Giuseppe Marrucci

Brownian simulations of a network of reptating primitive chains

A new model for Brownian dynamics simulations of entangled polymeric liquids is proposed here. Chains are coarse grained at the level of segments between consecutive entanglements; hence, the system is in fact a network of primitive chains. The model incorporates not only the “individual” mechanisms of reptation and tube length fluctuation, but also collective contributions arising from the 3D network structure of the entangled system, such as constraint release. Chain coupling is achieved by fulfilling force balance on the entanglement nodes. The Langevin equation for the nodes contains both the tension in the chain segments emanating from the node and an osmotic force arising from density fluctuations. Entanglements are modeled as slip links, each connecting two chain strands. The motion of monomers through slip links, which ultimately generates reptation as well as tube length fluctuations, is also described by a suitable Langevin equation. Creation and release of entanglements is controlled by the num...

A simple constitutive equation for entangled polymers with chain stretch

We propose a simple way of including chain stretch effects in convective constraint release theories for entangled polymers. The main idea is that the characteristic time of orientational relaxation depends in a series-parallel way on all three relevant mechanisms, i.e., reptation, constraint release (thermal and convective), and Rouse relaxation. As usual, a separate equation describes chain stretch, which however is assumed not to be affected by constraint release. The model is further simplified by writing the orientational equation in differential form. For step strains, the successful damping function of the Doi–Edwards theory is exactly preserved. Predictions in steady shear also favorably compare with typical data of nearly monodisperse polymers.

Entanglement molecular weight and frequency response of sliplink networks

Brownian dynamics simulations of the linear viscoelastic response of entangled polymers have been performed, and compared quantitatively with some existing solution data at a fixed concentration and variable molecular weight. The model is a three-dimensional network where the nodes are sliplinks connecting chains in pair. The simulations make use of Langevin equations both for the node motion in space, and for the one-dimensional monomer sliding through sliplinks. Comparison with data is very satisfactory, but the molecular weight between entanglements that emerges from the model is unconventionally small.

Nematic phase of rodlike polymers. II. Polydomain predictions in the tumbling regime

The two‐dimensional model previously considered is here used to obtain predictions in the complex situation of the tumbling regime which prevails at low shear rates. Although each domain is permanently in a time‐dependent, periodic regime, the macroscopic response can be stationary in time because of the well‐known polydomain structure. First, the average steady rheological response for this situation is calculated by taking a polydomain structure which neglects interdomain interactions. Although the steady state predictions thus obtained favorably compare with the experimental results throughout the range of shear rates, the transient start‐up responses do not, because of the crucial role played by the interactions in such a case. These interactions, due to Frank elasticity, are then introduced in the model in the simplest possible way, i.e., by use of a mean field potential. Under this assumption, also the predictions of transient behavior in the tumbling regime show the correct qualitative features.

Flow-induced orientation and stretching of entangled polymers.

A single–mode constitutive equation is proposed which accounts, in a very simple way, for the most important feature of the molecular theory for entangled polymers based on the ‘tube’ concept, i.e. that the orientation of the tubes and the stretching of the chain within them relax over different time–scales. The much faster relaxation of stretch is essentially a Rouse process, whereas orientational relaxation takes place by a combination of several factors, including reptation, tube–length fluctuations and constraint release, both thermal and convective. The model presented here accounts for all of these mechanisms, albeit in a simplified way, with the exception of fluctuations, which cannot be dealt with in a single–mode theory. Extension to a multi–mode version should, however, be easy.

A multi-mode CCR model for entangled polymers with chain stretch

Abstract The model recently proposed by the authors [J. Rheol., 45 (2001) 1305–1318] to account for convective constraint release (CCR) and chain stretch in entangled polymers is here extended to a multiple mode situation. Such an extension, indispensable for the polydisperse case, is believed to be important also for monodisperse polymers, especially in view of chain-end fluctuations. The model is compared with existing steady and transient start-up data of shear flows. It is also shown how the model can help explaining the frequently observed power-laws, especially for the case of melts.

Simple strain measure for entangled polymers

In the classical theory of Doi and Edwards for entangled polymers the strain measure Q arises from the assumption of affine deformation of the tube segments. On the other hand, we have recently argued [G. Marrucci, F. Greco, and G. Ianniruberto, “Possible role of force balance on entanglements,” Macromol. Symp. (in press)] that force balance on the nodes of the entangled network generates departures from affinity. An ad hoc “lattice” model of the network was then proposed to fulfill force balance automatically, at least for single-step deformations. The corresponding strain measure is linked to the square root of the Finger tensor, and is therefore easy to use. Predictions obtained with the new strain measure are here compared with a variety of step strain data.

Convective constraint release (CCR) revisited

The molecular mechanism known as convective constraint release (CCR) is here revisited to account for the fact that in fast flows topological entanglements decrease in number, as recently shown by the molecular dynamics simulations of Baig et al. [Macromolecules 43, 6886–6902 (2010)] and even before by the Brownian simulations of Yaoita et al. [J. Chem. Phys. 128, 154901 (2008)]. Based on the same Brownian dynamics code, Furuichi et al. [J. Chem. Phys. 133, 174902 (2010)] suggested that the time-strain separability in step strain relaxation is influenced by the entanglement density dynamics, an idea previously explored by Archer et al. [Macromolecules 35, 10216–10224 (2002)]. The simple model that is here proposed is therefore tested against literature data of stress relaxation following large step strains, where the time-strain separability is approached in a time much longer than the expected Rouse time, a mystery that has long remained unsolved. The new CCR theory gives a simple mathematical form to th...

Statics, linear, and nonlinear dynamics of entangled polystyrene melts simulated through the primitive chain network model

Simulation results of the primitive chain network (PCN) model for entangled polymers are compared here to existing data of diffusion coefficient, linear and nonlinear shear and elongational rheology of monodisperse polystyrene melts. Since the plateau modulus of polystyrene is well known from the literature, the quantitative comparison between the whole set of data and simulations only requires a single adjustable parameter, namely, a basic time. The latter, however, must be consistent with the known rheology of unentangled polystyrene melts, i.e., with Rouse behavior, and is therefore not really an adjustable parameter. The PCN model adopted here is a refined version of the original model, incorporating among other things a more accurate description of chain end dynamics as well as finite extensibility effects. In the new version, we find good agreement with linear rheology, virtually without adjustable parameters. It is also shown that, at equilibrium, Gaussian statistics are well obeyed in the simulated network. In the nonlinear range, excellent agreement with data is found in shear, whereas discrepancies and possible inadequacies of the model emerge in fast uniaxial elongational flows, even when accounting for finite extensibility of the network strands.

Structure of entangled polymer network from primitive chain network simulations

The primitive chain network (PCN) model successfully employed to simulate the rheology of entangled polymers is here tested versus less coarse-grained (lattice or atomistic) models for what concerns the structure of the network at equilibrium (i.e., in the absence of flow). By network structure, we mean the distributions of some relevant quantities such as subchain length in space or in monomer number. Indeed, lattice and atomistic simulations are obviously more accurate, but are also more difficult to use in nonequilibrium flow situations, especially for long entangled polymers. Conversely, the coarse-grained PCN model that deals more easily with rheology lacks, strictly speaking, a rigorous foundation. It is therefore important to verify whether or not the equilibrium structure of the network predicted by the PCN model is consistent with the results recently obtained by using lattice and atomistic simulations. In this work, we focus on single chain properties of the entangled network. Considering the significant differences in modeling the polymer molecules, the results here obtained appear encouraging, thus providing a more solid foundation to Brownian simulations based on the PCN model. Comparison with the existing theories also proves favorable.