Lifetime of spatially heterogeneous dynamic domains in polystyrene melts

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.

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.

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).

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

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.

Kinetics of azobenzene nitrene oxidation by molecular oxygen in glassy propylene carbonate

The kinetics of azobenzene nitrene oxidation by molecular oxygen dissolved in a matrix was studied in glassy propylene carbonate. The reaction was carried out in excess oxygen within its concentration range 0.008 to 0.048 M. The oxidation kinetics, controlled by oxygen diffusion, is not described by the exponential function. A specific reaction rate decreases in the course of the process. The higher the oxygen concentration in the matrix, the sharper is the decrease in the reaction rate. It is shown that at all concentrations, the oxidation kinetics is described in the framework of the model of heterogeneous matrix with a characteristic size of heterogeneities of 1.5 nm and a dispersion of the activation energy of oxygen molecule jump of 4 kJ/mol. The reaction radius is about 0.5 nm.

Dynamical heterogeneity in a highly supercooled liquid: consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ξ(4), intensity χ(4), and lifetime τ(hetero). We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime τ(hetero)(t) in two time intervals t = τ(α) and τ(ngp), where τ(α) is the α-relaxation time and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime τ(hetero)(t), we evaluated the correlation length ξ(4)(t) and the intensity χ({4)(t) from the same order parameter used for the lifetime τ(hetero)(t). We found that as the temperature decreases, the lifetime τ(hetero)(t) grows dramatically, whereas the correlation length ξ(4)(t) and the intensity χ(4)(t) increase slowly compared to τ(hetero)(t) or plateaus. Furthermore, we investigated the lifetime τ(hetero)(t) in more detail. We examined the time-interval dependence of the lifetime τ(hetero)(t) and found that as the time interval t increases, τ(hetero)(t) monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which τ(hetero)(t) plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.

Lifetime of dynamical heterogeneity in a highly supercooled liquid

We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals: τ(α) and τ(ngp). τ(α) is the α relaxation time, and τ(ngp) is the time at which non-gaussian parameter of the Van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)), by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between τ(hetero)(τ(α)) and τ(hetero)(τ(ngp)) increases with decreasing temperature. At low temperatures, τ(hetero)(τ(α)) is considerably larger than τ(α), while τ(hetero)(τ(ngp)) remains comparable to τ(α). Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.

Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids

A multitime probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular-dynamics simulations for simple glass-forming liquids are performed and a three-time correlation function is numerically calculated for general time intervals. It is demonstrated that the three-time correlation function is sensitive to the heterogeneous dynamics and that it reveals couplings of correlated motions over a wide range of time scales. Furthermore, the time scale of the heterogeneous dynamics tauhetero is determined by the change in the second time interval in the three-time correlation function. The present results show that the time scale of the heterogeneous dynamics tauhetero becomes larger than the alpha-relaxation time at low temperatures and large wavelengths. We also find a dynamical scaling relation between the time scale tauhetero and the length scale xi of dynamical heterogeneity as tauhetero approximately xiz with z=3.

Nanoparticle motion within glassy polymer melts

X-ray photon correlation spectroscopy is employed to investigate the motion of dilute suspensions of gold nanoparticles in low-molecular-weight polystyrene melts. At high temperatures, the observed motion is diffusive, with a rate that follows a Vogel-Fulcher temperature dependence. Closer to the glass transition temperature Tg, diffusion is superseded by a hyperdiffusive process that first becomes observable near a crossover temperature Tc approximately 1.1Tg and is identified with heterogeneous strain in the melts. Following rapid cooling to temperatures sufficiently below Tc, but still above Tg, the hyperdiffusive dynamics displays a time dependence similar to aging in polymer glasses.

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

We studied the temperature dependence of the structural relaxation in poly(vinyl acetate) near the glass transition temperature with single molecule spectroscopy from Tg-1 K to Tg+12 K. The temperature dependence of the observed relaxation times matches results from bulk experiments; the observed relaxation times are, however, 80-fold slower than those from bulk experiments at the same temperature. We attribute this factor to the size of the probe molecule. The individual relaxation times of the single molecule environments are distributed normally on a logarithmic time scale, confirming that the dynamics in poly(vinyl acetate) is heterogeneous. The width of the distribution of individual relaxation times is essentially independent of temperature. The observed full width at half maximum (FWHM) on a logarithmic time axis is approximately 0.7, corresponding to a factor of about 5-fold, significantly narrower than the dielectric spectrum of the same material with a FWHM of about 2.0 on a logarithmic time axis, corresponding to a factor of about 100-fold. We explain this narrow width as the effect of temporal averaging of single molecule fluorescence signals over numerous environments due to a limited lifetime of the probed heterogeneities, indicating that heterogeneities are dynamic. We determine a loose upper limit for the ratio of the structural relaxation time to the lifetime of the heterogeneities (the rate memory parameter) of Q<80 for the range of investigated temperatures.

Local viscosity of supercooled glycerol near Tg probed by rotational diffusion of ensembles and single dye molecules

We probe the rotational diffusion of a perylene dye in supercooled glycerol, 5-25 K above the glass-transition temperature (T(g) = 190 K) at the ensemble and the single-molecule level. The single-molecule results point to a broad distribution of local viscosities that vary by a factor of five or more for different individual fluorophores at a given temperature. By following the same single molecules at various temperatures, we find that the distribution of local viscosities itself broadens upon approaching T(g). This spatial heterogeneity is found to relax extremely slowly, persisting over hours or even days. These results convey a picture of heterogeneous liquid pockets separated by solid-like walls, which exist already well above the viscosimetric glass transition.

Dynamical Heterogeneity in Glassy o-Terphenyl: Manifestation of Environment Changes in Photoisomerization Kinetics of Probe Molecules

A new method for the investigation of dynamical heterogeneity in glassy matrixes is presented and illustrated by the example of o-terphenyl (OTP). UV-vis absorption spectroscopy has been used to monitor the cis-trans isomerization kinetics of probe molecules in glassy OTP. The dependence of isomerization quantum yield on light intensity has been established. This dependence is shown to be due to the change in the local environment of the probe molecules. The simple model is suggested to estimate the time required for the environment to change, tauex. The tauex values from 2.6 x 10(2) to 1.9 x 10(5) s have been obtained for environments of molecules of 1-naphthylazomethoxybenzene (NAMB) in OTP over a temperature range from 244 to 204 K (Tg+1 to Tg-39 K). The temperature dependence of exchange time has a non-Arrhenius character. As the temperature decreases, an increase in exchange time slows down. The activation energy of the relaxation process is 54 kJ/mol over the range of 224-239 K.

Heterogeneous dynamics, ageing, and rejuvenating in van der Waals liquids

It has been shown over the past ten years that the dynamics close to the glass transition is strongly heterogeneous: fast domains coexist with domains three or four decades slower, the size of these regions being about 3 nm at T(g). The authors extend here a model that has been proposed recently for the glass transition in van der Waals liquids. The authors describe in more details the mechanisms of the alpha relaxation in such liquids. It allows then to interpret physical ageing in van der Waals liquids as the evolution of the density fluctuation distribution towards the equilibrium one. The authors derive the expression of macroscopic quantities (volume, compliance, etc.). Numerical results are compared with experimental data (shape, times to reach equilibrium) for simple thermal histories (quenches, annealings). The authors explain the existence of a "Kovacs memory effect" and the temporal asymmetry between down jump and up jump temperatures experiments, even for systems for which there is no energy barriers. Their model allows also for calculating the evolution of small probe diffusion coefficients during ageing.

Local polarization fluctuations in an aging glass

Polarization fluctuations were measured in nanoscale volumes of a polymer glass during aging following a temperature quench through the glass transition. Statistical properties of the noise were studied in equilibrium and during aging. The noise spectral density had a larger temporal variance during aging; i.e., the noise was more non-Gaussian, suggesting stronger correlations during aging.

Nonresonant dielectric hole burning in neat and binary organic glass formers

Binary mixtures of the molecular glass former 2-picoline in oligostyrene, in which the dielectric response of 2-picoline exhibits a particularly broad distribution of correlation times, are investigated by nonresonant dielectric hole-burning (NDHB) spectroscopy and the results are compared with NDHB in neat systems, in particular, glycerol. It turns out that in both substance classes spectral selectivity is achieved, which indicates that dynamics is heterogeneous, i.e., slow and fast responses coexist in the material. However, in binary systems the position of the spectral modifications is completely determined by the spectral density of the pump field, and thus shifts linearly with burn frequency as expected, also at pump frequencies around the alpha-relaxation maximum. It is shown that in binary systems the lifetime tau(rec) of the spectral modifications is determined by the burn frequency omega(p) and exceeds its inverse by about one order of magnitude, indicating long-lived dynamic heterogeneity. The data are described in terms of a previously suggested model of dynamically selective heating, which was extended to include intrinsic nonexponential relaxation. It turns out that the spectral broadening in binary mixtures is not only due to pronounced dynamic heterogeneity, but partially also due to intrinsic broadening of the relaxation function.

Heterogeneous nature of the dynamics and glass transition in thin polymer films

Recent experiments have demonstrated that the dynamics in liquids close to and below the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. We use here a model proposed recently for explaining these features, and show that the heterogeneous nature of the dynamics has important consequences when considering the dynamics of thin films. We show how the dominant relaxation time in a thin film is changed as compared to the bulk, as a function of the thickness, the interaction energy with the substrate, and the temperature. The corresponding time scales cover the so-called VFT (or WLF) regime and vary between 10(-8) s to 10(4) s typically. In the absence of interaction, our model allows for interpreting suspended films experiments, in the case of small polymers for which the data do not depend on the polymer weight. The interaction leads to an increase of T(g) for an interaction per monomer of the order of the thermal energy T. This increase saturates at the value corresponding to strongly interacting films for adsorption energies slightly larger and still of order T. In particular, we predict that the T(g) shift can be non-monotonous as a function of the film thickness, in the case of intermediate interaction strength.

Dynamic heterogeneity of relaxations in glasses and liquids

We report an investigation of the heterogeneity in supercooled liquids and glasses using the non-Gaussianity parameter. We simulate selenium and a binary Lennard-Jones system by molecular dynamics. In the non-Gaussianity three time domains can be distinguished: an increase on the ps scale due to the vibrational (ballistic) motion of the atoms, followed by a growth, due to local relaxations ( beta relaxation) at not too high temperatures, and finally a slow drop at long times. The non-Gaussianity follows in the intermediate time domain a sqrt[t] law. This is explained by collective hopping and dynamic heterogeneity. We support this finding by a model calculation.