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The dynamic heat capacity is calculated from molecular dynamics simulations of a model glass former of simple bead-spring chains. The temperature is directly modulated and the energy tracked. The frequency-dependent heat capacity is found as the complex response function. There is agreement both with molecular dynamics simulations of related glass formers and with an energy-landscape-based, two state model. In particular, at high packing fraction, a low frequency loss peak is seen to split from the main, high frequency peak. This low frequency peak describes the configurational contribution to the heat capacity associated with the glass transition. Although the current application is in the linear response regime, this methodology paves the way for studies of nonlinear response that parallel experiment. [ABSTRACT FROM AUTHOR]

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole–Davidson function was used to fit the response functions with extensive use being made of Cole–Cole plots in the fitting procedure. For the systems studied, the Cole–Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch–Williams–Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or free rotation effects. The accuracy of the Cole–Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole–Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole–Davidson would provide a better frequency-domain description of the associated response function than the KWW function does. [ABSTRACT FROM AUTHOR]

Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch–Williams–Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent β to be tracked over a wide range of state points. The smoothness of β as a function of packing fraction η is a testimony both to the accuracy of the analytical methods and the appropriateness of (η0-η) as a measure of the distance to the ideal glass transition at η0. Relatively direct comparison is made with experiment by viewing β as a function of the KWW relaxation time τKWW. The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of α-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye–Stokes–Einstein relation), of motion on different length scales (i.e., the Stokes–Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of β across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features. [ABSTRACT FROM AUTHOR]

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems’ rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents β are found to be 0.75±0.02 for the freely jointed case and 0.68±0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-endrelaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed. [ABSTRACT FROM AUTHOR]

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, η. The functions D*(η) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*’s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, η0. This limiting packing fraction is interpreted to be the location of the glass transition, and (η0-η), the distance to the glass transition. [ABSTRACT FROM AUTHOR]

We performed molecular dynamics simulations of chain systems to investigate general relationships between the system mobility and computed scalar quantities. Three quantities were found that had a simple one-to-one relationship with mobility: packing fraction, potential energy density, and the value of the static structure factor at the first peak. The chain center-of-mass mobility as a function of these three quantities could be described equally well by either a Vogel-Fulcher type or a power law equation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations of the diffusion of penetrants in bead-spring polymers were performed along both constant volume and constant pressure paths at several temperatures. By using an effective hard sphere diameter, the packing fractions of these systems were calculated. It was found that all the data for a given polymer type collapsed to a single curve that can be well described using a modification of the Doolittle equation. Data on polymer simulations from the literature was analyzed in this manner and showed similar results. In this work we demonstrate that the packing fraction analysis that is used to describe hard sphere and colloidal systems can also be extended to polymeric systems. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]