Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

A significant body of evidence indicates that particles with excessively high or low mobility relative to Brownian particles form in dynamic equilibrium in glass-forming liquids. We examine whether these "dynamic heterogeneities" can be identified with a kind of equilibrium polymerization. This correspondence is first checked by demonstrating the presence of a striking resemblance between the temperature dependences of the configurational entropy s(c) in both the theory of equilibrium polymerization and the generalized entropy theory of glass formation in polymer melts. Moreover, the multiple characteristic temperatures of glass formation are also shown to have analogs in the thermodynamics of equilibrium polymerization, supporting the contention that both processes are varieties of rounded thermodynamic transitions. We also find that the average cluster mass (or degree of polymerization) varies in nearly inverse proportionality to s(c). This inverse relation accords with the basic hypothesis of Adam-Gibbs that the number of particles in the cooperatively rearranging regions (CRR) of glass-forming liquids scales inversely to s(c) of the fluid. Our identification of the CRR with equilibrium polymers is further supported by simulations for a variety of glass-forming liquids that verify the existence of stringlike or polymeric clusters exhibiting collective particle motion. Moreover, these dynamical clusters have an exponential length distribution, and the average "string" length grows upon cooling according to the predictions of equilibrium polymerization theory. The observed scale of dynamic heterogeneity in glass-forming liquids is found to be consistent with this type of self-assembly process. Both experiments and simulations have revealed remarkable similarities between the dynamical properties of self-assembling and glass-forming liquids, suggesting that the development of a theory for the dynamics of self-assembling fluids will also enhance our understanding of relaxation in glass-forming liquids.     

Tuning polymer melt fragility with antiplasticizer additives

A polymer-diluent model exhibiting antiplasticization has been developed and characterized by molecular dynamics simulations. Antiplasticizer molecules are shown to decrease the glass transition temperature Tg but to increase the elastic moduli of the polymeric material in the low-temperature glass state. Moreover, the addition of antiplasticizing particles renders the polymer melt a stronger glass-forming material as determined by changes in the characteristic temperatures of glass formation, the fragility parameter D from fits to the Vogel-Folcher-Tamman-Hesse equation, and through the observation of the temperature dependence of the size of cooperatively rearranging regions (strings) in each system. The length of the strings exhibits a weaker temperature dependence in the antiplasticized glass-forming system than in the more fragile pure polymer, consistent with the Adam-Gibbs model of glass formation. Unexpectedly, the strings become increasingly concentrated in the antiplasticizer particles upon cooling. Finally, we discuss several structural indicators of cooperative dynamics, and find that the dynamic propensity (local Debye-Waller factor p) does seem to provide a strong correlation with local molecular displacements at long times. The authors also consider maps of the propensity, and find that the antiplasticized system exhibits larger fluctuations over smaller length scales compared to the pure polymer.     

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

We study in detail the predictions of various theoretical approaches, in particular, mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wave vector dependence of multipoint correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multipoint correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular, explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multipoint correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.     

The role of temperature and density on the glass-transition dynamics of glass formers

A correlation between the monomeric volume and the dynamic quantity E*(V)/H*, used to provide a quantitative measure of the role of temperature and density on the dynamics, is demonstrated for a series of polymers and glass-forming liquids. We show that monomeric volume and local packing play a key role in controlling the value of this ratio and thus the dynamics associated with the glass temperature.     

On melting dynamics and the glass transition. I. Glassy aspects of melting dynamics

The following properties are in the present literature associated with the behavior of supercooled glass-forming liquids: faster than exponential growth of the relaxation time, dynamical heterogeneities, growing point-to-set correlation length, crossover from mean-field behavior to activated dynamics. In this paper we argue that these properties are also present in a much simpler situation, namely the melting of the bulk of an ordered phase beyond a first order phase transition point. This is a promising path toward a better theoretical, numerical and experimental understanding of the above phenomena and of the physics of supercooled liquids. We discuss in detail the analogies and the differences between the glass and the bulk melting transitions.     

Molecular mass dependence of point-to-set correlation length scale in polymers

We use a recently proposed metric, termed the point-to-set correlation functions, to probe the molecular weight dependence of the relevant static length scales in glass-forming oligomeric chain liquids of 4, 5, 8, and 10 repeat units. In agreement with the results for simple, monatomic fluids, we find that static length scales of the oligomers increase monotonically when the temperature is lowered towards the glass transition temperature of the fluid. More interestingly, the static length scale increases with increasing chain length. Within the bounds of error in our simulations, the static length scale appears to scale as the radius of gyration of the oligomer, but with a prefactor, which is much larger than unity and which grows with the temperature. The preceding behavior contrasts with the length scales extracted from the radial distribution function of the oligomer system, which is practically independent of the chain length.     

Revealing long-range density fluctuations in dialkylimidazolium chloride ionic liquids by dynamic light scattering

In this study, the structures and dynamics of ionic liquids of 1-allyl-3-methylimidazolium chloride ([AMIM][Cl]) and 1-n-butyl-3-methylimidazolium chloride ([BMIM][Cl]) were studied by dynamic light scattering with polarized and depolarized geometries in the temperature range from 300 to 400 K. The temperature range covered supercooled and liquid states for [BMIM][Cl] and covered the liquid state for [AMIM][Cl]. The results show that for these ionic liquids at all chosen temperatures only one ultraslow relaxation is observed in the polarized component of dynamic light scattering, however, the ultraslow relaxation is not observed in the depolarized component. The ultraslow relaxation exhibited several typical features of the "cluster" mode generally found in glass-forming liquids and polymer melts, such as diffusive, strongly scattering-vector-dependent, and nearly exponential characters, which thus corresponded to long-range density fluctuations. The physical origin for long-range density fluctuations was the existence of heterogeneities with large characteristic length scales in these ionic liquids. It was further considered that molecules of these ionic liquids not only tended to aggregate to form dynamic clusters but also possibly formed dynamic networks in the supercooled state and the heterogeneities could exist even at temperatures higher than the melting points.     

Mechanistic insight into the structure and dynamics of entangled and hydrated λ-phage DNA

Intrinsic dynamics of DNA plays a crucial role in DNA-protein interactions and has been emphasized as a possible key component for in vivo chromatin organization. We have prepared an entangled DNA microtube above the overlap concentration by exploiting the complementary cohesive ends of λ-phage DNA, which is confirmed by atomic force microscopy and agarose gel electrophoresis. Photon correlation spectroscopy further confirmed that the entangled solutions are found to exhibit the classical hydrodynamics of a single chain segment on length scales smaller than the hydrodynamic length scale of single λ-phage DNA molecule. We also observed that in 41.6% (gm water/gm DNA) hydrated state, λ-phage DNA exhibits a dynamic transition temperature (T(dt)) at 187 K and a crossover temperature (T(c)) at 246 K. Computational insight reveals that the observed structure and dynamics of entangled λ-phage DNA are distinctively different from the behavior of the corresponding unentangled DNA with open cohesive ends, which is reminiscent with our experimental observation.     

On the role of inherent structures in glass-forming materials: I. The vitrification process

In this work, we investigate the role of inherent structures in the vitrification process of glass-forming materials by using a two-component Lennard-Jones mixture. We start with a simplified model that describes the dynamics of the atomistic system as a Poisson process consisting of a series of transitions from one potential energy minimum (inherent structure) to another, the rate of individual transitions being described by a first-order kinetic law. We investigate the validity of this model by comparing the mean square displacement resulting from atomistic molecular dynamics (MD) trajectories with the corresponding mean square displacement based on inherent structures. Furthermore, in the case of vitrification via stepwise cooling, we identify the role of the potential energy landscape in determining the properties of the resulting glass. Interestingly, the cooling rate is not sufficient to define the resulting glass in a stepwise cooling process, because the time spent by the system at different temperatures (length of the steps) has a highly nonlinear impact on the properties of the resulting glass. In contrast to previous investigations of supercooled liquids, we focus on a range of temperatures close to and below the glass transition temperature, where the use of MD is incapable of producing equilibrated samples of the metastable supercooled state. Our aim is to develop a methodology that enables mapping the dynamics under these conditions to a coarse-grained first-order kinetic model based on the Poisson process approximation. This model can be used in order to extend our dynamical sampling ability to much broader time scales and therefore allow us to create computer glasses with cooling rates closer to those used experimentally. In a continuation to this work, we provide the mathematical formulation for lifting the coarse-grained Poisson process model and reproducing the full dynamics of the atomistic system.     

Local polymer dynamics under strong connectivity constraints: the dendrimer case

The characteristics of local motion are explored by molecular dynamics simulations in a series of AB(2)-type dendrimer melts. Systems of generations 3-5 were simulated in a wide temperature range, allowing the assessment of effects associated with molecular size, proximity to the detected glasslike transitions, and the strong connectivity constraints imposed by the dendritic topology. Investigation of the mechanisms involved in local motion at short temporal and spatial scales revealed the connection between the non-Gaussian nature of monomer displacements to alpha-relaxation and the caging/decaging process under different degrees of confinement. In the latter mechanism, two characteristic localization lengths were identified: at the low temperature limit spatial localization was realized within approximately 10% of the nearest neighbor distance while at temperatures higher than the glass transition, the existence of an analogous length scale is ascribed to the geometric constraints due to the dense connectivity pattern. As the results from this study are discussed in comparison to the behavior observed in linear polymers and supercooled liquids, new insight is provided on the universal/specific mechanisms involved in local dynamics of different glass-forming systems.     

Mosaic energy landscapes of liquids and the control of protein conformational dynamics by glass-forming solvents

Using recent advances in the Random First-Order Transition (RFOT) Theory of glass-forming liquids, we explain how the molecular motions of a glass-forming solvent distort the protein's boundary and slave some of the protein's conformational motions. Both the length and time scales of the solvent imposed constraints are provided by the RFOT theory. Comparison of the protein relaxation rate to that of the solvent provides an explicit lower bound on the size of the conformational space explored by the protein relaxation. Experimental measurements of slaving of myoglobin motions indicate that a major fraction of functionally important motions have significant entropic barriers.     

Unwinding dynamics of double-stranded polymers

We consider the unwinding of two lattice polymer strands of length N that are initially wound around each other in a double-helical conformation and evolve through Rouse dynamics. The problem relates to quickly bringing a double-stranded polymer well above its melting temperature, i.e., the binding interactions between the strands are neglected, and the strands separate from each other as it is entropically favorable for them to do so. The strands unwind by rotating around each other until they separate. We find that the process proceeds from the ends inward; intermediate conformations can be characterized by a tightly wound inner part, from which loose strands are sticking out, with length l～t(0.39). The total time needed for the two strands to unwind scales as a power of N as τ(u)～N(2.57±0.03). We present a theoretical argument, which suggests that during this unwinding process, these loose strands are far out of equilibrium.     

Solvation dynamics and electric field relaxation in an imidazolium-PF6 ionic liquid: from room temperature to the glass transition

Time-resolved phosphorescence spectra and anisotropy of quinoxaline were measured in an ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM-HFP), in its supercooled state near the glass-transition temperature. The solvation dynamics results are compared with the rotational motion of the probe and with the dielectric behavior of the neat ionic liquid. The dynamics in the viscous state are highly dispersive and show a super-Arrhenius temperature dependence, as typical for glass-forming materials. Combined with room-temperature results, solvation dynamics is observed to follow the structural relaxation times in terms of eta/T for more than 10 decades, from subnanoseconds at room temperature to seconds near the glass-transition temperature T(g). The dielectric modulus relaxation follows this trend only for temperatures T > 1.2T(g) and departs significantly from eta/T in the 1.1T(g) > T > T(g) range. This deviation is reminiscent of the enhanced translational diffusion or fractional Stokes-Einstein behavior observed in many fragile supercooled liquids. Because the electric field relaxation in BMIM-HFP includes dc conductivity, this correlation function involves translational motion and thus displays the effect of enhanced diffusivity. A microscopic model is required for rationalizing the decoupling of solvation dynamics from the longitudinal time scales and the limitation of this effect to the viscous regime with T < 1.2T(g).     

Effect of chain length on fragility and thermodynamic scaling of the local segmental dynamics in poly(methylmethacrylate)

Local segmental relaxation properties of poly(methylmethacrylate) (PMMA) of varying molecular weight are measured by dielectric spectroscopy and analyzed in combination with the equation of state obtained from PVT measurements. Significant variations of glass transition temperature and fragility with molecular weight are observed. In accord with the general properties of glass-forming materials, single molecular weight dependent scaling exponent gamma is sufficient to define the mean segmental relaxation time taualpha and its distribution. This exponent can be connected to the Gruneisen parameter and related thermodynamic quantities, thus demonstrating the interrelationship between dynamics and thermodynamics in PMMA. Changes in the relaxation properties ("dynamic crossover") are observed as a function of both temperature and pressure, with taualpha serving as the control parameter for the crossover. At longer taualpha another change in the dynamics is apparent, associated with a decoupling of the local segmental process from ionic conductivity.     

The short time regime of segmental dynamics of glass-forming polymers

The short time regime (10⁻¹³ s ≤ t ≤ 10⁻¹¹ s) of the segmental dynamics of several glass-forming polymers with different chemical microstructure and glass-transition temperature has been investigated by means of time of flight (TOF) neutron scattering techniques. In this paper we present a summary of the main results obtained as well as the theoretical framework proposed by us to interpret these results. The main conclusion is that the segmental dynamics of glass-forming polymers display in the very short time range (t = 2 ps) a crossover from a simple exponential behaviour towards a non-exponential regime. The first exponential decay, which is controlled by C-C rotational barriers, can be understood as a trace of the behaviour of the system in absence of the effects (correlations, cooperativity, memory effects…) which characterise the dense supercooled liquid like state against the normal liquid state. The non-exponential regime at t > 2 ps corresponds to what is usually understood as α and β relaxations. Some implications of these results are also discussed.     

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: geodesic pathways through the potential energy landscape

How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential-energy-landscape ensemble, it is possible to make direct connections between the geometry of the landscape and the long-time dynamical behaviors of systems such as supercooled liquids. We show, in particular, that the onset of slow dynamics in such systems is governed directly by the lengths of their geodesics--the shortest paths through their landscapes within the special ensemble. The more convoluted and labyrinthine these geodesics are, the slower that dynamics is. Geodesics in the landscape ensemble have sufficiently well-defined characteristics that it is straightforward to search for them numerically, a point we illustrate by computing the geodesic lengths for an ordinary atomic liquid and a binary glass-forming atomic mixture. We find that the temperature dependence of the diffusion constants of these systems, including the precipitous drop as the glass-forming system approaches its empirical mode-coupling transition, is predicted quantitatively by the growth of the geodesic path lengths.     

Dynamics of caged ions in glassy ionic conductors

At sufficiently high frequency and low temperature, the dielectric responses of glassy, crystalline, and molten ionic conductors all invariably exhibit nearly constant loss. This ubiquitous characteristic occurs in the short-time regime when the ions are still caged, indicating that it could be a determining factor of the mobility of the ions in conduction at longer times. An improved understanding of its origin should benefit the research of ion conducting materials for portable energy source as well as the resolution of the fundamental problem of the dynamics of ions. We perform molecular dynamics simulations of glassy lithium metasilicate (Li2SiO3) and find that the length scales of the caged Li+ ions motions are distributed according to a Levy distribution that has a long tail. These results suggest that the nearly constant loss originates from "dynamic anharmonicity" experienced by the moving but caged Li+ ions and provided by the surrounding matrix atoms executing correlated movements. The results pave the way for rigorous treatments of caged ion dynamics by nonlinear Hamiltonian dynamics.     

Thermodynamic, dynamic, structural, and excess entropy anomalies for core-softened potentials

Using molecular dynamic simulations, we study three families of continuous core-softened potentials consisting of two length scales: a shoulder scale and an attractive scale. All the families have the same slope between the two length scales but exhibit different potential energy gap between them. For each family three shoulder depths are analyzed. We show that all these systems exhibit a liquid-liquid phase transition between a high density liquid phase and a low density liquid phase ending at a critical point. The critical temperature is the same for all cases suggesting that the critical temperature is only dependent on the slope between the two scales. The critical pressure decreases with the decrease of the potential energy gap between the two scales suggesting that the pressure is responsible for forming the high density liquid. We also show, using the radial distribution function and the excess entropy analysis, that the density, the diffusion, and the structural anomalies are present if particles move from the attractive scale to the shoulder scale with the increase of the temperature indicating that the anomalous behavior depends only in what happens up to the second coordination shell.     

Kinetic paths, time scale, and underlying landscapes: a path integral framework to study global natures of nonequilibrium systems and networks

We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems.     

Dynamic light scattering from ternary polymer blends: critical behavior and bicontinuous microemulsions

We have used dynamic light scattering to study the dynamics of ternary polymer blends consisting of poly(dimethylsiloxane) (PDMS) and poly(ethylethylene) (PEE) homopolymers and a PDMS‐PEE diblock copolymer nearly symmetric in composition. The intensity autocorrelation functions for the binary blend are single‐exponential, and the associated correlation length ξ scales with reduced temperature ϵ in accordance with the Ising universality class (i.e., ξ ∼ ϵ^−ν, with ν = 0.63). An addition of copolymer depresses the critical temperature, but also increases the magnitude of ν. For compositions within the microemulsion channel, ξ exhibits a distinct maximum with decreasing temperature, near the Lifshitz line obtained from the static structure factor. For a particular composition, there is a “re‐entrant” microemulsion, as the system passes into and then out of the phase‐separated region upon cooling.