Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

The charge-assisted hydrogen-bonded organic framework (CAHOF) self-assembled from the conjugated acid of tetrakis(4-aminophenyl)methane and 2,6-naphthalenedisulfonate as a new class of recyclable Brønsted acid catalysts

The acid–base neutralization reaction of commercially available disodium 2,6-naphthalenedisulfonate (NDS, 2 equivalents) and the tetrahydrochloride salt of tetrakis(4-aminophenyl)methane (TAPM, 1 equivalent) in water gave a novel three-dimensional charge-assisted hydrogen-bonded framework (CAHOF, F-1). The framework F-1 was characterized by X-ray diffraction, TGA, elemental analysis, and 1H NMR spectroscopy. The framework was supported by hydrogen bonds between the sulfonate anions and the ammonium cations of NDS and protonated TAPM moieties, respectively. The CAHOF material functioned as a new type of catalytically active Brønsted acid in a series of reactions, including the ring opening of epoxides by water and alcohols. A Diels–Alder reaction between cyclopentadiene and methyl vinyl ketone was also catalyzed by F-1 in heptane. Depending on the polarity of the solvent mixture, the CAHOF F-1 could function as a purely heterogeneous catalyst or partly dissociate, providing some dissolved F-1 as the real catalyst. In all cases, the catalyst could easily be recovered and recycled. © 2020 Kuznetsova et al