Heterogeneous dynamics and dynamic heterogeneities at the glass transition probed with single molecule spectroscopy

On the origin of time-aging-time superposition

Time-aging-time superposition and the concept of single-parameter aging refer to the experimentally verified scenario in which the relaxation profile is shifted as a whole along the logarithmic time or frequency scale during physical aging, i.e., without changing the shape of the susceptibility spectrum or decay function. This homogeneous aspect of aging and structural recovery appears to contrast the heterogeneous nature of structural relaxation in equilibrium. A picture is proposed in which both structural recovery and relaxation are heterogeneous, but lacking a local correlation of time constants. This scenario is consistent with time-aging-time superposition and single-parameter aging, as well as with recovery and relaxation processes being subject to practically the same time constant dispersion.

Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.

Correlating fragility and heterogeneous dynamics in polystyrene through single molecule studies

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.

Which probes can report intrinsic dynamic heterogeneity of a glass forming liquid?

Using extrinsic probes to study a host system relies on the probes' ability to accurately report the host properties under study. Probes have long been used to characterize dynamic heterogeneity, the phenomenon in which a liquid near its glass transition exhibits distinct dynamics as a function of time and position, with molecules within nanometers of each other exhibiting dynamics that may vary by orders of magnitude. The spatial and temporal characteristics of dynamic heterogeneity demand the selection of probes using stringent criteria on their size and dynamics. In this report, we study the dynamic heterogeneity of the prototypical molecular glass former o-terphenyl by investigating single molecule rotation of two perylene dicarboximide probe molecules that differ in size and comparing this to results obtained previously with the probe BODIPY268. It is found that a probe's ability to accurately report dynamic heterogeneity in o-terphenyl depends on whether the reported distribution of dynamics overlaps with the intrinsic dynamics of the host, which is naturally related to the width of the intrinsic dynamics and the magnitude of dynamical shift in probe dynamics relative to the host. We show that a probe that rotates ≈15 times more slowly than the intrinsic dynamics of the host o-terphenyl senses the slowest ≈5% of the full dynamic heterogeneity whereas one that rotates ≈65 times more slowly than the host fails to report dynamic heterogeneity of the host.

Single molecule studies reveal temperature independence of lifetime of dynamic heterogeneity in polystyrene

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 (τ_α) of the polystyrene host at all temperatures studied.

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy

Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

Ideal probe single-molecule experiments reveal the intrinsic dynamic heterogeneity of a supercooled liquid

The concept of dynamic heterogeneity and the picture of the supercooled liquid as a mosaic of environments with distinct dynamics that interchange in time have been invoked to explain the nonexponential relaxations measured in these systems. The spatial extent and temporal persistence of these regions of distinct dynamics have remained challenging to identify. Here, single-molecule fluorescence measurements using a probe similar in size and mobility to the host o-terphenyl unambiguously reveal exponential relaxations distributed in time and space and directly demonstrate ergodicity of the system down to the glass transition temperature. In the temperature range probed, at least 200 times the structural relaxation time of the host is required to recover ensemble-averaged relaxation at every spatial region in the system.

Single molecule rotational probing of supercooled liquids

Much of the interesting behavior that has been observed in supercooled liquids appears to be related to dynamic heterogeneity, the presence of distinct dynamic environments - with no apparent underlying structural basis - in these systems. To most directly interrogate these environments, proposed to span regions just a few nanometers across, molecular length scale probes are required. Single molecule fluorescent microscopy was introduced to the field a decade ago and has provided strong evidence of dynamic heterogeneity in supercooled systems. However, only more recently has the full set of challenges associated with interpreting results of these experiments been described. With a fuller understanding of these challenges in hand, single molecule measurements can be employed to provide a more precise picture of dynamic heterogeneity in supercooled liquids and other complex systems. In this tutorial review, experimental and data analysis details are presented for the most commonly employed single molecule approach to studying supercooled liquids, the measurement of rotational dynamics of single molecule probes. Guidance is provided in experimental set-up and probe selection, with a focus on choices that affect data interpretation and probe sensitivity to dynamic heterogeneity.

A multi-property fluorescent probe for the investigation of polymer dynamics near the glass transition

In addition to the commonly observed single molecule fluorescence intensity fluctuations due to molecular reorientation dynamics, a perylene bisimide-calixarene compound (1) shows additional on-off fluctuations due to its ability to undergo intramolecular excited state electron transfer (PET). This quenching process is turned on rather sharply when a film of poly(vinylacetate) containing 1 is heated above its glass transition temperature (T g), which indicates that the electron transfer process depends on the availability of sufficient free volume. Spatial heterogeneities cause different individual molecules to reach the electron transfer regime at different temperatures, but these heterogeneities also fluctuate in time: in the matrix above T g molecules that are mostly nonfluorescent due to PET can become fluorescent again on timescales of seconds to minutes.

The two different mechanisms for intensity fluctuation, rotation and PET, thus far only observed in compound 1, make it a unique probe for the dynamics of supercooled liquids.

Librations of probe molecules in polymeric matrixes

Formation of optical anisotropy under linearly polarized light has been studied in films of poly(n-butyl methacrylate) and poly(n-hexyl methacrylate) doped with azo compound (1-naphthyl-p-azo-methoxybenzene). Time profiles of the absorption anisotropy and absorbance can not be fitted with a commonly used model of anisotropy formation, which includes the transition dipole turns upon cis-trans isomerization and the rotational diffusion: the experimental values of anisotropy happen to be much lower than the calculated ones. To explain the low anisotropy level, fast molecular librations, i.e., stochastic pendulum-like oscillations of azo molecules about their average orientations were introduced. Numerical simulation of anisotropy and absorbance time profiles with the modified model gives estimates for average libration amplitude of 45-60° at temperatures 25-65 K below T(g).

Heterogeneity in Single-Molecule Observables in the Study of Supercooled Liquids

Bulk approaches to studying heterogeneous systems obscure important details, as they report average behavior rather than the distribution of behaviors in such environments. Small-molecule and polymeric supercooled liquids, which display heterogeneity in their dynamics without an underlying structural heterogeneity that sets those dynamics, are important constituents of this category of condensed matter systems. A variety of approaches have been devised to unravel ensemble averaging in supercooled liquids. This review focuses on the ultimate subensemble approach, single-molecule measurements, as they have been applied to the study of supercooled liquids. We detail how three key experimental observables (single-molecule probe rotation, translation, and fluorescence lifetime) have been employed to provide detail on dynamic heterogeneity in supercooled liquids. Special attention is given to the potential for, but also the challenges in, discriminating spatial and temporal heterogeneity and detailing the length scales and timescales of heterogeneity in these systems.

Transport in supported polyelectrolyte brushes

Functional polymers have a wide variety of applications ranging from energy storage to drug delivery. For energy storage applications, desirable material properties include low cost, high charge storage and/or mobility, and low rates of degradation. Isotropic thin films have been used for many of these types of applications, but research suggests that different structures such as polymer brushes can improve charge transport by an order of magnitude. Supported polymer brush structures produced by "grafting-from" polymerization methods offer a framework for a controlled study of these materials on the molecular scale. Using these materials, researchers can study the basis of hindered diffusion because they contain a relatively homogeneous polyelectrolyte membrane. In addition, researchers can use fluorescent molecular probes with different charges to examine steric and Coulombic contributions to transport near and within polymer brushes. In this Account, we discuss recent progress in using fluorescence correlation spectroscopy, single-molecule polarization-resolved spectroscopy, and a novel three-dimensional orientational technique to understand the transport of charged dye probes interacting with the strong polyanionic brush, poly(styrene sulfonate). Our preliminary experiments demonstrate that a cationic dye, Rhodamine 6G, probes the brush as a counterion, and diffusion is therefore dominated by Coulombic forces, which results in a 10,000-fold decrease in the diffusion coefficient in comparison with free diffusion. We also support our experimental results with molecular dynamics simulations. Further experiments show that, up to 50% of the time, Rhodamine 6G translates within the brush without significant rotational diffusion, which indicates a strong deviation from Fickian transport mechanisms (in which translational and rotational diffusion are related directly through parameters such as chemical potential, size, solution viscosity, and thermal properties). To understand this oriented transport, we discuss the development of an experimental technique that allows us to quantify the three-dimensional orientation on the time scale of intrabrush transport. This method allowed us to identify a unique orientational transport direction for Rhodamine 6G within the poly(styrene sulfonate) brush and to report preliminary evidence for orientational dye "hopping".

Identification of intensity ratio break points from photon arrival trajectories in ratiometric single molecule spectroscopy

We describe a statistical method to analyze dual-channel photon arrival trajectories from single molecule spectroscopy model-free to identify break points in the intensity ratio. Photons are binned with a short bin size to calculate the logarithm of the intensity ratio for each bin. Stochastic photon counting noise leads to a near-normal distribution of this logarithm and the standard student t-test is used to find statistically significant changes in this quantity. In stochastic simulations we determine the significance threshold for the t-test's p-value at a given level of confidence. We test the method's sensitivity and accuracy indicating that the analysis reliably locates break points with significant changes in the intensity ratio with little or no error in realistic trajectories with large numbers of small change points, while still identifying a large fraction of the frequent break points with small intensity changes. Based on these results we present an approach to estimate confidence intervals for the identified break point locations and recommend a bin size to choose for the analysis. The method proves powerful and reliable in the analysis of simulated and actual data of single molecule reorientation in a glassy matrix.

Transient 3-Dimensional Orientation of Molecular Ions in an Ordered Polyelectrolyte Membrane

Single-molecule fluorescence spectroscopy is employed to reveal 3-dimensional details of the mechanisms underpinning ion transport in a polyelectrolyte thin film possessing polymer-brush nanoscale order. The ability to resolve fluorescence emission over three discrete polarization angles reveals that these ordered materials impart 3-dimensional orientation to charged, diffusing molecules. The experiments, supported by simulations, report global orientation parameters for molecular transport, track dipole angle progressions over time, and identify a unique transport mechanism: translational diffusion with restricted rotation. Generally, realization of this experimental method for translational diffusion in systems exhibiting basic orientation should lend itself to evaluation of transport in a variety of important, ordered, functional materials.

Single molecule probing of dynamics in supercooled polymers

Fluorescence experiments with single BODIPY molecules embedded in a poly(methyl acrylate) matrix have been performed at various temperatures in the supercooled regime. By using pulsed excitation, fluorescence lifetime and linear dichroism time trajectories were accessible at the same time. Both observables have been analyzed without data binning. While the linear dichroism solely reflects single particle dynamics, the fluorescence lifetime observable depends on the molecular environment, so that the dynamics from the polymer host surrounding a chromophore contributes to this quantity. We observe that the lifetime correlation decays slightly faster than polarization correlation, indicating the occurrence of large angular reorientations. Additionally, dichroism time trajectories have been adducted to reveal directly the geometry of rotational dynamics. We identify small but also significantly larger rotational jumps being responsible for the overall molecular reorientation.