It has recently been proposed that the miscibility of nanoparticles with a polymer matrix can be controlled by grafting polymer chains to the nanoparticle surface. As a first step to study this situation, we have used molecular dynamics simulations on a single nanoparticle of radius R (4σ ≤R≤ 16σ , where σ is the diameter of a polymer monomer) grafted with chains of length 500 in a polymer melt of chains of length 1000. The grafting density Σ was varied between 0.04-0.32 chains/σ 2 . To facilitate equilibration a Monte Carlo doublebridging algorithm is applied -new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. For the long brush chains studied here, the structure of the brush assumes its large particle limit even for R as small as 8σ , which is 1 consistent with recent experimental findings. We study autophobic dewetting of the melt from the brush as a function of increasing Σ. Even these long brush and matrix chains of length 6 and 12 N e , respectively, (the entanglement length is N e ∼ 85) give somewhat ambiguous results for the interfacial width, showing that studies of two or more nanoparticles are necessary to properly understand these miscibility issues. Entanglement between the brush and melt chains were identified using the primitive path analysis. We find that the number of entanglements between the brush and melt chains scale simply with the product of the local monomer densities of brush and melt chains.

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects.

The viscoelasticity of a number of polymer solutions was studied by subjecting the solutions to simple harmonic displacements in a pipe. Both water-based and organic-based solutions were used. Results were analyzed in terms of a modification of the operator equation of linear viscoelasticity. A three-constant model used earlier was found to correlate most of the data. Further experiments to verify the model are suggested.In previous papers ( 4 , 7), a quasilinear hereditary constitutive equation for incompressible materials exhibiting stress relaxation has been derived, and some properties of this equation have been discussed. The equation isThis equation and those derived from it are intended to be valid for very small strain rates only; this should be borne in mind in what follows. An experimental method for determining the relaxation function is the principal topic of this paper. PERTINENT LITERATUREIt has been shown ( 4 ) that the relaxation function of materials described by Equation (1) cannot be determined by steady, laminar shear flow experiments alone. In such experiments, one can determine the viscosity 71 and a normal stress coefficient 8. The viscosity is related to + ( t ) by and the normal stress coefficient is related to $ ( t ) byso that steady, laminar shear flow experiments can yield at most the integral and the first moment of the relaxation function.Kapoor et al. (7) have shown how recoil experiments could be used, in principle, to check the applicability of a given relaxation function. This method is not suitable for actual determination of + ( t ) , however, for two reasons: initial conditions necessary to keep solutions of the associated boundary value problem simple are difficult to attain experimentally, and solutions of the associated boundary value problem are Fourier-Bessel series so that the computational problem is extremely difficult.Oldroyd (9) suggested and analyzed an experiment whereby the properties of viscoelastic materials could be determined, at least for small rates of strain. This experiment utilized a simple harmonic deformation in a concentric cylinder apparatus. Subsequently, apparatus was constructed and utilized by Oldroyd and his co-workers (10, 11, 12) to determine properties of various polymer Saul Vela is with the Jersey Production Research Company, Houston, Texas.solutions. Analysis was confined to a certain kind of viscoelastic material; the constitutive equation of this idealized material is tantamount to Equation ( l ) , with the relaxation function given by 1"In a later paper, Walters ( 1 4 ) has analyzed the experimental results cited above in terms of a somewhat different relaxation function, which also gave a good fit of the data.The foregoing papers on simple harmonic deformation are subject to criticism on two grounds. First, one can determine two quantities (an amplitude ratio and a phase difference) from the experiment, but only one of them (the amplitude ratio) was fitted to equations derived. If the model is correct, both quantities must fit. Walters...

No abstract

No abstract