Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static (statistical) properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability ?? (s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed ?? (s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained ?? (s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.open342

Влияние лечения тиотриазолином на состояние перекисного окисления липидов и уровни иммуновоспалительных и вазоактивных эндотелиальных факторов у больных с хронической сердечной недостаточностью и helicobacter pylori-негативными гастропатиями

Показано, что включение в схему патогенетического лечения больных с ХСН, hp-негативной гастропатией и умеренным или высоким риском сердечно-сосудистых осложнений (ССО) антиоксиданта тиотриазолина сопровождается достоверно более выраженными позитивными эффектами на процессы перекисного окисления липидов и содержание в крови иммуновоспалительных и вазоактивных эндотелиальных факторов по сравнению с динамикой при лечении без использования тиотриазолина, причем степень положительной динамики у больных с высоким риском ССО достоверно больше.Показано, що включення у схему патогенетичного лікування хворих із ХСН, hр-негативною гастропатією і з помірним або високим ризиком серцево-судинних ускладнень (ССУ) антиоксиданта тіотриазоліна супроводжується достовірно більш вираженими позитивними ефектами на процеси перекисного окислення ліпідів та вміст у крові імунозапальних і вазоактивних ендотеліальних факторів порівняно з динамікою при лікуванні без використання тіотриазоліну, причому ступінь позитивної динаміки у хворих із високим ризиком ССУ достовірно більший.It is shown that the use of tiotriazolin in the scheme of pathogenetic treatment of patients with chronic heart failure, Hp-negative gastropathy, and moderate or high risk of cardiovascular complications (CVC) is accompanied by significantly higher positive effect on the processes of lipid peroxidation and the amount of immune inflammation and vasoactive endothelial factors in the blood when compared with the dynamics at treatment without the use of tiotriazolin, the degree of positive dynamics in patients with a high risk of CVC being significantly higher

The Role of Teachers ’ Self- and Collective-Efficacy Beliefs on Their Job Satisfaction and Experienced Emotions in School

This study aimed at investigating a) teachers ’ job satisfaction, experienced emotions at school, self-efficacy and school collective-efficacy beliefs; b) the influential role of self-efficacy in the school collectiveefficacy beliefs, and in the impact of the school collective-efficacy beliefs on job satisfaction and emotions; and c) the effect of self- and collective-efficacy beliefs on the impact of job satisfaction on emotions. The sample comprised 268 elementary school teachers (113 male, 155 female), who completed the scales at the middle of a school year. The results showed that a) the teachers experienced form moderate negative emotions to moderate positive emotions at school, particularly in the context-task- and self-related emotions; b) teachers ’ self-efficacy had positive effect on school collective-efficacy beliefs and job satisfaction, and on the impact of collective efficacy on job satisfaction; c) self-efficacy, collective efficacy and job satisfaction, as a group, explained from a small to moderate amount of the variance of the emotions, while the impact of job satisfaction on the emotions was to a significant extent mediated by teachers ’ perceptions about their school collective efficacy; and d) self-efficacy had direct and indirect effect, through the interaction of collective efficacy and job satisfaction, on the emotions. The findings are discussed for their applications in educational practice and future research

Mapping of atomistic simulation data for the dynamics of entangled polymers onto the tube model: Calculation of the segmental survival probability function for mono- and bi- disperse melts and comparison with modern tube models

Topological constraints, arising from chain and chain uncrossability, are of primary importance for the high molecular weight polymeric liquids which are typically employed in practical polymer processing. However, it is tremendously difficult to consider these topological interactions in a rigorous fashion due to the huge number of degrees of freedom associated with polymer configurations. The problem was considerably simplified by the notion of a confining tube, introduced for the very first time by Edwards and de Gennes, [1] through which a chain can execute a reptation-like motion, as small-length scale fluctuations, irrelevant to the large-scale rheological properties of the polymer, may be neglected. A few years later, Doi and Edwards [2] (DE) developed a more elaborate version of the reptation theory which, since then, has attracted considerable attention and development

Melt structure and dynamics of unentangled polyethylene rings: Rouse theory, atomistic molecular dynamics simulation, and comparison with the linear analogues

Atomistic configurations of model unentangled ring polyethylene (PE) melts ranging in chain length from C24 up to C400 have been subjected to detailed molecular dynamics (MD) simulations in the isothermal-isobaric statistical ensemble at temperature T = 450 K and P = 1 atm. Strictly monodisperse samples were employed in all cases. We present and discuss in detail simulation results for a variety of structural, thermodynamic, conformational and dynamic properties of these systems, and their variation with chain length. Among others, these include the mean chain radius of gyration, the pair correlation function, the intrinsic molecular shape, the local dynamics, the segmental mean square displacement (msd), the chain center-of-mass self-diffusion coefficient DG, the chain terminal relaxation time τd, the characteristic spectrum of the Rouse relaxation times τp, and the dynamic structure factor S(q,t). In all cases, the results are compared against the corresponding data from simulations with linear PE melts of the same chain length (the linear analogues) and the predictions of the Rouse theory for polymer rings which we derive here in its entirety. The Rouse theory is found to provide a satisfactory description of the simulation findings, especially for rings with chain length between C50 and C170. An important finding of our work (from the observed dependence of DG, τp, ζ, and η0 on chain length N) is that PE ring melts follow approximately Rouse-like dynamics even when their chain length is as long as C400; this is more than twice the characteristic crossover chain length (∼C 156) marking the passage from Rouse to reptation dynamics for the corresponding linear PE melts. In a second step, and by mapping the simulation data onto the Rouse model, we have managed to extract the friction coefficient ζ and the zero-shear rate viscosity η0 of the simulated ring melts. Overall, and in agreement with previous theoretical and experimental studies, our simulation results support that the structure of ring polymers in the melt is more compact than that of their linear analogues due to their nonconcatenated configurations. Additional results for the intermolecular mer-mer and center-of-mass pair correlation functions confirm that the effective correlation hole effect is more pronounced in melts of rings than in melts of linear chains. © 2010 American Chemical Society

Understanding Dynamics in Binary Mixtures of Entangled cis-1,4-Polybutadiene Melts at the Level of Primitive Path Segments by Mapping Atomistic Simulation Data onto the Tube Model

We study dynamics in bidisperse melts of linear cis-1,4-polybutadiene composed of probe and matrix chains at the level of the segment survival probability function ??(s,t) which is computed directly in the course of long atomistic molecular dynamics simulations [Stephanou et al. J. Chem. Phys. 2010, 132, 124904]. By controlling precisely the matrix chain length and composition, the effect of contour length fluctuations (CLFs) and constraint release (CR) on melt dynamics is quantified. Our study shows that (a) the values of the static topological properties of the probe chains (e.g., the average value of their primitive path (PP) contour length and its fluctuation) remain unaltered in the different matrices, but (b) their dynamical properties (including ??(s,t) and its average over all segments s, ??(t), the time autocorrelation function of the PP contour length, and the time autocorrelation function of the chain end-to-end vector) vary significantly from matrix to matrix. As the length of the matrix chains decreases, the functions ??(s,t) and ??(t) describing the reptation relaxation of the probe chains are found to decrease more rapidly. Furthermore, the relaxation of longer probe chains is seen to be delayed as the concentration of shorter matrix chains decreases. Overall, our direct computational study proves that CR is the dominant relaxation mechanism in melts of long and short cis-1,4-polybutadiene chains accounting for the majority of differences observed in their relaxation dynamics in different environments (since CLFs appear to be unaffected by compositional differences); as a result, it has a profound effect on the linear viscoelastic properties of the melt, such as the spectra of storage and loss moduli. By further analyzing the mean-square displacement of atomistic segments in the different matrices, we find that while the tube diameter is constant in the mixtures with MS ??? Me where MS is the molecular weight of short chains and Me the entanglement molecular weight, it gradually increases in the mixtures with MS < Me. How the simulation results compare with laboratory measurements on melts of bidisperse polymers reported in the literature is also discussed.close121

Melt Structure and Dynamics of Unentangled Polyethylene Rings Rouse Theory, Atomistic Molecular Dynamics Simulation, and Comparison with the Linear Analogues

Atomistic configurations of model unentangled ring polyethylene (PE) melts ranging in chain length from C24 up to C400 have been subjected to detailed molecular dynamics (MD) simulations in the isothermal-isobaric statistical ensemble at temperature T = 450 K and P = 1 atm. Strictly monodisperse samples were employed in all cases. We present and discuss in detail simulation results for a variety of structural, thermodynamic, conformational and dynamic properties of these systems, and their variation with chain length. Among others, these include the mean chain radius of gyration, the pair correlation function, the intrinsic molecular shape, the local dynamics, the segmental mean square displacement (msd), the chain center-of-mass self-diffusion coefficient DG, the chain terminal relaxation time ??d, the characteristic spectrum of the Rouse relaxation times ??p, and the dynamic structure factor S(q,t). In all cases, the results are compared against the corresponding data from simulations with linear PE melts of the same chain length (the linear analogues) and the predictions of the Rouse theory for polymer rings which we derive here in its entirety. The Rouse theory is found to provide a satisfactory description of the simulation findings, especially for rings with chain length between C50 and C170. An important finding of our work (from the observed dependence of DG, ??p, ??, and ??0 on chain length N) is that PE ring melts follow approximately Rouse-like dynamics even when their chain length is as long as C400; this is more than twice the characteristic crossover chain length (???C 156) marking the passage from Rouse to reptation dynamics for the corresponding linear PE melts. In a second step, and by mapping the simulation data onto the Rouse model, we have managed to extract the friction coefficient ?? and the zero-shear rate viscosity ??0 of the simulated ring melts. Overall, and in agreement with previous theoretical and experimental studies, our simulation results support that the structure of ring polymers in the melt is more compact than that of their linear analogues due to their nonconcatenated configurations. Additional results for the intermolecular mer-mer and center-of-mass pair correlation functions confirm that the effective correlation hole effect is more pronounced in melts of rings than in melts of linear chains.close302