Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

Looking inside the entanglement “tube” using molecular dynamics simulations

For 30 years, the dynamics of entangled polymers have been explained using the phenomenological “tube” model, where the “tube” represents the confining effects of surrounding chains, but the tube properties, such as its length and diameter, could only be inferred indirectly by fitting the tube model to rheological data. Now, however, molecular simulations are allowing these properties to be directly computed. The computational advances in molecular dynamics and related methods that have made this possible are here reviewed. In addition, it is discussed how new findings, such as an apparent time dependence of the tube diameter and direct observation of “hopping” of branch points along the tube, are helping to refine the tube model. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3240–3248, 2007     

Local Transient Jamming in Stress Relaxation of Bulk Amorphous Polymers

Bulk amorphous polymers become stretched and parallel-aligned under loading stress,and their intermolecular cooperation slows down the subsequent stress relaxation process.By means of dynamic Monte Carlo simulations,we employed the linear viscoelastic Maxwell model for stress relaxation of single polymers and investigated their intermolecular cooperation in the stress relaxation process of stretched and parallel-aligned bulk amorphous polymers.We carried out thermal fluctuation analysis on the reproduced Debye relaxation and Arrhenius fluid behaviors of bulk polymers.We found a transient state with stretch-coil coexistence among polymers in the stress relaxation process.Further structure analysis revealed a scenario of local jamming at the transient state,resulting in an entropy barrier for stretch-coil transition of partial polymers.The microscopic mechanism of intermolecular cooperation appears as unique to polymer stress relaxation,which interprets the hydrodynamic interactions as one of essential factors raising a high viscosity in bulk amorphous polymers.Our simulations set up a platform of molecular modeling in the study of polymer stress relaxation,which brought new insights into polymer dynamics and the related mechanical/rheological properties.     

Anatomy of an energy transfer event in a liquid: the high-energy rotational relaxation of OH in solution

The photochemical generation of highly rotationally excited diatomics affords us an intriguing way to study energy relaxation processes in solution. Because excited products involve only a single intramolecular degree of freedom and because their relaxations can lie well outside of the linear-response regime, it may be possible to infer detailed molecular mechanisms for these processes just from transient absorption measurements. In this paper we describe a theoretical study of the rotational relaxation of a new candidate for such measurements, OH radicals. Much as we saw in our previous studies of rotationally hot CN radicals, molecular dynamics simulations of OH relaxation predict that the rotational motion should trigger a structural change in the surrounding solvent, decreasing the rotational friction and allowing the OH to rotate coherently for a dozen rotational periods. The mass distribution in OH, however, gives it a much faster rotational period and significantly different kinematics. These differences end up making it possible to identify the separate molecular events taking place at the onset of the relaxation (an unusual occurrence for a liquid-state process) and to weigh in on what collisions are really like in a liquid.     

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.     

Modeling velocity autocorrelation functions for confined fluids using gamma distributions

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.     

Pressure calculation in hybrid particle-field simulations

In the framework of a recently developed scheme for a hybrid particle-field simulation techniques where self-consistent field (SCF) theory and particle models (molecular dynamics) are combined [J. Chem. Phys. 130, 214106 (2009)], we developed a general formulation for the calculation of instantaneous pressure and stress tensor. The expressions have been derived from statistical mechanical definition of the pressure starting from the expression for the free energy functional in the SCF theory. An implementation of the derived formulation suitable for hybrid particle-field molecular dynamics-self-consistent field simulations is described. A series of test simulations on model systems are reported comparing the calculated pressure with those obtained from standard molecular dynamics simulations based on pair potentials.     

Externally steered relaxation of tight polyethylene tangles with different initial knot topologies

Using single-molecule manipulations or sudden changes in solvent, it is possible to introduce knotted-loops (or “tangles”) in open linear polymers. It is still unclear how these tangles relax, and in particular, whether it is possible to trap knots locally by adopting very compact loop conformations. Here, we use steered molecular dynamics simulations to study a highly stressed polyethylene chain with three different knot topologies. Starting from stressed configurations, unknotting events are recognized as leading to sudden transitions in overcrossing number. By means of a soft compressing external force, we show that: (1) tangles with different complexities can be unknotted and (2) the potential energy decreases in a way that suggests that a similar relaxation mechanism might be at work for all the tested loop topologies. Contribution to the Serafín Fraga Memorial Issue.     

Energetics and dynamics in MbCN: CN--vibrational relaxation from molecular dynamics simulations

The dynamics of the cyanide anion bound to sperm-whale myoglobin is investigated using atomistic simulations. With density-functional theory, a 2D potential energy surface for the cyanide-heme complex is calculated. Two deep minima with a stabilization energy of approximately 50 kcal/mol corresponding to two different binding orientations (Fe-CN and Fe-NC) of the ligand are found. The Fe-CN conformation is favored over Fe-NC by several kcal/mol. Mixed quantum mechanics/molecular mechanics calculations show that the binding orientation affects the bond strength of the ligand, with a significantly different bond length and a 25 cm-1 shift in the fundamental CN-frequency. For the molecular dynamics (MD) simulations, a 3-center fluctuating charge model for the Fe-CN unit is developed that captures polarization and ligand-metal charge transfer. Stability arguments based on the energetics around the active site and the CN- frequency shifts suggest that the Fe-CN conformation with epsilon-protonation of His epsilon 64 are most likely, which is in agreement with experiment. Both equilibrium and nonequilibrium MD simulations are carried out to investigate the relaxation time scale and possible relaxation pathways in bound MbCN. The nonequilibrium MD simulations with a vibrationally excited ligand reveal that vibrational relaxation takes place on a time scale of hundreds of picoseconds within the active site. This finding supports the hypothesis that the experimentally observed relaxation rate (3.6 ps) reflects the repopulation of the electronic ground state.     

Coupling between lysozyme and glycerol dynamics: microscopic insights from molecular-dynamics simulations

We explore possible molecular mechanisms behind the coupling of protein and solvent dynamics using atomistic molecular-dynamics simulations. For this purpose, we analyze the model protein lysozyme in glycerol, a well-known protein-preserving agent. We find that the dynamics of the hydrogen bond network between the solvent molecules in the first shell and the surface residues of the protein controls the structural relaxation (dynamics) of the whole protein. Specifically, we find a power-law relationship between the relaxation time of the aforementioned hydrogen bond network and the structural relaxation time of the protein obtained from the incoherent intermediate scattering function. We demonstrate that the relationship between the dynamics of the hydrogen bonds and the dynamics of the protein appears also in the dynamic transition temperature of the protein. A study of the dynamics of glycerol as a function of the distance from the surface of the protein indicates that the viscosity seen by the protein is not the one of the bulk solvent. The presence of the protein suppresses the dynamics of the surrounding solvent. This implies that the protein sees an effective viscosity higher than the one of the bulk solvent. We also found significant differences in the dynamics of surface and core residues of the protein. The former is found to follow the dynamics of the solvent more closely than the latter. These results allowed us to propose a molecular mechanism for the coupling of the solvent-protein dynamics.     

Transient diffusion in a tube with dead ends

A particle diffusing in a tube with dead ends, from time to time enters a dead end, spends some time in the dead end, and then comes back to the tube. As a result, the particle spends in the tube only a part of the entire observation time that leads to slowdown of its diffusion along the tube. We study the transient diffusion in a tube with periodic identical dead ends formed by cavities of volume V(cav) connected to the tube by cylindrical channels of length L and radius a, which is assumed to be much smaller than the tube radius R and the distance l between neighboring dead ends. Assuming that the particle initial position is uniformly distributed over the tube, we analyze the monotonic decrease of the particle diffusion coefficient D(t) from its initial value D(0)=D, which characterizes diffusion in the tube without dead ends, to its asymptotic long-time value D(infinity)=D(eff)相似文献   

Finite system size effects in the interfacial dynamics of binary liquid films

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.     

CF3CH3 --> HF + CF2CH2: a non-RRKM reaction?

The experimental shock tube data recently reported by Kiefer et al. [J. Phys. Chem. A 2004, 108, 2443-2450] for the title reaction at temperatures between 1600 and 2400 K have been compared to master equation simulations using three models: (a) standard RRKM theory, (b) RRKM theory modified by local random matrix theory, which introduces dynamical corrections arising from slow intramolecular vibrational energy randomization, and (c) an ad hoc empirical non-RRKM model. Only the third model provides a good fit of the Kiefer et al. unimolecular reaction rate data. In separate simulations, all three models accurately reproduce the experimental 300 K chemical activation data of Marcoux and Setser [J. Phys. Chem. 1978, 82, 97-108] when the energy transfer parameters are freely varied to fit the data. When experimental energy transfer parameters for a geometrical isomer (1,1,2-trifluoroethane) are used, the standard RRKM model fits the chemical activation data better than the other models, but if energy transfer in the 1,1,1-trifluoroethane is significantly reduced in comparison to the 1,1,2 isomer, then the empirical ad hoc non-RRKM model also gives a good fit. While the ad hoc empirical non-RRKM model can be made to fit the data, it is not based on theory, and we argue that it is physically unrealistic. We also show that the master equation simulations can mimic the Kiefer et al. vibrational relaxation data, which was the first shock tube observation of double-exponential relaxation. We conclude that, until more data on the trifluoroethanes become available, the current evidence is insufficient to decide with confidence whether non-RRKM effects are important in this reaction, or whether the Kiefer et al. data can be explained in some other way.     

Communication: effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids

A microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformation-assisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.     

Simulations of the dynamics of thermal undulations in lipid bilayers in the tensionless state and under stress

The relaxation processes of height undulations and density fluctuations in a membrane have been studied by molecular dynamics simulations of a coarse grained amphiphilic bilayer model. We observe a double exponential decay in their time correlations, with relaxation rates in good quantitative agreement with the theory by Seifert and Langer [Europhys. Lett. 23, 71 (1993)]. Intermonolayer friction due to slippage between the two monolayers is shown to be the dominant dissipative mechanism at the high wave numbers, q>10 mum(-1), typically encountered in computer simulations. We briefly discuss the ramifications of the slow undulatory relaxation process for the calculation of bending rigidities from the static undulation structure factors. The relaxation rates are sensitive to the surface tension, and at high elongations an oscillatory contribution is observed in the time correlation of the undulations.     

Modeling of ionic relaxation around a biomembrane disk

A simplified Brownian dynamics model and the corresponding software implementation have been developed for the simulation of electrolyte dynamics on the mesoscopic scale. In addition to direct control simulations, the model system has been verified by a quantitative comparison with the Debye-Hückel theory. As a first application, the model was used to simulate ionic relaxation processes following abrupt intramembrane charge rearrangements in the case of a disk shaped membrane. In addition to its general implications, the obtained properties of the relaxation kinetics confirm the assumptions of the theory of the so-called suspension method, a technique capable of tracing molecular charge motions of membrane proteins in three dimensions.     

Analysis of uncertainties in polymer viscoelastic properties obtained from equilibrium computer simulations

We critically evaluate the uncertainties in the stress autocorrelation function obtained from equilibrium molecular dynamics simulation of model polymer melts. This quantity is central to evaluating transport properties, e.g., the complex modulus and the viscosity. In contrast to the intuitive expectation that simulations have to be run five to six orders of magnitude longer than the chain relaxation time to reduce uncertainties to acceptable levels, our analysis shows that the majority of the uncertainty is associated with rapidly oscillating bonded interactions. These fluctuations occur on time scales which are approximately 10(4) times shorter than the relaxation time of a chain of length 80. Consequently, the effects of these oscillations on the stress autocorrelation function can be dramatically reduced by (i) conducting long simulations (typically 10(6) times longer than the bond relaxation times or only 10(2) chain relaxation times) and (ii) by performing running averages with time windows whose time scales are much longer than these oscillations. Conducting such long simulations also allows for the accurate determination of the melt viscosity and the low-frequency complex modulus, but performing running averages do not impact these quantities since they are time integrals of the stress autocorrelation function.     

Comparison of aqueous molecular dynamics with NMR relaxation and residual dipolar couplings favors internal motion in a mannose oligosaccharide.

An investigation has been performed to assess how aqueous dynamical simulations of flexible molecules can be compared against NMR data. The methodology compares state-of-the-art NMR data (residual dipolar coupling, NOESY, and (13)C relaxation) to molecular dynamics simulations in water over several nanoseconds. In contrast to many previous applications of residual dipolar coupling in structure investigations of biomolecules, the approach described here uses molecular dynamics simulations to provide a dynamic representation of the molecule. A mannose pentasaccharide, alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->3)-alpha-D-Manp-(1-->2)-D-Manp, was chosen as the model compound for this study. The presence of alpha-linked mannan is common to many glycopeptides, and therefore an understanding of the structure and the dynamics of this molecule is of both chemical and biological importance. This paper sets out to address the following questions. (1) Are the single structures which have been used to interpret residual dipolar couplings a useful representation of this molecule? (2) If dynamic flexibility is included in a representation of the molecule, can relaxation and residual dipolar coupling data then be simultaneously satisfied? (3) Do aqueous molecular dynamics simulations provide a reasonable representation of the dynamics present in the molecule and its interaction with water? In summary, two aqueous molecular dynamics simulations, each of 20 ns, were computed. They were started from two distant conformations and both converged to one flexible ensemble. The measured residual dipolar couplings were in agreement with predictions made by averaging the whole ensemble and from a specific single structure selected from the ensemble. However, the inclusion of internal motion was necessary to rationalize the relaxation data. Therefore, it is proposed that although residual dipolar couplings can be interpreted as a single-structure, this may not be a correct interpretation of molecular conformation in light of other experimental data. Second, the methodology described here shows that the ensembles from aqueous molecular dynamics can be effectively tested against experimental data sets. In the simulation, significant conformational motion was observed at each of the linkages, and no evidence for intramolecular hydrogen bonds at either alpha(1-->2) or alpha(1-->3) linkages was found. This is in contrast to simulations of other linkages, such as beta(1-->4), which are often predicted to maintain intramolecular hydrogen bonds and are coincidentally predicted to have less conformational freedom in solution.