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.     

Unsolved problems in the theory of dynamics in homogeneous and heterogeneous polymer networks

A brief review related to some unsolved problems of the dynamic theory of polymer networks and to possible ways of solving them is presented. The comparative role of small‐scale intrachain and long‐scale collective interchain relaxation processes, the influence of long‐range hydrodynamic interactions between the network elements and the effective viscous medium, and the problem of the structure heterogeneity of polymer networks are considered. New approaches for theoretical treatment of these problems are proposed and discussed.     

Asymmetric electron spin relaxation in ClO2 solution. Deviation of the motional correlation time from modified Debye theory

In highly viscous solutions the ESR spectra of chlorine dioxide are asymmetrically broadened. Modulation of the anisotropic hyperfine and g tensors accounts for the observed broadening but the correlation time for the motion is much smaller than expected from Debye theory. The calculated hydrodynamic radius is compared with that derived from spin rotational relaxation.     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

Model Theory of Visco-Elastic Properties and Relaxation Spectra of Two Different Interpenetrating Polymer Networks

Dynamic viscoelastic models of the system of two different interpenetrating polymer networks with different topology and type of interactions were used for calculating spectra of relaxation times of the system under consideration. It was shown, that two branches of the relaxation spectrum appear for two models of interpenetrating networks with different components. One of the branches is the branch of the collective motion of double network consisting of two initial interacting networks. Parameters of this branch of relaxation spectrum are defined by both own elastic constants of each of interacting networks and by effective quasi-elastic interactions between two networks. This branch is the low frequency one and is described by broad relaxation time spectrum. The second branch is the high frequency one and characterizes mutual local motions of two interacting networks. The relaxation spectrum of this branch is comparatively narrow and depends on the quasi-elastic constants and mutual friction which is defined by the entanglements of the networks and by its effective rigidity. The second branch does not contain extremely large relaxation times for infinitely large networks.     

The relaxation spectra of polymer networks with different types of topology,ordering, heterogeneity

Many characteristic features of the relaxation spectra of the different types of polymer networks (meshlike and tree-like) manifesting in experimental behaviour are determined by manifold types of local and long-range irregularities or inclusions existing even in the simplest network structures. These irregularities in the local topology, in the fluctuations of the local orientational order existing due to stretching of the chains in the bulk elastomers (even in the non-ordered elastomers), also due to possible LC-ordering, the distribution of chain lengths between junctions and possible existence of cross-link agglomerations and domains at random cross-linking and the influence of the position of the chain element relative to junctions lead to variety of relaxation spectra, frequency and time-dependencies. The long-range hydrodynamic effects in bulk network can also lead to drastic variation of relaxation spectra. The inclusion of elongated rigid particles in polymer gels and network leads to the appearance of new branches of relaxation spectra changing and overlapping the relaxation spectra of the primary network system.     

Cooperative motion of spheres arranged in periodic grids between two parallel walls

In this article, we analyze the collective motion of a two-dimensional periodic array of spheres in a slit-pore confined by two parallel planar walls. We determine the friction coefficient of the spheres when all particles move with the same velocity along a particular direction and cooperate with each other in their motion. In order to solve this many-body problem, we use Stokesian dynamics algorithm and resolve multiparticle hydrodynamic interactions in wall-bounded geometry. Apart from particle-particle interactions, we also recognize that the aforementioned collective motion of all particles creates a cumulative effect on the fluid medium. This effect is manifested as either a net induced flow for a periodic pressure field or an additional pressure gradient for quiescent fluid. In our analysis, we focus on both periodic pressure and no-flow conditions. For both cases, the hydrodynamic friction on the translating particles is calculated using our multiparticle Stokesian dynamics simulation. The simulation for the no-flow condition is relatively straightforward-we only need to compute the multiparticle hydrodynamic interactions in quiescent fluid. However, for the periodic pressure condition, the net induced flow dragged by the particles has to be evaluated also. We express this net induced flow in terms of an additional pressure-driven velocity field. We present the hydrodynamic friction as a function of the dimensions of the two-dimensional periodic lattice. For closely packed arrays, the results show a considerable reduction in friction coefficients that usually increase with interparticle distance. Hence, our work renders the theoretical justification for other recent findings that indicate the importance of interparticle mutual cooperation.     

Simulation of semidilute suspensions of non-Brownian fibers in shear flow

Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in fair agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration. It was also found that the coefficient of friction has a strong influence on the tendency for flocculation as well as the apparent viscosity of the suspension in the semidilute regime.     

Effects of Nematic Ordering on the Relaxation Spectrum of a Polymer Network with Included rod‐like Particles: Mean‐Field Approximation

Summary: Equilibrium and local dynamic properties of ordered polymer networks with included rod‐like particles are considered using a simplified network model. Lagrange multipliers in the equations of motion of rigid rods are replaced by their averaged values. This approximation corresponds to modelling rod‐like particles by elastic Gaussian springs with mean‐square lengths independent of the orientational order. Nematic‐like interactions between network segments and rods are taken into account in terms of the Maier‐Saupe mean‐field approximation. Nematic ordering of rods induces network segments ordering and changes the relaxation spectrum of the network. The relaxation spectrum of the ordered network splits into two main branches for parallel and perpendicular components of chain segments with respect to the director. Relaxation times of a polymer network are calculated as functions of the wave number for the corresponding normal mode and of the order parameter taking into account both the dynamic factor (determined by friction effects) and the statistical factor (related to mean‐square fluctuations of segment projections). We compare the relaxation spectra of ordered unstretched polymer networks with fixed boundaries with those for polymer networks at free boundaries. A polymer network with free boundaries is stretched along the director. This produces additional fine structure of the two main branches in the relaxation spectrum.

Cell of a three‐chain network model with included rods.     

Hydrodynamic Permeability of the Membrane as a System of Rigid Particles Covered with Porous Layer (Cell Model)

Problem of uniform flow of viscous, incompressible liquid around a rigid particle covered with porous layer and located inside the spherical cell was solved at small Reynolds numbers. In order to describe the motion of liquid within porous layer, the Brinkman equations were used. Based on the Happel and Brenner cell method, the hydrodynamic permeability of the membrane consisting of the system of porous particles with rigid impermeable cores was calculated.     

Low-frequency velocity correlation spectrum of fluid in a rectangular microcapillary

In addition to the fast correlation for local stochastic motion, the velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. At late times, the flow approaches that of an incompressible fluid. Here, we consider the motion of a viscous fluid, at constant temperature, in a rectangular semipermeable channel. The fluid is driven through the rectangular capillary by a uniform main pressure gradient. Tiny pressure gradients are allowed perpendicular to the main flux. We solve numerically the three-dimensional Navier-Stokes equations for the velocity field to obtain the steady solution. We then set and solve the Langevin equation for the fluid velocity. We report hydrodynamic fluctuations for the center-line velocity together with the corresponding relaxation times as a function of the size of the observing region and the Reynolds number. The effective diffusion coefficient for the fluid in the microchannel is also estimated (Deff = 1.43 x 10(-10) m2.s-1 for Re = 2), which is in accordance with measurements reported for a similar system (Stepisnik, J.; Callaghan, P. T. Physica B 2000, 292, 296-301; Stepisnik, J.; Callaghan, P. T. Magn. Reson. Imaging 2001, 19, 469-472).     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.     

Effect of surface elasticity on the motion of a droplet in a viscous fluid

The motion of a droplet with adsorption layer in a viscous incompressible fluid is studied on the basis of the linearized Navier-Stokes equations. It is shown that dilatational elasticity of the layer has a strong effect on the decay of velocity after a sudden impulse. If the elasticity is sufficiently strong the droplet shows backtracking, i.e., during part of the time the velocity relaxation function becomes negative. The motion is independent of the surface shear modulus or surface shear viscosity. The friction coefficient of the droplet at zero frequency is the same as for a rigid sphere with stick boundary conditions, independent of the elasticity modulus.     

新型刺激响应性纤维素基含能凝胶的流变性能

研究了以不同基团含量的羧甲基纤维素硝酸酯(CMCN)为胶凝剂的含能凝胶细微结构与流变行为的关系.探讨了凝胶的形成机理,并采用线性的流变学方法研究了凝胶的屈服性、触变性、蠕变性及温敏性等动态黏弹性质,分别利用Herschel-Bulkley模型、Burger模型及Carreau-Yasuda模型对凝胶的流动曲线、蠕变曲线和频率曲线进行了数据拟合.研究发现,CMCN凝胶是由其分子结构上两亲性基团通过分子链间氢键及疏水键等非共价键相互作用形成的一种结构均匀的物理交联网络型凝胶.凝胶的非牛顿系数n均小于0.5.随着亲水性羧酸基团含量的增加,凝胶的屈服应力逐渐增大,触变恢复性逐渐增强,弹性与黏性柔量均减小,但其比值增加,蠕变的黏性响应性逐渐减弱而弹性响应性逐渐增强.凝胶的温敏性变化有一个力学松弛转变区,随着羧酸基团含量的增加,松弛转变区愈发明显,凝胶的温敏性也逐渐增强.     

Ionic liquid nanotribology: stiction suppression and surface induced shear thinning

The friction and adhesion between pairs of materials (silica, alumina, and polytetrafluoroethylene) have been studied and interpreted in terms of the long-ranged interactions present. In ambient laboratory air, the interactions are dominated by van der Waals attraction and strong adhesion leading to significant frictional forces. In the presence of the ionic liquid (IL) ethylammonium nitrate (EAN) the van der Waals interaction is suppressed and the attractive/adhesive interactions which lead to "stiction" are removed, resulting in an at least a 10-fold reduction in the friction force at large applied loads. The friction coefficient for each system was determined; coefficients obtained in air were significantly larger than those obtained in the presence of EAN (which ranged between 0.1 and 0.25), and variation in the friction coefficients between systems was correlated with changes in surface roughness. As the viscosity of ILs can be relatively high, which has implications for the lubricating properties, the hydrodynamic forces between the surfaces have therefore also been studied. The linear increase in repulsive force with speed, expected from hydrodynamic interactions, is clearly observed, and these forces further inhibit the potential for stiction. Remarkably, the viscosity extracted from the data is dramatically reduced compared to the bulk value, indicative of a surface ordering effect which significantly reduces viscous losses.     

Interchain coupling effects on dynamics of photoexcitations in conjugated polymers

Within an extended Su-Schrieffer-Heeger model including interchain interactions and the extended Hubbard model, the dynamical relaxation of photoexcitations in two coupled conjugated polymer chains is investigated by using a nonadiabatic evolution method. Initially, one of the two chains is photoexcited and the other chain is in the dimerized ground state. Due to the interchain interactions, the electron and/or the hole can be transferred from one chain to the other chain. For weak interchain coupling, the dynamical evolution of the lattice on the photoexcited chain is similar to that found in an isolate single chain case. With interchain interactions increasing, the amplitude of the distortions on the photoexcited chain decreases, and simultaneously, that on the other chain gradually increases. Until stronger interchain coupling, the deformations of the two chains have almost the same amplitude. Besides intrachain polaron-excitons and intrachain oppositely charged polaron pairs as found in single chain case, interchain polaron-excitons and interchain separated charged polaron pairs are obtained. The results show that the yield of interchain products increases and that of intrachain products decreases with interchain coupling increasing. Totally, the yield of charged polarons (including intrachain oppositely charged polaron pairs and interchain oppositely charged polaron pairs) is about 25%, in good agreement with results from experiments.     

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.