Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

Statics and dynamics of dense polymer systems studied by monte carlo simulation

Monte Carlo simulations of coarse–grained models of macromolecules offer a unique tool to study the interplay between coil conformations, thermodynamic properties, and chain configurational relaxation and diffusion. Two examples are discussed where the chain conformation strongly differs from a gaussian coil: (i) collapsed chains in a bad solvent, where anomalous diffusion occurs in the Rouse limit and the relaxation time increases at least with the third power of chain length. (ii) Expulsion of a chain from a semidilute polymer brush. The initially stretched chain contracts to a gaussian coil and the center of mass moves outward with constant velocity until it reaches the region of the “last blob” where crossover to diffusive behavior occurs.     

Relaxation of a semiflexible grafted polymer

The relaxation of single grafted semiflexible chains freely rotating around the grafting point is investigated by means of two dimensional computer simulations and scaling arguments. Both free chains and chains surrounded by topological obstacles are considered. We compute the autocorrelation of the end-to-end vector for the whole chain and for terminal sections of various lengths. Our results are relevant for the relaxation of star polymers with stiff arms or branched semiflexible polymers moving in an array of obstacles.     

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.     

Single-chain dynamics in a semidilute polymer solution under steady shear

We use Brownian dynamics computer simulations to investigate single-chain dynamics in a semidilute polymer solution undergoing a steady, uniform shear flow. In the presence of the shear flow, the system used in the present study exhibits anisotropic structure factors, often referred to as butterfly patterns, which rotate with increasing shear rate [P. P. Jose and G. Szamel, J. Chem. Phys. 127, 114905 (2007)]. The rotation of these patterns correlates with shear thinning of the solution. In order to elucidate the microscopic origin of this behavior, we have investigated the change in the single-chain dynamics in the solution: We have focused on the relaxation of the end-to-end vector, the Rouse modes, and the radius of gyration tensor. In equilibrium and for small shear rates, these quantities show double exponential relaxation. With increasing shear rate, they show oscillatory relaxation, which hints at the tumbling motion of the chain. In the high shear rate regime, the frequency of the oscillations of the end-to-end vector autocorrelation function shows a power law dependence on the shear rate. We have compared the single-chain dynamics in the semidilute solution with that in a dilute solution. An analysis of the instantaneous values of the radius of gyration tensor, the end-to-end distance, and the normal stress along the system's trajectory reveals a synchronization of the fluctuations of these quantities.     

Dielectric relaxation of polymer networks built from macromolecules with dipole moment directed along the end-to-end chain vector

The dielectric relaxation properties are considered for polymer networks built from polar macromolecules with the dipole moment directed along the end-to-end chain vector. The viscoeleastic cubic model of a regular network is used. The fixed average volume of a polymer network is ensured by the effective internal pressure. The dynamic models of polymer networks with external and interchain friction are studied. Two cases are considered: (1) polar chains cross-linked in a network at their ends, and (2) a densely cross-linked network with many network junctions per polar chain. The expressions for the autocorrelation functions of the total dipole moment of a network, which determine the dielectric susceptibility, are calculated. The relaxation spectrum of the autocorrelation function consists of two regions: the high-frequency relaxation spectrum of a chain fragment between two neighbouring junctions (intrachain relaxation spectrum) and the lowfrequency interchain relaxation spectrum. The interchain relaxation spectrum is determined by cooperative motions of chains which form a network. The characteristic time of this spectrum for networks of type (1) is the relaxation time of a chain between junctions τ_min. For networks of type (2) a second time scale τ₁ exists, which corresponds to motions inside the volume occupied by a single long polar chain included in a network. It leads to different time behaviour of the autocorrelation functions for both network models. The existence of only interchain friction in the network model leads to a cut-off of the relaxation spectrum at the time τ_max depending on the volume of viscous interchain interactions.     

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

A detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two-bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non-Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation-like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end-to-end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006     

Dynamics of Branched Polymers in Random Layered Flows with Intramolecular Hydrodynamic Coupling: Star and Dendrimer

The authors develop a theoretical formalism to incorporate the effect of intramolecular hydrodynamic interactions (HIs) on the dynamics of flexible branched polymer in the presence of random layered flows. The influence of HIs on the anomalous diffusive behavior of branched polymers is illustrated through the preaveraged Oseen tensor approach. Although the formalism is valid for polymer structures with arbitrary topology, particular attention is paid here to the study of stars and dendrimers. The macromolecular property that is evaluated is the average square displacement (ASD) of drift center of the polymer. Qualitatively, our analysis highlights two anomalous power‐law regimes, viz. subdiffusive (intermediate‐time polymer stretching and flow induced diffusion) and superdiffusive (long‐time flow induced diffusion). The time dependence of the ASD in the presence of HIs within the preaveraging approximation reveals the anomalous long‐time dynamics which is governed by scaling behavior, t ^{2 − α/2}. The introduction of HIs in random flows speeds up the dynamics resulting in the shorter crossover time (from subdiffusive to superdiffusive regime) with enhanced magnitude of ASD compared to the free‐draining limit.

     

Dynamics of Bond‐Fluctuation Model Chains in Good and Theta Solvents

The dynamic Monte Carlo algorithm is employed to explore the dynamics of flexible linear chains. The chains are represented by the bond‐fluctuation model with and without attractions between non‐bonded units placed at close distances. This mimics the behavior of real chains in the good and poorer solvents. We obtain the chain sizes, diffusion coefficients, Rouse modes, and their relaxation times. We also evaluate the time correlation function of the end‐to‐end vector at different concentrations. Subsequently, we compare the dependence of the simulation results on chain length, solvent quality, concentration, and mode order with the corresponding theoretical predictions. We observe a retardation of diffusion for non‐dilute systems close to the theta state. This retardation is too high to be exclusively attributed to the increase of global friction and can be caused by temporary adherence of the chains to transient clusters.     

A fluorescence polarization study of the effect of matrix molecular weight on the relaxation of a labeled molecule in a stretched polymer melt

Fluorescence polarization has been used to measure the orientation during stretching of a polystyrene chain embedded in a matrix of narrow-dispersion polystyrene chains of a different molecular weight and labeled by an anthracene group covalently bound at the middle of a chain. Strong coupling between the relaxation of the labeled chain and the matrix chains is evidenced, the orientation of the labeled chain being partially governed by the molecular weight of the matrix. This behavior is interpreted qualitatively on the basis of a molecular model showing that the relaxation of a polymer chain is strongly affected by the entanglements acting on the chain, the number of which is also related to the motion of the surroundings. Good agreement is found between experimental data and the behavior predicted by the model.     

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time‐dependent Ginzburg‐Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz‐Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order‐parameter fluctuations is observed. The growth behavior of domains was altered, and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench‐depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz‐Slyozov law. In addition, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.     

Nuclear magnetic resonance relaxation studies of polyacrylamide solution

 The cohesive interaction among polymer chains in a polyacrylamide (PAAm)–D₂O solution has been studied by NMR relaxation. The NMR relaxation times of PAAm in the good solvent D₂O were measured at different temperatures. The results show that the solution system has a high local viscosity and that its relaxation characteristic is soft-solid-like. The temperature dependence of the relaxation behavior of the solution is obviously different from that of ordinary polymer solutions. The difference lies in the relaxation behavior of the methylene protons in the main chain of PAAm, as shown by analyzing the relaxation process with single exponential and biexponential decays. As the temperature increases, the solvation is weakened, leading polymer chains to form curling coils, thus hindering the movement of the methylene protons among the main chains. It can be expected from the existence of 80% fast-relaxing protons that there are a zhigh number of entanglements among the polymer chains in PAAm solution. The information about entanglements among the polymer chains can be deduced from the biexponential dependence of the spin–spin relaxation on the concentration of the polymer solutions. Received: 14 April 1999/Accepted in revised form: 12 October 1999     

Stochastic entangled chain dynamics of dense polymer solutions

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.     

Computer simulation studies of the influence of side alkyl chain on glass transition behavior of carbazole trimer

In this work,all-atom molecular dynamics simulations were employed to study the influence of the side alkyl chain on glass transition behavior of several carbazole trimers(CT) in a temperature range from 423 to 183 K.The glass transition temperatures were obtained from the break in the slope of the volume-temperature curves and found to agree with the experimental values.The short time dynamics of four CT molecules were probed by usingvelocity autocorrelation functions and mean-square displacements.The current studies showed that the dynamics of CT systems can be easily interpreted through the cage effect.Furthermore,the investigation of the torsional autocorrelation function and P_(2-state)/P_(3-state) functions showed that the rotational barriers of side chains can slow down the conformational relaxation and lead to stronger temperature dependence of conformational relaxation.The relaxation time,characteristic time of P_(2-state)(t) and P_(3-state)(t) functions were all found to have Arrhenius-type temperature dependence.     

Molecular dynamics investigation of dynamical properties of phosphatidylethanolamine lipid bilayers

We describe the dynamic behavior of a 1-stearoyl-2-oleoyl-phosphatidylethanolamine (SOPE) bilayer from a 20 ns molecular dynamics simulation. The dynamics of individual molecules are characterized in terms of (2)H spin-lattice relaxation rates, nuclear overhauser enhancement spectroscopy (NOESY) cross-relaxation rates, and lateral diffusion coefficients. Additionally, we describe the dynamics of hydrogen bonding through an analysis of hydrogen bond lifetimes and the time evolution of clusters of hydrogen bonded lipids. The simulated trajectory is shown to be consistent with experimental measures of internal, intermolecular, and diffusive motion. Consistent with our analysis of SOPE structure in the companion paper, we see hydrogen bonding dominating the dynamics of the interface region. Comparison of (2)H T(1) relaxation rates for chain methylene segments in phosphatidylcholine and phosphatidylethanolamine bilayers indicates that slower motion resulting from hydrogen bonding extends at least three carbons into the hydrophobic core. NOESY cross-relaxation rates compare well with experimental values, indicating the observed hydrogen bonding dynamics are realistic. Calculated lateral diffusion rates (4 +/ -1 x 10(-8) cm(2)s) are comparable, though somewhat lower than, those determined by pulsed field gradient NMR methods.     

Polymer Chain Dynamics Predicted by n-Renormalized Rouse Models: Numerical Studies

Features of the renormalized and twice renormalized Rouse models were examined numerically. Based on numerical evaluations of the generalized Langevin equation in renormalization approaches, nonexponential normal mode autocorrelation functions were derived, that can be described over two orders of magnitude by stretched exponential functions. The mode number dependence of the stretching parameter was evaluated. The consequences of the nonexponential correlation functions on dynamical properties are discussed. As a basis for predictions for the behavior of diffusion and spin-lattice relaxation dispersion, the time dependence of the mean-squared segment displacement and of the autocorrelation function of the segment tangential vector, respectively, were obtained taking into account finite chain lengths.     

The ultrafast dynamics of hydrogen-bonded liquids: molecular structure-dependent occurrence of normal arrhenius or fractional Stokes-Einstein-Debye rotational diffusive relaxation

The ultrafast rotational-diffusive dynamics of the peptide linkage model compounds N-methylacetamide (NMA), acetamide (Ac), and N,N-dimethylacetamide (DMA) have been studied as a function of temperature using optically heterodyne-detected optical Kerr effect (OHD-OKE) spectroscopy. Both NMA and Ac exhibit a non-Arrhenius temperature dependence of the rotational diffusive relaxation time. By contrast, the non-hydrogen-bonding DMA exhibits normal hydrodynamic behavior. The unusual dynamics of NMA and Ac are attributed to the decoupling of single-molecule rotational diffusive relaxation from the shear viscosity via a transition between stick and slip boundary conditions, which arises from local heterogeneity in the liquid due to the formation of hydrogen-bonded chains or clusters. This provides new insight into the structure and dynamics of an important peptide model compound and the first instance of such a phenomenon in a room-temperature liquid. The OHD-OKE responses of carboxylic acids acetic acid (AcOH) and dichloroacetic acid (DCA) are also reported. These, along with the terahertz Raman spectra, show no evidence of the effects observed in amide systems, but display trends consistent with the presence of an equilibrium between the linear and cyclic dimer structures at all temperatures and moderate-to-high mole fractions in aqueous solution. This equilibrium manifests itself as hydrodynamic behavior in the liquid phase.     

Modelling of solid polymers in chemical detail - gases in amorphous polymers

The diffusion of gases in dense polymers, above and below the glass-transition temperature, is described with a new Transition State Theory model that is based on the concept that the dynamics of small molecules dissolved in dense polymers is separated from the structural relaxation of the dense polymers. The model is used to study the dynamics of rare gases dissolved in atomistic micro-structures of four polymers at 300 K: poly(dimethylsiloxane), poly(isobutylene), atactic poly(vinylchloride) and the polycarbonate of 4,4′-isopropylidenediphenol (bisphenol-A). Short-time-scale MD runs (5 ps) are used to characterize the elastic thermal motion of the host matrix; this information on mobility is then used for a stochastic simulation of solute dynamics up to ca. 1ms. All dissolved molecules show similar behavior by displaying three time regimes: a short-time, high-mobility domain, an intermediate time domain of anomalous diffusion, and a diffusive regime at long times. From the long-time data diffusion coefficients are estimated; comparison with experimental data results in good agreement.     

Simulation of the brownian motion of macromolecular chains. II. Chain dynamics

A simulation of the Brownian motion of polyethers and polyethylene is reported. The chains under consideration are confined to a tetrahedral lattice and subjected to conformational energy conditions. The dynamic behavior of the whole chain is studied. The diffusion of individual chain atoms reflects the chemical nature of the chain, and the diffusion of the center of mass, in connection with experimental results, affords a time scale for the simulation. The relaxation of bond orientation, which is connected with fluorescence depolarization, is found to be consistent with the theory of Valeur and co-workers. The relaxation of the total dipole is interpreted in terms of conformational features of the motions and correlations between neighboring dipoles. Finally, relations between chemical structure and dynamic behavior are established. Three classes of polyether chains are to be distinguished: the rigid chain poly(methylene oxide), the highly flexible poly(ethylene oxide) and an intermediate class typified by polyethylene.     

Dynamics of a single copolymer chain

The dynamics of a single copolymer chain in a solution containing identical chains is studied. The intermediate scattering function is calculated, and two different modes are identified and analyzed as a function of wave vector q. The first mode is characteristic of the copolymer system and leads to a peculiar constant relaxation frequency as q goes to zero. The second mode represents the diffusion of the chain in the solution.