Glass-forming Polymer Melts Research Articles

The measurement of mechanical properties of glycerol, m-toluidine, and sucrose benzoate under consideration of corrected rheometer compliance: An in-depth study and review

Determination of the mechanical response of materials can be fraught with error if rheometer compliance is not properly taken into account. The resulting inaccuracies in the determined mechanical properties of the materials of interest can result in mistakes in material modeling, design, and theory. In the present work, we build on our previous report [K. Schroter, S. A. Hutcheson, X. Shi, A. Mandanici, and G. B. McKenna, J. Chem. Phys. 125, 214507 (2006)] and investigate the effects of instrument compliance that result from use of a commercial rotary rheometer and its fixtures on the determination of the dynamic shear and stress relaxation responses of glycerol, m-toluidine, and sucrose benzoate near to the glass transition regime. We revisit the procedure for compliance corrections presented in earlier work and correct dynamic shear data for these materials. We also present a new correction procedure to obtain shear stress relaxation curves from data that was obtained using this instrument. In addition, we broaden our consideration of compliance effects to materials, such as polymer melts, that have lower moduli than the simple glass formers previously considered. We discuss the possible errors for the viscoelastic response of glass-forming liquids and polymer melts or rubber networks that have been reported in the literature. A major purpose of the present work is to alert the community to possible problems in modulus values and relaxation functions obtained for a large number of materials for which rotary rheometers were used in a range where material stiffness (modulus and geometry effects) was comparable to the rheometer stiffness. Finally, we include recommendations for both experimental protocol and instrument design to avoid, minimize, or correct for compliance effects.

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.

Characterization of the potential energy landscape of an antiplasticized polymer

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These "substrings" nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in "superstrings" that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

Fluorescence Lifetime of a Single Molecule as an Observable of Meta-Basin Dynamics in Fluids Near the Glass Transition

Using single molecule spectroscopy, we show that the fluorescence lifetime trajectories of single probe molecules embedded in a glass-forming polymer melt exhibit strong fluctuations of a hopping character. Using molecular dynamics simulations targeted to explain these experimental observations, we show that the lifetime fluctuations correlate strongly with the average square displacement function of the matrix particles. The latter observable is a direct probe of the meta-basin transitions in the potential energy landscape of glass-forming liquids. We thus show here that single molecule experiments can provide detailed microscopic information on system properties that hitherto have been accessible via computer simulations only.

Molecular dynamics simulations

A tutorial introduction to the technique of molecular dynamics (MD) is given, and somecharacteristic examples of applications are described. The purpose and scope of thesesimulations and the relation to other simulation methods is discussed, and the basicMD algorithms are described. The sampling of intensive variables (temperatureT, pressurep) in runs carried outin the microcanonical (NV E) ensemble (N = particle number, V = volume, E = energy) is discussed, as well as the realization of other ensembles (e.g. theNV T ensemble). For a typical application example, moltenSiO2, the estimation of various transport coefficients (self-diffusion constants, viscosity,thermal conductivity) is discussed. As an example of non-equilibrium moleculardynamics, a study of a glass-forming polymer melt under shear is mentioned.

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.

What Do We Learn from the Local Geometry of Glass-Forming Liquids?

We examine the local geometry of a simulated glass-forming polymer melt. Using the Voronoi construction, we find that the distributions of Voronoi volume P(v(V)) and asphericity P(a) appear to be universal properties of dense liquids, supporting the use of packing approaches to understand liquid properties. We also calculate the average free volume <v(f)> along a path of constant density and find that <v(f)> extrapolates to zero at the same temperature T0 that the extrapolated relaxation time diverges. We relate <v(f)> to the Debye-Waller factor, which is measurable by neutron scattering.

Features of the structural arrest in a glass-forming polymer melt

The segmental motion and the reorientation of a model polymeric glassformer is investigated by molecular-dynamics simulations under isobaric conditions. At lower temperatures and short times cage effects are apparent. At longer times the segmental anomalous diffusion and the reorientation of the monomers are evidenced.

Spatially correlated dynamics in a simulated glass-forming polymer melt: analysis of clustering phenomena.

In recent years, experimental and computational studies have demonstrated that the dynamics of glass-forming liquids are spatially heterogeneous, exhibiting regions of temporarily enhanced or diminished mobility. Here we present a detailed analysis of dynamical heterogeneity in a simulated "bead-spring" model of a low-molecular-weight polymer melt. We investigate the transient nature and size distribution of clusters of "mobile" chain segments (monomers) as the polymer melt is cooled toward its glass transition. We also explore the dependence of this clustering on the way in which the mobile subset is defined. We show that the mean cluster size is time dependent with a peak at intermediate time, and that the mean cluster size at the peak time grows with decreasing temperature T. We show that for each T a particular fraction of particles maximizes the mean cluster size at some characteristic time, and this fraction depends on T. The growing size of the clusters demonstrates the growing range of correlated motion, previously reported for this same system [C. Beneman et al. Nature (London) 399, 246 (1999)]. The distribution of cluster sizes approaches a power law near the mode-coupling temperature, similar to behavior reported for a simulated binary mixture and a dense colloidal suspension, but with a different exponent. We calculate the correlation length of the clusters, and show that it exhibits similar temperature- and time-dependent behavior as the mean cluster size, with a maximum at intermediate time. We show that the characteristic time of the maximum cluster size follows the scaling predicted by mode-coupling theory (MCT) for the beta time scale, revealing a possible connection between spatially heterogeneous dynamics and MCT.

Investigating the influence of different thermodynamic paths on the structural relaxation in a glass-forming polymer melt

We present results from molecular dynamics simulations of the thermal glass transition in a dense polymer melt. In previous work we compared the simulation data with the idealized version of mode-coupling theory (MCT) and found that the theory provides a good description of the dynamics above the dynamical critical temperature. In order to investigate the influence of different thermodynamic paths on the structural relaxation (α-process), we performed simulations for three different pressures and are thus able to give a sketch of the critical line of MCT in the pressure-temperature plane, where, according to the idealized version of MCT, an ergodic-nonergodic transition should occur. Furthermore, by cooling our system along two different paths (an isobar and an isochor), with the same intersection point of the critical line, we demonstrate that neither the dynamical critical temperature nor the exponent γ depend on which path is chosen.

Monte Carlo and molecular dynamics simulation of the glass transition of polymers

Two coarse-grained models for polymer chains in dense glass-forming polymer melts are studied by computer simulation: the bond fluctuation model on a simple cubic lattice is treated by Monte Carlo methods, and a continuum bead-spring model with a Lennard-Jones potential between the beads is treated by means of molecular dynamics. While the dynamics of the two models differ for short length scales and the associated timescales, the two models behave similarly on mesoscopic spatial and temporal scales. In particular, the mode-coupling theory of the glass transition can be used to interpret the slowing down of the undercooled polymer melt. For the off-lattice model, the approach to the critical point of mode coupling is studied both at constant pressure and constant volume. The lattice model allows a test of the Gibbs-Di Marzio entropy theory of the glass transition to be carried out, and our finding is that although the entropy does decrease significantly, there is no `entropy catastrophe' where the fluid entropy would turn negative. Finally, a forward look at the effects of confinement on the glass transition in thin-film geometry is given.

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation.

Lattice vibrations in time-fluctuating percolation networks: Application to Brillouin scattering from glasses and liquids.

A model of lattice vibrations in a percolation network which is stochastically fluctuating in time is treated within the effective-medium approximation (EMA). This work generalizes previous studies on vibrations in static percolation networks, which are characterized by phonon-fracton crossover, to the dynamical regime. Our result for the frequency-dependent effective force constant K(\ensuremath{\omega}) is that it depends on \ensuremath{\omega} through the combinations \ensuremath{\omega}-i${\mathrm{\ensuremath{\tau}}}_{\mathit{j}}^{\mathrm{\ensuremath{-}}1}$, where ${\mathrm{\ensuremath{\tau}}}_{\mathit{j}}$ are the matrix fluctuation times. For a single-exponential relaxation, we obtain the relation K(\ensuremath{\omega},${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$)=${\mathit{K}}_{0}$(\ensuremath{\omega}-i${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$), where ${\mathit{K}}_{0}$ is the effective force constant of the static (${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$=0) medium. We calculate the effect of lattice renewal on the dispersion relation and on the dynamical structure factor, for which we analyze separately the frequency-dependent linewidth and sound velocity. For the latter quantities, we also provide scaling Ansa$iuml---tze, which are shown to be obeyed by the EMA for sufficiently small fluctuation times \ensuremath{\tau}. We find that the dynamic fluctuation effects become dominant for small enough \ensuremath{\tau} and are manifested (as \ensuremath{\tau} decreases) first as a nonuniform broadening and later as a ``motional narrowing'' of the dynamical structure factor line. The implications of our results on Brillouin scattering from glass-forming polymer melts and polymer electrolytes are discussed.

Weak and strong localization in the theory of polymer melts

A stochastic model of slow molecular motions in glass forming polymer melts is suggested. “Kinetic interactions” are incorporated into this model in the sense that a conformational transition of a two-bond kink requires a monovacancy to appear nearby, a transition of a three-bond kink requires a bivacancy, etc. An essential feature of the model is its structural inhomogeneity, introduced in terms of the random distribution of the kinetic constants of the kinks. It is shown that the model can be reduced to the so-called schematic glass transition model of W. Götze, with the coupling constants being expressed in terms of the kinetic constants of the kinks. The one-dimensional diffusion of three-bond kinks along the chain contour controlled by appearance of vacancies is considered. It is shown that the three-bond kinks undergo dynamic transitions in a weak localized state at the temperature T = T w . This transition results in the following reptation time dependence: τ rep ∝ N θ, where N is the chain length and θ ⩾ 3. This exponent is shown to grow infinitely at the glass transition temperature T g < T w (strong localization).

Glass freezing as kinetics time scale singularity of new significance

The empirical law of Vogel and Fulcher announces a kinetics time scale with a singular temperature dependence: τ ∼ τ 0 ×exp[ T 1 (T − T 0) ] , observed in a very wide variety of systems with disorderly freezing, such as glass-forming liquids, polymer melts, and rubbers. Recently the universality, in the sense that is established for critical point singularities, of this law was enhanced by the inclusion of disparate systems as liquid crystals and spin glasses. The present discussion of the singularity behind the glass-freezing phenomena is based on the recently formulated principle of optimal network kinetics, whereby an exact analysis has become feasible due to certain results on diffusion in random structures. The singularity at T 0 indicates a new class of kinetic transitions in stochastic processes, from null-recurrence to transience. According to this concept, neither of T 0 or T 1 represent energy barriers in the conventional sense, but characterize the optimal network in a randomly hierarchical structure. The present simple and universal model points towards a new empirical model of characterizing the varieties within the universality class, suggesting a novel approach to the problem of relating the freezing phenomena to the structure and composition of the systems.

Temperature dependence of the configurational entropy of undercooled melts and the nature of glass transition

Abstract The configurational entropy as well as other related thermodynamic properties of a (poly)disperse glass-forming polymer melt have been calculated exactly in terms of a lattice-hole model and within the framework of the mean field approximation (MFA). One of the main results of the calculation, in which the average “stiffness” and the mean degree of polymerization (association) of the melt appear as temperature-dependent entities, is that for the first time a single analytical expression for the configurational entropy has been established which predicts a noncatastrophic behavior of the undercooled liquid. For certain, “realistic,” values of the energy parameters obtained, the results are consistent with previous theoretical and experimental investigations, although the entropy curve in the region of the supposed second-order phase transition (Gibbs and Di Marzio [1]) is considerably leveled off, and no abrupt changes of its derivatives are to be expected. Qualitative agreement with existing data...

Considerations of the “freezing-in” of flow-induced orientation in polymer melts by vitrification with application to processing

We develop the implications of the experimentally tested hypothesis that (i) birefringence developed during flow is quantitatively frozen-in during vitrification of glass-forming polymer melts and (ii) that the rheo-optical law may be combined with a knowledge of the stress field existing immediately prior to vitrification to yield birefringence distributions. This hypothesis is applied to various problems including multiaxial stretching of sheets, melt spinning, tubular film extrusion and injection molding. Special problems concerned with internal temperature distributions are discussed. We examine difficulties which may arise in application of the hypothesis due to residual thermal stresses. Comparisons are made to other methods of representing orientation development during flow.