Whereas the first part of this paper dealt with the relaxation in the beta-regime, this part investigates the final (alpha) relaxation of a simulated polymer melt consisting of short non-entangled chains above the critical temperature Tc of mode-coupling theory (MCT). We monitor the intermediate incoherent as well as the coherent chain and coherent melt scattering functions over a wide range of wave numbers q. Upon approaching Tc the coherent alpha-relaxation time of the melt increases strongly close to the maximum of the static structure factor of the melt. At q corresponding to the radius of gyration of the chain the melt relaxation time exhibits another maximum. The temperature dependence of the relaxation times is well described by a power-law with a q-dependent exponent in an intermediate temperature range. The time-temperature superposition principle of MCT is clearly bourne out in the whole range of wave numbers. An analysis of the alpha-decay using Kohlrausch-Williams-Watts (KWW) functions reveals that the collective melt KWW-stretching exponent and KWW-relaxation times are modulated with the structure factor. Furthermore, both incoherent and coherent KWW-times approach the large-q prediction of MCT at q comparable to the maximum of the structure factor. At small q a power law with exponent -3 is found for the coherent chain KWW-times similar to that of recent experiments.
We report results of molecular-dynamics simulations of a model polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of mode-coupling theory (MCT). To analyse the dynamics of the system we computed the incoherent, collective chain and melt intermediate scattering functions as well as the Van Hove correlation functions. We find good evidence for the space-time factorization theorem of MCT. From the critical amplitudes we could derive typical length scales of the beta-dyamics. In an extensive quantitative analysis the leading order descript…
We report results of molecular-dynamics simulations for a glassy polymer melt consisting of short, linear bead-spring chains. It was shown in previous work that this onset of the glassy slowing down is compatible with the predictions of the mode coupling theory. The physical process of `caging' of a monomer by its spatial neighbors leads to a distinct two step behavior in the particle mean square displacements. In this work we analyze the effects of this caging process on the Rouse description of the melt's dynamics. We show that the Rouse theory is applicable for length and time scales above …
A high-resolution calorimetric spectroscopy study has been performed on pure glycerol and colloidal dispersions of an aerosil in glycerol covering a wide range of temperatures from 300 K to 380 K, deep in the liquid phase of glycerol. The colloidal glycerol+aerosil samples with 0.05, 0.10, and 0.20 mass fraction of aerosil reveal glassy, activated dynamics at temperatures well above the $T_g$ of the pure glycerol. The onset of glass-like behavior appears to be due to the structural frustration imposed by the silica gel on the glycerol liquid. The aerosil gel increases the net viscosity of the …
We present simulation results for a model polymer melt, consisting of short, nonentangled chains, in the supercooled state. The analysis focuses on the monomer dynamics, which is monitored by the incoherent intermediate scattering function. The scattering function is recorded over six decades in time and for many different wave-vectors. The lowest temperatures studied are slightly above the critical temperature of mode-coupling theory (MCT), which was determined from a quantitative analysis of the beta- and alpha-relaxations. We find evidence for the space-time factorization theorem in the bet…
Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to qnaitify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molec…
We study the heterogeneous dynamics of attractive colloidal particles close to the gel transition using confocal microscopy experiments combined with a theoretical statistical analysis. We focus on single particle dynamics and show that the self part of the van Hove distribution function is not the Gaussian expected for a Fickian process, but that it reflects instead the existence, at any given time, of colloids with widely different mobilities. Our confocal microscopy measurements can be described well by a simple analytical model based on a conventional continuous time random walk picture, a…
We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hyper-netted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this re-entrant fluid-glass transition to particle softness, and c…
An extended Molecular-Dynamics study of the short-time "glassy" elasticity exhibited by a polymer melt of linear fully-flexible chains above the glass transition is presented. The focus is on the infinite-frequency shear modulus $G_\infty$ manifested in the picosecond time scale and the relaxed plateau $G_p$ reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbours of each monomer exhibits marked distribution with average value given by $G_\infty$. In particular, the neighbourhood of the end monomers of each chain are …
We examine the vitrification and melting of asymmetric star polymers mixtures by combining rheological measurements with mode coupling theory. We identify two types of glassy states, a {\it single} glass, in which the small component is fluid in the glassy matrix of the big one and a {\it double} glass, in which both components are vitrified. Addition of small star polymers leads to melting of {\it both} glasses and the melting curve has a non-monotonic dependence on the star-star size ratio. The phenomenon opens new ways for externally steering the rheological behavior of soft matter systems.
We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (g…
We have carried out computer simulations of overcompressed suspensions of hard monodisperse ellipsoids and observed their crystallization dynamics. The system was compressed very rapidly in order to reach the regime of slow, glass-like dynamics. We find that, although particle dynamics become sub-diffusive and the intermediate scattering function clearly develops a shoulder, crystallization proceeds via the usual scenario: nucleation and growth for small supersaturations, spinodal decomposition for large supersaturations. In particular, we compared the mobility of the particles in the regions …
The relaxation of polymers around and below their glass transition temperature is governed by a range of correlated unit processes with a wide range of timescales. The fast deformation rates of shock loading can negate a significant fraction of these processes resulting in the dynamical glass transition in rubbers. In this letter we report the inverse, a transient melting of glassy polymer under shock loading. The large deviatoric stresses near the shock front induce fast transitions in backbone dihedral angles and a stress relaxation characteristic of polymer melts. This is followed by the sl…
We report on quantitative comparisons between simulation results of a bead-spring model and mode-coupling theory calculations for the structural and conformational dynamics of a supercooled, unentangled polymer melt. We find semiquantitative agreement between simulation and theory, except for processes that occur on intermediate length scales between the compressibility plateau and the amorphous halo of the static structure factor. Our results suggest that the onset of slow relaxation in a glass-forming melt can be described in terms of monomer-caging supplemented by chain connectivity. Furthe…
Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…
The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals,…
Hard electromagnetic radiation diffraction experiments on copper(I)-bromide melt are presented. Combining the result of this experiment with earlier neutron diffraction experiments the partial pair distribution functions of CuBr have been determined. The differing results for two of these functions obtained recently by various techniques are discussed. A potential inversion scheme has been applied to generate three dimensional structures from the partial pair distribution function. The angular correlations between near neighbor atoms have been determined. These show characteristic differences …
We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the `self' component having only one particle, the `distinct' component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Browni…
In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled vs. well-entangled systems and (ii) melts vs. glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary vs. binary and (iv) cooperative vs. nonccoperative relaxation dynamics. I discuss the applicability of (iii-iv) to understanding the functional form of glassy strain hardening. Results from molecular dynamics simulations show that the "dramatic" strain hardening observed in densely entangled …
We apply microcanonical ensemble considerations to suggest that, whenever it may thermalize, a general disorder-free many-body Hamiltonian of a typical atomic system has solid-like eigenstates at low energies and fluid-type (and gaseous, plasma) eigenstates associated with energy densities exceeding those present in the melting (and, respectively, higher energy) transition(s). In particular, the lowest energy density at which the eigenstates of such a clean many body atomic system undergo a non-analytic change is that of the melting (or freezing) transition. We invoke this observation to analy…
Molecular dynamics simulations are used to investigate the connection between thermal history and physical aging in polymer glasses, in particular the effects of a temperature square step. Measurements of two-time correlation functions show that a negative temperature step causes "rejuvenation" of the sample: the entire spectrum of relaxation times appears identical to a younger specimen that did not experience a temperature step. A positive temperature step, however, leads to significant changes in the relaxation times. At short times, the dynamics are accelerated (rejuvenation), whereas at l…
Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time $t$ as $t^{1/2}$ in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the on…
We introduce a mesoscale method for simulating hydrodynamic transport and self assembly of inhomogeneous polymer melts in pressure driven and drag induced flows. This method extends dynamic self consistent field theory (DSCFT) into the hydrodynamic regime where bulk material transport and viscoelastic effects play a significant role. The method combines four distinct components as a single coupled system, including (1) non-equilibrium self consistent field theory describing block copolymer self-assembly, (2) multi-fluid Navier-Stokes type hydrodynamics for tracking material transport, (3) cons…
In polymers melts and supercooled liquids, the glassy dynamics is characterized by the rattling of monomers or particles in the cage formed by their neighbors. Recently, a direct correlation in such systems, described by a universal scaling form, has been established between the rattling amplitude and the structural relaxation time. In this paper we analyze the glassy dynamics emerging from the formation of a persistent network in a model colloidal gel at very low density. The structural relaxation time of the gel network is compared with the mean squared displacement at short times, correspon…
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 …
Performing molecular dynamics simulations for all-atom models, we characterize the conformational and structural relaxations of poly(ethylene oxide) and poly(propylene oxide) melts. The temperature dependence of these relaxation processes deviates from an Arrhenius law for both polymers. We demonstrate that mode-coupling theory captures some aspects of the glassy slowdown, but it does not enable a complete explanation of the dynamical behavior. When the temperature is decreased, spatially heterogeneous and cooperative translational dynamics are found to become more important for the structural…
All liquids in nature can be supercooled to form a glass. Surprisingly, although this phenomenon has been employed for millennia, it still remains ill-understood. Perhaps the most puzzling feature of supercooled liquids is the dramatic increase in their viscosity as the temperature ($T$) is lowered. This precipitous rise has long posed a fundamental theoretical challenge. Numerous approaches currently attempt to explain this phenomenon. When present, data collapse points to an underlying simplicity in various branches of science. In this Letter, we report on a 16 decade data collapse of the vi…
The generalized entropy theory (GET) offers many insights into how molecular parameters influence polymer glass-formation. Given the fact that chain rigidity often plays a critical role in understanding the glass-formation of polymer materials, the GET was originally developed based on models of semiflexible chains. Consequently, all previous calculations within the GET considered polymers with some degree of chain rigidity. Motivated by unexpected results from computer simulations of fully flexible polymer melts concerning the dependence of thermodynamic and dynamic properties on the cohesive…
The breakdown of the time-temperature superposition (TTS) near its glass transition temperature (Tg) in simple bead-spring polymer melts with and without the chain angle potential was numerically investigated. The stress relaxation modulus at different temperatures G(t,T) was calculated by the Green-Kubo relation. The TTS of G(t,T) of bead-spring polymer melts worked well at temperatures sufficiently higher than its Tg. However, when the system temperature is approaching the glass transition regime, the breakdown of TTS is observed. At temperatures near the Tg, the temperature dependence of th…
Diffusion of long ring polymers in a melt is much slower than the reorganization of their internal structures. While direct evidences for entanglements have not been observed in the long ring polymers unlike linear polymer melts, threading between the rings is suspected to be the main reason for slowing down of ring polymer diffusion. It is, however, difficult to define the threading configuration between two rings because the rings have no chain end. In this work, evidences for threading dynamics of ring polymers are presented by using molecular dynamics simulation and applying a novel analys…
The binary hard-sphere mixture is one of the simplest representations of a many-body system with competing time and length scales. This model is relevant to fundamentally understand both the structural and dynamical properties of materials, such as metallic melts, colloids, polymers and bio-based composites. It also allows us to study how different scales influence the physical behavior of a multicomponent glass-forming liquid; a question that still awaits a unified description. In this contribution, we report on distinct dynamical arrest transitions in highly asymmetric binary colloidal mixtu…
This paper reviews recent Monte Carlo simulation studies of the glassy behavior in thin polymer films. The simulations employ a version of the bond-fluctuation lattice model, in which the glass transition is driven by the competition between a stiffening of the polymers and their dense packing in the melt. The melt is geometrically confined between two impenetrable walls separated by distances ranging from once to about fifteen times the bulk radius of gyration. The confinement influences static and dynamic properties of the films: Chains close to the wall preferentially orient parallel to it.…
By the adoption of a quaternion orientational order parameter to describe solidification, the topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein. Global orientational order, achieved by spontaneous symmetry breaking, is prevented at finite temperatures for systems that exist in restricted dimensions (Mermin-Wagner theorem). Just as complex ordered systems exist in restricted dimensions in 2D and 1D, owing to the dimensionality of the order parameter, quaternion ordered systems in 4D and 3D exist in restricted dimensions…
We analyze structural and conformational properties in a simulated bead-spring model of a non-entangled, 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 [Krakoviack et al., Europhys. Lett. 58, 53 (2002)], remain essentially unchanged on cooling toward the critical glass transition temperature of mode-coupling theory. Spatial correlations between mon…
A basic concept in chain-particle cluster-motion, from frozen glassy state to melt state, is the 2D soft nano-scale mosaic structure formed by 8 orders of 2D interface excitation (IE) loop-flows, from small to large in inverse cascade and re-arrangement structure in cascade along local one direction. IE has additional repulsive energy and extra vacancy volume. IE results from that the instantaneous synchronal polarized electron charge coupling pair is able to parallel transport on the interface between two neighboring chain-particles with antiparallel delocalization. This structure accords wit…
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 $τ_α$ and ultimately follows the Rouse dynamics characterized by the time $τ_{\rm R} \sim N^2 τ_α$. After application of shear $\gdot$, transient stress growth $σ_{xy}(t)/\gdot$ first obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 but saturates into a non…
Models of 3D confluent tissue as under-constrained glasses
Department of Physics, Emory University（埃默里大学物理系）；Aix Marseille Univ, Université de Toulon, CNRS, CPT (UMR 7332), Turing Centre for Living systems（艾克斯马赛大学、土伦大学、法国国家科学研究中心、CPT（UMR 7332）、图灵生命系统中心）
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian variational approach. In constructing the solution, we assume that the chain is very long and impose the translational invariance which is expected to be present in the bulk of the globule by averaging over the center the of mass coordinate. In this way we derive equations of motion for the correlation and response functions C(t,t') and R(t,t'). The order pa…
We show that incoherent quasi-elastic neutron scattering (QENS) from molecular liquids reveals a two-state dynamic heterogeneity on a 1 ps timescale, where molecules are either highly confined or are free to undergo relatively large excursions. Data ranging from deep in the glassy state to well above the melting point allows us to observe temperature-dependent population levels and exchange between these two states. A simple physical picture emerges from this data, combined with published work, that provides a mechanism for "hopping" and for the Johari-Goldstein ($β_{JG}$) relaxation, and allo…
We study the shear induced fluidization of amorphous solids subjected to external loading by investigating the relaxation dynamics of the deformed states using computer simulation. A simple shear deformation is employed at constant rate to the thermal glassy materials. The shear localization and the plastic deformation heterogeneity with strain is investigated in terms of the non-affine displacement field. The mean square displacement shows an enhanced mobility of the particles with strain, indicating the fluidization of the material. Using the time correlation function we estimate the relaxat…
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and, yet, they display a large number of topological constraints. To understand their role, here we systematically probe the response of solutions of rings at various densities to "random pinning" perturbations. We show that these perturbations trigger non-Gaussian and heterogeneous dynamics, eventually leading to non-ergodic and glassy behaviours. We then derive un…
Bonding between polymeric interfaces is encountered widely in several industrial applications. Many of these bonding processes rely on time-consuming and temperature-dependent classical mechanism of polymer interdiffusion via reptation in a melt state. Here, for the first time, we report a new mechanistic pathway for achieving solid-state polymer bonding by triggering rapid macromolecular acceleration through mechanical deformation. Large-scale molecular simulations reveal that active plastic deformation in glassy polymers, at temperatures well-below the bulk (and surface) glass transition tem…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we presen…
Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in the preceding paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a r…
We study the effect of a random Flory-Huggins parameter in a symmetric diblock copolymer melt which is expected to occur in a copolymer where one block is near its structural glass transition. In the clean limit the microphase segregation between the two blocks causes a weak, fluctuation induced first order transition to a lamellar state. Using a renormalization group approach combined with the replica trick to treat the quenched disorder, we show that beyond a critical disorder strength, that depends on the length of the polymer chain, the character of the transition is changed. The system be…
Potential energy landscape picture of zero-temperature avalanche criticality governing dynamics in supercooled liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专攻）
