Session W42: Focus Session: Multiscale Modeling of Polymers

Coarse graining of polystyrene sulfonate

Capturing large length scales in soft matter while retaining atomistic properties is imperative to computational studies. Here we develop a new coarse-grained model for polystyrene sulfonate (PSS) that often serves as a model system because of its narrow molecular weight distribution and defined degree of sulfonation. Four beads are used to represent polymer where the backbone, the phenyl group, and the sulfonated group are each represented by a different bead and the fourth one represents counterion, which is sodium in our case. Initial atomistic simulations of PSS melt with sulfonation levels of 2-10{\%}, with a dielectric constant $\varepsilon =$1 revealed a ``locked'' phase where motion of the polymer is limited. Dielectric constant of $\varepsilon =$5 was used to accelerate the dynamics. Bonded interactions were obtained using Boltzmann inversion on the bonded distributions extracted from atomistic simulation. Non-bonded interaction of polystyrene monomer was taken from our previous work and potential of mean force was used as the initial guess for interaction of the ionic beads. This set of potential was subsequently iterated to get a good match with radial distribution functions. This potential and its transferability across dielectric constants and temperatures will be presented.   

Morphology and Dynamics of Tapered Diblock Copolymers from fDFT-initialized MD Simulations

Tapered block copolymers are similar to AB diblock copolymers, but with a statistical A-to-B (normal) or B-to-A (inverse) gradient ``taper'' between the A and B blocks. Depending on the sequence of monomers along the chain and the segregation strength, the A and B monomers are known to microphase separate into various ordered morphologies. Tapering introduces an additional parameter, independent of molecular weight or polymer choice, to tune morphology, and has been shown previously to widen the gyroid region of the phase diagram.In this study, we use classical, fluids density functional theory (fDFT) and molecular dynamics (MD) simulations to study the morphology and dynamics of tapered systems. Using fDFT allows us to accurately compare free energies between different potential microphases as a function of interaction parameter and fraction of A. Because of the similarity of the fDFT and MD models, the fDFT results map very closely with the corresponding MD model. We use the fDFT density profiles to generate the initial state of the chains for the simulations. Lamellae, cylinders, and other phases can be generated in this way with approximately correct spacing and density. We apply the streamlined simulation setup to analyze the effect of tapering on conformations and dynamics.   

Properties of Coarse-Grained Polymer Models: Statics, Dynamics, and Crystallinity

To capture large length and time scales, coarse-grained (CG) models that combine multiple atoms into one bead have been developed to model polymer melts. In the process microscopic detail is discarded in exchange for computational efficiency. However it is not well-understood how the scale of coarse-graining affects the polymer structure and dynamics. We compare results of atomistic simulations with CG models in which each CG bead represents three, four, or six methylene groups for C$_{96}$H$_{194}$, C$_{480}$H$_{962}$, and C$_{960}$H$_{1922}$. The CG potential is developed at 500K by iterative Boltzmann inversion. While static properties such as end-to-end distance and radius of gyration are captured by all CG models, the entanglement length deviates from experimental results with increased CG scale. The mean squared displacement of CG models is used to determine scale factors between the atomistic and CG models. During cooling to low temperature, the three and four-carbon models form a semi-crystalline structure while the six-carbon model and a four-carbon model based on the MARTINI force field remain amorphous at all temperatures. These findings show that the level of coarse-graining and CG interactions can strongly affect model temperature transferability.   

Thermodynamically Consistent Coarse-Graining of Polymers

Structural and dynamical properties of macromolecular liquids, melts and mixtures, bridge an extensive range of length- and time-scales. For these systems, the computational limitations of the atomistic description prevent the study of the properties of interest and coarse-grained models remain the only viable approach. In coarse-grained models, structural and thermodynamic consistency across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. This talk presents a coarse-graining approach that conserves structural and thermodynamic quantities independent of the extent of coarse-graining, and describes a model for the reconstruction of the dynamics measured in mesoscale simulations of the coarse-grained system. Some of the general challenges of preserving structural and thermodynamic consistency in coarse-grained models are discussed together with the conditions by which the problem is lessened.   

Modelling and multiscale simulations of meta aromatic polyurea: microscopic geometry and dielectric properties

BOPP is the state-of-art material for high-power-density capacitors. However, its efficiency drastically drops at high electric fields. Recently, polymers in the polyurea/polythiourea family have been shown to have much higher energy density and efficiency at high fields than BOPP [1-2]. We perform multiscale simulations to investigate dielectric and structural properties of meta aromatic polyurea (mAP). Both crystalline and disordered structures have been studied, and much larger ionic contribution to permittivity is found in disordered structures. The specific volume is 10\% to 20\% larger in the latter, leading to greater structural flexibility. For example, the orientation variations of polar units are 100\% larger than in the crystal structure, and the phonon density of states in the low frequency regime is significantly enhanced. At the same time, we find that meta aromatic polyurea has a higher tendency to be disordered than other members in the polyurea family. All these facts lead to a significantly larger permittivity of mAP.\\[4pt] [1] Wu et al, Advanced Materials, 25, 1734 (2013).\\[0pt] [2] Wang et al, APL 94, 202905 (2009).   

The conditional reversible work method for molecular coarse graining of soft matter

I will discuss a recently introduced systematic coarse-graining method that provides transferable coarse-grained potentials for scale-bridging simulations of soft matter systems. The method [1-3] is based on direct calculation of pair potentials in the gas or liquid phase with thermodynamic integration or free energy perturbation methods and has been coined the Conditional Reversible Work (CRW) method. I will discuss the CRW method in the general context of systematic coarse graining, a recent extension to dynamically-consistent coarse-grained simulations [4], and show some practical examples, including coarse-grained simulations of molecular liquids and polymers. \\[4pt] [1] E. Brini, N.F.A. van der Vegt, J. Chem. Phys. 137, 154113 (2012).\\[0pt] [2] E. Brini, V. Marcon, N.F.A. van der Vegt, Phys.Chem.Chem.Phys. 13, 10468-10474 (2011).\\[0pt] [3] E. Brini et al. Soft Matter 9, 2108-2119 (2013).\\[0pt] [4] G. Deichmann, V. Marcon, N.F.A. van der Vegt, submitted   

Systematic and Simulation-Free Coarse Graining of Polymeric Systems: A Structure-based Study

We propose a systematic and simulation-free strategy for coarse graining of multicomponent polymeric systems, where we use the Polymer Reference Interaction Site Model theory, instead of many-chain molecular simulations, to calculate the structure and thermodynamic properties of both the original and coarse-grained (CG) models, and quantitatively examine how the effective CG pair potentials and properties of CG systems vary with the coarse-graining level. Our strategy is general and versatile, is much faster than those using many-chain simulations, and practically solves the transferability problem of coarse graining. As an example, here we apply it to structure-based coarse graining of homopolymer melts, which matches the structure correlations of CG segments between the original and CG systems. Our numerical results clearly show that structure-based coarse graining cannot give thermodynamic consistency between the original and CG systems at any coarse-graining level due to the information loss of coarse graining.   

Systematic and Simulation-Free Coarse Graining of Polymeric Systems: A Relative-Entropy-based Study

Relative-entropy-based coarse graining minimizes the relative entropy (RE) quantifying the information loss due to coarse graining.[1] When pair potentials are used for coarse-grained (CG) segments, RE-based coarse graining becomes equivalent to structure-based coarse graining if the pair potentials are unconstrained.[1] Here we apply our systematic and simulation-free strategy to RE-based coarse graining of homopolymer melts; that is, we use the Polymer Reference Interaction Site Model (PRISM) theory, instead of many-chain molecular simulations, to calculate the structure and thermodynamic properties of both the original and CG systems, and quantitatively examine how the CG pair potentials and properties of CG systems vary with the coarse-graining level. We consider various analytic functional forms of CG pair potential as suggested by structure-based coarse graining, and minimize RE to obtain the associated parameters. Values of minimized RE are then used to select the appropriate analytic form of CG pair potential, which is much easier to use than the tabulated (numerical) CG pair potential obtained from structure-based coarse graining. This is the first application of RE-based coarse graining to polymers. [1] M. S. Shell, \textbf{J. Chem. Phys. 129}, 144108 (2008).   

A proposed method for directed self-assembly of graphene nanoribbons

There is an opportunity for modeling to inform the experimental synthesis and design of graphene nanoribbons (GNRs). We present here a new course-grained algorithm for simulating GNR synthesis by the self-assembly of aromatic carbon precursor molecules. The model uses a Gillespie algorithm to form a network of possible coupling reactions between these molecules, and exploits a novel way of representing their geometries to speed up the simulations. Based on this method, we identify areas in parameter space given by temperature, binding energy, functional groups, and concentration of precursor molecules, which lead to GNRs with desirable properties. We demonstrate use of the model based on two precursors that self-assemble together to form a nanoporous GNR, namely, functionalized tetrabenzanthracene and benzene. We demonstrate that, unlike a pristine GNR, the GNRs formed by these molecules have regular repeating holes, and exhibit a band gap of 1.6eV independent of the ribbon width.   

Universal aspects of conformations and transverse fluctuations of a two-dimensional semi-flexible chain

In this talk we compare the results obtained from Monte Carlo (MC) and Brownian dynamics (BD) simulation for the universal properties of a semi-flexible chain. Specifically we compare MC results obtained using pruned-enriched Rosenbluth method (PERM) with those obtained from BD simulation. We find that the scaled plot of root-mean-square (RMS) end-to-end distance $\langle R_N^2 \rangle/2L\ell_p$ and RMS transverse transverse fluctuations $\sqrt{\langle l^2_\perp \rangle}/\ell_p$ as a function of $L/\ell_p$ (where $L$ and $\ell_p$ are the contour length, and the persistence length respectively) are universal and independent of the definition of the persistence length used in MC and BD schemes. We further investigate to what extent these results agree for a semi-flexible polymer confined in a quasi one dimensional channel.   

Stretching wormlike chain: interplay between chain stiffness and excluded volume in the long chain limit

Nearly 20 years ago, Marko and Siggia ($Macromolecules$ \textbf{1995}, 8759-8770) proposed an approximate interpolation formula for the force-extension ($f$-$z$) behavior of a wormlike chain that has found widespread use in biophysics and polymer physics. We have extended their result to account for excluded volume interactions. Our analysis takes advantage of Pruned-Enriched-Rosenbluth Method (PERM) simulations of wormlike chains of varying monomer anisotropy. Our simulations use up to 80,000 hard beads, allowing us to reach the long chain limit with sub-persistence length resolution. The simulations produce the Pincus scaling $z \sim f^{2/3}$, followed by a crossover to the linear behavior $z \sim f$, and subsequent saturation approaching the fully stretched limit. We also developed an approximate interpolation formula that captures these three regimes. This interpolation formula is in good agreement with PERM simulation results and can be reduced to the Marko-Siggia interpolation formula when the excluded volume effect is eliminated. Practically, our work provides a handy description of force-extension behavior for real wormlike chain, which will be useful for coarse-grained simulations and interpreting experiment results.   

Accelerated dynamics of bead-spring polymer chains

We present results from the application of the recently generalized parallel replica method to a system of bead-spring polymer chains. The statistics of chain breakage show that individual chains, after a relatively short dephasing time, display an exponential distribution of breakage times over a wide range of extension ratios, thereby allowing us to exploit the notion of the quasi-stationary distribution and accelerate the dynamical evolution of a representative volume element.