Effects of bubble size and approach velocity on bubble–particle interaction – a theoretical study

A theoretical analysis of the atomic force microscopy (AFM) approach–retract dynamic interaction between an air bubble and a hydrophilic silica plane was carried out based on the well-established Stokes–Reynolds–Young–Laplace model. An air bubble with different radii attached to the end of a cantilever approached the silica surface with different approach velocities in a 10^?3?M KCl solution. Results showed that with increasing approach velocity (0.1, 1, and 10?µm/s), the repulsive force, flattened area of the film, and hydrodynamic suction force between the 100-µm bubble and the silica plane increased. The film continued thinning at the initial stages of bubble retraction because of the attractive hydrodynamic pressure. When the bubble size decreased, the influence of hydrodynamic pressure was less evident. The final film thickness before bubble retraction was similar to the theoretical equilibrium thickness when the Laplace pressure was equal to the disjoining pressure.     

A Monte Carlo Method to Quantify the Effect of Reactor Residence Time Distribution on Polyolefins Made with Heterogeneous Catalysts: Part I—Catalyst/Polymer Particle Size Distribution Effects

Polyolefins are commercially produced in continuous reactors that have a broad residence time distribution (RTD). Most of these polymers are made with heterogeneous catalysts that also have a particle size distribution (PSD). These are totally segregated systems, in which the catalyst/polymer particle can be seen as a microreactor operated in semibatch mode, where the reagents (olefins, hydrogen, etc.) are fed continuously to the catalyst/polymer particle, but no polymer particle can leave. The reactor RTD has a large influence on the PSD of the polymer particles leaving the reactor, as well as in polymer microstructure and properties, polymerization yield, and composition of reactor blends. This article proposes a Monte Carlo model that can describe how particle RTD in a single or a series of reactors can affect the PSD of polymer particles made under a variety of operation conditions. It is believed that this is the most flexible model ever proposed to model this phenomenon, and can be easily modified to track all properties of interest during polyolefin production in continuous reactors with heterogeneous catalysts.     

The Effect of Residence Time Distribution on the Slurry‐Phase Catalytic Ethylene Polymerization: An Experimental and Computational Study

This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions.     

Stimuli‐responsive polymer nanocomposites based on styrene‐butadiene rubber and bacterial cellulose whiskers

Water‐induced mechanically adaptive rubber nanocomposites were prepared by mixing bacterial cellulose whiskers (BCWs) suspension with styrene‐butadiene rubber (SBR) latex, followed by evaporation method. The structure, morphology, dynamic mechanical properties, water stimuli‐responsive behavior, and biodegradability of SBR/BCWs nanocomposite films were investigated. The results showed that the hydrophilic whiskers had a significant reinforcement effect on the storage modulus of SBR matrix, which originated from the formation of a rigid three‐dimensional filler network within matrix by strong hydrogen bonding between whiskers. The SBR/BCWs nanocomposites showed pronounced water stimuli‐responsive behavior compared with neat SBR. The storage modulus of SBR/BCWs nanocomposite could be decreased by 99.2% after equilibrium water swelling. This remarkable water‐triggered modulus change is attributed to the disentanglement of BCWs network via competitive hydrogen bonding with water.     

Kinetic and particle size studies of emulsion polymerization of methyl methacrylate and styrene with using polyamidoamine dendrimer as seed

The emulsion polymerization of methyl methacrylate (MMA) and styrene (St) were investigated with using polyamidoamine (PAMAM) dendrimer as seed, potassium persulfate as initiator and sodium dodecyl sulfate as emulsifier. The effects of 4.0GPAMAM dendrimer concentration, initiator concentration, emulsifier concentration, monomer concentration, and polymerization temperature on the monomer conversion and polymerization rate were investigated. At the same time, the influence of the generation of PAMAM dendrimer on latex particle size was studied also. The results showed that the monomer conversion and polymerization rate increased with increasing initiator concentration, emulsifier concentration, monomer concentration, and polymerization temperature. But polymerization rate increased firstly with an increase in the 4.0GPAMAM dendrimer from 0.03 g to 0.09 g and then decreased with further increase to 0.12 g. When the concentration of 4.0GPAMAM dendrimer less than 1.449 × 10^?4 mol/L, the kinetic equation can be expressed by Rp∝[4.0GPAMAM]^0.772[SDS]^0.562[KPS]^0.589[M]^0.697, and the activation energy (Ea) of emulsion polymerization is 62.56kJ/mol. In additional, the copolymer latex particle size decreased and possessed monodispersity with increasing the generation of PAMAM dendrimer. According to FT-IR spectrum analysis, PAMAM dendrimer is successfully incorporated into the poly(PAMAM-St–MMA) latex particles.     

Structure and Dynamics in the Nucleosome Revealed by Solid‐State NMR

Eukaryotic chromatin structure and dynamics play key roles in genomic regulation. In the current study, the secondary structure and intramolecular dynamics of human histone H4 (hH4) in the nucleosome core particle (NCP) and in a nucleosome array are determined by solid‐state NMR (SSNMR). Secondary structure elements are successfully localized in the hH4 in the NCP precipitated with Mg²⁺. In particular, dynamics on nanosecond to microsecond and microsecond to millisecond timescales are elucidated, revealing diverse internal motions in the hH4 protein. Relatively higher flexibility is observed for residues participating in the regulation of chromatin mobility and DNA accessibility. Furthermore, our study reveals that hH4 in the nucleosome array adopts the same structure and show similar internal dynamics as that in the NCP assembly while exhibiting relatively restricted motions in several regions consisting of residues in the N‐terminus, Loop 1, and the α3 helix region.     

Scaling of particle trajectories on a lattice

The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. On both lattices, for most concentrations of the scatterers the trajectories close exponentially fast. For special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters.At criticality, in addition to the two critical exponents =15/7 andd _f=7/4 found before, the critical exponent =3/7 appears. This exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity. New scaling behavior was found for the square lattice partially occupied by rotators, indicating a different universality class than that of percolation clusters.Near criticality, in the critical region, two scaling functions were determined numerically:f(x), related to the trajectory length (S) distributionn _s, andh(x), related to the trajectory sizeR _s (gyration radius) distribution, respectively. The scaling functionf(x) is in most cases found to be a symmetric double Gaussian with the same characteristic size exponent =0.433/7 as at criticality, leading to a stretched exponential dependence ofn _S onS, n_Sexp(–S ^6/7). However, for the rotator model on the partially occupied square lattice an alternative scaling function is found, leading to a new exponent =1.6±0.3 and a superexponential dependence ofn _S onS.h(x) is essentially a constant, which depends on the type of lattice and the concentration of the scatterers. The appearance of the same exponent =3/7 at and near a critical point is discussed.     

Finite Range of Large Perturbations in Hamiltonian Dynamics

The dynamics defined by the Hamiltonian , where the _m are fixed random phases, is investigated for large values of A, and for . For a given P ^* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ – nt + _m) with \Delta \upsilon$$ " align="middle" border="0"> , is a random variable whose r.m.s. with respect to the _m is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing . For practical purposes close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.     

Some Infinite-Dimensional Algebras Arising in Spin Systems and in Particle Physics and their Grand Algebra

We indicate similarities in the structure of two types of infinite-dimensional algebras, one introduced 28 years ago in connection with the mass problem of elementary particles and the other seven years ago in connection with spin systems (XY models). We show that these algebras can be considered as representations of a single Grand Algebra, the enveloping algebra of an affine Kac–Moody algebra built on the Poincaré Lie algebra. As an associative and coassociative bialgebra of operators, the latter representation of the grand algebra is a preferred nontrivial deformation of the Ising case bialgebra.     

A Remark on the Use of Differential Forms for the Skyrme Problem

We introduce a formulation of the Skyrme problem using differential forms. By means of this formulation, we prove first that the homothetic map between the standard three-sphere of radius R, S³ _r R⁴, and S³ ₁ is the unique minimizer, modulo isometries, of the Skyrme energy in its homotopy class, for any R less than some critical value R₀ (3/2, 2]. We then establish a stability result for this Skyrme-form problem from which we can recover the result of M. Loss and N. S. Manton which states that this homothetic map is stable only up to R = 2.