic growth may result from the crystallographic control of the existing underlying crystal structure or from impurity incorporation into the growing surface. The formation of a solid solution may show very significant growth differences from crystal growth of phases with fixed compositions. Here a number of experiments using calcite and barite are described to illustrate crystal growth mechanisms.