Mobility of Spherical Probe Objects in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement ?Δr(2)? of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (?Δr(2) (t)? ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (?Δr(2) (t)? ~ t(1/2)) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ(e) of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ(e)) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τ(rep). At longer times t > τ(rep), the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.     

Analysis of Polymer Dynamics by NMR Modulated Gradient Spin Echo

NMR modulated gradient spin echo method, which allows the quantification of polymer segmental displacement via the measurement of the velocity autocorrelation, requires the formulation of theoretical predictions in the frequency domain in order to test their validity. We worked out the velocity autocorrelation spectrum of the segmental motion according to the Rouse and the tube/reptation model to compare it to the experimental results obtained by the new NMR technique. The analysis of polybutadiene shows the segmental velocity autocorrelation spectrum typical for the reptation-like motion of polymer in a “tube”. The measurement of bulk water indicates a kind of Rouse motion in a network of hydrogen bonds.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Constitutive equations for the flow behavior of entangled polymeric systems: application to star polymers

A semimicroscopic derivation is presented of equations of motion for the density and the flow velocity of concentrated systems of entangled polymers. The essential ingredient is the transient force that results from perturbations of overlapping polymers due to flow. A Smoluchowski equation is derived that includes these transient forces. From this, an equation of motion for the polymer number density is obtained, in which body forces couple the evolution of the polymer density to the local velocity field. Using a semimicroscopic Ansatz for the dynamics of the number of entanglements between overlapping polymers, and for the perturbations of the pair-correlation function due to flow, body forces are calculated for nonuniform systems where the density as well as the shear rate varies with position. Explicit expressions are derived for the shear viscosity and normal forces, as well as for nonlocal contributions to the body force, such as the shear-curvature viscosity. A contribution to the equation of motion for the density is found that describes mass transport due to spatial variation of the shear rate. The two coupled equations of motion for the density and flow velocity predict flow instabilities that will be discussed in more detail in a forthcoming publication.     

对聚合物玻璃化转变的几点新认识

基于聚合物玻璃化转变的定义,探讨了聚合物宏观单晶体和聚合物单链单晶的玻璃化转变问题,指出玻璃化转变的温度依赖性不服从普适的Arrhenius方程,可以把WLF方程看作是聚合物玻璃化转变的特有温度依赖关系。介绍了二维状态下聚合物可能的玻璃化转变。     

Non-markovian effects in NMR relaxation processes: An application to molecular dynamics in branched and cross-linked solid polymers

The dynamic of restricted rotatranslation of mobile structural defects along a polymer chain are treated with an equation of motion with a non-Markovian, stochastic force. The MORI/KUBO/ZWANZIG representation gives a stochastic process with a memory where the loss of correlation is dependend on the restriction of diffusional motion of defects. The influence of crosslinks and branchings of the polymer chains on the molecular dynamics are discussed. The analytical spectral densities of ω^−-α-type characterized by the fractal dimensions of the relevant processes in the different polymeric systems, e. g. cis-polybutadiene, cis-polyisoprene, styrene-butadiene-rubber, high density and linear low density polyethylenes, are compared with the observed NMR data.     

Analysis of polymer mobility by fluorescence spectroscopy

Fluorescence spectroscopy using an intramolecular excimer-forming probe has been used to investigate chain mobility in various polybutadienes. The spectroscopic technique is completed by a rheological study carried out in order to identify the molecular parameters governing polymer dynamics. The temperature dependence of the correlation time of the probe motion can be fitted to a WLF equation which shows that the probe mobility reflects the glass transition phenomenon of the host matrix.     

Numerical and theoretical study on the mechanism of biopolymer translocation process through a nano-pore

We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.     

Multi-stage mixer-settler planet centrifuge. Preliminary studies on partition of macromolecules with organic-aqueous and aqueous-aqueous two-phase solvent systems

A rotary-seal-free planetary centrifuge holds a separation column which consists of multiple partition units (ca. 200) connected in series with transfer tubes. In the cavity of each partition unit the transfer tube extends to form a mixer which vibrates to stir the contents under an oscillating force field generated by the planetary motion of the centrifuge. Consequently, solutes locally introduced at the inlet of the column are subjected to an efficient partition process in each partition unit and separated according to their partition coefficients. The mixer tube equipped with a flexible silicone rubber joint was found to produce excellent results for partition with viscous polymer phase systems. The capability of the method was demonstrated on separation of cytochrome c and lysozyme using a PEG-aqueous dibasic potassium phosphate-aqueous two-phase solvent system.     

Reptation theory: geometrical and topological aspects

This paper discusses topological and geometrical aspects of reptation theory which are common to all versions of reptation theory. These are: the postulated existence of the tube, the functional relationship between the tube diameter a and the polymer/monomer density p, the crossover from the Rouse to reptation regime. Statistical mechanics of the geometrically confined polymer chain is reanalyzed by careful separation of the diffusive motion of the chain into the longitudinal and transversal parts. Connection between old results and the new formalism is established. It is shown that the longitudinal motion resembles that known for directed polymers. This provides a source of the effective rigidification of the reptating chain's backbone thus facilitating the viscosity exponent to be larger than 3. The transversal motion is also reanalyzed. It is shown that the diffusion on the Bethe lattice used before to describe the transversal (planar) motion (conformational statistics) of the trapped chain is actually the diffusion on the universal covering of the corresponding Riemannian surface. This fact allows to reanalyze the tube stability using topological arguments. Detailed numerical comparison of the obtained new theoretical results with available experimental and Monte Carlo data is provided. Very good agreement between theory and experiment is found. It is also shown that the emerging physical picture of the tube destruction is isomorphic to that which was developed earlier with the help of the quantum Hall effect analogy (J. Phys. I 4 , 843 (1994)). Remarkable connections between the reptation theory and the theory of quantum chaotic/mesoscopic systems are established thus making the reptation theory part of the more general theory of quantum chaotic systems.     

Pom-Pom分子在平面收缩流场中的流变行为

用基于管子理论发展的XPP(extended Pom-Pom)模型描述支化高分子熔体——低密度聚乙烯(LDPE)的分子流变特性,实现了从分子微观结构到宏观响应的跨尺度模拟.引入有限增量微积分(FIC)过程重构了压力稳定质量守恒方程以克服因流体不可压缩性引发的压力场空间分布虚假振荡现象.采用离散的弹性——黏性应力分裂技术(DEVSS)以在缺失纯黏性项情况下保持动量方程弱形式中的椭圆项贡献.利用迎风流线(SU)方法离散黏弹性XPP本构方程中的对流项,以基于Crank-Nicolson隐式差分格式的迭代稳定分步算法求解质量、动量守恒方程和本构方程.采用等低阶有限元模拟了平面黏弹性收缩流,考察了不同Weissenberg数、支化程度和分子结构参数对Pom-Pom分子在收缩流场中流变行为的影响,数值结果与相关文献和试验结果吻合得较好.     

在“高聚物的结构与性能”课程中讲透高聚物的特点

通过对高分子链的柔性、聚合物独有的熵弹性、显著的粘弹性、特有的描述链段运动的WLF方程,可能实现的大尺寸取向和小尺寸解取向、银纹、单链凝聚态、折叠链片晶和伸直链晶体、分子量的多分散性、高分子溶液特性和高聚物熔体的弹性行为等的讨论,希望能突出“高聚物的结构与性能”课程中高聚物的特点。     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

RHEOLOGICAL PROPERTIES OF POLY(VINYLIDENE FLUORIDE) IN MOLTEN STATE

The theological behavior of poly(vinylidene fluoride)(PVDF)samples of different molecular weights was investigated by means of high pressure capillary rheometer and rotational rheometer.Information on the rheological properties of such materials above melt temperatures is of interest as this can lead to an improved understanding of polymer behavior in processing and fabrication technologies.Shift factors derived from time-temperature superposition showed good fit to the Arrhenius equation with a flow act...     

Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments.     

The elementary softening event in glassy systems in terms of the model of the excited state

The pressure dependence of the glass-transition temperature (glass-transition lines) is described through a relationship similar to the Clausius-Clapeyron equation. The criterion for the glass-liquid transition for polymer and other glasses is calculated. According to the proposed speculations, an elementary softening event in glasses is reduced to the critical deformation of interatomic (intermolecular) linkage, which corresponds to the maximum force of attraction between atoms. A glass (an amorphous polymer) softens when the mean energy of the thermal motion of the kinetic units responsible for the viscous flow is ∼3 times higher than the work of the ultimate deformation of the interatomic bond. The nature of structural changes occurring in the course of critical displacement (excitation) of kinetic units in liquids and glasses is discussed.     

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.     

Controllable Assembly and Separation of Colloidal Nanoparticles through a One‐Tube Synthesis Based on Density Gradient Centrifugation

Self‐assembly of gold nanoparticles into one‐dimensional (1D) nanostructures with finite primary units was achieved by introducing a thin salt (NaCl) solution layer into density gradient before centrifugation. The electrostatic interactions between Au nanoparticles would be affected and cause 1D assembly upon passing through the salt layer. A negatively charged polymer such as poly(acrylic acid) was used as an encapsulation/stabilization layer to help the formation of 1D Au assemblies, which were subsequently sorted according to unit numbers at succeeding separation zones. A centrifugal field was introduced as the external field to overcome the random Brownian motion of NPs and benefit the assembly effect. Such a facile “one‐tube synthesis” approach couples assembly and separation in one centrifuge tube by centrifuging once. The method can be tuned by changing the concentration of interference salt layer, encapsulation layer, and centrifugation rate. Furthermore, positively charged fluorescent polymers such as perylenediimide‐poly(N,N‐diethylaminoethyl methacrylate) could encapsulate the assemblies to give tunable fluorescence properties.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.