Size- and shape-dependent transformation of nanosized titanate into analogous anatase titania nanostructures

A size- and shape-dependent morphological transformation was demonstrated during the hydrothermal soft chemical transformation, in neutral solution, of titanate nanostructures into their anatase titania counterparts. Specifically, lepidocrocite hydrogen titanate nanotubes with diameters of approximately 10 nm were transformed into anatase nanoparticles with an average size of 12 nm. Lepidocrocite hydrogen titanate nanowires with relatively small diameters (average diameter range of < or = 200 nm) were converted into single-crystalline anatase nanowires with relatively smooth surfaces. Larger diameter (>200 nm) titanate wires were transformed into analogous anatase submicron wire motifs, resembling clusters of adjoining anatase nanocrystals with perfectly parallel, oriented fringes. Our results indicate that as-synthesized TiO2 nanostructures possessed higher photocatalytic activity than the commercial titania precursors from whence they were derived.     

Spinodal Decomposition¶for the Cahn–Hilliard–Cook Equation

This paper gives theoretical results on spinodal decomposition for the stochastic Cahn–Hilliard–Cook equation, which is a Cahn–Hilliard equation perturbed by additive stochastic noise. We prove that most realizations of the solution which start at a homogeneous state in the spinodal interval exhibit phase separation, leading to the formation of complex patterns of a characteristic size. In more detail, our results can be summarized as follows. The Cahn–Hilliard–Cook equation depends on a small positive parameter ε which models atomic scale interaction length. We quantify the behavior of solutions as ε→ 0. Specifically, we show that for the solution starting at a homogeneous state the probability of staying near a finite-dimensional subspace ?_ε is high as long as the solution stays within distance r _ε=O(ε ^R ) of the homogeneous state. The subspace ?_ε is an affine space corresponding to the highly unstable directions for the linearized deterministic equation. The exponent R depends on both the strength and the regularity of the noise. Received: 2 May 2000 / Accepted: 8 July 2001     

Spinodal Decomposition for Multicomponent Cahn–Hilliard Systems

We consider the initial-stage phase separation process in multicomponent Cahn–Hilliard systems through spinodal decomposition. Relying on recent work of Maier-Paape and Wanner, we establish the existence of certain dominating subspaces determining the behavior of most solutions originating near a spatially homogeneous state. It turns out that, depending on the initial concentrations of the alloy components, several distinct phenomena can be observed. For ternary alloys we observe the following two phenomena: If the initial concentrations of the three components are almost equal, the dominating subspace consists of two copies of the finite-dimensional dominating subspace from the binary alloy case. For all other initial concentrations, only one copy of the binary dominating subspace determines the behavior. Thus, in the latter case we observe a strong mutual coupling of the concentrations in the alloy during the initial separation process.