Time-dependent orientation coupling in equilibrium polymer melts

The motion in concentrated polymer systems is described by either the Rouse or the reptation model, which both assume that the relaxation of each polymer chain is independent of the surrounding chains. This, however, is in contradiction with several experiments. In this Letter, we propose a universal description of orientation coupling in polymer melts in terms of the time-dependent coupling parameter κ(t). We use molecular dynamics simulations to show that the coupling parameter increases with time, reaching about 50% at long times, independently of the chain length or blend composition. This leads to predictions of component dynamics in mixtures of different molecular weights from the knowledge of monodisperse dynamics for unentangled melts. Finally, we demonstrate that entanglements do not play a significant role in the observed coupling. © 2010 The American Physical Societ

Determining tube theory parameters by slip-spring model simulations of entangled star polymers in fixed networks

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual ``slip-links'', each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight $N_e$, a key tube theory parameter, can be extracted. The procured $N_e$ value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of $N_e$ as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms $\mu(t)$, or equivalently arm end-to-end vector relaxation function $\phi(t)$, through the mean FP time spectrum $\tau(s)$ of the tube segments after careful consideration of the inner-most entanglements

Shear banding in molecular dynamics of polymer melts

In order to establish constitutive equations for a viscoelastic fluid uniform shear flow is usually required. However, in the last 10 years S. Q. Wang and co-workers have demonstrated that some entangled polymers do not flow with the uniform shear rate as usually assumed, but instead choose to separate into fast and slow flowing regions. This phenomenon, known as shear banding, causes flow instabilities and in principle invalidates all rheological measurements when it occurs. In this Letter we report the first observation of shear banding in molecular dynamics simulations of entangled polymer melts. We show that our observations are in a very good agreement with the phenomenology developed by Fielding and Olmsted. Our findings provide a simple way of validating the empirical macroscopic phenomenology of shear banding. © 2012 American Physical Societ

Dynamic contact angle at nano-scale: a unified view

Generation of dynamic contact angle in the course of wetting is a fundamental phenomenon of nature. Dynamic wetting processes have a direct impact on flows at nano-scale, and therefore their understanding is exceptionally important to emerging technologies. Here, we reveal the microscopic mechanism of dynamic contact angle generation. It has been demonstrated using large-scale molecular dynamics simulations of bead-spring model fluids that the main cause of local contact angle variations is the distribution of microscopic force acting at the contact line region. We were able to retrieve this elusive force with high accuracy. It has been directly established that the force distribution can be solely predicted on the basis of a general friction law for liquid flow at solid surfaces by Thompson and Troian. The relationship with the friction law provides both an explanation of the phenomenon of dynamic contact angle and a methodology for future predictions. The mechanism is intrinsically microscopic, universal and irreducible, and is applicable to a wide range of problems associated with wetting phenomena

Arm retraction dynamics of entangled star polymers: a forward-flux sampling method study

The study of dynamics and rheology of well-entangled branched polymers remains a challenge for computer simulations due to the exponentially growing terminal relaxation times of these polymers with increasing molecular weights. We present an efficient simulation algorithm for studying the arm retraction dynamics of entangled star polymers by combining the coarse-grained slip-spring (SS) model with the forward-flux sampling (FFS) method. This algorithm is first applied to simulate symmetric star polymers in the absence of constraint release (CR). The reaction coordinate for the FFS method is determined by finding good agreement of the simulation results on the terminal relaxation times of mildly entangled stars with those obtained from direct shooting SS model simulations with the relative difference between them less than $5\%$. The FFS simulations are then carried out for strongly entangled stars with arm lengths up to $16$ entanglements that are far beyond the accessibility of brute force simulations in the non-CR condition. Apart from the terminal relaxation times, the same method can also be applied to generate the relaxation spectra of all entanglements along the arms which are desired for the development of quantitative theories of entangled branched polymers. Furthermore, we propose a numerical route to construct the experimentally measurable relaxation correlation functions by effectively linking the data stored at each interface during the FFS runs. The obtained star arm end-to-end vector relaxation functions $\Phi(t)$ and the stress relaxation function $G(t)$ are found to be in reasonably good agreement with standard SS simulation results in the terminal regime. Finally, we demonstrate that this simulation method can be conveniently extended to study arm-retraction problem in entangled star polymer melts with CR by modifying the definition of the reaction coordinate

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes

Dynamics in supramolecular polymer networks formed by associating telechelic chains

We present hybrid molecular dynamics/Monte Carlo simulations of supramolecular networks formed by unentangled telechelic chains with sticky end monomers (or stickers) of finite functionality. The reversible bonding between sticky monomers leads to the formation of sticker clusters with well-defined size distribution, which in turn work as cross-links for transient polymer networks. We study the kinetics of sticky monomer association, the topological structure and the resulting dynamic and rheological behavior of the supramolecular systems as a function of the sticker bonding energy $\varepsilon$ and the parent polymer chain length. Percolated transient networks are formed above a threshold bonding energy around $4.3 k_B T$. At high bonding energies $\varepsilon \geq 10 k_B T$, the majority of the stickers are fully reacted and the fraction of open stickers is less than $1\%$. The conventional picture of a single sticker hopping from one cluster to another is energetically unfavorable. We find the dynamic and rheological behavior of such strongly associated supramolecular networks are dominated by a partner exchange mechanism in which the stickers exchange their associated partners, and so release the imposed topological constraints, through the association and disassociation of sticker clusters. The characteristic time of the partner exchange events grows exponentially with the bonding energy and is up to $2$ orders of magnitude longer than the average lifetime of the reversible bonds. As a result, three relaxation regimes can be clearly identified in the stress and chain end-to-end vector relaxation functions as well as the mean-squared displacements of the stickers, which are the initial Rouse regime, the intermediate rubbery regime and the terminal relaxation regime. A phantom chain hopping model based on the microscopic understanding is proposed to describe the chain relaxation dynamics in the supramolecular networks, which provides numerical predictions in reasonably good agreement with our simulation results

Relaxation of surface tension in the liquid-solid interfaces of Lennard-Jones liquids

We have established the surface tension relaxation time in the liquid-solid interfaces of Lennard-Jones (LJ) liquids by means of direct measurements in molecular dynamics (MD) simulations. The main result is that the relaxation time is found to be almost independent of the molecular structures and viscosity of the liquids (at seventy-fold change) used in our study and lies in such a range that in slow hydrodynamic motion the interfaces are expected to be at equilibrium. The implications of our results for the modelling of dynamic wetting processes and interpretation of dynamic contact angle data are discussed

Whither tube theory: From believing to measuring

This short contribution examines the difficulties that have not yet been fully overcome in the many developments made from the simplest (and original) tube model for entangled polymers. It is concluded that many more length scales have to be considered sequentially when deriving a continuum rheological model from molecular considerations than have been considered in the past. In particular, most unresolved issues of the tube theory are related to the length scales of tube diameter, and molecular dynamics simulations is the perfect route to resolve them. The power of molecular simulations is illustrated by two examples: stress contributions from bonded and non-bonded interaction, and the inter-chain coupling, which is usually neglected in the tube theory