Colloidal Nanocrystals of Lithiated Group 14 Elements

The synthesis of colloidal nanocrystals (NCs) of lithiated group 14 elements (Z=Si, Ge, and Sn) is reported, which are Li_4.4Si, Li_3.75Si, Li_4.4Ge, and Li_4.4Sn. Li_xZ compounds are highly reactive and cannot be synthesized by existing methods. The success relied on separating the surface protection from the crystal formation and using a unique passivating ligand. Bare Li_xZ crystals were first produced by milling elemental Li and Z in an argon‐filled jar. Then, under the assistance of additional milling, hexyllithium was added to passivate the freshly generated Li_xZ NCs. This ball‐milling‐assisted surface protection method may be generalized to similar systems, such as Na_xZ and K_xZ. Moreover, Li_4.4Si and Li_4.4Ge NCs were conformally encapsulated in carbon fibers, providing great opportunities for studying the potential of using Li_xZ to mitigate the volume‐fluctuation‐induced poor cyclability problem confronted by Z anodes in lithium‐ion batteries.     

Steric interactions between finite objects and end-grafted polymer chains: a two-dimensional mean-field analysis

We examine the usefulness of a two-dimensional self-consistent mean-field theory for predicting polymer-induced forces between a finite object and a surface. The predictions are compared with scaling results for the compression of a single, end-grafted chain by a disk and for the compression of a brush with an athermal wall. For the former, the mean-field predictions agree with scaling theory and, in addition, provide the necessary prefactor in the scaling expressions for the Helmholtz potential and force of compression. For the brush, the mean-field results agree with the Alexander-de Gennes scaling result at moderate compressions and also provide an analytical expression for the force without any unknown parameters. We also use the mean-field theory to examine the interaction of a model bacterium with a planar substrate and show that steric interactions due to a single polymer chain alone can dominate van der Waals attraction under typical practical conditions and thus prevent bacterial adhesion to the surface.     

Explicit solution for a vector-valued LQG homing problem

In this note, a vector-valued LQG homing problem subject to a controlled stock-wealth process is formulated. Under certain conditions, the problem is solved explicitly via an auxiliary scalar LQG homing problem.     

Enhancing sensitivity of the white-light speckle method in terrestrial applications

Noncoherent-light speckle interferometry techniques have been used for terrestrial motion measurements. The long imaging distances typical of these applications limit sensitivity and accuracy because of atmospheric turbidity. Experiments show that the performance of camera systems used to record glacier surface speckle agrees with the predictions of theory developed for astronomical work. Several methods to enhance the technique are suggested.     

Surface and interior strain fileds measured by multiple-embedded-grid moiré and strain gages

Surface and interior straini fields in thick specimens of polycarbonate have been measured by an embedded-multiple-grid moiré method. Interior gratings are photographed through intervening gratings. Coherent optical processing of grating records creates moiré fringe pattern. A correction procedure was developed to eliminate moiré errors caused by strain-induced gradients of refractive index. This procedure utilizes the refraction distribution as obtained from observation of a grating from opposite sides of a specimen. No measurements other than the normal moiré observations are required in order to find actual strains. The correction technique should be useful in refining the results obtained when other optical methods are used in three-dimensional situations. The method is utilized to determine strains on the surfaces and at the mid-and quarter-planes of thick compact tension specimens. Results obtained, after correction, agree with measurements made with embedded strain gages. Maximum tensile strain occurs on the midplane. The findings are rationalized by consideration of thickness and proximity to the crack tip.