Session C4: Bridging Time and Length Scales: From Nano Assemblies to Bio-Polymers

Going up in time and length scales in modeling polymers

Polymer properties depend on a wide range of coupled length and time scales, with unique macroscopic viscoelastic behavior stemming from interactions at the atomistic level. The need to probe polymers across time and length scales and particularly computational modeling is inherently challenging. Here new paths to probing long time and length scales including introducing interactions into traditional bead-spring models and coarse graining of atomistic simulations will be compared and discussed. Using linear polyethylene as a model system, the degree of coarse graining with two to six methylene groups per coarse-grained bead derived from a fully atomistic melt simulation were probed. We show that the degree of coarse graining affects the measured dynamic. Using these models we were successful in probing highly entangled melts and were able reach the long-time diffusive regime which is computationally inaccessible using atomistic simulations. We simulated the relaxation modulus and shear viscosity of well-entangled polyethylene melts for scaled times of ~500 µs. Results for plateau modulus are in good agreement with experiment. The long time and length scale is coupled to the macroscopic viscoelasticity where the degree of coarse graining sets the minimum length scale instrumental in defining polymer properties and dynamics. Results will be compared to those obtained from simple bead-spring models to demonstrate the additional insight that can be gained from atomistically inspired coarse grained models. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Multi-scale modelling and dynamics

Moving from a fine-grained particle model to one of lower resolution leads, with few exceptions, to an acceleration of molecular mobility, higher diffusion coefficient, lower viscosities and more. On top of that, the level of acceleration is often different for different dynamical processes as well as for different state points. While the reasons are often understood, the fact that coarse-graining almost necessarily introduces unpredictable acceleration of the molecular dynamics severely limits its usefulness as a predictive tool. There are several attempts under way to remedy these shortcoming of coarse-grained models. On the one hand, we follow bottom-up approaches. They attempt already when the coarse-graining scheme is conceived to estimate their impact on the dynamics. This is done by excess-entropy scaling. On the other hand, we also pursue a top-down development. Here we start with a very coarse-grained model (dissipative particle dynamics) which in its native form produces qualitatively wrong polymer dynamics, as its molecules cannot entangle. This model is modified by additional temporary bonds, so-called slip springs, to repair this defect. As a result, polymer melts and solutions described by the slip-spring DPD model show correct dynamical behaviour. Read more: ``Excess entropy scaling for the segmental and global dynamics of polyethylene melts'', E. Voyiatzis, F. M\"{u}ller-Plathe, and M.C. B\"{o}hm, Phys. Chem. Chem. Phys. \textbf{16}, 24301--24311 (2014). [DOI: 10.1039/C4CP03559C] ``Recovering the Reptation Dynamics of Polymer Melts in Dissipative Particle Dynamics Simulations via Slip-Springs'', M. Langeloth, Y. Masubuchi, M. C. B\"{o}hm, and F. M\"{u}ller-Plathe, J. Chem. Phys. \textbf{138}, 104907 (2013). [DOI: 10.1063/1.4794156].   

Role of Ionic Clusters in Dynamics of Ionomer Melts: From Atomistic to Coarse Grained Simulations

Ionomers, polymers decorated with ionizable groups, have found application in numerous technologies where ionic transport is required. The ionic groups associate into random clusters resulting in substantial effect on structure, dynamics and transport of these materials. The effects of topology, size and dynamics of these aggregates however remain an open question. Here we probe cluster formation correlated with polymer dynamics through a model system of randomly sulfonated polystyrene (SPS) melts with molecular dynamics (MD) simulations over a broad time and length scales ranging from that within the ionic clusters through polymer segmental dynamics to the motion of the entire molecules. The cluster evolution was probed by fully atomistic studies. We find ladder-like aggregates that transform to globule-like with increasing the dielectric constant of media for sodium neutralized SPS. With increasing dielectric constant, the size of the aggregates decrease and their number increases. Concurrently, the mobility of the polymer increases. The counterion radius and valency affect both morphology and dynamics as is evident in the calculated static and dynamic structure factors. It is further manifested in the results of viscosity obtained through non-equilibrium molecular dynamics technique. Finally, to access larger length scales a three bead coarse-grained model to describe sulfonated styrene that we have developed will be discussed in view of the outstanding challenges in ionic polymers.   

\textbf{Protein free energy landscapes from long equilibrium simulations }

Many computational techniques based on molecular dynamics (MD) simulation can be used to generate data to aid in the construction of protein free energy landscapes with atomistic detail. Unbiased, long, equilibrium MD simulations---although computationally very expensive---are particularly appealing, as they can provide direct kinetic and thermodynamic information on the transitions between the states that populate a protein free energy surface. It can be challenging to know how to analyze and interpret even results generated by this direct technique, however. I will discuss approaches we have employed, using equilibrium MD simulation data, to obtain descriptions of the free energy landscapes of proteins ranging in size from tens to thousands of amino acids.   

\textbf{Electrostatic Interactions and Self-Assembly in Polymeric Systems}

Electrostatic interactions between macroions play an important role in different areas ranging from materials science to biophysics. They are main driving forces behind layer-by-layer assembly technique that allows self-assembly of multilayer films from synthetic polyelectrolytes, DNA, proteins and nanoparticles. They are responsible for complexation and reversible gelation between polyelectrolytes and proteins. In this talk, using results of the molecular dynamics simulations and analytical calculations, I will demonstrate what effect electrostatic interactions, counterion condensation and polymer solvent affinity have on a collapse of polyelectrolyte chain in a poor solvent conditions for the polymer backbone, on complexations and reversible gelation between polyelectrolytes and polyamholytes (unstructured proteins), on microphase separation transitions in spherical and planar charged brushes, and on a layer-by-layer assembly of charged nanoparticles and linear polyelectrolytes on charged surfaces.