Supercooled Polymer Melt Research Articles

Surface roughness of supercooled polymer melts

We report on in situ x-ray reflectivity measurements of the surface roughness of supercooled glass forming polymers in a temperature range from 190 to 330 K. The experimentally determined rms roughness has been found to obey the capillary wave model of a single liquid/vapor interface over the entire temperature range. An expression for the surface roughness below the bulk glass transition (T(G) approximately equal to 200 K) is deduced from the viscoelastic theory of surface fluctuations; however, no indication of a frozen-in surface roughness has been observed in the experiment. Additionally, it is shown that precise values of the surface tension of highly viscous liquids in the supercooled state can be determined by x-ray reflectivity.

Memory effects in classical and quantum mean-field disordered models

We apply the Kovacs experimental protocol to classical and quantum p-spin models. We show that these models have memory effects as those observed experimentally in super-cooled polymer melts. We discuss our results in connection to other classical models that capture memory effects. We propose that a similar protocol applied to quantum glassy systems might be useful to understand their dynamics.

Static properties of a simulated supercooled polymer melt: structure factors, monomer distributions relative to the center of mass, and triple correlation functions.

We analyze structural and conformational properties in a simulated bead-spring model of a nonentangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Europhys. Lett. 58, 53 (2002)]], remain essentially unchanged on cooling toward the critical glass transition temperature T(c) of mode-coupling theory. Spatial correlations between monomers on different chains, however, depend on temperature, albeit smoothly. This implies that the glassy behavior of our model cannot result from static intrachain or CM-CM correlations. It must be related to interchain correlations at the monomer level. Additionally, we study the dependence of interchain correlation functions on the position of the monomer along the chain backbone. We find that this site dependence can be well accounted for by a theory based on the polymer reference interaction site model. We also analyze triple correlations by means of the three-monomer structure factors for the melt and for the chains. These structure factors are compared with the convolution approximation that factorizes them into a product of two-monomer structure factors. For the chains this factorization works very well, indicating that chain connectivity does not introduce special triple correlations in our model. For the melt deviations are more pronounced, particularly at wave vectors close to the maximum of the static structure factor.

Publisher’s Note: “Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt” [J. Chem. Phys. 119, 5290 (2003)

a! Present address: Department of Physics, Wesleyan University, Middletown, CT 06459. b!Author to whom correspondence should be addressed. Electronic mail: baschnag@ics.u-strasbg.fr c!Author to whom correspondence should be addressed. Electronic mail: sglotzer@umich.edu FIG. 8. Temperature dependence of the ratio of ^sseg(tstr )& and ^s(tstr )&. tstr max is the peak time of ^sseg& and ^s& at different temperatures. TMCT 50.45. JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER 14 8 APRIL 2004

Confinement effects on the slow dynamics of a supercooled polymer melt: Rouse modes and the incoherent scattering function.

Results of large-scale molecular-dynamics simulations of a supercooled polymer film are presented (F. Varnik, J. Baschnagel, K. Binder, J. Phys. IV 10, 239 (2000)). The dynamic and static properties of the system are studied for a wide range of film thicknesses (from 3 to about 55 times the bulk radius of gyration) and temperatures (from the normal liquid state to the supercooled region). The system is confined between two completely smooth and purely repulsive walls. Motivated by the previous results on the enhancement of the local relaxation dynamics due to the confinement (F. Varnik, J. Baschnagel, K. Binder, Eur. Phys. J. E 8, 175 (2002); Phys. Rev. E. 65, 021507 (2002)), we now study the effect of the walls on the dynamics of the Rouse modes. It has been reported from Monte Carlo studies of the Bond Fluctuation Model (BFM) that, contrary to the enhancement of the "cage dynamics" (exemplified by a faster relaxation of the incoherent scattering function in the film), Rouse modes exhibit a slower relaxation in the confined system (C. Mischler, J. Baschnagel, K. Binder, Adv. Colloid Interface Sci. 94, 197 (2001)). However, we do not observe such a discrepancy for our continuum model: At a given temperature, the relaxation of a given Rouse mode is faster in the film than in the bulk in accordance with the acceleration of the dynamics around the cage.

Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt

We analyze dynamical heterogeneities in a simulated “bead-spring” model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature TMCT of the mode-coupling theory, but generally remains small, although large strings involving ten or more monomers are observed. An important contribution to this replacement comes from directly bonded neighbors in the chain. However, mobility is not concentrated along the backbone of the chains. Thus, a relaxation mechanism in which neighboring mobile monomers along the chain move predominantly along the backbone of the chains, seems unlikely for the system studied.

Shear viscosity of a supercooled polymer melt via nonequilibrium molecular dynamics simulations

Using nonequilibrium molecular dynamics simulations, we compute the shear viscosity, ηs, of a glass forming polymer melt at temperatures ranging from the normal liquid state down to the supercooled state. For this purpose, the polymer melt is confined between two solid walls and a constant force pointing in direction parallel to the walls is applied on each monomer thus giving rise to a Poiseuille flow. It is shown that ηs(T) does not exhibit an Arrhenius-type behavior but can be described both by a power law (mode coupling theory) and by a Vogel–Fulcher–Tammann law. A similar behavior is observed in recent experiments above the glass transition temperature. The diffusion coefficient is computed using the mean square displacements in direction perpendicular to the flow. Combined with the knowledge of ηs(T), it is then shown that the Stokes–Einstein relation is valid at high temperatures, whereas deviations are observed in the supercooled regime in agreement with experiments. Moreover, the local viscosity, η(z), is also computed and its reliability is discussed. Using the sharp rise of η(z) close to the wall, we estimate zwall, the effective position of the wall. It is found that zwall moves towards the film center at lower T thus leading to a decrease of the (hydrodynamic) width of the system. Furthermore, we observe that the curves for η(z)/ηs at various temperatures superimpose if the data are depicted versus z−zwall(T). This suggests that the spatial and temperature dependence of the local viscosity separate if the effective position of the wall is chosen as a new reference plane.

Dynamics and rheology of a supercooled polymer melt in shear flow

Using molecular dynamics simulations, we study dynamics of a model polymer melt composed of short chains with bead number N=10 in supercooled states. In quiescent conditions, the stress relaxation function G(t) is calculated, which exhibits a stretched exponential relaxation on the time scale of the α relaxation time τα and ultimately follows the Rouse dynamics characterized by the time τR∼N2τα. After application of shear γ̇, transient stress growth σxy(t)/γ̇ first obeys the linear growth ∫0tdt′G(t′) for strain less than 0.1 but saturates into a non-Newtonian viscosity for larger strain. In steady states, shear thinning and elongation of chains into ellipsoidal shapes take place for shear γ̇ larger than τR−1. In such strong shear, we find that the chains undergo random tumbling motion taking stretched and compact shapes alternatively. We examine the validity of the stress–optical relation between the anisotropic parts of the stress tensor and the dielectric tensor, which are violated in transient states due to the presence of a large glassy component of the stress. We furthermore introduce time-correlation functions in shear to calculate the shear-dependent relaxation times, τα(T,γ̇) and τR(T,γ̇), which decrease nonlinearly as functions of γ̇ in the shear-thinning regime.

Static and dynamic properties of supercooled thin polymer films.

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time alpha-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT beta-process. An analysis of the temperature dependence of the alpha-relaxation time suggests that the critical temperature, T(c), of MCT decreases with D. If the confinement is not too strong ( D>or=10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T(c)( D), to the critical temperature. This suggests that T - T(c)( D) is an important temperature scale of our model both in the bulk and in the films.

Formation of Chain-Folded Structures in Supercooled Polymer Melts Examined by MD Simulations

We report the first computer experiments with supercooled polymer melts of chains long enough to form chain-folded structures. These structures resemble the lamellae of polymer crystals, and the inverse of the lamellar thickness is related linearly to the crystallization temperature as found in experiments. The small- and wide-angle scattering intensities start growing at about the same time. However, the wide-angle scattering signal is very weak at the beginning. We use molecular dynamics (MD) simulations with a coarse-grained polymer model for chain lengths of N = 100 monomers. The model consists of spherical beads connected by harmonic springs with an additional angle bending potential reflecting the torsional states of the underlying atomistic backbone. It demonstrates that chain stiffness alone without an attractive interparticle potential is a sufficient driving force for the formation of chain-folded structures. We discuss the evolution of structure in the homogeneous nucleation regime as well as the melting process. The influence of the finite size accessible in direct MD simulation of polymer crystallization is discussed critically.

Formation of chain-folded structures in supercooled polymer melts

Molecular dynamics simulations of supercooled polymer melts are reported for long chains. This is the first simulation study at melt densities where the formation of chain-folded structures resembling the lamellae of polymer crystals is observed. Crystallization and subsequent melting temperatures are related linearly to the inverse lamellar thickness. Analysis of the single chain conformations in the crystal shows that most chains reenter the same lamella by tight backfolds. Simulations are performed with a mesoscopic bead-spring model including a specific angle bending potential. They demonstrate that chain stiffness alone, without an attractive inter-particle potential, is a sufficient driving force for the formation of chain-folded lamellae.

Polymer motions from localization to Rouse dynamics in supercooled melts

Laboratory and simulation studies of relaxation in supercooled polymer melts provide a view of the approach to the glass transition that is complementary to that obtained from study of small molecule liquids, because of the additional length scales characteristic of macromolecules. Recent molecular dynamics simulations of a supercooled melt of bead–spring polymers have shown that the motions of a coarse-grained polymer bead on length scales smaller than the bead diameter closely resemble dynamics in a supercooled simple liquid, in which molecules are spatially localized in accordance with the predictions of mode coupling theory. On longer length scales, the connectivity of the polymer becomes significant and molecular motions may be described by the Rouse model. We present calculations of chain dynamics in a supercooled melt from the dynamically disordered Rouse model. This dynamical mean field model shows qualitative agreement with the simulation data in describing both the short time regime of spatial localization at low temperature and the longer time regimes of Rouse dynamics.

Dynamics of a supercooled polymer melt above themode-coupling critical temperature: cage versus polymer-specificeffects

This paper reports results of molecular dynamics simulations for aglassy polymer melt consisting of short, non-entangled chains. Thetemperature region studied covers the supercooled state of the meltabove the mode-coupling critical temperature. The analysis focuseson the interplay of simple-liquid and polymer-specific effects. Onecan clearly distinguish two regimes: a regime of small and one of largemonomer displacements. The first regime corresponds to motion of amonomer in its local environment. It is dominated by the cage effectand well described by the idealized mode-coupling theory. Thesecond regime is governed by the late-β/early-α process.In this regime the connectivity of the monomers begins tointerfere with the cage dynamics and finally becomes dominant. Themonomer displacement is compared with simulation results for abinary Lennard-Jones mixture to highlight the differences which areintroduced by the connectivity of the particles.

Relaxation in a supercooled polymer melt within the dynamically disordered Rouse model

Dielectric and rheological measurements on polymer melts have demonstrated that rates of dynamical processes on short length scales decrease more rapidly than relaxation rates associated with longer length scales as the melt is cooled towards its glass transition temperature. We demonstrate here that the dynamically disordered Rouse model is consistent with these observations and provides a simple physical picture of molecular motions in supercooled melts. In this coarse-grained model of the dynamics of a single molecule, the beads of a harmonic chain are characterized by mobilities that fluctuate between zero and a finite value at a rate that is determined self-consistently. We present calculations of two observables whose temperature dependence near the glass transition has revealed the inadequacies of the Rouse model: Je, the steady-state compliance, and ωs/ωn, the ratio of segmental and normal mode peak frequencies in the dielectric spectrum of a polar polymer.

Collective dynamics in simple supercooled and polymer liquids

The Dynamic Lattice Liquid (DLL) model for molecular rearrangements in liquids is discussed in application to both simple supercooled liquids and polymer melts. It is shown, that the model is able to reproduce a broad class of various temperature dependencies of relaxation times, lying between the extremal cases represented by the Arrhenius relation on one and by the Vogel-Fulcher-Tamman (VFT) relation on the other hand. Rates of rearrangements are considered as being controlled by thermal activation with activation energy barriers dependent on local density. Various dependencies of the activation energy barriers on local density are examined. All cases are based on the uniform microscopic picture of cooperative molecular rearrangements operating in a dense system under conditions of the excluded volume and continuity of the system. The model is implemented as a simulation algorithm, which is used to describe dynamic properties of liquids and polymer melts. Simulation results obtained for systems representing simple liquids as well as linear polymers, multiarm star polymers and microgels are presented. An analogy in the dynamic behavior between the low molecular liquids and melts of macromolecules with complex compact architectures is discussed.

Molecular dynamics of supercooled polymer films

We present results of molecular dynamics simulations for a supercooled polymer melt confined between two smooth and purely repulsive walls. The thickness D of the film is about 7 times the bulk radius of gyration. For all temperatures studied, a significant increase of the monomer and chain mobilities with respect to the bulk is observed. Preliminary results suggest that structural relaxation times exhibit a power-law behavior in the vicinity of a critical temperature T c (D) 0.39 (in Lennard-Jones units). This estimate of T c (D) is about 14% smaller than the corresponding bulk value. Despite this significant decrease the time dependence of various mean-square displacements seems to be unaffected by confinement if data for the same reduced temperatures T - T c of the bulk and the film are compared.

Observation of shish crystal growth into nondeformed melts

Thin films of isotactic polystyrene (iPS) were deformed on a carbon supported TEM grid at temperatures between 210 °C and 240 °C. The elongation of the supercooled polymer melt films is localized in a deformation zone due to the formation of cracks within the brittle carbon support film, whereas the adjoining areas stay in a relaxed state. Since the nucleation of fibrous (“shish”) crystals needs an orientation mechanism to align the molecular chains, their origin is located in the deformation zone. It is shown that the subsequent growth of the shish crystal can propagate into the relaxed melt although it has to surmount the adhesion to the carbon substrate. From these results the conclusion is drawn that the shish crystal growth can be an autocatalytic process, which induces a self-orientation of the molecules in the growth front of the crystal tip and does not necessarily need an external flow field. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1183–1187, 2000

Dynamics and Rheology of a Supercooled Polymer Melt

Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions in supercooled states. In quiescent states, while the self chain motions are excellently described by the Rouse model, the stress relaxation function G(t) exhibits a stretched exponential decay in a relatively early stage and ultimately follows the Rouse function. Transient stress evolution after application of shear obeys the linear growth ∫0tdt′G(t′) for strain less than 0.1 and then saturates into a non-Newtonian viscosity. A glassy component of the stress is much enhanced as compared to the entropic component.

Monte Carlo simulation of stretched exponential relaxation near the glass transition

The dynamical behavior of a supercooled polymer melt is studied by means of Monte Carlo simulation. The simulation uses a version of the bond-fluctuation (lattice) model in which long bond vectors are favored energetically. The expansion on the length scale of a bond also induces an increase of the chains' size and stiffness during supercooling. In a dense melt the tendency of an individual chain to stretch has to compete with that of all others. This competition between the internal energy of a chain and the density of the melt strongly slows down the structural relaxation at low temperatures. In order to analyze the dynamical behavior of this model different relaxation functions were calculated in a temperature region ranging from the normal liquid-like to the supercooled state of the melt. Among these relaxation functions are the end-to-end vector correlation function and the correlation function of the Rouse modes. Both functions exhibit a time-temperature superposition property at all times. The corre sponding superposition (relaxation) times can be fitted by a Vogel-Fulcher equation, yielding a common Vogel-Fulcher temperature of about T 0 ≈ 0.12–0.13. As in experiments, this temperature is smaller than the critical temperature of mode-coupling theory (T 0 < T c ≈ 0.15). In addition to this temperature dependence another characteristic feature of the correlation functions is that their relaxation is stretched. For the Rouse modes this stretching is unexpected from the Rouse theory. However, as the theory predicts, the modes remain statically uncorrelated for all studied temperatures.

A model of relaxation in supercooled polymer melts

We present a dynamical mean-field model for molecular motions in a supercooled polymer melt. A macromolecule is represented by a harmonic chain undergoing Brownian motion whose bead mobilities fluctuate between zero and a finite value. These fluctuations mimic the dynamic obstacles formed by the chain segments surrounding a given segment, whose effects become more pronounced as T decreases. The rate of these mobility fluctuations is determined self-consistently by equating it to the asymptotic long-time relaxation rate of the shortest-wavelength Rouse mode. The resulting fluctuating rate vanishes as c, the equilibrium fraction of mobile beads, approaches a threshold value c*. As c→c*, relaxation times become arbitrarily large, permitting the modeling of fluids as T approaches Tg. Calculations of autocorrelation functions of Rouse mode coordinates and of segmental mean-squared displacements are presented and compared to results from recent simulations of melts at low temperatures. The deviations from the Rouse model observed in the simulations are features of this theory.