Session A18: Focus Session: Multiscale Modeling: Polymers, Nanocomposites, and Biomacromolecules

Aneesur Rahman Prize Talk: Dynamics of Entangled Polymer Melts: Perceptive from Molecular Dynamics Simulations

Twenty years ago at the APS March Meeting, Kurt Kremer and I presented the first numerical evidence from computer simulations that the reptation model of Edwards and de Gennes correctly describes the dynamics of entangled linear polymer melts. For chains longer than the entanglement length $N_e$, the monomers of a chain move predominantly along their own contour. The distinctive signature of reptation dynamics, which we observed, was that on intermediate time scales, the mean squared displacement of a monomer increases with time as $t^ {1/4}$. Though these early simulations were limited to chains of a few $N_e$, they demonstrated the potential of computer simulations to contribute to our understanding of polymer dynamics. Here I will review the progress over the past twenty years and present an outlook for the future in modeling entangled polymer melts and networks. With present day computers coupled with efficient parallel molecular dynamics codes, it is now possible to follow the equilibrium dynamics of chains of length $10-20N_e$ from the early Rouse regime to the long time diffusive regime. Result of these simulations support the earlier results obtained on chains of only a few $N_e$. Further evidence for the tube models of polymer dynamics has been obtained by identifying the primitive path mesh that characterizes the microscopic topological state of the computer- generated conformations of the chains. In particular, the plateau moduli derived on the basis of this analysis quantitatively reproduce experimental data for a wide spectrum of entangled polymer liquids including semi-dilute theta solutions of synthetic polymers, the corresponding dense melts, and solutions of semi-flexible (bio)polymers such as f-actin or suspensions of rodlike viruses. We also find that in agreement with the reptation model, the stress, end-to-end distance and entanglement length of an entangled melt subjected to uniaxial elongation, all relax on the same time scale.   

Microrheology of Nanospheres in Rod Suspensions

Many biological processes and applications involve the motion of small (nanoscale) spherical particles through a dense (typically) semiflexible polymer matrix. While much theoretical work has characterized the motion of such particles in the limit of its size being much larger than the mesh size of the matrix, very limited understanding exists of the (more biologically relevant) crossover regime to the case where the particle size becomes comparable to the mesh size. Recently we have developed a new computer simulation method to simulate the dynamical and rheological properties of colloid suspensions of in a variety of complex fluids. We first present the results of its generalization to the dynamics and linear rheological properties of dilute, semidilute and concentrated rods suspensions in a simple fluid. Subsequently, we use this method to characterize the mobility and diffusive dynamics of nanoscale spheres in rod matrices, while paying special attention to the length scales of the fluid which characterize the hydrodynamic screening and overall viscous motion.   

Peptide binding to sheet silicate and metal nanoparticles: Insight from atomistic simulation

Short peptides (8 to 12 amino acids, excluding Cys) bind selectively to nanoparticles composed of Au, Pd, and montmorillonite depending on the sequence of amino acids, as evidenced by laboratory screening of several billion peptides. The molecular reasons for binding versus non-binding and the specificity toward a certain surface are analyzed by molecular dynamics simulation, using recent force field extensions for fcc metals and sheet silicates to reproduce surface and interface energies with $<$10{\%} deviation compared to experiment. Polarization on even metal surfaces ranges from 3 to 5 kcal/mol and non-covalent binding energies from 0 and 80 kcal/mol per dodecapeptide. Adsorption energies, changes in chain conformation, Ramachandran plots, and orientational parameters, are analyzed in conjunction with NMR, TEM, and other experimental data. On montmorillonite, an ion exchange reaction of Lys side groups against alkali ions as well as interactions between alkali cations and polar groups in the peptide are explained.   

Adsorption-desorption of peptide chains on Au surface by a coarse-grained Monte Carlo simulation

Using a coarse grained description, we study stability of the structure and dynamics of several peptide chains (A3, Flg, Pro10, Gly10, Pd2, Pd4) at gold surfaces on a cubic lattice. Although the structural details within the amino acid groups are ignored, the specificity of their interactions is incorporated in our computer simulation modeling of these peptide chains on a cubic lattice. Appropriate coarse-grained interactions (Lennard-Jones) among the amino acid nodes, solvent, and the gold surface with different strength are guided by the atomistic simulations and X-ray crystallographic data; the molecular weight of each amino acid groups is also considered. Peptide chains execute their stochastic motion and their proximity to the generic gold surface is monitored. Mobility of each amino acid (node), its energy, and correlations to their neighboring constituents are analyzed. Some of these results are consistent with the atomistic simulation.   

Characterization of the translocation of polymers driven through nanopores using molecular dynamics simulations

The passage of a polymer through a narrow pore (translocation) is a fundamental process with a wide range of biological applications.~ In particular, threading DNA through nanopores promises to have important implications for the next generation of DNA sequencing techniques.~ In this work, simulations of the translocation of polymers being driven through a narrow, short nanopore are conducted via the Espresso Molecular Dynamics simulation package using the Lattice-Boltzmann algorithm to include hydrodynamics.~ In this talk, results from simulations in which an external field is applied within the pore or to one end of the polymer are presented and compared.~ Characterization of the scaling of the translocation time with the number of monomers as well as details of the anomalous diffusion exhibited by the translocation coordinate will be given.   

Coupling of atomistic and mesoscopic scales: visualizing the translocation of biopolymers through nanopores

We investigate the process of biopolymer translocation through a narrow pore using a multiscale approach, which combines Langevin Molecular-Dynamics with a mesoscopic Lattice-Boltzmann method for the solvent dynamics. We analyze the statistical features of the translocation process through extensive simulations over various polymer conformations and lengths. The translocation time obeys a power law dependence to the polymer length with an exponent $1.28 \pm 0.01$ in very good agreement with experiments of DNA translocation through solid state pores. We focus on the morphological aspects of the translocation dynamics, the folding behavior of the translocating molecule and the associated cooperation of the surrounding solvent, and report the first computational evidence of quantized current blockades.   

Coarse-Grained Kinetic Modeling of Polymer Networks with Non-Affine Slip-Tube Behavior and Heterogeneous Microstructure

Elements of existing entanglement network models have been extended to better account for non-affice slip-tube behavior and to incorporate the effect of heterogeneous spatial domains. Starting with the Density Cloud Model (DCM) framework from Terzis et. al., an entanglement bond potential acting at each entanglement point is introduced. This potential mimics the non-affine tethering from network theories, and in combination with slippage accurately reproduces Non-Affine Slip-Tube behavior. This framework can easily be extended to study the effect of polymer architecture on the mechanical response of the resulting networks. Secondly, the temporary bond from the model of Termonia and Smith is combined with the DCM framework to simulate rigid domains within a matrix of soft polymer network. The modulus of the additional bonds sets the elastic properties of the rigid domain, while DCM entanglement relaxation assures that local deformation remains consistent with the bulk polymer density. The effect of rigid domain size on initial modulus is reported.   

Simulating thermal transport in high contrast composite media

In dealing with transport in composites systems, high contrast materials pose a special problem for numerical simulation: the time scale or step size in the high thermal conductivity material must be much smaller than in the low conductivity material. High conductivity inclusions can be treated as having an infinite conductivity, removing the need to model transport within the high conductivity inclusions. We develop a random walk algorithm to model thermal transport in composites with high conductivity. We observed the standard random walk algorithm leads to non uniform temperature distribution at the vicinity of the high conductivity inclusion violating the second law of thermodynamics. We show how a standard random walk algorithm can be altered to improve speed while still preserving the second law of thermodynamics. We demonstrate the algorithm in 1D and 3D systems.   

Predictive Morphology Models for Crystalline Polymers

Modeling of small-angle scattering data provides information on heterogeneities on sizes on the order of 10 Angstroms and larger. The typical size, shape and arrangement of the heterogeneity can be determined by applying models to the scattering intensity $I(q)$. When there is a distribution in the size of structures present and when a system is densely packed, it is likely that models that can be used for analysis may not provide a unique description of the structure. With the recent interest developing predictive models for molecular level control over the properties of polymers, it is desirable to determine all unique structural and morphological contributions to a scattering curve without assuming a model. However, by using a multi-scale approach (i.e. light and X-ray scattering spanning multiple size scales), it may be possible to build unique models for crystalline polymers. We will show that hybrids of statistical methods can be used to decouple scattering data into unique structural components. We will show how our approach can be used to discover analytical models and to develop a set of descriptors that can be used to predict scattering curves for several other polymers that share a similar structure or crystallization condition.   

Coarse-grained Molecular Dynamics Simulations and Analysis of Poly(L-lactic Acid) (PLLA) Melt

We present coarse-grained (CG) MD simulations of the melt structure of PLLA, a very useful biodegradable polymer. Our CGMD simulations consider entire repeat unit as a one bead and use IBI scheme. The CG potentials and forces are obtained after performing atomistic MD of 52 PLLA tetramer molecules and employing the probability distributions for the corresponding CG lengths, angles, dihedrals, and the radial distribution function. The initial energy-minimized samples are equilibrated for density in NPT ensemble, followed by structural equilibration. The simulated characteristic ratio (2.13) and density (1.123g/cc) at 450K are in excellent agreement with the expt. values$^{1}$ of 2.2 and 1.152g/cc at 413K. The equilibrated structures were analyzed for primitive path properties, tube diameter, $a_{pp}$, entanglement length, $N_{e}$, etc., using Kroger's Z-code$^{2}$. This yields $N_{e}$=61.8 and $a_{pp}$=55.7A$^{o}$ for longest chains (N=1000) and compare favorably with expt.$^{ }$values.$^{1}$, 55 and 47.7A$^{o}$ (413K). \newline \newline [1] Dorgan, J R., Janzen, J and Clayton, M.,\textit{J. Rheology},49,607,\textbf{2005} \newline (a) Kroger, M., \textit{Comput. Phys. Commun}., 168, 209, \textbf{2005}.   

Modeling the Thermodynamics of the Interaction of Nanoparticles with Cell Membranes

Interactions between nanoparticles and cell membranes may play a crucial role in determining the cytotoxicity of nanoparticles as well as their potential application as drug delivery vehicles or therapeutic agents. It has been shown that such interactions are often determined not by biochemical but by physico-chemical factors (e.g., nanoparticle size, hydrophobicity, and surface charge density). Here, we propose a mesoscale thermodynamic model describing the transitions in membrane morphology observed after exposure to various types of nanoparticles. Our simulations demonstrate under which conditions (determined by particle size and hydrophilic/hydrophobic interactions) the particles can adsorb into the membrane or compromise the membrane integrity to result in the formation of nano-sized holes. The model could be refined to include a more accurate description of various phospholipid membranes, and its results could be applied in the design of specific nanoparticles for various biomedical applications.   

Structure and dynamics of a model polymer nanocomposites

We investigate the structure and the dynamics of a model polymer nanocomposite (PNC) through molecular dynamics (MD) simulations in the canonical ensemble (NVT). Several computer experiments have been carried out at different temperatures for different Lennard-Jones well-depth and filler volume fraction. We studied the real space pair correlation functions and collective scattering structure factors of the PNC melt. This structural analysis has been compared with the previous theoretical and experimental works. The reinforcement of the nanocomposite have been investigated using stress-stress autocorrelation ($\sigma_{xy}(t)$) function for different temperatures. At lower temperatures, $\sigma_{xy}(t)$ shows strong reinforcement of the nanocomposite while at higher temperatures it relaxes quite fast. Diffusion of nanoparticles in the composite has been investigated and compared with earlier works. The effect of sizes and shapes of the nanoparticles has also been investigated in this work.   

Strategies for design of polymeric nanoparticles

Recently polymer nanoparticles have been synthesized using single chains as macromolecular precursors, providing unprecedented control of nanoparticle size and function. We present the results of molecular dynamics simulations which provide detailed insight into the formation kinetics of specific polymeric nanoparticles and which also predict design strategies for formation of interesting new targets. Nanoparticles are formed through chemical crosslinking which is possible when reactive species on the chain backbone are in close proximity. Since the chemical crosslinking is highly irreversible, nanoparticles formed in this way do not unfold on heating, in contrast to the familiar case of thermal denaturing of proteins. Synthesis of precursors with an alphabet of orthogonal crosslinkers provides a rich phase space for design of polymeric nanoparticles. For example, our simulations indicate that an alphabet of three orthogonal crosslinkers enables self-assembly of two-faced or Janus nanoparticles and a variety of other morphologies.