Exact Phase Diagram of a model with Aggregation and Chipping

We revisit a simple lattice model of aggregation in which masses diffuse and coalesce upon contact with rate 1 and every nonzero mass chips off a single unit of mass to a randomly chosen neighbour with rate $w$. The dynamics conserves the average mass density $\rho$ and in the stationary state the system undergoes a nonequilibrium phase transition in the $(\rho-w)$ plane across a critical line $\rho_c(w)$. In this paper, we show analytically that in arbitrary spatial dimensions, $\rho_c(w) = \sqrt{w+1}-1$ exactly and hence, remarkably, independent of dimension. We also provide direct and indirect numerical evidence that strongly suggest that the mean field asymptotic answer for the single site mass distribution function and the associated critical exponents are super-universal, i.e., independent of dimension.Comment: 11 pages, RevTex, 3 figure

Transition from 2D to 3D SBA‐15 by High‐Temperature Fluoride Addition and its Impact on the Surface Reactivity Probed by Isopropanol Conversion

A systematic variation of the SBA‐15 synthesis conditions and their impact on the structural and chemical characteristics are reported. An incremental alteration of the hydrothermal aging temperature and time was used to induce changes of the highly ordered SBA‐15 structure. Any effects on the total surface area, mesopores size, micropore contributions, and pore connectivity are amplified by a combined incremental increase of the NH4F concentration. Based on changes of the unit‐cell parameter as a function of the mesopore size, and a feature in the low‐angle XRD pattern, useful descriptors for the disorder of the corresponding SBA‐15 are identified. An additional analysis of the Brunauer–Emmett–Teller (BET) surface area and pore size distributions enables investigations of the structural integrity of the material. This systematic approach allows the identification of coherencies between the evolution of physical SBA‐15 properties. The obtained correlations of the surface and structural characteristics allow the discrimination between highly ordered 2D SBA‐15, disordered 3D SBA‐15, and highly nonuniform silica fractions with mainly amorphous character. The fluoride‐induced disintegration of the silica structure under hydrothermal conditions was also verified by TEM. A direct influence of the structural adaption on the chemical properties of the surface was demonstrated by isopropanol conversion and H/D exchange monitored by FTIR analysis as sensitive probes for acid and redox active surface sites