Glass-forming Polymer Melts Research Articles

Experimental Tests of a Theoretically Predicted Noncausal Correlation between Dynamics and Thermodynamics in Glass-forming Polymer Melts

The connection between slow activated relaxation in glass-forming liquids and various equilibrium thermodynamic properties remains intensely debated. The microscopic elastically collective nonlinea...

A Simple New Way To Account for Free Volume in Glassy Dynamics: Model-Free Estimation of the Close-Packed Volume from PVT Data.

In this article we focus on the important role of well-defined free volume (Vfree) in dictating the structural relaxation times, τ, of glass-forming liquids and polymer melts. Our definition of Vfree = V - Vhc, where V is the total system volume, means the use of Vfree depends on determination of Vhc, the system's volume in the limiting closely packed state. Rejecting the historically compromised use of Vfree as a dynamics-dependent fitting function, we have successfully applied a clear thermodynamics-based route to Vhc using the locally correlated lattice (LCL) model equation of state (EOS). However, in this work we go further and show that Vhc can be defined without the use of an equation of state by direct linear extrapolation of a V(T) high-pressure isobar down to zero temperature (T). The results from this route, tested on a dozen experimental systems, yield ln τ vs 1/Vfree isotherms that are linear with T-dependent slopes, consistent with the general ln τ ∼ f(T) × (1/Vfree) form of behavior we have previously described. This functional form also results by implementing a simple mechanistic explanation via the cooperative free volume (CFV) rate model, which assumes that dynamic relaxation is both thermally activated and that it requires molecular segmental cooperativity. With the degree of the latter, and thus the activation energy, being determined by the availability of free volume, the new route we demonstrate here for determination of Vfree expands the potential for understanding and predicting local dynamic relaxation in glass-forming materials.

Investigation of the Temperature Dependence of Activation Volume in Glass-Forming Polymer Melts under Variable Pressure Conditions

Motivated by empirical observations suggesting that changes in the activation volume ΔV# upon varying temperature (T), determined from the pressure (P) dependence of the segmental structural relaxa...

Microscopic Theory of Dynamically Heterogeneous Activated Relaxation as the Origin of Decoupling of Segmental and Chain Relaxation in Supercooled Polymer Melts

We combine our force-based theory of activated segmental relaxation for glass-forming polymer melts, with our new formulation of how nm-scale effectively static structural fluctuations induce dynam...

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear.

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated β-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the "stretching exponent" β quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

COOPERATIVE FREE VOLUME RATE MODEL APPLIED TO THE PRESSURE-DEPENDENT SEGMENTAL DYNAMICS OF NATURAL RUBBER AND POLYUREA

ABSTRACT We apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts, focusing on two new applications of the model, to natural rubber and to polyurea. In CFV, segmental relaxation times, τ, are analyzed as a function of temperature (T) and free volume (Vfree), where the latter provides an insightful route to expressing dynamics relative to using the system's overall total volume (V). Vfree is defined as the difference between the total volume and the volume at close packing and is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice equation-of-state analysis of characteristic thermodynamic data. The new results for natural rubber and polyurea are discussed in the context of results on a set of polymeric and small-molecule glass formers that had previously been modeled with CFV. We also discuss the results in the context of recent connections that we have made with the density-scaling approach.

The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach⋆.

In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, [Formula: see text] , as a function of temperature (T and free volume ( [Formula: see text] , and make substantive comparisons with the density scaling approach. [Formula: see text] , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling [Formula: see text] parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find [Formula: see text] , where [Formula: see text] is the value predicted by the LCL EOS at the ambient [Formula: see text] . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct [Formula: see text] parameter.

Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities.

From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g0(t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Influence of Pressure on Glass Formation in a Simulated Polymer Melt

We investigate the thermodynamic and dynamic properties of a model unentangled glass-forming polymer melt over a wide range of pressures (P) and temperatures (T) using molecular dynamics simulation. We show that the T dependence of the reduced thermal expansion coefficient and isothermal compressibility becomes weaker for higher P. Based on the generalized entropy theory, these trends suggest that the isobaric fragility of glass formation decreases with increasing P, consistent with our analysis from the structural relaxation time (τα). Moreover, we confirm previous findings that the onset and end of the glass formation process in our model can be estimated solely based on the static structure factor. We then provide a detailed analysis for the T and P dependence of τα as well as other quantities characterizing the dynamic heterogeneity of glass-forming liquids. In particular, we discuss how T and P influence the average extent L of the stringlike cooperative motion of monomers in our model polymer melt, ...

Stringlike Cooperative Motion Explains the Influence of Pressure on Relaxation in a Model Glass-Forming Polymer Melt.

Numerous experiments reveal that the dynamics of glass-forming polymer melts are profoundly influenced by the application of pressure, but a fundamental microscopic understanding of these observations remains incomplete. We explore the structural relaxation of a model glass-forming polymer melt over a wide range of pressures (P) by molecular dynamics simulation. In accord with experiments for nonassociating polymer melts and the generalized entropy theory, we find that the P dependence of the structural relaxation time (τα) can be described by a pressure analog of the Vogel-Fulcher-Tammann equation and that the characteristic temperatures of glass formation increase with P, while the fragility decreases with P. Further, we demonstrate that τα for various P can quantitatively be described by the string model of glass formation, where the enthalpy and entropy of activation are found to be proportional, an effect that is expected to apply to polymeric materials under various applied fields.

Influence of Cohesive Energy on Relaxation in a Model Glass-Forming Polymer Melt

The wide range of chemical compositions exhibited by polymers enables the fabrication of materials having highly tunable cohesive energy strength ϵ, and many of the properties that make polymers so useful as structural and responsive materials in both manufacturing and living systems derive from the variability of this basic property. The design and characterization of polymer materials then inevitably leads to a consideration of how ϵ impacts the thermodynamic and relaxation properties of polymer liquids. Our prior paper uses molecular dynamics simulations of a model coarse-grained polymer melt to systematically investigate the dependence of commonly measured thermodynamic properties on ϵ, while the present work focuses on the relaxation dynamics of the same molecular model. After demonstrating, as expected, that ϵ greatly influences the segmental relaxation time, we obtain a universal reduction of all our data for relaxation in terms of an activated transport model in which the activation free energy is...

Simulated glass-forming polymer melts: dynamic scattering functions, chain length effects, and mode-coupling theory analysis.

We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.

Temperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation

We present a Molecular Dynamics simulation study of a micro-rheological probing of the glass transition in a polymer melt. Our model system consists of short bead-spring chains and the temperature ranges from well above the glass transition temperature to about 10% above it. The nano-particle clearly couples to the slowing down of the polymer segments and the calculated storage and loss moduli reveal the approach to the glass transition. At temperatures close to the mode coupling Tc of the polymer melt, the micro-rheological moduli measure the local viscoelastic response of the cage of monomers surrounding the nano-particle and no longer reveal the true melt moduli. The incoherent scattering function of the nano-particle exhibits a stretched exponential decay, typical for the α-process in glass forming systems. We find no indication of a strong superdiffusive regime as has been deduced from a recent experiment in the same temperature range but for smaller momentum transfers.

Quantitative Model for Clusters of String-like Cooperative Motion in a Coarse-Grained Glass-Forming Polymer Melt

ABSTRACTWe apply a living polymerization theory to describe cooperative string-like particle rearrangement clusters observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs (AG) model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann ‘entropy crisis’.

Simulated glass-forming polymer melts: Glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.

Modifying Fragility and Collective Motion in Polymer Melts with Nanoparticles

We investigate the impact of nanoparticles (NP) on the fragility and cooperative stringlike motion in a model glass-forming polymer melt by molecular dynamics simulation. The NP cause significant changes to both the fragility and the average length of stringlike motion, where the effect depends on the NP-polymer interaction and NP concentration. We interpret these changes via the Adam-Gibbs (AG) theory, assuming the strings can be directly identified with the abstract "cooperatively rearranging regions" of AG. Our findings indicate that fragility is primarily a measure of the temperature dependence of the cooperativity of molecular motion.

Nature and interrelations of fast dynamic properties in a coarse-grained glass-forming polymer melt

Recent experimental studies have demonstrated that the dynamics of glass-forming liquids on fast picosecond timescales are directly relevant to developing effective formulations for protein drug preservation. In these systems, short-time dynamic properties, including the Debye–Waller factor, non-ergodicity parameter, and the ‘fast beta’ relaxation time, are ‘tuned’ by the addition of antiplasticizer additives, with associated improvements in protein preservation. We employ molecular dynamics simulations of a coarse-grained polymer melt with and without the addition of an antiplasticizer additive to characterize how these fast dynamic properties interrelate and how they are altered by the addition of antiplasticizer additives. We find that the Gaussian approximation for the van Hove correlation function holds to an excellent approximation at short times, facilitating the establishment of precise interrelations between these properties and the characterization of their temperature and composition dependence. Following previous studies, we first fit the fast relaxation process to an empirical ‘stretched Gaussian’ form (exp[−(t/τ)β] with 1 < β < 2) and find that β equals 3/2 over a wide range of temperature for the post-inertial relaxation process. We then consider a more theoretically motivated description of fast beta relaxation inspired by an earlier model for the relaxation of a fractal network of elastic clusters in glass-forming colloids, and we find that this description provides an excellent fit to the entire short time relaxation over a large range of temperatures with physically meaningful parameters. Finally, we show that it is possible to tune the fast beta relaxation process with antiplasticizer additives, resulting in effects that rationally enhance protein preservation in glassy sugar matrices.

Antiplasticization and the elastic properties of glass-forming polymer liquids

We investigate the effect of antiplasticizer additives on long-wavelength thermodynamic properties relating to the efficiency of molecular packing (density ρ and isothermal compressibility κT) and material stiffness (bulk modulus K, shear modulus G, and Poisson ratio ν) of model glass-forming polymer melts. Variations in the stiffness (G and molecular force constant km from the Debye–Waller factor 〈u2〉) and density ρ at a molecular scale are also considered. We find that antiplasticizer additives cause significant changes in the long-wavelength properties that are associated with an enhanced packing efficiency in the glass state, such as a decrease in κT and an increase in K, G, and ν. Moreover, values of the local elastic moduli in the glass state follow a nearly universal (approximately log-normal) distribution and a Fourier transform of the elastic constant fluctuations in space reveals a general −2 wave vector q scaling, as in order parameter fluctuations in critical fluids and magnetic systems near their critical point for phase separation and ordering, respectively. No discernible large-scale fluctuations in the density were observed, however, indicating that the local elastic constant fluctuations do not reflect density (free volume) fluctuations, as often assumed. These observations provide essential insights into how varying the fragility of glass formation, through the addition of antiplasticizer additives, alters the local mechanical properties of polymer melts and other glass-forming liquids.

Dynamics of a Polyphosphazene Melt Studied by Solid-State 2H NMR

Poly[bis(methoxy)phosphazene] (PBMP) is used as a model to investigate the backbone dynamics of polyphosphazenes approaching their glass transitions. Specifically, we study PBMP featuring deuterated methyl groups so that, as a consequence of fast rotation of the methyl groups, 2H NMR probes the reorientation of their 3-fold symmetry axes and, thus, of the inorganic backbone. Combining 2H NMR spin−lattice relaxation, line-shape, and stimulated-echo analyses, we follow the slowdown of the segmental motion upon cooling over a broad temperature/time range. Comparison of present and previous results provides no evidence that polymers featuring inorganic and organic backbones, respectively, show fundamentally different dynamical behaviors during vitrification. In particular, typical of glass-forming polymer melts, we find for the α-process of PBMP that its temperature dependence deviates from an Arrhenius law and its time dependence differs from a single-exponential function. 2H NMR three-time correlation functions indicate that both homogeneous and heterogeneous dynamics contribute to the nonexponential relaxation. In addition, 2H NMR spin−lattice relaxation and line-shape analyses reveal the existence of some large-angle anisotropic precursor motion in the moderately viscous melt, which may be a peculiarity of polyphosphazene.