Heterogeneous Dynamics and Domains in Supercooled o-Terphenyl: A Single Molecule Study

Characterizing Rotational Dynamics and Heterogeneity via Single-Molecule Intensity Measurements

Dynamic heterogeneity in glassy systems has typically been characterized at the single-molecule level by extracting rotational relaxation time scales from linear dichroism (LD) collected via two orthogonally polarized channels. However, in such measurements, localization precision is diminished due to photons lost relative to collection in a single detection channel. This poses challenges in characterizing rotational and translational dynamics simultaneously, as translational measurements require high localization precision. In this paper, we present a method for extracting rotational dynamics of glassy systems at the single-molecule level from intensity fluctuations of fluorescent probe molecules in a wide-field configuration without the use of a polarizing optical component. Through numerical analysis, we show that LD and intensity measurements probing rotational dynamics report similar, approximately second-order rotational correlation decays even at low signal to noise. Thus, within the assumptions of small, isotropic rotations, LD and intensity autocorrelation analysis should provide identical information on the time scale and heterogeneity of rotational dynamics. We then present experimental results that validate this numerical result, with direct comparison of LD and intensity-based approaches across probe molecules in both polymeric and small-molecule glass formers as well as across optical configurations. Our results demonstrate moderate correlation on a per-probe basis between rotational time scales obtained from both approaches, with deviations consistent with those expected in a dynamically heterogeneous system. We envision that this easily accessible strategy will be of use across disciplines for characterizing single-molecule rotational dynamics in limited signal situations and/or when high-precision localization is required.

Dynamic Heterogeneity in the Optical Signals from Single Nano-Objects

In contrast to ensemble-averaged measurements, single-molecule experiments directly display the heterogeneity of molecular properties in space and time. In many complex systems, spatial heterogeneity is regularly accompanied by temporal or dynamic heterogeneity; if a property differs from molecule to molecule, it will often vary in time for one and the same molecule. In this short paper, we discuss a few examples of complex systems where dynamical heterogeneity was observed in single-molecule or single-particle optical signals. For single biomolecules, the first demonstration of dynamic heterogeneity in a single enzyme was provided by Xie and colleagues. Other examples are found in glassy systems, and very recently in the magnetic relaxation of single superparamagnetic nanoparticles. The ubiquity of this phenomenon suggests that, rather than an exception, dynamic heterogeneity is the rule in complex systems with multiple degrees of freedom.

Viscosity Measurement in Biocondensates Using Deep-Learning-Assisted Single-Particle Rotational Analysis

Viscoelastic characterization is of great importance for the investigation of biomolecular condensates. Single-particle-tracking-based rotational diffusion analysis of single nanorods is an effective approach for quantitative viscosity measurement. However, in the case of high background and noise with high-speed image acquisition, accurate extraction of diffusivity from the data is a challenging task. Here, we develop a novel frequency-domain-based deep learning (DL) method for single nanorod rotational tracking analysis. We synthesized Brownian rotational time-series data for training, designed a data preprocessing module to reduce the effect of noise, and extracted rotational diffusion coefficient using recurrent neural networks in the frequency domain. Compared with the traditional curve-fitting-based methods, our method shows higher accuracy and a wider detection range for viscosity measurement. We verified our method using experimental data from plasmonic imaging of single gold nanorods (AuNRs) in glycerol solution and PGL droplets. Our method can be potentially applied to the viscosity measurement of different biomolecular condensates in vitro and in vivo.

Progress and perspectives in single-molecule optical spectroscopy

We review some of the progress of single-molecule optical experiments in the past 20 years and propose some perspectives for the coming years. We particularly focus on methodological advances in fluorescence, super-resolution, photothermal contrast, and interferometric scattering and briefly discuss a few of the applications. These advances have enabled the exploration of new emitters and quantum optics; the chemistry and biology of complex heterogeneous systems, nanoparticles, and plasmonics; and the detection and study of non-fluorescing and non-absorbing nano-objects. We conclude by proposing some ideas for future experiments. The field will move toward more and better signals of a broader variety of objects and toward a sharper view of the surprising complexity of the nanoscale world of single (bio-)molecules, nanoparticles, and their nano-environments.

Polarization-resolved single-molecule tracking reveals strange dynamics of fluorescent tracers through a deep rubbery polymer network

Tracking the movement of fluorescent single-molecule (SM) tracers has provided several new insights into the local structure and dynamics in complex environments such as soft materials and biological systems. However, SM tracking (SMT) remains unreliable at molecular length scales, as the localization error (LE) of SM trajectories (∼30-50 nm) is considerably larger than the size of molecular tracers (∼1-2 nm). Thus, instances of tracer (im)mobility in heterogeneous media, which provide indicators for underlying anomalous-transport mechanisms, remain obscured within the realms of SMT. Since the translation of passive tracers in an isotropic media is associated with fast dipolar rotation, we propose that authentic pauses within the LE can be revealed by probing the hindrance of SM reorientational dynamics. Here, we demonstrate how polarization-resolved SMT (PR-SMT) can provide emission anisotropy at each super-localized position, thereby revealing the tumbling propensity of SMs during random walks. For rhodamine 6G tracers undergoing heterogeneous transport in a hydrated polyvinylpyrrolidone (PVP) network, analysis of PR-SMT trajectories enabled us to discern instances of genuine immobility and localized motion within the LE. Our investigations on 100 SMs in (plasticized) PVP films reveal a wide distribution of dwell times and pause frequencies, demonstrating that most probes intermittently experience complete translational and rotational immobilization. This indicates that tracers serendipitously encounter compact, rigid polymer cavities during transport, implying the existence of nanoscale glass-like domains sparsely distributed in a predominantly deep-rubbery polymer network far above the glass transition.

Rheological behavior of molecular vs network chalcogenide supercooled liquids

The viscoelastic behavior of supercooled glass-forming liquids along the binary join As₄S₃-GeS₂ with As₄S₃ contents varying from 81.25 to 9 mol. % and correspondingly with structures varying from predominantly molecular to a three-dimensional tetrahedral network is studied by small-amplitude oscillatory shear parallel plate rheometry. The storage shear modulus G' shows a scaling behavior of G'(ω) ∼ ωⁿ in the terminal (low-frequency) regime, where n varies between 1 and 2 and shows an increasingly anomalous departure from the expected value of 2 (Maxwell scaling) with increasing molecule content. A concomitant departure from the Maxwell scaling is also observed for the loss modulus G″ at frequencies above the G'-G″ crossover. On the other hand, the variation in the phase angle δ with the complex modulus indicates that the molecular liquid does not display a purely viscous response even at the lowest frequencies. These results, combined with an analysis of the relaxation spectra of these liquids, suggest that the anomalous behavior of molecular liquids may be linked to their rather broad relaxation spectrum and the presence of slow relaxation processes associated with molecular clusters. Additionally, these liquids are also characterized by a wide high-frequency plateau in the relaxation spectral density that can be linked to the rotational dynamics of the constituent molecules. Such fundamental differences between the rheological behavior of molecular and network liquids may explain the significantly higher fragility of the former.

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.

Faster Convergence of Diffusion Anisotropy Detection by Three-Step Relation of Single-Particle Trajectory

We focus on the issue of limited number of samples in the single particle tracking (SPT) when trying to extract the diffusion anisotropy that originates from the particle asymmetry. We propose a novel evaluation technique of SPT making use of the relation of the consecutive three steps. More specifically, the trend of the angle comprised of the three positions and the displacements are plotted on a scatter diagram. The particle anisotropy dependence of the shape of the scatter diagram is examined through the data from the standard numerical model of anisotropic two-dimensional Brownian motion. Comparison with the existing method reveals the faster convergence in the evaluation. In particular, our proposed method realizes the detection of diffusion anisotropy under the conditions of not only less number of data but also larger time steps. This is of practical importance not only when the abundant data is hard to achieve but also when the rotational diffusion is fast compared to the frame rate of the camera equipment, which tends to be more common for smaller particles or molecules of interest.

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.

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.

Length and time scales of structural heterogeneities in deeply supercooled propylene carbonate

Deactivation of excited phenanthrene by molecular oxygen is utilized to probe the structural heterogeneity of supercooled propylene carbonate. The diffusion rate of oxygen molecules in different regions varies over two orders of magnitude. The size of the regions of different oxygen mobility was determined to be 1.5 nm. Values from 0.2 to 30 s have been obtained for the lifetime of these regions over a temperature range from T(g)-1 to T(g)+4 K (T(g)=158 K). The heterogeneity lifetime is in close agreement with the α-relaxation time determined by dielectric spectroscopy. The obtained results argue in favor of the statement that the heterogeneous cooperative dynamics of host molecules (so-called dynamical heterogeneity) is of structural origin.

Relaxation in Thin Polymer Films Mapped across the Film Thickness by Astigmatic Single-Molecule Imaging

We have studied relaxation processes in thin supported films of poly(methyl acrylate) at the temperature corresponding to 13 K above the glass transition by monitoring the reorientation of single perylenediimide molecules doped into the films. The axial position of the dye molecules across the thickness of the film was determined with a resolution of 12 nm by analyzing astigmatic fluorescence images. The average relaxation times of the rotating molecules do not depend on the overall thickness of the film between 20 and 110 nm. The relaxation times also do not show any dependence on the axial position within the films for the film thickness between 70 and 110 nm. In addition to the rotating molecules we observed a fraction of spatially diffusing molecules and completely immobile molecules. These molecules indicate the presence of thin (<5 nm) high-mobility surface layer and low-mobility layer at the interface with the substrate.

Short time behavior of fluorescence intensity fluctuations in single molecule polarization sensitive experiments

Recent developments in the field of single molecule orientation imaging have led us to devise a simple framework for analyzing fluorescence intensity fluctuations in single molecule polarization sensitive experiments. Based on the new framework, rotational dynamics of individual molecules are quantified, in this paper, from the short time behavior of the time averaged fluorescence intensity fluctuation trajectories. The suggested model can be applied in single molecule fluorescence fluctuations experiments to extract accurate expectation values of photon counts during very short integration time in which rotational diffusion is likely not to be averaged out.

Manifestations of probe presence on probe dynamics in supercooled liquids

Experimental studies that follow behavior of single probes embedded in heterogeneous systems are increasingly common. The presence of probes may perturb the system, and such perturbations may or may not affect interpretation of host behavior from the probe observables typically measured. In this study, the manifestations of potential probe-induced changes to host dynamics in supercooled liquids are investigated via molecular dynamics simulations. It is found that probe dynamics do not necessarily mirror host dynamics as they exist either in the probe-free or probe-bearing systems. In particular, for a binary supercooled liquid, we find that smooth probes larger than the host particles induce increased translational diffusion in the host system; however, the diffusion is anisotropic and enhances caging of the probe, suppressing probe translational diffusion. This in turn may lead experiments that follow probe diffusion to suggest Stokes-Einstein behavior of the system even while both the probe-free and probe-bearing systems exhibit deviations from that behavior.

When the Heterogeneous Appears Homogeneous: Discrepant Measures of Heterogeneity in Single Molecule Observables

Supercooled liquids demonstrate stretched exponential relaxations consistent with the presence of spatially heterogeneous dynamics. Many experimental results are consistent with this picture, but differences in experimental approach may lead to different conclusions about the degree of heterogeneity in a given system. Here, we investigate whether observables accessible with single molecule (SM) approaches are consistent with each other and with ensemble measurements. In particular, the distribution of rotational relaxation times, τ(c), obtained from SM measurements is compared with the stretching exponent determined from a quasi-ensemble treatment of the same data. It is shown that the time-limited trajectories typical of SM experiments can lead to a stretching exponent that suggests homogeneous dynamics even in the presence of heterogeneous dynamics. After correction for the time-limited trajectories, additional discrepancy remains between stretching exponents measured via SM experiments and ensemble techniques. The remaining difference is attributed to the limited dynamic range of the SM experiments.

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.

Gel-like elasticity in glass-forming side-chain liquid-crystal polymers

We study the complex shear modulus G of two side-chain liquid-crystal polymers (SCLCPs), a methoxy-phenylbenzoate substituted polyacrylate (thereafter called PAOCH3 ), and a cyanobiphenyl substituted polyacrylate supplied by Merck (thereafter called LCP105) using a piezoelectric rheometer. Two methods of filling the cell are used: (a) a capillary method, which can be used only at high temperature because of the low value of the viscosity, and (b) the classical one, thereafter called compression method, which consists in placing the sample between the two slides of the cell and to bring them closer. By filling the cell at high temperature either with the compression or the capillary method, we show that the response of both compounds is liquidlike ( G' approximately f2 and G'' approximately f , where f is the frequency) for temperatures higher than a certain temperature T0 and gel-like (G' approximately const, G'' approximately f) below T0. This change in behavior from the conventional flow response to a gel-like response, when approaching the glass transition, is observed for nonsliding conditions and for very weak-imposed shear strains. It can be explained by a percolation-type mechanism of preglassy elastic clusters, which correspond to long-range and long-lived density fluctuations that are frozen at the time scale of the experiment. The sample response is therefore the sum of two contributions: one is due to the flow response of the polymer melt and the other to the elastic response of the network formed by the preglassy elastic clusters. By filling the cell below T0 with the compression method, both compounds exhibit a gel-type behavior by gently bringing closer the slides of the cell and an anomalous low-frequency behavior characterized by G'=const and G''=const by increasing the pressure used to bring closer the slides of the cell. A compression-assisted aggregation of the preglassy elastic clusters can explain both the increase in the low-frequency elastic plateau when the sample thickness is decreased and the anomalous low-frequency behavior. Further evidence for the existence of these elastic clusters is provided by the following results: (a) the nonlinear response of the samples as a function of the strain amplitude, which can be explained by the Payne effect, and (b) the aggregation effects, which can be mimicked by a polydimethylsiloxane melt filled with silica particles, the silica particles playing the role of the preglassy elastic clusters. All these observations show that PAOCH3 is not a macroscopically solidlike material with an unconventional type of elasticity, as claimed by Mendil [Phys. Rev. Lett. 96, 077801 (2006)]. The gel-type behavior observed here on two SCLCPs ( PAOCH3 and LCP105) and previously on some conventional flexible polymers (atactic polystyrene, poly-n-butylacrylate) seems to be a generic effect of the glass transition. The presence of the preglassy elastic clusters questions the widely accepted hypothesis of ergodicity in the supercooled state.