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.     

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.

Open image in new window

     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

Internal viscosity in the dynamics of polymer molecules

We consider the internal viscosity (IV) of polymer molecules in solution, and investigate how the IV might depend on solvent viscosity η₀. From the Kirkwood model of a polymer, we derive in a nonrigorous manner two equations containing an IV, one equation valid for low η₀ and the other for high η₀, and we show that in these respective cases the coefficient of the IV is independent of η₀ and linearly dependent on η₀.     

Local dynamics and glass transition

The dynamics of polymer chains in the bulk state are discussed at three different temperature scales: (i) Well above the glass transition temperature where the basic step of motion is the rotameric transition of bonds. In this regime, the dynamics may conveniently be analyzed by the rotational isomeric state model, (ii) In the vicinity of glass transition where friction forces from the environment dominate. In this regime, the dynamics may be modeled according to the cooperative kinematics model, (iii) Well below glass transition. Here, an analogy with a native protein is made, and the mean-squared fluctuations are analyzed by adopting the Gaussian Network Model, which recently proved successful in describing fluctuations in native proteins.     

Monte Carlo modelling of the polymer glass transition

We are proposing a lattice model with chemical input for the computer modelling of the polymer glass transition. The chemical input information is obtained by a coarse graining procedure applied to a microscopic model with full chemical detail. We use this information on Bisphenol-A-Polycarbonate to predict it's Vogel-Fulcher temperature out of a dynamic Monte Carlo Simulation. The microscopic structure of the lattice model is that of a genuine amorphous material, and the structural relaxation obeys the time temperature superposition.     

Enthalpic relaxation and the glass transition in polymer blends

The kinetics of enthalpic relaxation are reviewed and applied to the ageing of a range of blends made from polyether imide and polyether ether ketone. DSC has been used to follow the development of enthalpic relaxation and a Williams-Watt stretched exponential equation relating the extent of relaxation, ϕ(t), to the ageing time t and an average relaxation time, t́_a', has been used to quantify the ageing process. where β' is inversely related to the breadth of the relaxation spectrum such that 0<β>1.0. The relationship was modified to incorporate non-linearity in the relaxation behaviour. ϕ(t) was measured directly from the enthalpy change observed in the endotherms on heating aged specimens through the glass transition in the DSC. The PEI/PEEK blends were compatible over the full composition range in that they exhibited a single glass transition with a temperature that varied almost linearly with composition between those of the homopolymers. Enthalpic relaxation was found to be a useful technique for probing the molecular relaxations of polymer blends and confirming the degree of compatibility of the system. The β' values changed systematically with the blend composition between those of the homopolymers suggesting that the breadth of the relaxation spectra were similar in the blends to that in the homopolymers. Physical ageing was observed to embrittle the blends, and there was a close correlation between the extent of enthalpic ageing and the change in mechanical and impact behaviour. The yield stress increased and the elongation to break decreased progressively with ϕ(t) in addition to a reduction in impact strength. The model of enthalpic relaxation and the kinetic relationships, outlined above, have been used to determine the onset of the glass transition temperature and subsequent progress of enthalpic relaxation at fixed ageing temperatures, for direct comparison with the change in specific heat observed in DSC experiments. Good agreement was observed between experiment and calculated glass transitions and the effect of variables, such as activation enthalpies, pre-exponential factors, non-linear factors such as X and β' and fictive temperature on the observed glass transition temperatures and the temperature range over which the glass transition occurred determined. Modifications to the model for the enthalpic relaxation have been suggested.     

The glass transition temperature of polymer melts

We develop an analytic theory to estimate the glass transition temperature T(g) of polymer melts as a function of the relative rigidities of the chain backbone and side groups, the monomer structure, pressure, and polymer mass. Our computations are based on an extension of the semiempirical Lindemann criterion of melting to locate T(g) and on the use of the advanced mean field lattice cluster theory (LCT) for treating the thermodynamics of systems containing structured monomer, semiflexible polymer chains. The Lindemann criterion is translated into a condition for T(g) by expressing this relation in terms of the specific volume, and this free volume condition is used to calculate T(g) from our thermodynamic theory. The mass dependence of T(g) is compared to that of other characteristic temperatures of glass-formation. These additional characteristic temperatures are determined from the temperature variation of the LCT configurational entropy, in conjunction with the Adam-Gibbs model for long wavelength structural relaxation. Our theory explains generally observed trends in the variation of T(g) with polymer microstructure, and we find that T(g) can be tuned either upward or downward by increasing the length of the side chains, depending on the relative rigidities of the side groups and the chain backbone. The elucidation of the molecular origins of T(g) in polymer liquids should be useful in designing and processing new synthetic materials and for understanding the dynamics and controlling the preservation of biological substances.     

Single particle jumps in a binary Lennard-Jones system below the glass transition

We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events (jumps) where a particle escapes the cage formed by its neighbors. Using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position. We find two kinds of jumps: "reversible jumps," where a particle jumps back and forth between two or more average positions, and "irreversible jumps," where a particle does not return to any of its former average positions, i.e., successfully escapes its cage. For all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur. With increasing temperature, relaxation is enhanced by an increasing number of jumps and growing jump lengths in position and potential energy. However, the waiting time between two successive jumps is independent of temperature. This temperature independence might be due to aging, which is present in our system. We therefore also present a comparison of simulation data with three different histories. The ratio of irreversible to reversible jumps is also increasing with increasing temperature, which we interpret as a consequence of the increased likelihood of changes in the cages, i.e., a blocking of the "entrance" back into the previous cage. In accordance with this interpretation, the fluctuations both in position and energy are increasing with increasing temperature. A comparison of the fluctuations of jumping particles and nonjumping particles indicates that jumping particles are more mobile even when not jumping. The jumps in energy normalized by their fluctuations are decreasing with increasing temperature, which is consistent with relaxation being increasingly driven by thermal fluctuations. In accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position.     

A study of the surface anchoring at a polymer/liquid crystal interface in the neighbourhood of the glass transition

Abstract

Recently, we have observed dramatic changes in the electro-optic properties of PDLC films composed of droplets of the liquid crystal E7 in a matrix of polyvinylformal (PVFM) in the vicinity of the glass transition temperature of the matrix. One plausible explanation for these changes is a decrease in the surface anchoring strength on passing through the glass transition. For this reason, we undertook a study of the surface anchoring strength between E7 and a thin film of PVFM using the technique of Yokoyama and van Sprang. To mimic the properties of the matrix more closely, we dissolved 20 per cent E7 liquid crystal into the PVFM film. The surface anchoring for this film was compared with that of a pure PVFM film. From these data, we observed no obvious changes in the surface anchoring on passing through the glass transition of the matrix. However, the incorporation of liquid crystal into the matrix did cause a decrease in the surface anchoring strength. We discuss the impact of these results on the interpretation of the PDLC electro-optic properties.     

Photoinduced intramolecular charge separation in a polymer solid below the glass transition temperature

Photoinduced intramolecular charge separation (CS) in a polar polymer glass, cyanoethylated pullulan (CN-PUL), was studied below the glass transition temperature (Tg=395 K). A series of three carbazole (Cz: donor)-cyclohexane (S: spacer)-acceptor (A: acceptor) molecules (Cz-S-A) was used as intramolecular donor-acceptor dyads. The photoinduced CS rate was evaluated by the fluorescence decay measurement at temperatures from 100 to 400 K. The CS rate (kCS) increased above 200 K even far below Tg where micro-Brownian motions of the whole polymer chain are frozen. Below 200 K, on the other hand, kCS showed weak dependence on temperature. The temperature dependence of kCS is discussed in terms of the dielectric relaxation time of the polymer matrix. Consequently, CS below Tg was well explained by a thermally nonequilibrium electron transfer (ET) formula above 200 K and by a two-mode quantum-mechanical ET formula below 200 K. The increase in kCS above 200 K is mainly caused by a thermally activated low-frequency matrix mode originating from the side-chain relaxation of polar cyano groups. The weak temperature dependence of kCS can be explained by a nuclear-tunneling effect caused by a high-frequency matrix mode (variant Planck's over 2piomegH=250 cm-1) and an intramolecular vibrational mode (variant Planck's over 2piomegaQ=1300 cm-1). The high-frequency mode of the polymer matrix was attributed to a vibrational or librational motion of polar groups in the CN-PUL glassy solid.     

Theory of heterogeneities in polymer networks

Following Edwards’ ideas we present main experimental results and the theory of random heterogeneities in neutral and charged networks obtained by instantaneous as well as chemical cross-linking of a melt and semidilute solution of linear chains. We study how random monomer density patterns in such networks change after swelling and stretching. We also describe main features of monomer density correlation functions, which determine the neutron and light scattering on spatial heterogeneities. We show that largescale cross-link density patterns written into network structure in the melt or semidilute state, can be revealed upon swelling by monitoring the monomer density patterns. We demonstrate that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image. We study how the monomer density image changes under different solvent conditions and discuss the difference between deformations of the density images in gels and ordinary solids. Possible tests of our predictions and some potential applications are proposed.     

Response of water to electric fields at temperatures below the glass transition: a molecular dynamics analysis

The electric field dependence of the structure and dynamics of water at 77 K, i.e., below the glass transition temperature (136 K), is investigated using molecular dynamics simulations. Transitions are found at two critical field strengths, denoted E(1) and E(2). The transition around E(1)≈3.5 V/nm is characterized by the onset of significant structural disorder, a rapid increase in the orientational polarization, and a maximum in the dynamical fluctuations. At E(2)≈40 V/nm, the system crystallizes in discrete steps into a body-centered-cubic unit cell that minimizes the potential energy by simultaneous superpolarization of the water molecular dipoles and maximization of the intermolecular hydrogen bonds. The stepwise and discontinuous increase of the orientational polarization with the increasing electric field indicates that the dipole relaxation in the electric field is highly cooperative.     

Molecular dynamics investigation of a density-driven glass transition in a liquid crystal system

Molecular dynamics simulations are carried out to address the density-driven glass transition in a system of rodlike particles that interact with the Gay-Berne potential. Since crystallization occurs in this system on the time scale of the simulations, direct simulation of the glass transition is not possible. Instead, glasses with isotropic orientational order are heated to a temperature T, and the relaxation times by which nematic orientational order develops are determined. These relaxation times appear to diverge at a critical density rho(c); i.e., the system can equilibrate at rhorho(c) (at the temperature T). The relaxation times follow a power-law scaling as the critical density is approached, suggesting that this density-driven glass transition concurs with mode coupling theory.     

Single polymer dynamics of topologically complex DNA

Single molecule studies allow for the direct observation of polymer dynamics in dilute and concentrated solutions, thereby revealing polymer chain conformations and molecular sub-populations that may be obscured in ensemble-level measurements. Over the past two decades, researchers have used DNA as a model system to study polymer dynamics at the molecular level. The vast majority of studies have focused on linear DNA molecules; however, researchers have recently begun to study polymers with complex topologies and architectures at the single molecule level. Here, we explore recent work in single polymer dynamics focused on topologically complex DNA, including knots, ring polymers, and branched polymers. Experimental, computational, and theoretical advances have enabled in-depth studies of topologically complex DNA, with recent efforts focused on complex molecular conformations, intermolecular interactions, and topology-dependent dynamics. In this article, we highlight recent work aimed at understanding the interplay between molecular-scale behavior and the emergent properties of polymeric materials.     

The dimensions of a polymer chain at the coil-to-globule transition

Simple models of the star-branched and linear polymers were studied by means of a Monte Carlo method. The chains were confined on a simple cubic lattice. Star-branched polymers consisted of f=3 arms of equal length. The total number of beads in both types of polymers was varied from N=49 to N=799. The simulations were performed in different solvent qualities—from a good solvent to a collapsed globule regime. The static properties of the chains under consideration were measured as functions of the temperature of the system. It appeared that the ratio of the radius of gyration to the mean end-to-end vector is very sensitive to solvent quality. It shows that the coil-to-globule transition is a complicated phenomenon. The possible explanation of the phenomenon is discussed.     

Hofmeister effect on the interfacial dynamics of single polymer molecules

The Hofmeister effect on interfacial dynamics has been discovered for single charged polymer molecules (sodium polystyrene sulfonate) adsorbed on a hydrophobic surface from an aqueous solution. The presence of ions in the aqueous solution affects the surface diffusivity, and its amplitudes and the surface friction follow the Hofmeister series-the kosmotropic ions slowed down the surface diffusivity and the chaotropic ions speeded it up. The amplitude of the surface friction exhibits a good correlation with the surface tension increment, indicating the interfacial feature of the Hofmeister effect.     

Critical dynamics of dimers: implications for the glass transition

The Adam-Gibbs view of the glass transition relates the relaxation time to the configurational entropy, which goes continuously to zero at the so-called Kauzmann temperature. We examine this scenario in the context of a dimer model with an entropy-vanishing phase transition and stochastic loop dynamics. We propose a coarse-grained master equation for the order parameter dynamics which is used to compute the time-dependent autocorrelation function and the associated relaxation time. Using a combination of exact results, scaling arguments, and numerical diagonalizations of the master equation, we find nonexponential relaxation and a Vogel-Fulcher divergence of the relaxation time in the vicinity of the phase transition. Since in the dimer model the entropy stays finite all the way to the phase transition point and then jumps discontinuously to zero, we demonstrate a clear departure from the Adam-Gibbs scenario. Dimer coverings are the "inherent structures" of the canonical frustrated system, the triangular Ising antiferromagnet. Therefore, our results provide a new scenario for the glass transition in supercooled liquids in terms of inherent structure dynamics.