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.     

Nano‐scaled intrachain ordering and dynamics in two‐dimensional orientational polymer domains1)

Statistical and local relaxation properties of two‐dimensional finite polymer systems (domains) are considered. The domains consist of a large number of semirigid chains with the finite contour length at free, half‐free and fixed boundary conditions for chain ends. The intermolecular orientational order at short distances between chains in the thick domains is similar to the order in infinite two‐dimensional systems. The correlations of orientation between sufficiently distant elements of different chains decay by the exponential law, but the effective constant of interchain interactions in the domain is proportional to the molecular weight of the chain. At the given intra‐and interchain interactions an elongtation of the chains leads to a local ordering of chains in the domain (at free boundary conditions) or, on the contrary, to the decreasing of the parameter of short‐range orientational order (at fixed and half‐free boundary conditions). Independently of type of boundary conditions the parameter of large‐range orientational order tends to zero with increasing of the chain contour length. Dynamical equations and relaxation spectrums for times of local motions are obtained. From time correlation functions of local relaxation the times of nano‐scaled mobility of chains were calculated in depending on the bending rigidity of chains, the parameter of interchain interactions, and the contour length of chains. At the given intra‐and interchain interactions an elongtation of chains forming the domain leads to to the slowing‐down of local mobility of chains in the domain. The comparison with experimental date obtained by dielectric relaxation and polarized luminescence methods on investigation of nano‐scaled mobility in the dilute melts of comb‐shaped polymers has been carried out.     

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.     

Molecular dynamics in liquid-crystalline side chain polymers studied by dielectric relaxation spectroscopy: A comparative study

A series of liquid-crystalline side chain copolymers with different main chains have been studied by the dielectric method in a maximum frequency range of 9 decades. Oriented samples were used throughout. The data were analysed in terms of the Havriliak-Negami and Fuoss-Kirkwood formulae for the relaxation functions. Two well separated dispersion regions with their strengths depending strongly on the macroscopic orientation were found. The low frequency or δ-relaxation shows a marked change in its curve form and width with different main chain structure, its strength being determined by the longitudinal dipole moment of the mesogenic unit. The high frequency relaxation shows a more complicated dependence of its characteristic parameters on the molecular structure. In some cases a decomposition into two underlying relaxations was successfully attempted. We discuss the models for molecular motions developed for low molecular weight liquid crystals and for amorphous polymers, in order to explain the behaviour of the different dispersions found.     

PEEK链分子内γ-松弛过程构象机理的研究

使用AM1半经验量化计算,研究在PEEK链分子内γ-松弛的构象机理。指出部分链段作曲柄式运动时,各相连苯环不断调节其相对位置。γ-松弛的活化能与苯环间相对转动势垒、链骨架绕骨架平面作曲柄式运动势垒及链间相互作用有关,本文估算各部分的大小,并对苯环在PEEK链内相对取向作进一步的计算,得到十分接近实验数据的结果。     

Orientation of amorphous polymers

Orientation of amorphous polymers stretched at a temperature above their glass-transition temperature, is involved in thermoforming processing. The molecular processes controlling the orientation and chain relaxation of polymers have been investigated by infrared dichroism in a large series of materials: polystyrene, polymethylmethacrylate of various tacticity and its copolymers with styrene and acrylonitrile. Polystyrene with hydrogenated and deuterated blocks leads to information on the behavior of each block (central part, chain ends) and allows a quantitative comparison with the Doi-Edwards model for chain relaxation. In order to analyse the effect of polydispersity, blends of hydrogenated and deuerated polystyrene chains with various molecular weights have been studied. Short chains with molecular weights smaller than the molecular weight between entanglements, enhance the relaxation of long chains. Furthermore an anisotropic orientational coupling effect exists between a chain segment and its oriented surrounding. By comparing the orientation of polymers with different chemical structures, it results that they behave differently under temperature conditions where T - T_g = const, but they undergo identical relaxations when the experiments are performed at temperatures chosen in such a way that the monomer friction coefficients are identical. In copolymers of styrene and methylmethacrylate, the two monomer units have different orientations due to local conformational constraints. This effect also accounts for the difference observed between an alternated and a random copolymer.     

Simulation of the brownian motion of macromolecular chains. I. Local motions and chain conformations

Chains confined to a tetrahedral lattice can be considered as models for aliphatic polyethers and polyethylene. The deformations of such chains are analyzed by computer simulation using the Monte Carlo method. The elementary motions that are taken into consideration are three-bond and four-bond motions. The local mobility is analyzed in terms of conformational characteristics and compared with some NMR relaxation data.     

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.     

Theory of relaxation properties of two‐dimensional polymer networks, 2. Local dynamic characteristics

Using normal mode transformation obtained in Part 1 of this series^[1], the exact analytical expressions for the mean‐square displacements of junctions and non‐junction beads, the autocorrelation functions of the end‐to‐end chain vectors between neighboring junctions, and those of subchain vectors of a two‐dimensional regular network consisting of "bead and spring" Rouse chains are obtained. Contributions of intra‐ and interchain relaxation processes to the local dynamic characteristics considered are compared. The time behavior of dynamic quantities obtained is estimated for different scales of motions. The possibility of describing long‐time relaxation of a two‐dimensional network by a simplified coarse‐grained network model is demonstrated. It is shown that the local relaxation properties of a two‐dimensional polymer network (as well as a three‐dimensional network) on scales smaller than the average distance between cross‐links are very close to those of a single Rouse chain. The large‐scale collective relaxation of the polymer networks having a two‐dimensional connectivity differs considerably from that of the three‐dimensional networks.     

The relationship between chemical structure and viscoelastic properties of linear aliphatic polyesters

The effects of Chemical structure on the molecular motions in linear aliphatic polyesters have been investigated with a free-oscillation torsion pendulum. Broad-line NMR provided supplementary information. In the γ relaxation which corresponds to the local-mode motions of main chains in the noncrystalline region, the polyesters which are composed of two methylene units in the diol part of the chemical repeat unit showed an extremely asymmetric loss curve with a relatively high-loss peak temperature compared with that of the other polyesters. In addition to the two relaxations (β,γ) which have been observed in earlier dielectric measurements, a new relaxation (α) was found on the high-temperature side of the glass transition of the polyesters. The α relaxation was assigned to molecular motions of methylene segments in the crystalline region. The α and β relaxations of the two-dimensional series are situated close to the temperatures found for other polyesters with rather long methylene sequence in the chemical repeat unit. The results were explained in terms of a difference on the chain mobility in the noncrystalline regions which may be related to the difference of chemical structure of the polyesters.     

Dynamic heterogeneity in diblock copolymer systems

Dynamic light scattering from diblock copolymers in melt and solution in a non-selective solvent reveals different mechanisms for relaxing the composition and orientation fluctuations near the order to disorder transition (ODT). For the former, internal relaxation and copolymer chain diffusion are the main relaxation processes whereas the latter relate to collective orientation of the copolymer chains near the ODT and induced form anisotropy of coherently ordered microstructures below ODT.     

Influence of the molecular weight on the elongational behaviour of polypropylene and on the fibre orientation factors

This study shows that the elongational behaviour depends upon molecular weight and upon elongational rate. If the molecular weight is low, elongational viscosity reaches rapidly a steady value but, if the molecular weight is high, the viscosity (or the elongational stress) increases continuously with the time. These behaviours may be explained in comparison of the relaxation rate determined by shear rheology as the reciprocal relaxation time with the elongation rate ϵ. If the elongation rate is lower than the relaxation rate the polypropylene chains may relax and the elongational viscosity reaches a steady value with the time. For high fluidity polypropylene the range of elongation rates within of which the elongational viscosity is constant with time is very large. On the contrary, if the elongational rate is higher than relaxation rate the polypropylene chains undergo a continuous deformation and then the elongational viscosity increases with time. The range of elongational rates within of which the stress is constant is narrow for high-molecular-weight polypropylene. Furthermore, the elongational behaviour influences the chain orientation in the crystalline and amorphous phases of the fibres. If the polymer chains are quenched in a relaxed state the orientation is lowered as shown with high fluidity polypropylenes. On the contrary, if the chains are cooled in extended state their orientation may subsist during crystallisation and the orientation factors may reach high values as shown with high-molecular-weight polypropylene.     

Diluting the hydrogen bonds in viscous solutions of n-butanol with n-bromobutane: II. A comparison of rotational and translational motions

Mixtures of the monohydroxy alcohol n-butanol with n-bromobutane are investigated via dielectric and nuclear magnetic resonance (NMR) techniques. Static- and pulsed-field gradient proton NMR yielded self-diffusion coefficients as a function of concentration and temperature. To monitor reorientational motions, broadband dielectric and (13)C-spin relaxation time measurements were carried out. The latter demonstrate that the structural relaxation stems from the motion of the alkyl chains. By combining data from translational diffusion coefficients with published shear viscosities, hydrodynamic radii were determined that compare favorably with the van der Waals radii of single molecules. The results for the neat alcohol and for the binary mixtures are discussed with respect to a recent transient chain model. The approach of Debye and structural relaxation times at high temperatures, identified as a general feature of monohydroxy alcohols, is also discussed within that framework.     

Segmental orientation and chain relaxation of polymers by fourier transform infrared dichroism

Fourier transform infrared dichroism has been used to investigate molecular orientation in polymeric materials. It is first applied to characterize network behavior in some elastomeric systems such as model networks of poly(dimethylsiloxane). The strain dependence of segmental orientation is analyzed through networks of known degree of cross-linking and experimental results are compared with calculation predictions based on the rotational isomeric state formalism. Infrared dichroism spectroscopy has also been used to analyze orientational relaxation in binary blends of long and short polystyrene chains. The effect of short deuterated chains (M_w = 3000 to 72000) on the orientational relaxation of long entangled chains (Mw = 2 000 000) is examined in the bidisperse melts uniaxially deformed above the glass transition temperature. While the long chain relaxation is found to be dependent on the short-chain concentration, the local orientational order of the latter is molecular weight dependent in agreement with the classical relaxation theories.     

Dielectric relaxations and electrical conductivities of poly(alkyl methacrylates) under high pressure

Dielectric properties of four methacrylate polymers (methyl, ethyl, n-butyl and n-octyl) were studied in the frequency range 0.0001 cps–300 kcps at temperatures above and below the glass transition temperature and at various pressures up to 2500 atm. At temperatures well above T_g a single relaxation peak (α′ peak) was observed in the case of the higher n-alkyl methacrylates. However, this peak was split into two peaks, α and β, with decrease in temperature or increase in pressure. The molecular motions corresponding to the α and the β relaxation processes are the micro-Brownian motions of amorphous main chains and of flexible side chains, respectively. From the temperature and the pressure dependence of the average dielectric relaxation time of these polymers the single relaxation process (the α′ process) was attributed to the micro-Brownian motion of the main chain coupled with that of the side chain. The effects of temperature and pressure on the d.c. conductivity of these polymers were also studied.     

Dielectric relaxation and molecular motion in poly(vinylidene fluoride)

The dielectric properties of poly(vinylidene fluoride) have been studied in the frequency range 10 Hz to 100 kHz at temperatures between ?196 and 150°C. Three dielectric relaxations were observed: the α relaxation occurred near 130°C, the β near 0°C, and the γ near ?30°C at 100 kHz. In the α relaxation the magnitude of loss peak and the relaxation times increased not only with increasing lamellar thickness, but also with decrease of crystal defects in the crystalline regions. In the light of the above results, the α relaxation was attributed to the molecular motion in the crystalline regions which was related to the lamellar thickness and crystal defects in the crystalline phase. In the β relaxation, the magnitude of the loss peak increased with the amount of amorphous material. The relaxation times were independent of the crystal structure and the degree of crystallinity, but increased slightly with orientation of the molecular chains by drawing. The β relaxation was ascribed to the micro-Brownian motions of main chains in the amorphous regions. The Arrhenius plots were of the so-called WLF type, and the “freezing point” of the molecular motion was about ?80°C. The Cole-Cole distribution parameter of the relaxation time α increased almost linearly with decreasing temperature in the temperature range of the experiment. The γ relaxation was attributed to local molecular motions in the amorphous regions.     

Relaxations of confined chains in polymer nanocomposites: Glass transition properties of poly(ethylene oxide) intercalated in montmorillonite

The relaxation behavior of poly(ethylene oxide) (PEO), intercalated in montmorillonite, a naturally occurring mica-type silicate, was studied by differential scanning calorimetry (DSC) and thermally stimulated dielectric depolarization (or thermally stimulated current, TSC). The materials were synthesized by melt or solution-mediated intercalation. In both intercalates, the PEO chains were confined to ca. 0.8-nm galleries between the silicate layers. The solution intercalate contained a fraction of unintercalated PEO chains which exhibited a weak and depressed PEO melting endotherm in DSC. In contrast, the melt intercalate was “starved” such that almost all the PEO chains were effectively intercalated. For these melt intercalates, no thermal events were detected by DSC. TSC thermal sampling technique was used to examine the glass transition regions and to estimate the extent of cooperativity of chain motions. The motions of the intercalated PEO chains are inherently noncooperative relative to the cooperative T_g motions in the amorphous portion of the bulk polymer. This is presumably due to the strong confining effect of the silicate layers on the relaxations of the intercalated polymer. © 1997 John Wiley & Sons, Inc.     

Structural changes and chain radius of gyration in cold-drawn polyethylene after annealing: small- and wide-angle X-ray scattering and small-angle neutron scattering studies

Samples made from linear polyethylene were drawn at room temperature and subsequently annealed at high temperatures below the melting point. The structural changes of the crystalline lamellae and lamellar superstructures as well as the single chain radius of gyration were studied by means of combined small- and wide-angle X-ray scattering and small-angle neutron scattering (SANS). After drawing, the polymeric chain segments in the crystalline phase are preferentially oriented along the drawing direction with a high degree of orientation whereas the lamellae in the samples are found to be slightly sheared exhibiting oblique surfaces as evidenced by X-ray scattering. SANS indicates that the chains are highly elongated along the drawing direction. Annealing the deformed samples at temperatures where the mechanical alpha-process of polyethylene is active leads to a thickening of both crystalline lamellae and amorphous layers. The chains in the crystalline phase retain their high degree of orientation after annealing while the lamellae are sheared to a larger extent. In addition, there is also lateral growth of the crystalline lamellae during high-temperature annealing. Despite the structural changes of the crystalline and amorphous regions, there is no evidence for global chain relaxation. The global anisotropic shape of the chains is preserved even after prolonged annealing at high temperatures. The results indicate that the mobility of polyethylene chains-as seen, e.g., by 13C NMR-is a local phenomenon. The results also yield new insight into mechanical properties of drawn PE, especially regarding stress relaxation and creep mechanisms.     

Models for the dynamics of monodisperse polymer melts based on lateral chain motions

A recently developed model for the dynamics of monodisperse polymer melts of linear chains is briefly reviewed. Within the simplifications inherent in the model, it is found that the obstacles to the motion of a given chain, which are imposed by neighboring chains, do not suppress the lateral chain motion. The model associates a length scale with each obstacle, and compares it with the length scale for chain motion. If the obstacle length is greater than the length scale for chain motion, the obstacle is deemed impassable. The cooperative motion of the mutually impassable obstacles is considered, and this gives rise to predictions that are in excellent agreement with experimental observations. If the model were modified to include the additional complexities of real polymer systems, various features of the model might change. The implications of a number of possible modifications in the model are explored. Specifically, the impact of varying the behavior of the function which determines the fraction of obstacles that are impassable is examined in detail. In addition, in the original model it is assumed that chain memory is relaxed due to the slowing of lateral chain motion by the obstacles imposed by neighboring chains. The effect of the opposite assumption of essentially no memory relaxation is also studied. Finally, the influence of limiting the extent of the correlations between the motions of various chain segments because of finite chain length is also considered. It is found that these features have effects that can largely cancel each other. As a result, a range of lateral motion models, which are consistent with the known phenomenology of these systems, are possible.