Dynamics of free chains in polymer nanocomposites

The dynamics of entangled polymeric chains in a polymer filled with nanoparticles is studied by means of molecular dynamics simulations of a model system. The primary objective is to study to what extent the reptation of polymers not in direct contact with fillers is modified with respect to the neat material. To this end, two systems are considered: A regular filled material in which the filler-polymer affinity is controlled, and a system in which the beads in contact with the filler at the beginning of the production phase of the simulation are tethered to the filler surface. This second system represents the limit case of long polymer-filler attachment time. In this case attention is focused on the free chains of the melt. The dynamics in the two models is different. In the filled system uniform slowing down for all Rouse modes is observed. The effect varies monotonically with the filler-polymer affinity. Up to saturation, this behavior may be captured by usual models with an effective, affinity-dependent, friction coefficient. In the system with grafted chains, the free chain Rouse dynamics is identical to that in the neat material, except for the longest modes which are significantly slowed down. More interestingly, the dynamics of the free chains depends in a nonmonotonic way on the polymer-filler affinity, although the free chains do not come in direct contact with the filler. This effect is due to small changes in the structure of the polydisperse brush upon modification of the affinity. Specifically, the density of the brush and the amount of interpenetration of free and grafted chains depend on the filler-polymer affinity. The use of a reptation model with modified tube diameter to capture this behavior is discussed.     

A model for the plateau in the relaxation modulus for linear chain polymer melts

A simple model is considered for the free energy associated with the relaxation of a linear chain polymer melt. The relaxation of the chain configurations results in an adjustment of the locations of the interchain contacts. The change in the distribution of the positions of the contacts between a pair of relaxing chains is hindered by the presence of other nearby chains in the melt. There is less configuration space available to the relaxing chains, due to the noncrossability of the chain backbones, than would be the case for phantom chains. This results in an increase in the free energy of the relaxing system. The analysis presented indicates that, given the free energy models considered, the extent of relaxation decreases as the length scale for relaxation increases. This results in a plateau in the relaxation modulus. This qualitative prediction of a plateau does not rely on the assumption of a specific mechanism for the chain dynamics, and is relatively insensitive to the form chosen for the terms in the free energy. If reasonable assumptions are made concerning the form of the free energy, then it is shown that the plateau which results depends on monomer length, Kuhn length, the monomer density for the melt, and, for solutions, the polymer concentration in a manner consistent with experimental data.     

Dielectric Relaxation of Type‐A Polymers in Melts and Solutions

This article describes the dielectric relaxation behavior of flexible polymer chains having the so‐called type‐A dipoles parallel along the chain backbone. This behavior reflects the global chain motion. Viscoelastically well known features of this motion, such as the power‐law relationship between the relaxation time and molecular weight of entangled linear chains (τ₁ ∝ M^3.5), are also observed dielectrically. More importantly, the dielectric behavior of linear chains having once‐inverted type‐A dipoles enables us to find some detailed dynamic features such as changes in the eigenfunctions f_p of a local correlation function with the chain concentration in solutions. These changes are discussed in relation to motional coupling of concentrated chains. The dielectric properties detect the orientational correlation of two submolecules in the chain at two separate times, while the viscoelastic properties reflect the isochronal orientational anisotropy of individual submolecules. Thus the chain motion is differently averaged in the dielectric and viscoelastic properties, and comparison of these properties enables us to find novel dynamic features. Specifically, this comparison reveals the validity of the tube dilation molecular picture for entangled linear chains and weakening of the short‐time coherence of the submolecule motion due to the constraint release mechanism. Moreover, the dielectric method enables us to investigate the chain dynamics under strong flow and/or in a molecularly narrow space. In particular, the retarded dielectric relaxation found for homopolymers and block copolymers in such narrow spaces (in the microdomains for the latter) indicates important effects of the spatial and thermodynamic constraints on the global chain motion. All the above results in turn demonstrate the importance of the dielectric method in investigations of the polymer dynamics.     

Model filled rubber. II. Particle composition dependence of suspension rheology

Monodisperse size colloidal particles varying in chemical composition were synthesized by emulsifier‐free emulsion polymerization. Using a stress‐controlled rheometer, the rheological behavior of colloidal suspensions in a low molecular weight liquid polysulfide was investigated. All suspensions exhibited shear thinning behavior. The shear viscosity, dynamic moduli, and yield stress increased as interactions between particles and matrix increased. The rheological properties associated with network buildup in the suspensions were sensitively monitored by a kinetic recovery experiment. We propose that interfacial interactions by polar and hydrogen bonding between particles and matrix strongly promote affinity of matrix polymer to the filler particles, resulting in adsorption or entanglement of polymer chains on the filler surface. A network structure was formed consisting of particles with an immobilized polymer layer on the particle surface with each particle floc acting as a temporary physical crosslinking site. As the interfacial interaction increases, the adsorbed layer thickness on the filler particles, hence, the effective particle volume fraction, increases. As a result, the rheological properties were enhanced in the order PS < PMMA < PSVP. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 815–824, 1999     

Polymer-nanoparticle interfacial behavior revisited: a molecular dynamics study

By tuning the polymer-filler interaction, filler size and filler loading, we use a coarse-grained model-based molecular dynamics simulation to study the polymer-filler interfacial structural (the orientations at the bond, segment and chain length scales, chain size and conformation), dynamic and stress-strain properties. Simulated results indicate that the interfacial region is composed of partial segments of different polymer chains, which is consistent with the experimental results presented by Chen et al. (Macromolecules, 2010, 43, 1076). Moreover, it is found that the interfacial region is within one single chain size (R(g)) range, irrespective of the polymer-filler interaction and the filler size, beyond which the bulk behavior appears. In the interfacial region, the orientation and dynamic behaviors are induced by the interfacial enthalpy, while the size and conformation of polymer chains near the filler are controlled by the configurational entropy. In the case of strong polymer-filler interaction (equivalent to the hydrogen bond), the innerest adsorbed polymer segments still undergo adsorption-desorption process, the transport of chain mass center in the interfacial region exhibits away from the glassy behavior, and no plastic-like yielding point appears in the stress-strain curve, which indicates that although the mobility of interfacial polymer chains is restricted, there exist no "polymer glassy layers" surrounding the filler. In addition, it is evidenced that the filler particle prefers selectively adsorbing the long polymer chains for attractive polymer-filler interaction, validating the experimental explanation of the change of the bound rubber (BR). In short, this work provides important information for further experimental and simulation studies of polymer-nanoparticle interfacial behavior.     

Dynamics of relaxation of entangled polymers in shear flow

The application of shear flow to entangled polymer melts can strongly modify its rheological and physicochemical behaviors, giving rise to an acceleration of several chemical processes such as diffusion-controlled reactions. In the present work, we investigate the modification of conformational and diffusive properties of an entangled polymer in shear flow by numerical methods. The flow affects both the conformational and diffusive properties of the system, giving rise to a quasinematic ordering of the macromolecules which take prolate spheroid shape with the main axis aligned to the shear direction. The shear flow is found to accelerate the overall diffusion of the chains in all directions at times longer than the polymer relaxation time. The polymer chains display a quite peculiar displacement behavior in direction parallel to the flow. At the same conditions, the linear relation between the diffusion constant in direction perpendicular to the flow and the inverse of the relaxation time, usually adopted in equilibrium regimes, is shown to hold even in the presence of flow.     

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Molecular modeling of matrix chain deformation in nanofiber filled composites

The effects of the oriented fiber filler particles on the microscopic properties of the matrix network chains were investigated by using nanofiber filler particles as reinforcing material. Monte Carlo Rotational Isomeric State simulations were carried out for filled poly(ethylene) (PE) networks to study the dependence of the conformational distribution functions of polymer chains and their elastomeric properties on filler loadings. We were especially interested how the excluded volume effect of the nanofiber particles and their orientation (specifically orientational anisotropy) in the matrix influence elastomeric properties of the network. Distribution functions of the end-to-end distances of polymer chains for both unfilled and filled networks were calculated. Effects of nanofiber reinforcements with varying fiber radii and fiber volume fractions were investigated. We have found that the presence of nanofibers significantly increase the non-Gaussian behavior of polymer chains in the composite. The anisotropic effects of the nanofibers on mechanical properties of polymeric composites were studied as a function of their relative orientation to the direction of deformation. The modulus (reduced nominal stress per unit strain) was calculated from the distribution of end-to-end distances of polymer chains using the Mark–Curro method. Relatively small amount of nanofibers was found to increase the normalized moduli of the composite. Our results are quite in satisfactory qualitative agreement with experimental data reported in the literature. This shows that computer simulations provide a powerful tool in predicting physical properties of composite materials.     

A molecular model for cohesive slip at polymer melt/solid interfaces

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.     

Dynamics of entangled supramolecular polymer networks in presence of high‐order associations of strong hydrogen bonding groups

Dynamics of entangled polymer chains in the melt state are deliberately excluded in most of the studies on supramolecular polymer networks by utilizing nonentangled precursor chains. Relaxation of the system mainly depends on the dissociation of the associative groups in latter case and nonentangled chains deliver nothing to resist afterward. Conversely, in an entangled system, relaxation of polymer chains and dissociation of associative groups can occurred parallel. Supramolecular networks based on an entangled precursor polymer with different levels of strong associating ureidopyrimidinone (UPy) groups are synthesized to screen the corresponding effects on the dynamics of the system. Binary‐associated UPy groups phase separate into collective assemblies by stacking and form high‐order, needle‐like domains at higher UPy contents. Relaxation of polymer chains is significantly hindered due to the trapping of polymer segments between UPy stacks. Above a certain threshold of UPy content (~4 mol%), the plateau level and final relaxation time of networks show a significant jump, which is attributed to the onset of high‐order association of UPy groups.     

Communication: effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids

A microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformation-assisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.     

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γ_σm and γ_Nm, corresponding to the peaks of σ and N₁ lay on the universal functions of γ˙τ_R, respectively, proposed for dilute solutions in pure solvent. Here τ_R is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γ_σm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τ_R < 10⁻². This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γ_σm and γ_Nm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000     

Dynamics of polymer melts confined by smooth walls: crossover from nonentangled region to entangled region

The authors present the results of molecular dynamics simulations of polymer films confined by smooth walls. Simulations were performed for a wide range of chain lengths covering both nonentangled and entangled regions, as well as film thicknesses ranging from the order of unperturbed chain size to the bulk state. The simulation results for the chain size dependence on the film thickness are compared with the prediction of the scaling model. By measuring the correlation function of the end-to-end vectors, we have determined the relaxation time of confined polymer chains in different entangled states. It is shown that there is a minimum in the relaxation time of long chains when decreasing the film thickness, which is partially due to the confinement-induced disentanglement effect.     

Structure and dynamics of a bisurea-based supramolecular polymer in n-dodecane

The structure and dynamics of a supramolecular polymer formed by a bisurea-type compound, 2,4-bis(2-ethylhexylureido)toluene (EHUT), in an apolar solvent, n-dodecane (C12), were examined in detail. The EHUT/C12 organo-gel system forms long, dynamic chain-like supramolecular polymers, which lead to an entangled network showing remarkable viscoelastic behavior with two major relaxation modes. A slow relaxation mode with an approximately constant relaxation time, tauS, was observed in a flow region and the other, fast, relaxation mode with a time tauF1 (相似文献   

Comparison of optical and mechanical limits of linear relaxation behavior in glassy polycarbonate

The decay in birefringence of glassy polycarbonate held at constant extension has been studied at 23°C, in the time-scale range 10–10³ sec, up to about 6% strain. The results show that, under these conditions, the birefringence can be validly expressed as a linear hereditary integral of the strain history up to a relatively high strain level which is about 3.4% for an experimental time-scale of 100 sec. Comparison with previously obtained data on the stress relaxation behavior of the same polymer shows that, other factors remaining constant, mechanical relaxation is linear only up to about 1.1% strain. The earlier onset of mechanical nonlinearity is discussed and it is suggested that the mechanical relaxation spectrum is richer than the optical spectrum in relatively long relaxation times, corresponding to relatively slow molecular motions. It is further suggested that these slow molecular motions are accelerated first as the polymer is extended beyond the limit of linear viscoelastic behavior. The observed nonidentity between strain limits for linear mechanical and linear optical behavior is discussed in the light of current practices in photomechanical stress analysis.     

Structure and dynamics of carbon black‐filled elastomers

The linear and nonlinear melt viscoelastic properties for a series of carbon black‐filled polymer composites were studied. Complementary tapping‐mode atomic force microscopy (AFM) studies were used to examine the dispersion and structural correlations of the filler particles in these composites. The low‐frequency dependence of the linear viscoelastic moduli gradually changes from liquidlike behavior for the unfilled polymer to pseudosolid character for composites with more than 9 vol % carbon black filler. The plateau modulus, inferred from the linear viscoelastic response, exhibits a somewhat discontinuous change at about 9 vol % filler. On the basis of the linear viscoelastic response, we postulate that the carbon black filler forms a continuous percolated network structure beyond 9 vol % filler, considerably lower than that expected from theoretical calculations for overlapping spheres and ellipsoids. We suggest that the lower threshold for percolation is due to the polymer mediation of the filler structure, resulting from the low functionality of the polymer and, consequently, few strong polymer–filler interactions, allowing for long loops and tails that can either bridge filler particles or entangle with one another. Furthermore, the strain amplitude for the transition from linear behavior to nonlinear behavior of the modulus for the composites with greater than 9 vol % filler is independent of frequency, and this critical strain amplitude decreases with increasing filler concentration. Complementary AFM measurements suggest a well‐dispersed carbon black structure with the nearest neighbor distance showing a discontinuous decrease at about 9 vol % filler, again consistent with the formation of a filler network structure beyond 9 vol % carbon black. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 256–275, 2001     

Monte Carlo Simulation of Thin Film Polymer Melts

We present Monte Carlo simulation data on conformations and dynamics of polymer melts confined in narrow slits of different widths and compare with data of bulk systems. We find that in confined geometries the chains swell laterally; they retain and even expand their spatially long-range correlations compared to bulk polymers and in contrast to the assumption of a complete screening of excluded volume. Long chains in bulk melts show entangled dynamics with a clear signature of a t^1/4-power law for the mean square displacements of innermost monomers at intermediate time scales. This behavior is gradually lost by confining the melts in slits with decreasing width. For ultra-thin films, the dynamics appears to follow a Rouse-like behavior over the entire subdiffusive regime. However, the terminal relaxation time is significantly increased compared to Rouse relaxation. This interesting observation was not reported previously and is the focus of our ongoing research.