Glassy Dynamics of Polystyrene by Quasielastic Neutron Scattering

Response of Elementary Structural Transitions in Glassy Atactic Polystyrene to Temperature and Deformation

The effects of temperature, pressure, and imposed strain on the structural transition pathways of glassy atactic polystyrene (aPS) are studied for a wide range of conditions. By employing an atomistic description of the system, we systematically explore its free energy landscape, emphasizing connections between local free energy minima. A triplet of two minima connected to each other via a first-order saddle point provides the full description of each elementary structural relaxation event. The basis of the analysis is the potential energy landscape (PEL), where efficient methods for finding saddle points and exploring transition pathways have been developed. We then translate the stationary points of the PEL to stationary points of the proper free energy landscape that obeys the macroscopically imposed constraints (either stress- or strain-controlled). By changing the temperature under isobaric conditions (i.e., Gibbs energy landscape), we probe the temperature dependence of the transition rates of the subglass relaxations of aPS, thus obtaining their activation energies by fitting to the Arrhenius equation. The imposition of different strain levels under isothermic conditions allows us to estimate the apparent activation volume of every elementary transition. Our findings are in good agreement with experimental observations for the same system, indicating that both length- and time-scales of the structural transitions of glassy aPS can be obtained by proper free energy minimization of atomistically detailed configurations.

A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy–enthalpy compensation and dynamic gradients near the free surface

We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin–lattice relaxation time [Formula: see text] was measured near the free surface and in the bulk. Spin–lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence [Formula: see text]. There is no clear correlation of the average entropy of activation [Formula: see text] and enthalpy of activation [Formula: see text] with MW, but there is a clear correlation between [Formula: see text] and [Formula: see text], i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, [Formula: see text], being approximately independent of MW. Measurements of the temperature dependence of [Formula: see text] as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to [Formula: see text] = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in [Formula: see text] near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a “double-exponential” depth dependence. This model can explain the depth dependence of [Formula: see text] in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Transition pathways on the energy landscape of atactic polystyrene (aPS) glassy specimens are probed below its glass-transition temperature. Each of these transitions is considered an elementary structural relaxation event, whose corresponding rate constant is calculated by applying multidimensional transition-state theory. Initially, a wide spectrum of first-order saddle points surrounding local minima on the energy landscape is discovered by a stabilized hybrid eigenmode-following method. Then, (minimal-energy) “reaction paths” to the adjacent minima are constructed by a quadratic descent method. The heights of the free energy, the potential energy, and the entropy barriers are estimated for every connected triplet of transition state and minima. The resulting distribution of free energy barriers is asymmetric and extremely broad, extending to very high barrier heights (over 50 k_BT); the corresponding distribution of rate constants extends over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene. Analysis of the curvature along the reaction paths reveals a multitude of different rearrangement mechanisms; some of them bearing multiple distinct phases. Finally, connections to theoretical models of the glass phenomenology allows for the prediction, based on first-principles, of the “ideal” glass-transition temperature entering the Vogel–Fulcher–Tammann (VFT) equation describing the super-Arrhenius temperature dependence of glassy dynamics. Our predictions of the time scales of the subglass relaxations and the VFT temperature are in favorable agreement with available experimental literature data for systems of similar molecular weight under the same conditions.

Dynamics of polystyrene probed by muon spin spectroscopy

Muon spin spectroscopic measurements were made on atactic low-molecular-weight (LMW) (1.3 kg mol^-1) and high-molecular-weight (HMW) (202 kg mol^-1) polystyrene. Muoniated cyclohexadienyl radicals, which are formed by muonium addition to the phenyl side groups, are used as local probes of bulk dynamics. Muon spin relaxation is caused by the secondary γ-relaxation process, which involves motion of the phenyl rings, and is sensitive to the glass transition. The activation energy of the γ-relaxation process in the rubbery state is 0.60(2) eV in the HMW sample and 0.37(3) eV in the LMW sample.

Direct measurements of the temperature, depth and processing dependence of phenyl ring dynamics in polystyrene thin films by β-detected NMR

There is indirect evidence that the dynamics of a polymer near a free surface are enhanced compared with the bulk but there are few studies of how dynamics varies with depth. β-Detected nuclear spin relaxation of implanted 8Li+ has been used to directly probe the temperature and depth dependence of the γ-relaxation mode, which is due to phenyl rings undergoing restricted rotation, in thin films of atactic deuterated polystyrene (PS-d8) and determine how the depth dependence of dynamics is affected by sample processing, such as annealing, floating on water and the inclusion of a surfactant, and by the presence of a buried interface. The activation energy for the γ-relaxation process is lower near the free surface. Annealing the PS-d8 films and then immersing in water to mimic the floating procedure used to transfer films had negligible effects on the thickness of the region near the free surface with enhanced mobility. Measurements on a bilayer film indicate enhanced phenyl ring dynamics near the buried interface compared with a single film at the same depth. PS-d8 films annealed with the surfactant sodium dodecyl sulfate (SDS) deposited on the surface show enhanced dynamics in the bulk compared with a pure PS-d8 film and a PS-d8 film where the SDS was washed away. There is less contrast between the surface and bulk in the SDS-treated sample, which could account for the elimination of the Tg confinement effect observed in films containing SDS [Chen and Torkelson, Polymer, 2016, 87, 226].