Jonathan R. Brown

Simulation of a small molecule analogue of a lithium ionomer in an external electric field

We have investigated the ion dynamics in lithium-neutralized 2-pentylheptanoic acid, a small molecule analogue of a precise poly(ethylene-co-acrylic acid) lithium ionomer. Atomistic molecular dynamics simulations were performed in an external electric field. The electric field causes alignment of the ionic aggregates along the field direction. The energetic response of the system to an imposed oscillating electric field for a wide range of frequencies was tracked by monitoring the coulombic contribution to the energy. The susceptibility found in this manner is a component of the dielectric susceptibility typically measured experimentally. A dynamic transition is found and the frequency associated with this transition varies with temperature in an Arrhenius manner. The transition is observed to be associated with rearrangements of the ionic aggregates.

Fluids density functional theory and initializing molecular dynamics simulations of block copolymers

Classical, fluids density functional theory (fDFT), which can predict the equilibrium density profiles of polymeric systems, and coarse-grained molecular dynamics (MD) simulations, which are often used to show both structure and dynamics of soft materials, can be implemented using very similar bead-based polymer models. We aim to use fDFT and MD in tandem to examine the same system from these two points of view and take advantage of the different features of each methodology. Additionally, the density profiles resulting from fDFT calculations can be used to initialize the MD simulations in a close to equilibrated structure, speeding up the simulations. Here, we show how this method can be applied to study microphase separated states of both typical diblock and tapered diblock copolymers in which there is a region with a gradient in composition placed between the pure blocks. Both methods, applied at constant pressure, predict a decrease in total density as segregation strength or the length of the tapered region is increased. The predictions for the density profiles from fDFT and MD are similar across materials with a wide range of interfacial widths.

Effect of sequence dispersity on morphology of tapered diblock copolymers from molecular dynamics simulations

Tapered diblock copolymers are similar to typical AB diblock copolymers but have an added transition region between the two blocks which changes gradually in composition from pure A to pure B. This tapered region can be varied from 0% (true diblock) to 100% (gradient copolymer) of the polymer length, and this allows some control over the microphase separated domain spacing and other material properties. We perform molecular dynamics simulations of linearly tapered block copolymers with tapers of various lengths, initialized from fluids density functional theory predictions. To investigate the effect of sequence dispersity, we compare systems composed of identical polymers, whose taper has a fixed sequence that most closely approximates a linear gradient, with sequentially disperse polymers, whose sequences are created statistically to yield the appropriate ensemble average linear gradient. Especially at high segregation strength, we find clear differences in polymer conformations and microstructures between these systems. Importantly, the statistical polymers are able to find more favorable conformations given their sequence, for instance, a statistical polymer with a larger fraction of A than the median will tend towards the A lamellae. The conformations of the statistically different polymers can thus be less stretched, and these systems have higher overall density. Consequently, the lamellae formed by statistical polymers have smaller domain spacing with sharper interfaces.

Driven simulations of the dynamic heat capacity

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.

The potential energy landscape contribution to the dynamic heat capacity

The dynamic heat capacity of a simple polymeric, model glassformer was computed using molecular dynamics simulations by sinusoidally driving the temperature and recording the resultant energy. The underlying potential energy landscape of the system was probed by taking a time series of particle positions and quenching them. The resulting dynamic heat capacity demonstrates that the long time relaxation is the direct result of dynamics resulting from the potential energy landscape. Moreover, the equilibrium (low frequency) portion of the potential energy landscape contribution to the heat capacity is found to increase rapidly at low temperatures and at high packing fractions. This increase in the heat capacity is explained by a statistical mechanical model based on the distribution of minima in the potential energy landscape.

Nonlinear dynamic heat capacity of a bead-spring polymeric glass former

Nonlinear dynamics of a simple bead-spring glass-forming polymer were studied with molecular dynamics simulations. The energy response to sinusoidal variations in the temperature was tracked in order to evaluate the dynamic heat capacity. The amplitude dependence of the response is the focus of the current paper where pronounced nonlinear behavior is observed for large amplitudes in the temperature driving force. We generalize the usual linear response analysis to the nonlinear regime so that higher order terms in the Fourier series of the energy response can be compactly analyzed. This is done by grouping all Fourier terms contributing to entropy generation into a loss contribution and the remainder yields the storage term. Finally, the bead-spring system is mapped onto three simpler models. First is a potential energy inspired trap model consisting of interconnected potential energy meta-basins and barriers. Second is the Tool-Narayanaswamy-Moynihan (TNM) model. Third is a version of the TNM model with a temperature dependent heat capacity. Qualitatively similar nonlinear behaviors are observed in all cases.

Theory and simulation of the dynamic heat capacity of the east Ising model

A recently developed methodology for the calculation of the dynamic heat capacity from simulation is applied to the east Ising model. Results show stretched exponential relaxation with the stretching exponent, beta, decreasing with decreasing temperature. For low temperatures, the logarithm of the relaxation time is approximately proportional to the inverse of the temperature squared, which is the theoretical limiting behavior predicted by theories of facilitated dynamics. In addition, an analytical approach is employed where the overall relaxation is a composite of relaxation processes of subdomains, each with their own characteristic time. Using a Markov chain method, these times are computed both numerically and in closed form. The Markov chain results are seen to match the simulations at low temperatures and high frequencies. The dynamics of the east model are tracked very well by this analytic procedure, and it is possible to associate features of the spectrum of the dynamic heat capacity with specific domain relaxation events.