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We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for the shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of the shear rate, as well as molecular parameters (molar mass, blend composition, and decreasing molar mass of linear component in the blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with the shear rate. The universal scaling of the strain at overshoot and fractional overshoot (the ratio of the maximum to the steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends. The shear thinning behavior of pure rings yields a slope nearly identical to predictions (−4/7) of a recent shear slit model and molecular dynamics simulations. Data for the second normal stress difference are reported for rings and ring-linear blends. While N2 is negative and its absolute value stays below that of N1, as for linear polymers, the ratio –N2/N1 is unambiguously larger for rings compared to linear polymer solutions with the same number of entanglements (almost by a factor of 2), in agreement with recent nonequilibrium molecular dynamics simulations. Furthermore, –N2 exhibits slightly weaker shear rate dependence compared to N1 at high rates, and the respective power-law exponents can be rationalized in view of the slit model (3/7) and simulations (0.6), although further work is needed to unravel the molecular original of the observed behavior. The comparison of shear and elongational stress growth coefficients for blends reflects the effect of ring-linear threading, which leads to significant viscosity enhancement in elongation. Along the same lines, the elongational stress is much larger than the first normal stress in shear, and their ratio is much larger for rings and ring-linear blends compared to linear polymers. This confirms the interlocking scenario of rings and their important role in mechanically reinforcing linear matrices. [ABSTRACT FROM AUTHOR]

The second virial coefficient, A[SUB2], is evaluated between pairs of short chain molecules by direct simulations using a parallel tempering Monte Carlo method where the centers of mass of the two molecules are coupled by a harmonic spring. Three off-lattice polymer models are considered, one with rigid bonds and two with flexible bonds, represented by the finitely extensible nonlinear elastic potential with different stiffness. All the models considered account for excluded volume interactions via the Lennard-Jones potential. In order to obtain the second virial coefficient we calculate the effective intermolecular interaction between the two polymer chains. As expected this intermolecular interaction is found to be strongly dependent upon chain length and temperature. For all three models the θ temperature (θ[SUBn]), defined as the temperature at which the second virial coefficient vanishes for chains of finite length, varies as θ[SUBn]-θ[SUB∞]∝n[SUP-1/2], where n is the number of bonds in the polymer chains and θ[SUB∞] is the θ point for an infinitely long chain. Introducing flexibility into the model has two effects upon θ[SUBn]; the θ temperature is reduced with increasing flexibility, and the n dependence of θ[SUBn] is suppressed. For a particular choice of spring constant an n-independent θ temperature is found. We also compare our results with those obtained from experimental studies of polystyrene in decalin and cyclohexane, and for poly(methyl methacrylate) in a water and tert-butyl alcohol mixture, and show that all the data can be collapsed onto a single universal curve without any adjustable parameters. We are thus able to relate both A[SUB2] and the excluded volume parameter v, to the chain interaction parameter z, in a way relating not only the data for different molecular weights and temperatures, but also for different polymers in different solvents. [ABSTRACT FROM AUTHOR]

Determines the interaction between identically charged surfaces immersed in a polyampholyte solution in the framework of the linear response approximation. Similarity of interaction between charged surfaces to that in electrolyte solutions; Effect of the charge redistribution on the length scales of the polymer coils; Result of the charge density fluctuations.

We study piecewise polynomial functions γk(c) that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the inverse Fourier transform of a Hankel determinant that satisfies a Painlevé V equation. We prove that γk(c) is very smooth at its transition points and also determine the asymptotics of γk(c) in a large neighbourhood of k = c/2. Finally, we consider the coefficients that appear in the asymptotics of elliptic aliquot cycles. [ABSTRACT FROM AUTHOR]

The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self-consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube—those due to its reptation—as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functions μ(t) and R(t). μ(t) is the fraction of tube occupied at time t=0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self-consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled. [ABSTRACT FROM AUTHOR]

Central concepts of the reptation model of polymer relaxation by disentanglement are the confining tube, the primitive path, and the entanglement net. These are given more precise definitions and are expounded upon here. The entanglement net is regarded as the set of primitive paths of the molecules. The scaling relation connecting distance between entanglements and concentration is derived by a self-consistency argument. Explicit results on probability distributions characterizing unentangled loops and primitive path lengths are derived. The polymers are modeled as random walks in a regular entanglement net. Results are presented as a function of the spacing between entanglements. [ABSTRACT FROM AUTHOR]

Acoustics are commonly used for borehole (i.e., oil well) imaging applications, under conditions where temperature and pressure reach extremes beyond that of conventional medical ultrasonics. Recently, there has been an interest in the application of encapsulated microbubbles as borehole contrast agents for acoustic assessment of fluid composition and flow. Although such microbubbles are widely studied under physiological conditions for medical imaging applications, to date there is a paucity of information on the behavior of encapsulated gas-filled microbubbles at high pressures. One major limitation is that there is a lack of experimental systems to assess both optical and acoustic data of micrometer-sized particles data at these extremes. In this paper, we present the design and application of a high-pressure cell designed for acoustical and optical studies of microbubbles at hydrostatic pressures up to 27.5 MPa (271 atm). [ABSTRACT FROM AUTHOR]