ABSTRACT
Many macroscopic properties of polymers depend on their molecular weight, with one notable example being glass transition temperature: polymers with higher molecular weights typically have higher glass transition temperatures than their lower molecular weight polymeric and oligomeric counterparts. Polymeric systems close to their glass transition temperatures also exhibit interesting properties, showing both high (and molecular weight dependent) fragility and strong evidence of dynamic heterogeneity. While studies have detailed the correlations between molecular weight and fragility, studies clearly detailing correlations between molecular weight and degree of heterogeneous dynamics are lacking. In this study, we use single molecule rotational measurements to investigate the impact of molecular weight on polystyrene's degree of heterogeneity near its glass transition temperature. To this end, two types of fluorescent probes are embedded in films composed of polystyrene ranging from 0.6 to 1364.0 kg mol-1. We find correlation between polystyrene molecular weight, fragility, and degree of dynamic heterogeneity as reported by single molecule stretching exponents but do not find clear correlation between these quantities and time scales associated with dynamic exchange.
ABSTRACT
Polymeric systems close to their glass transition temperature are known to exhibit heterogeneous dynamics that evolve both over time and space, comparable to the dynamics of small molecule glass formers. It remains unclear how temperature influences the degree of heterogeneous dynamics in such systems. In the following report, a fluorescent perylene dicarboximide probe molecule that reflects the full breadth of heterogeneity of the host was used to examine the temperature dependence of the dynamic heterogeneity lifetime in polystyrene at several temperatures ranging from the glass transition to 10 K above this temperature via single molecule microscopy. Contrary to prior reports, no apparent temperature dependence of time scales associated with dynamic heterogeneity was detected; indeed, the probe molecules report characteristic dynamic heterogeneity lifetimes 100-300 times the average alpha-relaxation time (τα) of the polystyrene host at all temperatures studied.
ABSTRACT
Supercooled liquids are proposed to be dynamically heterogeneous, with regions exhibiting relaxation time scales that vary in space and time. Measurement of the distribution of such time scales could be an important test of various proposed theories of vitrification. Single molecule fluorescence experiments attempt to uncover this distribution, typically by embedding single molecule probes into these systems and monitoring their individual rotational relaxations from a computed autocorrelation function (ACF). These ACFs may exhibit stretched exponential decays, with the value of the stretching exponent assumed to report the set of dynamical environments explored by the probe. Here, we use simulated trajectories of rotation to investigate how the time scale of dynamic exchange relative to underlying relaxation time scales in the system affects probe ability to report the distribution relaxation of time scales present. We find that dynamically heterogeneous regions must persist for approximately 50 times the median relaxation time scale for a single molecule to accurately report the full distribution of time scales it has experienced. In systems with faster dynamic exchange, single molecule ACFs average over successive environments, limiting the reported heterogeneity of the system. This leads to degeneracies in stretching exponent for systems with different underlying relaxation time distributions. We show that monitoring single molecule median stretching exponent as a function of trajectory length or simultaneously measuring median stretching exponent and measured relaxation time distribution at a given trajectory length can resolve these degeneracies, revealing the underlying set of relaxation times as well as median exchange time.
