Constraint Release Effects Research Articles

Testing the Ability of the Slip-Spring Model to Describe Constraint Release Effects Using Experimental Linear and Nonlinear Rheology

Testing the Ability of the Slip-Spring Model to Describe Constraint Release Effects Using Experimental Linear and Nonlinear Rheology

Molecular dynamics simulations of active entangled polymers reptating through a passive mesh

The dynamics of active entangled chains using molecular dynamics simulations of a modified Kremer–Grest model. The active chains are diluted in a mesh of very long passive linear chains, to avoid constraint release effects, and an active force is applied to the monomers in a way that it imparts a constant polar drift velocity along the primitive path. The simulation results show that, over a wide range of activity values, the conformational properties of the chains and the tubes are not affected, but the dynamics of the chains are strongly modified. Despite not having an explicit tube, the simulations verify the predictions of the active reptation theory very accurately, including a diffusion coefficient that becomes independent of the molecular weight at moderate values of the activity and a relaxation that results in low viscosity. Overall, this work provides information on the study of active entangled polymers, giving a route map for studying this phenomenon and an efficient way of simulating linear active polymers with a markedly preferential direction along the contour that reproduces the physics of active reptation theory.

Effects of Constraint-Release on Entangled Polymer Dynamics in Primitive Chain Network Simulations

Effects of Constraint-Release on Entangled Polymer Dynamics in Primitive Chain Network Simulations

Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids.

We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number ) of long ( for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of where , and are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight () polymers in fast flows (), where conventional simulation techniques are less applicable due to computational cost.

Unraveling Dynamics of Entangled Polymers in Strong Extensional Flows

The traditional Doi–Edwards tube model, applied to extensional flows at strain rates above the inverse Rouse time, predicts that the tube deforms affinely, which implies that the extensional stress reaches its plateau as soon as the chain has become locally fully stretched, even if the chain is still folded, and far from being completely unraveled. By starting from a state in which the chain is in a locally fully stretched, but folded, state, we develop an “entangled kink dynamics algorithm” that predicts the final unraveling of an ensemble of mutually entangled, folded chains, driven by a combination of drag forces and chain tension, with negligible Brownian motion. Equations for motions of both entangled folds and unentangled folds in which two chains hook together at a single fold point are derived and solved, including the effects of constraint release that occurs when the end of one chain passes through the fold at which that chain is entangled. This model predicts that the stress approaches its fina...

Humidity affects the viscoelastic properties of supramolecular living polymers

We investigate the linear and nonlinear viscoelastic response of a supramolecular gelator formed by association of a bisurea monomer (EHUT) via hydrogen bonds, in a nonpolar organic solvent (dodecane). Past experimental studies reported contradictory results concerning the concentration dependence and the magnitude of the terminal relaxation time. The discrepancies among data were attributed to the presence of water and, in particular, its chain stopper effects on the EHUT supramolecular assembly. Here, we present new measurements with this system under conditions of controlled humidity, achieved by means of a simple setup developed for this purpose. We resolve the discrepancy and demonstrate that humidity (both during sample storage and measurement) can substantially affect the linear viscoelastic response (frequency spectra). The magnitude of the terminal relaxation time, τt, is significantly reduced (by as much as 1 order of magnitude) and its concentration dependence follows τt ∼ c0.77 ± 0.06. This scaling differs from the theoretical prediction with nearly double exponent (1.25). We tentatively attribute this difference to the polydispersity in the supramolecular chain length, which results mainly from the EHUT self-assembly association mechanism, and propose that constraint release effects of smaller chains should be considered as they may weaken the concentration dependence of the terminal relaxation. On the other hand, the magnitude of the plateau modulus G0 is affected by humidity to a lesser degree (not exceeding 50%), whereas its concentration dependence is in accordance with predictions, G0 ∼ c2 ± 0.21. Finally, the nonlinear viscoelastic properties are also affected, again experiencing weakening in the presence of humidity.

Binary Blends of Entangled Star and Linear Poly(hydroxybutyrate): Effect of Constraint Release and Dynamic Tube Dilation

In order to further understand the relaxation behavior of binary blends of star and linear chains, new polymer blends consisting of linear poly(hydroxybutyrate) (PHB) matrix and PHB star molecules are designed, and their dynamics is investigated by varying the star concentrations and the molar mass of the linear matrix, while keeping few or no star–star entanglements in the blends. By studying the constraint release Rouse (CRR) relaxation of the star polymer diluted in the linear matrix at concentrations low enough to neglect star–star entanglements, we first point out the importance of the number of short linear chain entanglements on the CRR time of the long chains. For the blends composed of a larger proportion of star molecules, we then use this new definition of CRR time to determine the necessary time of a star–star entanglement segment to relax by CRR and explore its dilated tube, at the rhythm of the disentanglement/re-entanglements of the short chains. By considering this as the new reference tim...

Microscopic Picture of Constraint Release Effects in Entangled Star Polymer Melts

The constraint release (CR) effect in entangled branched polymers is generally described by the widely accepted dynamic tube dilation (DTD) theory based on the tube model, which predicts the stress relaxation function reasonably well, but not the dielectric or arm end-to-end vector relaxation. The microscopic picture of entanglement dynamics even in the simple case of star polymers is still not fully resolved. In this work, we first perform molecular dynamics (MD) simulations of symmetric star polymer melts using the Kremer–Grest bead–spring model. The entanglement events are analyzed microscopically using the persistent close contacts between mean paths of neighboring polymer strands. The resulting survival probability function of these entanglements or close contacts shows reasonably good agreement with the stress relaxation function, which provides qualitative evidence for the binary picture of entanglements. On the basis of this understanding, we further investigate the star arm retraction and CR effects using the coarse-grained single-chain slip-spring model originally developed by Likhtman and also a simplified single-chain stochastic model. In both MD and slip-spring simulations we verified the mechanism proposed by Shanbhag et al. that constraint release events lead to the insertion of new entanglements in between the branch points and deepest entanglements so that the last remaining deepest entanglements are deleted by relatively shallow arm retractions. Our simulations further revealed that for the entanglements sitting on a target star arm, only those destroyed by the free end of the given arm dominate the arm end-to-end vector relaxation, while the broad constraint release spectrum, together with the excluded volume of entanglements and the reflecting boundary at the branch point, produces an accelerated drift of the mean positions of these specific entanglements toward the arm-end, which is an essential mechanism for understanding the relaxation of star polymers in concentrated solutions or melts. Our findings call for an examination of the microscopic foundation of conventional DTD picture and inspire the development of quantitative theories with consideration of more microscopic details.

Stress Relaxation Behavior of Bidisperese Polystyrenes in Shear and Biaxial Extension

Two bidisperse PS samples B1 and B2 (blend of monodisperse polystyrenes) are employed to investigate the effects of bimodal molecular weight distribution on damping behavior of stress relaxation in shear and biaxial extension. The order of characteristic relaxation times, reptation time τd and contraction time τs of each component, for B1 is (τs,1 < τs,2 < τd,1 <τd,2) and that for B2 is (τs,1 < τd,1 < τs,2 < τd,2), where suffixes 1 and 2 denote lower and higher molecular weight component respectively. Time dependent damping functions in shear h(t,γ) and in biaxial extension hB(t,εB) are employed to confirm the time-strain separability for bidisperse polymer systems. Time dependent damping functions of B1 are almost constant, but B2 vary with time in both shear and biaxial extension. To investigate effects of reptative constraint release (RCR) via double reptation scheme and convective constrain release (CCR) in shear and biaxial stress relaxation for bidisperse polymer systems, we use multi-mode extension of the Ianniruberuto and Marrucci (IM) model and the Mead-Larson-Doi (MLD) model. The model predictions of h(t,γ) and hB(t,εB) well describe experimental tendency. Time dependent damping functions become independent of time after contraction of long chain and the multi mode model prediction seems almost the same strain dependence. Effect of CCR is very important to describe damping behavior for bidisperse polymer systems.

NMR Observation of Entangled Polymer Dynamics: Tube Model Predictions and Constraint Release

We use a benchtop NMR technique to monitor entangled polymer melt dynamics over 5 decades in time covering regimes II-IV of the tube model. We confirm the familiar molar mass scaling exponents of the regime transitions, but we observe a mass-dependent time scaling exponent describing segmental fluctuations in the constrained-Rouse regime II up to high molecular weights. Local chain motions are thus governed by modes that are much less restricted than predicted by the tube model. Diluting protonated chains in deuterated invisible matrix chains, we prove that the exponent is determined by the matrix molecular weight, suggesting constraint-release effects as the origin.

Modeling the solid-like behavior of entangled polymer nanocomposites at low frequency regimes

A theory for the linear viscoelastic behavior of entangled polymeric liquids reinforced with non-aggregated colloidal nanoparticles is presented. Composites with low filler concentration and strong polymer–particle interaction are considered. A fraction of entangled chains is assumed to be reversibly adsorbed on the surface of fillers, due to the affinity between the polymer molecules in the matrix and dispersed filler particles. The relaxation of the system is analyzed by the combination of stress relaxation functions for free and adsorbed polymer chains. It is demonstrated that the emergence of solid-like behavior at low frequency regimes, is due to the significant slow down in relaxation of adsorbed chains. Fitting the model predictions with relevant experimental data indicates that while the effect of constraint release should be considered to obtain a reasonable estimation of neat polymer behavior, the linear combination of stress relaxation functions of free and adsorbed chains (i.e., no thermal constraint release) leads to a better agreement with experimental data of filled systems.

Pom-pom model predictions on nonlinear stress relaxation in single-step strain flow

A phenomenological pom-pom model, which utilizes linear stress relaxation data as an input, is proposed for simulating the detailed retraction behavior of a full pom-pom chain as well as the associated nonlinear stress relaxation in single-step shear flows. Specifically, the initial, Rouse-like arm and/or backbone retraction as well as the long-time, renormalized (dumbbell-like) backbone retraction is simulated at one time, and a possible coupling between linear orientation relaxation and nonlinear stretch relaxation due to diffusive or convective constraint release is self-consistently accounted for. The model’s predictions are systematically tested against nonlinear stress relaxation data on three nearly monodisperse pom-pom melts, including two six-arm pom-pom polybutadienes (PPBDs) and an H-shaped polyisoprene (PPI). The model can describe the present data reasonably well by incorporating a previously proposed effect of drag–strain coupling. Accounting further for the effect of constraint release, due primarily to arm diffusive motion and its coupling with a known polydispersity in arm molecular weight distribution, appreciably broadens the predicted nonlinear stress relaxation and substantially improves the results of theory/data comparisons. The significance of the current findings is discussed.

Primitive Chain Network Simulations of Damping Functions for Shear, Uniaxial, Biaxial and Planar Deformations

Damping functions of entangled polymers for shear, uniaxial, biaxial, and planar deformations, as well as normal stress ratios for shear deformations, were obtained from Brownian simulations making use of the primitive chain network model. To investigate the effect of the force balance over the entanglements and of the convective constraint release mechanism, comparisons with predictions of earlier theories and with experimental data in the literature were performed. It was found that the obtained damping functions are close to the three-chain theory [Marrucci, Greco, and Ianniruberto, Macromol Symp, 158, 57 (2000)] suggesting that the force balance is a dominant correction over the basic Doi-Edwards theory as compared with the effect of convective constraint release. Furthermore, the predicted normal stress ratio in shear, i.e., a quantity very sensitive to the different assumptions, is in good agreement with experiments, suggesting that the combination of force balance, convective constraint release, and other relaxation modes, as accounted for through the primitive chain network model, is quite acceptable.

Molecular Observation of Constraint Release in Polymer Melts

The dynamics of binary polymer blends of few labeled long chains in successively shorter matrix chains has been investigated by neutron spin echo (NSE) spectroscopy. For the first time the effect of constraint release on the chain relaxation has been directly observed on a microscopic scale. Decreasing the matrix chain length reduces the topological confinement until unconfined Rouse motion is observed, when the matrix chains are too short to confine the long chain in a tube. Whereas an analytical description of the effect is not yet available, a new simulation based on the slip-link model shows perfect agreement with the NSE data over the full range of matrix molecular weights.

A tube-based constitutive equation for polydisperse entangled linear polymers

We present a tube-based constitutive model for polydisperse entangled linear polymers. The model is constructed as the non-linear extension of a linear model [A. Leygue, C. Bailly, R. Keunings, A differential tube-based model for predicting the linear viscoelastic moduli of polydisperse entangled linear polymers, J. Non Newton. Fluid Mech., in press] capable of predicting quantitatively the linear viscoelasticity of polydisperse linear systems. The constitutive equation accounts for the major linear and non-linear phenomena thought to be important in the description of entangled linear polymers: reptation, contour-length fluctuations, thermal constraint release, convective constraint release and chain stretch effects. In the non-linear regime convective constraint release couples the relaxation of the different masses and provides a non-linear mixing rule for the model. The predictive capabilities of the model are tested on published results for mono- and bi-disperse entangled solutions [C. Pattamaprom, R.G. Larson, Constraint release effects in monodisperse and bidisperse polystyrenes in fast transient shearing flows, Macromolecules 34 (2001) 5229–5237; X. Ye, R.G. Larson, C.J. Pattamaprom, T. Shridar, Extensional properties of monodisperse and bidisperse polystyrene solutions, J. Rheol. 47 (2) (2003) 443–468], both in shear and extension.

Convective constraint release with chain stretch: Solution of the Rouse-tube model in the limit of infinite tubes

This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics (tube diameter, persistence length, and CCR hop length) in response to chain stretch. It is found that the CCR-stretch equations are highly sensitive to the nature of the tube upon deformation, and in particular to the lower lengthscale cutoff used to describe the CCR process. The effect of CCR on chain stretch is explicitly derived from the microscopic model. The behavior of the constitutive equations is described for steady states under shear and startup under steady shear (where the results are compared against experiment).

Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release

A refined version of the Doi and Edwards tube model for entangled polymer liquids is presented. The model is intended to cover linear chains in the full range of deformation rates from linear to strongly nonlinear flows. The effects of reptation, chain stretch, and convective constraint release are derived from a microscopic stochastic partial differential equation that describes the dynamics of the chain contour down to the length scale of the tube diameter. Contour length fluctuations are also included in an approximate manner. Predictions of mechanical stresses as well as the single chain structure factor under flow are shown. A comparison with experimental data is made in which all model parameters are fixed at universal values or are obtained from linear oscillatory shear measurements. With no parameter modification the model produces good agreement over a wide range of rheological data for entangled polymer solutions, including both nonlinear shear and extension.

Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

AbstractThe nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003

Sieving mechanisms in polymeric matrices.

A critical review of the existing theoretical models and experimental evidences for sieving mechanisms during separation of macromolecules, paying particular attention to capillary electrophoresis applications is presented. Gel models (Ogston and reptation) have been successfully applied to highly entangled polymer solutions, where fast and efficient separations can occur. In order to account for the DNA/polymers collision-interaction mechanisms during separation in dilute solutions - characterized by a poorer resolution -, approximated analytical models have been developed. An insight in the mechanism regulating the intermediate case of moderately entangled polymer solutions, for low fields and concentrations of small multiples of the overlap concentration c*, is given by the constraint release approach. This model proposes an upper limit of size separation, increasing with matrix concentration and molecular mass. Finally, the coupling between the reptative motion of the analytes and the effect of matrix constraint release very likely plays a fundamental role in the separation mechanism and requires therefore further and deeper investigation, both theoretically and experimentally.

Tracer diffusion of four arm polystyrene star molecules into linear and star polymer matrices from nuclear reaction analysis

A series of linear and four arm star polystyrene polymers have been synthesised by anionic polymerisation and using deuterated star polymers the tracer diffusion coefficients for diffusion of star polymers into linear and star polymer hydrogenous matrices have been determined using nuclear reaction analysis. For diffusion into linear polystyrene, constraint release effects are evident for linear polymer molecular weights up to circa 250 000 g mol−1, the scaling relation between the tracer diffusion coefficient, D*, and the matrix degree of polymerisation below this molecular weight is D* = 6.82 × 10−11N−1.4matrix, the exponent being smaller than observed previously. This weakened dependence is attributed to the non-equivalence of constraints along a star arm and the contribution of the arm molecular weight to the overall dependence of constraint release leading to a weaker dependence of D* on matrix molecular weight. Tracer diffusion coefficients for the diffusion of star polymers into star polymer matrices were compared with theoretical predictions by combining expressions for the self-diffusion coefficient with a proposed relation that incorporates both self-diffusion and constraint release in star polymers. Although the data available is somewhat limited at present, the predictions of a dilated tube theory, i.e. dynamic dilution, describe the observed dependence of D* on the star arm degree of polymerisation more faithfully than in the absence of tube dilation.