Marina Guenza

Viscoelastic relaxation of segment orientation in dilute polymer solutions

Time autocorrelation and memory functions for segment orientation are derived for a general diffusion model of a linear polymer chain in solution. Exact analytical results for the orientation and alignment memories P1(t), P2(t) (averages of the first and second order Legendre polynomial of the cosine of the angle of rotation of a segment) are obtained as a function of the time autocorrelation function M1(t) of the segment vector. These expressions significantly depart from the results for the diffusional rotation of a sphere: P1=M1, P2=M31.

Theoretical models for bridging timescales in polymer dynamics

The dynamics of macromolecules are characterized by the presence of several length scales and related timescales in which relevant phenomena take place. This defines the complex nature of the liquid and renders its theoretical treatment a difficult matter. The necessity of developing theoretical approaches that can describe in a comprehensive manner properties observed at many different length scales is a fundamental challenge in polymer physics. This review paper summarizes some key problems arising from this challenge and different approaches taken so far in attempting to solve them. Theoretical models play a pivotal role in building the infrastructure that allows one to model these multiscale properties. We present methods for coarse-graining the structure of soft-matter systems, which provide effective potentials that are input to multiscale simulations. We also present methods for coarse-graining the dynamics of macromolecules in dilute solutions and in the melt state. Although much progress has already been made, obtaining comprehensive theoretical tools that are efficient and reliable in predicting complex fluid dynamics across many timescales of interest still remains an open challenge.

Cytoskeletal-assisted dynamics of the mitochondrial reticulum in living cells

Subcellular organelle dynamics are strongly influenced by interactions with cytoskeletal filaments and their associated motor proteins, and lead to complex multiexponential relaxations that occur over a wide range of spatial and temporal scales. Here we report spatio-temporal measurements of the fluctuations of the mitochondrial reticulum in osteosarcoma cells by using Fourier imaging correlation spectroscopy, over time and distance scales of 10−2 to 103 s and 0.5–2.5 μm. We show that the method allows a more complete description of mitochondrial dynamics, through the time- and length-scale-dependent collective diffusion coefficient D(k,τ), than available by other means. Addition of either nocodazole to disrupt microtubules or cytochalasin D to disassemble microfilaments simplifies the intermediate scattering function. When both drugs are used, the reticulum morphology of mitochondria is retained even though the cytoskeletal elements have been de-polymerized. The dynamics of the organelle are then primarily diffusive and can be modeled as a collection of friction points interconnected by elastic springs. This study quantitatively characterizes organelle dynamics in terms of collective cytoskeletal interactions in living cells.

Cooperative dynamics in unentangled polymer fluids.

We present a generalized Langevin equation for the dynamics of interacting semiflexible polymer chains undergoing slow cooperative dynamics. The calculated Gaussian intermolecular center-of-mass and monomer potentials are in quantitative agreement with computer-simulation data. The experimentally observed short-time subdiffusive regime of the polymer mean-square displacement emerges from the competition between intra- and intermolecular mean-force potentials.

Cooperative Dynamics in Homopolymer Melts : A Comparison of Theoretical Predictions with Neutron Spin Echo Experiments

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.

An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale

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.

Thermodynamic consistency in variable-level coarse graining of polymeric liquids.

Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, n(b), of size N(b). The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of N(b)(1/4). This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length, highlighting the importance of the long, repulsive, potential tail for the model to correctly predict both structural and thermodynamic properties of the macromolecular liquid.

Analytical soft-core potentials for macromolecular fluids and mixtures

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.

Viscoelastic relaxation of segment orientation in dilute polymer solutions. II. Stiffness dependence of fluorescence depolarization

The memory functions for the orientation of a segment in any position on a linear chain are calculated for a diffusion Gaussian model in the optimized Rouse–Zimm approximation for semiflexible polymer models. The crossover from flexible to rod chains is described and expectations for fluorescence anisotropy, fluorescence quenching, and the mean orientational relaxation time are outlined and discussed.

Mapping of polymer melts onto liquids of soft-colloidal chains

Microscopic computer simulations of fluids of long polymers are greatly restricted by the limits of current computational power, and so course-grained descriptions, accurate on molecular length scales, are essential to extending the range of accessible systems. For some phenomena, particularly dynamical entanglement, descriptions that eliminate all internal degrees of freedom from the polymers are too drastic, as intermediate wavelength degrees of freedom are essential to the effect. Employing first-principles liquid-state theory, we have developed a course-grained model for the intermolecular structure of melts of long homopolymer chains that maps each chain of hard-sphere monomers onto a chain of connected soft colloids. All dependence on system parameters is analytically expressed so the results may be immediately applied to melts with different polymer and thermodynamic properties to calculate effective potentials between the soft colloids on the chains, which can then be used to perform molecular dynamics simulations. These simulations will be able to capture the large wavelength structure of the system at greatly reduced computational cost, while still retaining enough internal degrees of freedom explicitly to describe the phenomena that occur on length scales much larger than the monomeric units that comprise the chain, but shorter than the size of the molecule.