An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters reproduce those computed from united atom molecular dynamics simulations. The coarse-grained description correctly bridges micro-and mesoscopic fluid properties. Molecular dynamics simulations of soft colloidal particles interacting through the calculated effective pair potentials are consistent with data from microscale simulations and analytical formulas.The formulation of an accurate mesoscopic description of macromolecular fluids has been a longstanding goal in polymer physics. Experimentally-relevant polymer dynamics span a wide range of timescales, for which large-scale, long-time properties still depend strongly on the local molecular structure [1]. Pertinent information on structure and dynamics of polymer liquids has been gained from united atom (UA) molecular dynamics (MD) simulations. However, the MD computational time increases as the squared number of interacting units, and the latter has to be large to approximate the thermodynamic limit, rendering an all-atom simulation of long-time polymer dynamics a prohibitive task. One strategy devised to overcome this problem is to renormalize the liquid structure and dynamics using effective-unit coarse-grained descriptions [1]. Specifically, polymers can be described mesoscopically as soft interpenetrating spheres having the overall size of the polymer, i.e., the radius of gyration R g . However, to correctly perform the renormalization procedure, a theoretical framework that bridges properly different lengthscales of interest is needed. Phenomenological mesoscopic potentials were implemented by Dautenhahn and Hall, and later on by Murat and Kremers, to describe polymer melts and blends [2,3]. Hansen and coworkers have recently developed a rigorous numerical description of polymer solutions as liquids of soft interacting colloidal particles [4].In this Letter we start from first-principles liquid-state theory and derive an analytical form of center-of-mass (c.o.m.) pair correlation functions, from which the effective pair soft-core potential acting between molecules in polymer liquids (melts) and their mixtures (blends) is obtained. The c.o.m. pair correlation functions reproduce mesoscale liquid structures obtained from UA-MD simulations [5,6,7] without adjustable parameters. Test systems are polymer melts with different architecture, local semiflexibility, and degree of polymerization (Table I), as well as their mixtures (Table II). Finally, the mesoscopic potential derived by an inversion procedure is used in MD simulations of soft colloidal particles, which reproduce the liquid structure at the level of c.o.m. pair correlation functions.The renormalized pair interaction potential is a function of the c.o.m. total pair correlation function h(r). In reciprocal space,, after a procedure devised by Krakoviack, Hansen, and Loui...

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.

We present a Generalized Langevin Equation for the dynamics of interacting semiflexible polymer chains, undergoing slow cooperative dynamics. The calculated Gaussian intermolecular center-ofmass and monomer potentials, wich enter the GLE, are in quantitative agreement with computer simulation data. The experimentally observed, short-time subdiffusive regime of the polymer meansquare displacements, emerges here from the competition between the intramolecular and the intermolecular mean-force potentials.PACS numbers:61.25.HqDespite its intrinsic complexity, the dynamics of low molecular weight unentangled polymer fluids has been considered for a long time to be a well understood problem in polymer physics. It is commonly accepted that when the degree of polymerization, N , does not exceed the entanglement value, N e , a molecule is free to diffuse in the liquid, and follows Fickian dynamics. In this case, the Rouse approach successfully describes several key features of the polymer dynamics. These include the scaling with N of the bulk viscosity and the single-−1 , with k B the Boltzmann constant, T the temperature, and ζ the monomer friction coefficient [1].Upon closer examination, however, the dynamics of unentangled polymer fluids still presents important unresolved questions. In the Rouse theory, local intermolecular interactions are completely neglected; the single chain dynamics is driven by intramolecular entropic restoring forces and segmental friction, while the dynamics of the surrounding chains provide a heat bath. In this description the polymer center of mass is free to diffuse following Brownian dynamics, and the mean-square displacement is expected to scale linearly in time at all time scales. In reality, a single polymer in a fluid spans a volume V ∝ R 3 g , with R g = √ N l/ √ 6 the polymer radius of gyration, and l the statistical segment length. Inside this volume are contained an average of n ∝ √ N chains, that interact with each-other through the potential of mean force [2]. The range of the potential is the same as that of the correlation hole [3] in the pair correlation function g(r), a distance of order R g in polymer fluids [4]. Such interactions on length scales shorter than or equal to R g leads to the Rouse equation's failure to adequately describe short-time polymer dynamics.The inconsistency of the Rouse equation with computer simulation data of short-time unentangled [5,6] and entangled polymer dynamics in the melt state, and in concentrated solutions [7,8], has been known for many years. In the short-time regime, t ≪ τ Rouse = 2R mean-square-displacement, ∆R 2 (t), of unentangled polymers shows anomalous diffusion. For times t ≪ τ Rouse ∆R 2 (t) crosses over from the short-time ballistic dynamics to long-time Fickian diffusion (∆R 2 (t) ∝ t) through an intermediate regime (∆R 2 (t) ∝ t 0.8÷0.9 ) [5,6,9]. Only at long times (t ≥ τ Rouse ) does the system obey Rouse dynamics and Fickian diffusion is recovered. Entangled polymer fluids show the same behavior in the shorttime regime whe...

Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k → 0 limit, c0. A numerical solution to the PRISM integral equations is used to determine c0, by adjusting the value of the effective hard sphere diameter, dHS, to agree with the predicted equation of state. This single quantity parameterizes the coarse-grained potential, which is used to perform mesoscale simulations that are directly compared with atomistic-level simulations of the same system. We test our coarse-graining formalism by comparing structural correlations, isothermal compressibility, equation of state, Helmholtz and Gibbs free energies, and potential energy and entropy using both united atom and coarse-grained descriptions. We find quantitative agreement between the analytical formalism for the thermodynamic properties, and the results of Molecular Dynamics simulations, independent of the chosen level of representation. In the mesoscale description, the potential energy of the soft-particle interaction becomes a free energy in the coarse-grained coordinates which preserves the excess free energy from an ideal gas across all levels of description. The structural consistency between the united-atom and mesoscale descriptions means the relative entropy between descriptions has been minimized without any variational optimization parameters. The approach is general and applicable to any polymeric system in different thermodynamic conditions.

The analytic Polymer Reference Interaction Site Model (PRISM) theory of structurally and interaction symmetric Gaussian diblock copolymer fluids is reformulated, extended, and applied to make predictions for experimentally observable equilibrium properties of the disordered state. These include the temperature, degree of polymerization, copolymer composition, and polymer density or concentration dependences of the peak scattering intensity, effective chi-parameter, and heat capacity. The location of the order-disorder transition is empirically estimated based on the disordered, strongly fluctuating state scattering function. Detailed numerical applications of PRISM theory demonstrates it provides an excellent and consistent description of the data. An in depth comparison of the mathematical structure and predictions of PRISM theory with the highly coarse-grained, incompressible Brazovski–Leibler–Fredrickson–Helfand (BLFH) fluctuation corrected field theory is also carried out. Under some conditions (nearly symmetric composition, high melt densities, moderate temperatures) there are striking mathematical similarities between the predictions of the physically very different theories, although quantitative differences always persist. However, for strongly asymmetric copolymer compositions, short chains, compressible copolymer solutions, and low temperatures many qualitative differences emerge. The possibility of multiple, self-consistent fluctuation feedback mechanisms within the most general PRISM approach are identified, their qualitative features discussed, and contrasted with alternative versions of the fluctuation-corrected incompressible field theories due to BLFH and Stepanow. The predictions of PRISM and BLFH theory for the composition, copolymer density, temperature, and molecular weight dependence of the effective chi-parameter are presented, contrasted, and qualitatively compared with recent experiments.