Origin of Internal Viscosity Effects in Flexible Polymers: A Comparative Neutron Spin-Echo and Light Scattering Study on Poly(dimethylsiloxane) and Polyisobutylene

Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations

Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.

Molecular Dynamics of Polyrotaxane in Solution Investigated by Quasi-Elastic Neutron Scattering and Molecular Dynamics Simulation: Sliding Motion of Rings on Polymer

In this study, we investigated the molecular dynamics of polyrotaxane (PR), composed of α-cyclodextrins (CDs) and a poly(ethylene glycol) (PEG) axial chain, in solution by means of quasi-elastic neutron scattering (QENS) measurements and full-atomistic molecular dynamics (MD) simulations. From QENS experiments, we estimated the diffusion coefficients of CD and PEG monomers in PR, which are in quantitative agreement with those obtained by MD simulations. By analyzing the simulation results, we succeeded, for the first time, in observing and quantifying the sliding motion of CD along a PEG chain. The diffusion coefficient for the sliding motion is almost 6 times lower than that of the translational diffusion of CD in PR at room temperature. The retardation of the sliding motion is caused by the energy barrier on PEG produced by molecular interactions between CD and PEG. We propose a simple equation to describe the diffusion coefficient of the sliding dynamics in PR by combining the Einstein-Stokes diffusion model and a one-dimensional jump diffusion model. This work provides a general strategy for the molecular designs to control the sliding motion in PR.

Applicability of mode-coupling theory to polyisobutylene: a molecular dynamics simulation study

The applicability of Mode Coupling Theory (MCT) to the glass-forming polymer polyisobutylene (PIB) has been explored by using fully atomistic molecular dynamics simulations. MCT predictions for the so-called asymptotic regime have been successfully tested on the dynamic structure factor and the self-correlation function of PIB main-chain carbons calculated from the simulated cell. The factorization theorem and the time-temperature superposition principle are satisfied. A consistent fitting procedure of the simulation data to the MCT asymptotic power-laws predicted for the α-relaxation regime has delivered the dynamic exponents of the theory-in particular, the exponent parameter λ-the critical non-ergodicity parameters, and the critical temperature T(c). The obtained values of λ and T(c) agree, within the uncertainties involved in both studies, with those deduced from depolarized light scattering experiments [A. Kisliuk et al., J. Polym. Sci. Part B: Polym. Phys. 38, 2785 (2000)]. Both, λ and T(c)/T(g) values found for PIB are unusually large with respect to those commonly obtained in low molecular weight systems. Moreover, the high T(c)/T(g) value is compatible with a certain correlation of this parameter with the fragility in Angell's classification. Conversely, the value of λ is close to that reported for real polymers, simulated "realistic" polymers and simple polymer models with intramolecular barriers. In the framework of the MCT, such finding should be the signature of two different mechanisms for the glass-transition in real polymers: intermolecular packing and intramolecular barriers combined with chain connectivity.

The thermodynamics of polymer mixing and compression in the semidilute regime

Polymers present a fascinating range of mechanical properties in the extension, compression, and flow of soft condensed matter. Entropy determines the physics of the elastic material behavior of polymeric systems in deformation. Classical models of polymer dynamics have assumed chain entanglement and resulting reptation in concentrated polymer solutions. Here, we present a thermodynamic treatment of interacting chains in solution with increasing concentration from the dilute to concentrated regimes. As the polymer chain concentration increases above the critical overlap, the chains must either compress or overlap and entangle, resulting in a decrease in chain configurational entropy. The free energy of chain entanglement is shown to be less favored than compression at concentrations above the critical overlap. Elastic forces act on the chains to reduce the dimensions to the ideal random walk size with increasing concentration. At significantly higher concentrations, the free energies reach an asymptote where chain compression and entanglement are simultaneously possible. Entanglement and reptation are shown to be statistically improbable in the semidilute regime, and it is concluded that the compression of polymer chains is favored at semidilute concentrations.

Characterization of the "simple-liquid" state in a polymeric system: coherent and incoherent scattering functions

By means of time-of-flight neutron scattering, we have characterized the dynamic structure factor and the hydrogen motions of polyethylene above its melting point. As signatures of simple-liquid dynamics, we observe that (i) in the explored dynamic window, the intermediate scattering functions display a single-step decay, without reminiscence of cage effects, and (ii) the structural relaxation as observed at the intermolecular structure factor peak shows a weak temperature dependence, indicating a low degree of interchain cooperativity. However, stretched functional forms are observed for all length scales and temperatures investigated. An apparent direct crossover from the microscopic regime to Rouse-like dynamics suggests an essential role of connectivity in the observed stretching. Finally, while at momentum-transfer values above the structure factor peak the relation between coherent and incoherent characteristic times is reasonably described by the de Gennes narrowing, at larger length scales it is not reproduced by any existing approach.

Static Rouse modes and related quantities: corrections to chain ideality in polymer melts

Following the Flory ideality hypothesis intrachain and interchain excluded-volume interactions are supposed to compensate each other in dense polymer systems. Multichain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume ("hard monomers") to no excluded volume ("phantom chains"). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.

Sliding friction between polymer surfaces: A molecular interpretation

For two contacting rigid bodies, the friction force F is proportional to the normal load and independent of the macroscopic contact area and relative velocity V (Amonton's law). With two mutually sliding polymer samples, the surface irregularities transmit deformation to the underlying material. Energy loss along the deformation cycles is responsible for the friction force, which now appears to depend strongly on V [see, e.g., N. Maeda et al., Science 297, 379 (2002)]. We base our theoretical interpretation on the assumption that polymer chains are mainly subjected to oscillatory "reptation" along their "tubes." At high deformation frequencies-i.e., with a large sliding velocity V-the internal viscosity due to the rotational energy barriers around chain bonds hinders intramolecular mobility. As a result, energy dissipation and the correlated friction force strongly diminish at large V. Derived from a linear differential equation for chain dynamics, our results are basically consistent with the experimental data by Maeda et al. [Science 297, 379 (2002)] on modified polystyrene. Although the bulk polymer is below T(g), we regard the first few chain layers below the surface to be in the liquid state. In particular, the observed maximum of F vs V is consistent with physically reasonable values of the molecular parameters. As a general result, the ratio FV is a steadily decreasing function of V, tending to V(-2) for large velocities. We evaluate a much smaller friction for a cross-linked polymer under the assumption that the junctions are effectively immobile, also in agreement with the experimental results of Maeda et al. [Science 297, 379 (2002)].

Collective motion in poly(ethylene oxide)/poly(methylmethacrylate) blends

We present neutron spin echo and structural measurements on a perdeuterated miscible polymer blend: poly(ethylene oxide)[PEO]/poly(methyl methacrylate)[PMMA], characterized by a large difference in component glass transition temperatures and minimal interactions. The measurements cover the q range 0.35 to 1.66 A(-1) and the temperature range Tg -75 to Tg +89 K, where Tg is the blend glass transition. The spectra, obtained directly in the time domain, are very broad with stretching parameters beta approximately 0.30. The relaxation times vary considerably over the spatial range considered however at none of the q values do we see two distinct relaxation times. At small spatial scales relaxations are still detectable at temperatures far below Tg. The temperature dependence of these relaxation times strongly resembles the beta-relaxation process observed in pure PMMA.

Dynamics of poly(ethylene oxide) in a blend with poly(methyl methacrylate): a quasielastic neutron scattering and molecular dynamics simulations study

In this paper, we have addressed the question of the dynamic miscibility in a blend characterized by very different glass-transition temperatures, Tg, for the components: poly(ethylene oxide) and poly(methyl methacrylate) (PEO/PMMA). The combination of quasielastic neutron scattering with isotopic labeling and fully atomistic molecular dynamics simulations has allowed us to selectively investigate the dynamics of the two components in the picosecond-10 nanoseconds scale at temperatures close and above the Tg of the blend. The main focus was on the PEO component, i.e., that of the lowest Tg, but first we have characterized the dynamics of the other component in the blend and of the pure PEO homopolymer as reference. In the region investigated, the dynamics of PMMA in the blend is strongly affected by the alpha-methyl rotation; an additional process detected in the experimental window 65 K above the blend-Tg can be identified as the merged alphabeta process of this component that shows strong deviations from Gaussian behavior. On the other hand, pure PEO displays entropy driven dynamics up to very large momentum transfers. Such kind of motion seems to freeze when the PEO chains are in the blend. There, we have directly observed a very heterogeneous and moreover confined dynamics for the PEO component. The presence of the hardly moving PMMA matrix leads to the creation of little pockets of mobility where PEO can move. The characteristic size of such confined islands of mobility might be estimated to be of approximately 1 nm. These findings are corroborated by the simulation study, which has been an essential support and guide in our data analysis procedure.

Polymer nanodroplets forming liquid bridges in chemically structured slit pores: A computer simulation

Using a coarse-grained bead-spring model of flexible polymer chains, the structure of a polymeric nanodroplet adsorbed on a chemically decorated flat wall is investigated by means of molecular dynamics simulation. We consider sessile drops on a lyophilic (attractive for the monomers) region of circular shape with radius R(D) while the remaining part of the substrate is lyophobic. The variation of the droplet shape, including its contact angle, with R(D) is studied, and the density profiles across these droplets also are obtained. In addition, the interaction of droplets adsorbed on two walls forming a slit pore with two lyophilic circular regions just opposite of one another is investigated, paying attention to the formation of a liquid bridge between both walls. A central result of our study is the measurement of the force between the two substrate walls at varying wall separation as well as the kinetics of droplet merging. Our results are compared to various phenomenological theories developed for liquid droplets of mesoscopic rather than nanoscopic size.

New interpretation of local dynamics of poly(dimethyl siloxane) observed by quasielastic neutron scattering

Synthetic and natural polymers have complex dynamic behavior with distinct motions taking place on a wide range of time and length scales. For poly(dimethyl siloxane) we show that, at temperatures above the melting point, the reorientation of the CH3 groups provides a non-negligible contribution to the incoherent dynamic structure factor. Analysis of the quasielastic neutron scattering data is carried out using a model function that includes fast rotational motion of the CH3 groups and local conformational transitions between isomeric states. By using this model, detailed comparison between experimental data and theoretical predictions at distances where deviations from the traditional Rouse model are expected becomes possible.

Effect of internal friction on biofilament dynamics

We consider biofilaments-flexible multimolecule structures common in cell biology-and show how "internal" friction associated with either conformational fluctuations or with fluid flow through narrow pores inside the filaments can dominate the external hydrodynamic friction usually considered to be the main energy dissipation process. The signature of this is wave-number-independent relaxation time of bending fluctuations. Preliminary experimental data for bending fluctuations of single folded (mitotic) chromosomes display these dynamics.

Intermediate length scale dynamics of polyisobutylene

We report on a neutron spin echo investigation of the intermediate scale dynamics of polyisobutylene studying both the self-motion and the collective motion. The momentum transfer (Q) dependences of the self-correlation times are found to follow a Q(-2/beta) law in agreement with the picture of Gaussian dynamics. In the full Q range of observation, their temperature dependence is weaker than the rheological shift factor. The same is true for the stress relaxation time as seen in sound wave absorption. The collective times show both temperature dependences; at the structure factor peak, they follow the temperature dependence of the viscosity, but below the peak, one finds the stress relaxation behavior.

Dynamic regimes and correlated structural dynamics in native and denatured alpha-lactalbumin

Understanding the mechanisms of protein folding requires knowledge of both the energy landscape and the structural dynamics of a protein. We report a neutron-scattering study of the nanosecond and picosecond dynamics of native and the denatured alpha-lactalbumin. The quasielastic scattering intensity shows that there are alpha-helical structure and tertiary-like side-chain interactions fluctuating on sub-nanosecond time-scales under extremely denaturing conditions and even in the absence of disulfide bonds. Based on the length-scale dependence of the decay rate of the measured correlation functions, the nanosecond dynamics of the native and the variously denatured proteins have three dynamic regimes. When 0.05<Q<0.5 A(-1) (where the scattering vector, Q, is inversely proportional to the length-scale), the decay rate, Gamma, shows a power law relationship, Gamma proportional to Q(2.42+/-0.08), that is analogous to the dynamic behavior of a random coil. However, when 0.5<Q<1.0 A(-1), the decay rate exhibits a Gamma proportional to Q(1.0+/-0.2) relationship. The effective diffusion constant of the protein decreases with increasing Q, a striking dynamic behavior that is not found in any chain-like macromolecule. We suggest that this unusual dynamics is due to the presence of a strongly attractive force and collective conformational fluctuations in both the native and the denatured states of the protein. Above Q>1.0 A(-1) is a regime that displays the local dynamic behavior of individual residues, Gamma proportional to Q(1.8+/-0.3). The picosecond time-scale dynamics shows that the potential barrier to side-chain proton jump motion is reduced in the molten globule and in the denatured proteins when compared to that of the native protein. Our results provide a dynamic view of the native-like topology established in the early stages of protein folding.