Transport Coefficients in Some Stochastic Models of the Revised Enskog Equation

A stochastic model of the revised Enskog equation is considered. A choice of the smearing function suggested by the work of Leegwater is used to apply the model to the repulsive part of the Lennard-Jones potential and the inverse-power soft-sphere potential. The virial coefficients obtained from the equilibrium properties of the models are in excellent agreement with the known exact coefficients for these models. The transport coefficients for the repulsive Lennard-Jones (RLP) model are also computed and appear to be of comparable accuracy to the Enskog-theory coefficients applied directly to a hard-sphere system, although exact results for the RLP with which to make an extensive comparison are not yet available. The pressure and the transport coefficients obtained from the model (shear viscosity, thermal conductivity, and self-diffusion) are compared with the pressure and the corresponding transport coefficients predicted by the Enskog and square-well kinetic theories.     

Coalescence suppression in model immiscible polymer blends by nano-sized colloidal particles

The effect of nanometer sized silica particles (R16 nm) on the flow-induced morphology of immiscible polymer blends is studied. Polydimethylsiloxane (PDMS) and polyisobutylene (PIB) are chosen as model components. A stable droplet/matrix microstructure is obtained for blends of 30% PIB in 70% PDMS or vice versa. Rheological measurements are used to show that the silica particles alter the sensitivity of the of dispersed phase/matrix microstructure to shear flow. Coalescence is suppressed or at least slowed down on a practical time scale, especially when PDMS is the matrix phase. The effect of mixing conditions, pre-shear rate and particle concentration on the blend morphology are studied. Cryo-SEM is used to observe the accumulation of the particles at the interface. Blends stabilized by solid particles could provide an interesting alternative to blends compatibilized by block-copolymers.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

<Emphasis Type="Italic">N</Emphasis>-dimensional space-time unit spheres and Lorentz transformation

By using hyperbolic virtual unit of Clifford algebra, the concept of n-dimensional space-time unit spheres is introduced. It is used as n-dimensional Minkowski space-time and Lorentz transformation.     

Nanometer Calibration Particles: What is Available and What is Needed?

Information on available polystyrene calibration spheres is presented regarding the particle diameter, uncertainty in the size, and the width of the size distribution for particles in a size range between 20 and 100nm. The use of differential mobility analysis for measuring the single primary calibration standard in this size range, 100nm NIST Standard Reference Material®1963, is described along with the key factors in the uncertainty assessment. The issues of differences between international standards and traceability to the NIST Standard are presented. The lack of suitable polystyrene spheres in the 20–40nm size range will be discussed in terms of measurement uncertainty and width of the size distributions. Results on characterizing a new class of molecular particles known as dendrimers will be described and the possibilities of using these as size calibration standards for the size range from 3 to 15nm will be discussed.     

Facile one‐pot method of initiator fixation for surface‐initiated atom transfer radical polymerization on carbon hard spheres

An efficient and novel one‐pot process is developed to immobilize the atom transfer radical polymerization (ATRP) initiators onto the surface of fully pyrolyzed carbon hard spheres (CHSs) via a radical trapping process from the in situ thermal decomposition of bis(bromomethylbenzoyl)peroxide. The CHSs do not require any additional preparative treatment prior to the initiator immobilization. Styrene and methyl methacrylate are polymerized onto initiator‐immobilized CHSs by surface‐initiated atomic transfer radical polymerization (SI‐ATRP). Samples are characterized using Fourier transform infrared, thermogravimetric analysis, scanning electron microscopy, and transmission electron microscopy. These methods of characterization confirmed that all the CHSs are coated with a uniform layer of grafted polymer. This efficient, one‐pot immobilization of ATRP‐initiators represents an exceptionally simple route for the rapid preparation of various polymer‐coated carbon‐based nanomaterials using SI‐ATRP. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3314–3322     

Three-bridge links with infinitely many three-bridge spheres

We construct infinitely many three-bridge links each of which admits infinitely many three-bridge spheres up to isotopy.     

Self-diffusion of multiarm star polymers in solution far from and near the ordering transition

The self-diffusion of three 128-arm polybutadiene star solutions in toluene was investigated over a broad concentration range from dilute to the ordering region with pulsed field gradient NMR (PFG-NMR). The strong concentration dependence of the self-diffusion coefficient in the fluid state is distinguished clearly from that of linear chains and can be described by a non-Arrhenius VFT-like equation with the concentration playing the role of inverse temperature. In the concentrated regime, the observation of two dynamic phases reflects the coexistence of crystalline and liquid phases over a limited concentration region. The concentration dependences of both the ordinary (fluid-like) diffusion and the completely restricted in-cage motion of these hyper stars are in agreement with the behavior of concentrated colloidal suspensions.     

The Kinetic Theory of Simple Reacting Spheres: I. Global Existence Result in a Dilute-Gas Case

Existence of global-in-time, spatially inhomogeneous, and L ¹-renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass, energy, and entropy.     

Hard-sphere binary-collision operators

The time displacement operator is described for a system of hard-sphere particles. We show how to avoid needing a representation for this operator in unphysical regions of phase space, and how to construct a useful representation in terms of binary collision operators in the physical region. The various binary collision operators used for hard-sphere systems are derived for the case of a system of two spheres, and the results are generalized toN-particle systems.Dedicated to Prof. E. G. D. Cohen on the occasion of his 65th birthday.     

Nanoparticles and Nanolayers In Commercial Applications

This paper presents particulate and layered materials used in industry with at least one dimension under 500 nm. The objective is to bring to the attention of researchers areas of investigation where new properties and phenomena may manifest. The most relevant materials are natural and synthetic platelets and spherical and coated silica particles.