Identifying the primitive path mesh in entangled polymer liquids (original) (raw)
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Computer Physics Communications, 2005
Topological constraints, referred to as entanglements in the literature, dominate the viscoelastic behavior of high molecular weight polymeric liquids. To give a microscopic foundation of the phenomenological tube models which successfully describe this behavior, we have recently introduced a method for identifying the so-called primitive path mesh that characterizes the microscopic topological state of (computer generated) conformations of long-chain polymer networks, melts and solutions. Here we give a short account of this approach and discuss some applications.
Polymers
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees–Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of th...
Writhe versus mutual entanglement of linear polymer chains in a melt
One of the reasons why the notion of entanglement in polymer melts is elusive is because it refers to both local and global characteristics of the conformations of the chains that compose it. Here we propose to use a combination of topological and geometrical measures of entanglement. Both the writhe and number of kinks (entanglements) of the primitive path of linear polymer chains in a melt are analysed over a range of molecular weights. Our numerical results show that the mean absolute writhe of linear semiflexible chains follows a scaling with respect to chain length and stiffness that is similar to the one known for semiflexible ring polymers. Focusing on linear finitely extendable chains, we find that the writhe of the corresponding primitive paths does not exhibit similar scaling behavior. Using the number of kinks in a chain and the writhe of both the original and primitive chains, we calculate the mean writhe and the mean squared writhe of an entanglement strand. Following this analysis, a new method to estimate the number of monomers in an entanglement strand, Ne, is presented and compared to existing Ne-estimators.
The Journal of Chemical Physics, 2010
The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static ͑statistical͒ properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics ͑MD͒ trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ͑s , t͒ that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time.
Microscopic Definition of Polymer Entanglements
Macromolecules, 2014
The dynamics of polymer melts and concentrated solutions is notoriously slow due to the fact that long polymer chains can not cross each other and therefore …nd themselves entangled. This popular belief is very di¢ cult to quantify and convert into mathematical model because there is still no clear de…nition of what entanglement really is. In this paper we propose to de…ne entanglement as a persistent contact between mean paths of the chains. In molecular dynamics (MD) simulations of well-entangled linear chains we discovered that such very tight and longlived contacts exist in signi…cant numbers. Moreover, once such contact is formed, it exists at every time step of the simulation until its destruction, which allows one to de…ne its life time. We study several properties of individual entanglements and discover several unexpected features not taken into account in the tube theory or slip-links models. We believe that our simple and versatile de…nition opens the way to the truly microscopic understanding of polymer dynamics.
Individual Polymer Chain Dynamics in an Entangled Polymeric Liquid Using a Stochastic Tube Model
2021
This study focuses on comparing the individual polymer chain dynamics in an entangled polymeric liquid under different shear and extension rates. Polymer chains under various shear rates and extension rates were simulated using a stochastic-tube model [J. Rheol. 56: 1057 (2012)]. We developed a Matlab code to visualize and analyze the simulated configurations from the stochastic-tube model. We introduced new variables to determine how the extent of linearity changes with time for different shear rates, which is more useful than a typical end-to-end distance analysis. We identified whether the polymer chains undergo a “tumbling” motion (rotation with slight elongation not accompanying contraction) or “flipping” motion (rotation with elongation accompanying contraction). The simulation results indicate that the polymer chains exhibit a significant tendency to elongate at higher shear rates and occasionally experience flipping, while lower shear rates tend to exhibit very frequent tumb...
Journal of Physics: Condensed Matter, 2011
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts
Polymers
We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of “entanglement” phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as “soft” particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric ...
Foundational issues in nonlinear rheology of entangled polymeric liquids
Bulletin of the American Physical Society, 2010
Foundational issues in nonlinear rheology of entangled polymeric liquids 1 SHI-QING WANG, University of Akron, POUYAN BOUKANY, SHAM RAVIDRANATH, YANGYANG WANG, XIN LI, POLYMER RHEOLOGY TEAM -Nonlinear dynamic and mechanic responses of entangled polymeric liquids to external deformations determine processing behavior of a hundred billion pounds of thermoplastic and rubber materials that are produced every year. The emerging phenomenology and theoretical concepts suggest that we need to go beyond the conventional description of polymer rheology involving high external deformations. The new understanding emphasizes the need to monitor the deformation field without predicating that homogeneous deformation would prevail in these highly viscoelastic materials. Entangled polymeric liquids are transient soft solids with finite cohesion and necessarily have to transform from a solid-like network state to a state of flow. Apparently, this yielding often results in inhomogeneous flow. About two dozen movies of particle-tracking velocimetric observation and publications can be found at our website: 1 Sponsored by a grant (DMR-0821697) from the National Science Foundation.