Single Molecule Experiments Reveal the Dynamic Heterogeneity and Exchange Time Scales of Polystyrene near the Glass Transition

A Monte Carlo simulation of tracer diffusion in amorphous polymers

Tracer diffusion in amorphous polymers is a sought-after quantity for a range of technological applications. In this regard, a quantitative description of the so-called decoupling from the reverse proportionality between viscosity and diffusion coefficient into a fractional one remains a challenge requiring a deeper insight. This work employs a Monte Carlo simulation framework in 3 dimensions to investigate the consequences of different scenarios for estimating this fractional exponent on the diffusion coefficient of tracers in polymers near glass transition. To this end, we adopted a continuous-time random walk model for tracer diffusion in the supercooled liquid state. The waiting time distribution of the diffusants was computed based on the rotational correlation times of the polymer. This proposed procedure is of particular interest because it brings the quantity of waiting time (and its statistics) in connection with the measurable observable of rotational times. In the framework of our simulations the aforementioned fractional exponent appears in the relation between the diffusant's waiting time and the rotational time of the diffusion medium. A limited comparison with experimental diffusivities from the literature revealed a reasonable agreement with a fractional exponent on the basis of the molar volumes of the diffusant and the monomeric unit. Finally, an analysis of time-averaged mean squared displacement pointed to normal Brownian dynamics for tracer diffusion in polymers above the glass transition temperature.

Segmental dynamics of polystyrene near polymer-polymer interfaces

This study investigated the segmental dynamics of polymers near polymer-polymer interfaces by probing the rotation of polymer-tethered fluorescent molecules using imaging rotational fluorescence correlation microscopy. Multilayered films were utilized to provide spatial selectivity relative to different polymer-polymer interfaces. In the experimental setup, for the overlayer polymer, polystyrene (PS) was employed and a 15 nm-thick probe-containing layer was placed ≈25 nm apart from different underlayer polymers with glass transition temperatures (Tg) either lower or higher than that of PS. The underlayer of poly-n-butyl methacrylate had 72 K lower Tg than that of PS, whereas polymethyl methacrylate and polysulfone had 22 and 81 K higher Tg, respectively, than that of PS. Two key dynamic features of the glass transition, the non-Arrhenius temperature dependence and stretched relaxation, were examined to study the influence of soft and hard confinements on the segmental dynamics of the overlayer polymer near the polymer-polymer interfaces. Although complications exist in the probing location owing to the diffusion of the polymer-tethered probe during the annealing protocol to consolidate the multilayers, the results suggest that either the segmental dynamics of the polymer near the polymer-polymer interface do not change owing to the soft and hard confinements or the interfacial perturbation is very short ranged.

Interplay between dynamic heterogeneity and interfacial gradients in a model polymer film

Glass-forming liquids exhibit long-lived, spatially correlated dynamical heterogeneity, in which some nm-scale regions in the fluid relax more slowly than others. In the nanoscale vicinity of an interface, glass-formers also exhibit the emergence of massive interfacial gradients in glass transition temperature Tg and relaxation time τ. Both of these forms of heterogeneity have a major impact on material properties. Nevertheless, their interplay has remained poorly understood. Here, we employ molecular dynamics simulations of polymer thin films in the isoconfigurational ensemble in order to probe how bulk dynamic heterogeneity alters and is altered by the large gradient in dynamics at the surface of a glass-forming liquid. Results indicate that the τ spectrum at the surface is broader than in the bulk despite being shifted to shorter times, and yet it is less spatially correlated. This is distinct from the bulk, where the τ distribution becomes broader and more spatially organized as the mean τ increases. We also find that surface gradients in slow dynamics extend further into the film than those in fast dynamics-a result with implications for how distinct properties are perturbed near an interface. None of these features track locally with changes in the heterogeneity of caging scale, emphasizing the local disconnect between these quantities near interfaces. These results are at odds with conceptions of the surface as reflecting simply a higher "rheological temperature" than the bulk, instead pointing to a complex interplay between bulk dynamic heterogeneity and spatially organized dynamical gradients at interfaces in glass-forming liquids.

Free Space Makes the Polymer "Dead Layer" Alive

The effect of free space on molecular motion inside the polymer "dead layer" or adsorbed nanolayers on solid surfaces is investigated. Free space is introduced into the nanolayer by choosing a polymer with a relatively big side group, poly n-butyl methacrylate (PnBMA), and polarization-resolved single-molecule fluorescence microscopy is adopted as the method. The rotational motion of the doped fluorescent probes is found to be considerably excited at moderate temperatures, attributed to the free space brought by the side group of the PnBMA. The development of the adsorbed nanolayer by the prolonged annealing of the parent film is carefully monitored, together with the evolution of the molecular motion and the glass transition temperature (T_g). The T_g values of the exposed nanolayers are considerably lower than that of the bulk system, while they become higher than those in the bulk situation when the nanolayer is covered with a polymer top layer. The experimental evidence has demonstrated that the free space made available by the side group and the air-polymer interface has considerably promoted the molecular motion inside the adsorbed nanolayers, even under the situation of overwhelming surface attraction.

Single molecule demonstration of Debye-Stokes-Einstein breakdown in polystyrene near the glass transition temperature

Rotational-translational decoupling, in which translational motion is apparently enhanced over rotational motion in violation of Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) predictions, has been observed in materials near their glass transition temperatures (T_g). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this work, ensemble and single molecule experiments are performed in parallel on a fluorescent probe in high molecular weight polystyrene near its T_g. Ensemble results show decoupling onset at approximately 1.15T_g, increasing to over three orders of magnitude at T_g. Single molecule measurements also show a high degree of decoupling, with typical molecules at T_g showing translational diffusion coefficients nearly 400 times higher than expected from SE/DSE predictions. At the single molecule level, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and SE/DSE breakdown.

Experiments with high-molecular-weight polystyrene provide insights into the mechanisms behind rotational-translational decoupling in glassy systems. Specifically, particularly mobile molecules exhibiting anisotropic trajectories are found to play a key role in Debye-Stokes-Einstein breakdown.

Environmentally Sensitive Luminescence Reveals Spatial Confinement, Dynamics, and Their Molecular Weight Dependence in a Polymer Glass

Polymer glasses have an irregular structure. Among the causes for such complexity are the chemically distinct chain end groups that are the most abundant irregularities in any linear polymer. In this work, we demonstrate that chain end induced defects allow polymer glasses to create confined environments capable of hosting small emissive molecules. Using environmentally sensitive luminescent complexes, we show that the size of these confinements depends on molecular weight and can dramatically affect the photoluminescence of free or covalently bound emissive complexes. We confirm the impact of chain end confinement on the bulk glass transition in poly(methyl acrylate) (pMA) and show that commonly observed T g changes induced by the chain ends should have a structural origin. Finally, we demonstrate that the size and placement of luminescent molecular probes in pMA can dramatically affect the probe luminescence and its temperature dependence, suggesting that polymer glass is a highly irregular and complex environment, marking its difference with conventional small molecule solvents. Considering the ubiquity of luminescent glassy materials, our work lays down a blueprint for designing them with structural considerations in mind, ones where packing density and chain end size are key factors.

Dynamic Polymer Free Volume Monitored by Single-Molecule Spectroscopy of a Dual Fluorescent Flapping Dopant

Single-molecule spectroscopy (SMS) of a dual fluorescent flapping molecular probe (N-FLAP) enabled real-time nanoscale monitoring of local free volume dynamics in polystyrenes. The SMS study was realized by structural improvement of a previously reported flapping molecule by nitrogen substitution, leading to increased brightness (22 times) of the probe. In a polystyrene thin film at the temperature of 5 K above the glass transition, the spectra of a single N-FLAP molecule undergo frequent jumps between short- and long-wavelength forms, the latter one indicating planarization of the molecule in the excited state. The observed spectral jumps were statistically analyzed to reveal the dynamics of the molecular environment. The analysis together with MD and QM/MM calculations show that the excited-state planarization of the flapping probe occurs only when sufficiently large polymer free volume of more than, at least, 280 ų is available close to the molecule, and that such free volume lasts for an average of 1.2 s.

The microscopic origins of stretched exponential relaxation in two model glass-forming liquids as probed by simulations in the isoconfigurational ensemble

The origin of stretched exponential relaxation in supercooled glass-forming liquids is one of the central questions regarding the anomalous dynamics of these fluids. The dominant explanation for this phenomenon has long been the proposition that spatial averaging over a heterogeneous distribution of locally exponential relaxation processes leads to stretching. Here, we perform simulations of model polymeric and small-molecule glass-formers in the isoconfigurational ensemble to show that stretching instead emerges from a combination of spatial averaging and locally nonexponential relaxation. The results indicate that localities in the fluid exhibiting faster-than-average relaxation tend to exhibit locally stretched relaxation, whereas slower-than-average relaxing domains exhibit more compressed relaxation. We show that local stretching is predicted by loose local caging, as measured by the Debye-Waller factor, and vice versa. This phenomenology in the local relaxation of in-equilibrium glasses parallels the dynamics of out of equilibrium under-dense and over-dense glasses, which likewise exhibit an asymmetry in their degree of stretching vs compression. On the basis of these results, we hypothesize that local stretching and compression in equilibrium glass-forming liquids results from evolution of particle mobilities over a single local relaxation time, with slower particles tending toward acceleration and vice versa. In addition to providing new insight into the origins of stretched relaxation, these results have implications for the interpretation of stretching exponents as measured via metrologies such as dielectric spectroscopy: measured stretching exponents cannot universally be interpreted as a direct measure of the breadth of an underlying distribution of relaxation times.

100th Anniversary of Macromolecular Science Viewpoint: Enabling Advances in Fluorescence Microscopy Techniques

In the past few decades there has been a revolution in the field of optical microscopy with emerging capabilities such as super-resolution and single-molecule fluorescence techniques. Combined with the classical advantages of fluorescence imaging, such as chemical labeling specificity, and noninvasive sample preparation and imaging, these methods have enabled significant advances in our polymer community. This Viewpoint discusses several of these capabilities and how they can uniquely offer information where other characterization techniques are limited. Several examples are highlighted that demonstrate the ability of fluorescence microscopy to understand key questions in polymer science such as single-molecule diffusion and orientation, 3D nanostructural morphology, and interfacial and multicomponent dynamics. Finally, we briefly discuss opportunities for further advances in techniques that may allow them to make an even greater contribution in polymer science.

Color-Based Optical Detection of Glass Transitions on Microsecond Timescales Enabled by Exciplex Dynamics

Every measurement technique operates on a given timescale and measurements using emissive small molecule sensors are no exception. A family of luminescent sensors providing first optical characterization of dynamic phenomena in polymers at a timescale of several microseconds is described. This performance originates from the dynamics manifested in the excited state of the sensor molecules where diffusioncontrolled events select the emission color while radiative phenomena define the global operation timescale. Since the mechanism responsible for signal generation is confined to the short lived excited state of emissive probe, it is possible observe an unprecedented link between the timescale of sensory action and that of photoluminescence. An application of this new methodology is demonstrated by performing general, short timescale detection of glass transitions in a temperature ranges precluding the informative range of conventional techniques by tens of degrees.

How Tethered Probes Report the Dynamics of a Polymer near the Glass Transition

How tethered probes report dynamics of host polymers near the glass transition was investigated by changing the length of the flexible linkers and the number of tethering points via imaging rotational fluorescence correlation microscopy and compared with free probes of different sizes. The results show that tethering did not alter the temperature-dependence of polymer dynamics and the shape of the correlation decay reported by the probe; however, the rotation slowed down up to ≈1 decade when both ends of the probe were restricted with short alkyl chain linkers. Upon comparison with the bigger free probe, the mechanism of the slowdown was attributed to the restricted motion upon tethering for tethered probes compared to averaging over different regions of the dynamic heterogeneity for the bigger probe. If the size of the probe was comparable to that of the dynamic heterogeneity of the system, tethered probes accurately report dynamics relevant to glass transition, regardless of tethering conditions.

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.

Segmental dynamics of polymer by rotational fluorescence correlation microscopy

The segmental dynamics of polymers is known to be closely related to the glass transition where the glass transition is the single most important parameter in its application. In this study, we designed an efficient and reliable experimental method to study the ensemble segmental dynamics of polymers by probing rotation of fluorescent molecules in the polymer matrix using a home-built microscope setup. The rotational dynamics of fluorescent molecules was analyzed using a fluorescence correlation method that extracts information through orthogonally polarized fluorescence images. From fluorescence intensities, autocorrelation functions (ACFs) were obtained in many areas simultaneously and by averaging several ACFs, well-defined ACF and precise experimental values were obtained from a single measurement movie. The robustness of the method and optimal experimental conditions were investigated by performing experiments with various probe concentrations, frame rates, and measurement lengths. By employing a home-built vacuum chamber, a wide temperature range was achieved, and we demonstrate the versatility and efficiency of imaging rotational FCM (fluorescence correlation microscopy) by probing segmental dynamics of different polymeric systems with glass transition temperature that differ by ≈100 K and with fragility ranging from 49 to 131. The imaging rotational FCM covers dynamics up to 4 orders of magnitude near the glass transition, and it was found that the rapidity of the stretching exponent β variation with temperature correlates with the fragility of polymers.

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.

Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods

We propose a novel approach to analyze random walks in heterogeneous medium using a hybrid machine-learning method based on a gamma mixture and a hidden Markov model. A gamma mixture and a hidden Markov model respectively provide the number and the most probable sequence of diffusive states from the time series position data of particles/molecules obtained by single-particle/molecule tracking (SPT/SMT) method. We evaluate the performance of our proposed method for numerically generated trajectories. It is shown that our proposed method can correctly extract the number of diffusive states when each trajectory is long enough to be frame averaged. We also indicate that our method can provide an indicator whether the assumption of a medium consisting of discrete diffusive states is appropriate or not based on the available amount of trajectory data. Then, we demonstrate an application of our method to the analysis of experimentally obtained SPT data.

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.

Fluorescent Diarylethene Photoswitches-A Universal Tool for Super-Resolution Microscopy in Nanostructured Materials

Super-resolution fluorescence microscopy allows for unprecedented in situ visualization of biological structures, but its application to materials science has so far been comparatively limited. One of the main reasons is the lack of powerful dyes that allow for labeling and photoswitching in materials science systems. In this study it is shown that appropriate substitution of diarylethenes bearing a fluorescent closed and dark open form paves the way for imaging nanostructured materials with three of the most popular super-resolution fluorescence microscopy methods that are based on different concepts to achieve imaging beyond the diffraction limit of light. The key to obtain optimal resolution lies in a proper control over the photochemistry of the photoswitches and its adaption to the system to be imaged. It is hoped that the present work will provide researchers with a guide to choose the best photoswitch derivative for super-resolution microscopy in materials science, just like the correct choice of a Swiss Army Knife's tool is essential to fulfill a given task.