Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Modeling diffusion of adsorbed polymer with explicit solvent

Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.     

Translocation of a confined polymer through a hole

Based on an analogy between polymer translocation across a free energy barrier associated with polymer worming through a hole and classical nucleation and growth process, the escape time tau is predicted asymptotically to be N(N/rho)(1/3nu). N is the polymer length, rho is the monomer density prior to escape, and nu is the radius of gyration exponent. Monte Carlo simulation data collected in the high salt limit (nu approximately 3/5) are in agreement with the asymptotic law and provide vivid details of the escape.     

Scaling laws of single polymer dynamics near attractive surfaces

We present a molecular dynamics study of a generic model for single polymer diffusion on surfaces, which have variable atomic-scale corrugation but no artificial, impenetrable obstacles. The diffusion coefficient D scales as D is proportional to (-3/2) with the degree of polymerization N for strongly adsorbed, linear polymers on solid substrates in good solvents. Weaker scaling, i.e., D is proportional to (-1), is found if (i) the substrate is a fluid, e.g., a membrane, (ii) the polymer is a ring polymer, and (iii) the polymer is commensurate with the substrate. In poor solvents, diffusion on solids slows exponentially fast with N. Reptation is not observed in any of the simulations presented here.     

Diffusion coefficient depends on time, not on absorption

The recent controversy over whether the photon diffusion coefficient depends on absorption is addressed by use of the analytical solution of the photon transport equation in an infinite homogeneous scattering medium. The diffusion coefficient is found to be independent of absorption but temporally dependent. After a long period of time, the photon diffusion coefficient approaches D=1/3mu(s)(?) , which supports a claim made by Furutsu and Yamada [Phys. Rev. E 50, 3634 (1994)]. At early times, the diffusion coefficient is smaller than D=1/3mu(s)(?) , but this reduction cannot be expressed as D=1/3(mu(s)(?)+mu(a)) , since the time-dependent diffusion coefficient is found to be unrelated to absorption.     

Molecular dynamics simulation of gas diffusion behavior in polyethylene terephthalate/aluminium/polyethylene interface

Molecular dynamics (MD) simulations were performed to estimate the diffusion coefficients of O₂ and H₂O molecules in polyethylene terephthalate/aluminum/polyethylene interface at the temperature of 298 K. It came out that the diffusion coefficient of gasses in the interface is smaller than that of a single polymer, and the diffusion coefficients compare well with experimental data as well as previously published work. Furthermore, the diffusion coefficients of H₂O molecules in the interface are preferable to that of O₂ molecules. Interestingly, the largest diffusion coefficient was detected in the polyethylene terephthalate/aluminum(1 0 0)/polyethylene interface, while the smallest value of the diffusion coefficients was found in the polyethylene terephthalate/aluminum(1 1 1)/polyethylene interface. Calculation and analysis of the interaction between aluminum and polymers indicated that the interaction of polymer/aluminum(1 1 0) has the most interface strength, and crystal density of the metal surface has a definite effect on the planar interface energy. What’s more, the figure of gas molecule concentration is further resulted that the interface make contribution to adsorption of gas molecules. Moreover, the diffusion is belonging to the Einstein diffusion in the multilayer materials, and this work provides some key clues to improve the performance of polymer materials.     

Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios l( ||)/l( perpendicular). We find, in addition to the fact that a higher fluctuation level deltaB/B(0) makes the system more stochastic, that by increasing the ratio l( ||)/l( perpendicular) at fixed deltaB/B(0), the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number R=(deltaB/B(0))(l( ||)/l( perpendicular)). The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When R<1 weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When R approximately 1 the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(2) is recovered. Finally, for R>1 the percolation scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(0.7) is obtained.     

Postexposure evolution of a photoinduced grating in a polymer material with phenanthrenequinone

The specific features of the postexposure evolution of photoinduced (holographic) gratings in a model medium that consists of poly(methyl methacrylate) with distributed phenanthrenequinone and is characterized by a diffusion enhancement are investigated using the holographic relaxation technique. It is established that the evolution process occurs in four stages controlled by different mechanisms: (i) initial nonmonotonic changes governed by the diffusion of an intermediate radical photoreaction product and its transformation into a stable product due to attachment to the macromolecules, (ii) hologram enhancement through the diffusion of phenanthrenequinone molecules, (iii) rapid partial degradation associated with the spatially confined motion of polymer chain segments, and (iv) slow degradation as a result of macromolecular diffusion. In the course of polymer relaxation after a temperature jump, the processes associated with the mobility of molecules are retarded and the depth of rapid degradation decreases. The effective diffusion coefficient characterizing the destruction of reflection gratings is smaller than that for transmission gratings. This can be explained by the spatial inhomogeneity of the polymer.     

Two-dimensional dynamics of metal nanoparticles on the surface of thin polymer films studied with coherent X rays

X-ray photon-correlation spectroscopy is used to measure the dynamic structure factor f(q,tau) of gold particles moving on the surface of thin polymer films. Above the glass transition of the polymer the peculiar form f(q,tau) approximately exp[-(Gamma tau)(alpha)] is found with 0.7 < alpha < 1.5, depending on sample age and temperature. The relaxation rates Gamma scale linearly with q, excluding a simple Brownian diffusive motion. This type of behavior, already observed in aging bulk soft matter systems, is explained by a power law distribution of particle velocities due to ballistic motion.     

First observation of two-stage collapsing kinetics of a single synthetic polymer chain

Using a narrowly distributed poly(N-isoporpylacrylamide) (PNIPAM) chain with a degree of polymerization (N) of 3100, randomly labeled with pyrene, we have, for the first time, observed the two-stage kinetics of the coil-to-globule transition. Two characteristic relaxation times, tau(fast) for the crumpling of a random coil (approximately 12 ms) and tau(slow) for the collapsing of the crumpled chain to a compact globule (approximately 270 ms), were measured. To our knowledge, this is the first experimental evidence supporting the two-stage collapsing kinetics of single synthetic polymer chain previously proposed by de Gennes, Dawson, and Grosberg.     

Assessment of diffusion coefficients of general solvents by PFG-NMR: investigation of the sources error

Accurate measurements of the diffusion coefficients, including an estimate of uncertainty, of various solvent molecules using the PFG-NMR method were performed in this study. Accurate diffusion coefficients were obtained using the Shigemi NMR tube. The relative combined standard uncertainties of the diffusion coefficients were found to be within approximately 0.4%. The three uncertainty sources (signal decay of the standard and the solvent, and diffusion coefficient of standard) equally affect the combined standard uncertainties. Unreliable data were obtained using a normal NMR tube, indicating that convection and background gradient effects significantly affected the accurate measurement of the diffusion coefficients.     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

Molecular mobility and transport in polymer membranes and polyelectrolyte multilayers

Polyelectrolyte multilayers prepared by the layer-by-layer technique provide an efficient way to generate planar structures of tailored surface charge and hydrophobicity, which are used as membranes for pervaporation. The use of polyelectrolyte multilayers to form the membrane permits tailoring the surface charge of the membrane and, thus, selectivity; at the same time, it reduces fouling of the membrane by adsorption of organic matter. Pulsed field gradient (PFG) nuclear magnetic resonance has been used to investigate the diffusion of probe molecules into polymer systems. Evaluation of the apparent diffusion coefficient in porous poly(amide) results in a pore size of 4 microm, as found in electron micrographs. For the pore size obtained for polyelectrolyte multilayers, no equivalent pores could be found in microscopy. Propagators for the diffusion of propanol and propanol-water mixture into multilayers reveal that there might be selective interaction of probe molecules with the polyelectrolyte system.     

模耦合理论计算纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数 (cited: 2)

分析和计算了纳米粒子在聚合物熔体中的含时扩散系数与常规扩散常数. 采用广义朗之万方程描述扩散动力学,并通过模耦合理论计算摩擦记忆内核.为简单起见,只考虑了来自两体碰撞和溶剂密度涨落耦合作用两类微观因素对摩擦记忆内核的贡献. 采用聚合物参考作用点模型以及Percus-Yevick闭合条件计算了聚合物-纳米粒子复合溶液的平衡态结构信息函数;详尽分析了纳米粒子的尺寸与聚合物链的尺寸对扩散动力学的影响. 揭示了结构函数、摩擦记忆内核以及扩散系数等随着纳米粒子半径和聚合物链长的变化关系. 结果表明,对于小尺寸的纳米粒子或者短链的聚合物,短时间的非马尔可夫扩散 动力学特征比较显著,含时扩散系数需要更长的时间弛豫到常规扩散常数. 微观因素对扩散常数的贡献随着纳米粒子尺寸的增加而减小,却随着聚合物链长的增加而增大. 此外,模耦合理论得到的扩散常数与Stokes-Einstein关系的预测值进行比较,发现对于小尺寸的纳米粒子或者长链的聚合物,微观因素对扩散常数的的贡献占主导地位. 相反,当纳米粒子较大或者聚合物链长较短时,流体力学的贡献会发挥重要作用.     

Universal aging features in the restructuring of fractal colloidal gels

We use multispeckle dynamic light scattering to measure the dynamic structure factor, f(q,tau), of gels formed by aggregation of colloids. Although the gel is an elastic solid, f(q,tau) nearly completely decays on long time scales, with an unusual form, f(q, tau) approximately exp{-(tau/tau(f))(mu)}, with mu approximately 1.5 and with tau(f) proportional variant q(-1). A model for restructuring of the gel with aging correctly accounts for this behavior. Aging leads to a dramatic increase in tau(f); however, all data can be scaled on a single master curve, with tau(f) asymptotically growing linearly with age. This behavior is strikingly similar to that predicted for aging in disordered glassy systems, offering convincing proof of the universality of these concepts.     

Diffusion relaxation of photoinduced gratings in polyvinyl acetate latex films

The features of the postexposure relaxation of holographic gratings recorded in inhomogeneous polyvinyl acetate latex films with photosensitive agents (photochromic molecules of fulgide dyes and phenanthrenequinone) have been considered. The diffusion coefficients and rms displacements of izomerized probe in polymer latex particles and aqueous environment are determined within the model of two diffusion states. The effective diffusion coefficient of the molecular probe, which is responsible for the relaxation of gratings, increases with an increase in their period in wet films, whereas in dry films, this parameter is independent of the grating period. In the films subjected to high-temperature treatment the effective diffusion coefficient decreases with an increase in the grating period. The successive stages of grating relaxation in latex films with phenanthrenequinone are related to the diffusion of free molecules, radicals, and polymer chains, as well as to the local displacement of macromolecular segments at distances of 5–25 nm.     

Two-pulse nutation echoes generated by gradients of the radiofrequency amplitude and of the main magnetic field

A two-pulse NMR nutation spectroscopy scheme is suggested that leads to a new type of spin echoes. The amplitude of the radiofrequency (RF) pulses as well as the external magnetic field are assumed to be subject to gradients G(1) and G(0), respectively, in the same but otherwise arbitrary direction. Multiple echoes are predicted and observed at times k(G(1)/G(0))tau(1) and tau -/+ k(G(1)/G(0))tau(1) (k = 1, 2, 3, ...) after the second RF pulse, where tau(1) represents the radiofrequency pulse duration, and tau is the spacing of the RF pulses. Based on these echoes, a method for diffusion measurements is proposed that simultaneously provides the spin-lattice relaxation time and the self-diffusion coefficient.     

利用单分子光学探针测量幂律分布的聚合物动力学

研究聚合物薄膜纳米尺度的动力学特性对于高性能材料的制备具有重要的意义.本文利用尼罗红单分子作为光学探针吸附在聚丙烯酸甲酯(PMA)聚合物链上,研究该聚合物薄膜的动力学特性.通过单分子散焦宽场荧光成像显微镜技术测量了单分子随PMA聚合物链转动弛豫的三维再取向特性,当环境温度高于PMA的玻璃点温度19 K时,发现处于PMA聚合物薄膜中的单分子光学探针的转动态和非转动态的持续时间概率密度服从指数截止的幂律分布.研究结果表明该温度下PMA聚合物薄膜的纳米环境动力学仍存在空间和时间异构性.     

Effect of a monomeric sequence on the structure of hydrated Nafion in the sandwich model and solvent dynamics in nano-channels: a molecular dynamic study

Molecular dynamics simulations are performed to obtain insight into the structural properties of hydrated Nafion using the sandwich model of the polymer membrane. It is shown that a larger distance between the sulfonate groups of a chain leads to the polymer forming a better inverted micelles structure. Water– and hydronium–polymer interfaces are investigated. Comparing our results with others indicates that, from the perspective of distance, the formation of shells of water and hydronium ions is independent of the model and monomer type, but depends on both if the coordination number is considered. The behaviour of water molecules and hydronium ions is also studied dynamically. Our survey shows that there is an increasing jump in the diffusion coefficient of water at a certain distance between the sulfonate groups of a chain, which then tends to change slightly. Such behaviour is discussed on the basis of density, the available space, as well as the loss of one translational degree of freedom of the water molecules at larger distances. The diffusion coefficient for the hydronium ions was also determined to be much smaller than that for water (by 3.5–6.1 times). The diffusion coefficient of the hydronium ions shows a declining jump at a certain distance between the sulfonate groups of a chain, but the jump is not significant as that for the water molecules.     

Computational modeling of cerebral diffusion-application to stroke imaging

Water diffusion within the structure of a brain extracellular space is analyzed numerically for various diffusion parameters of brain tissue namely extracellular space porosity and tortuosity. An algorithm for predicting diffusion pattern of water molecules within human brain considering the mechanics of water diffusion within porous media is developed. The extracellular space is modeled as a homogeneous porous medium with uniform porosity and permeability. Discretization of the fluid flow, heat transfer and mass transport equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Concentration maps are developed in this study for various clinical conditions. The effect of the space porosity and the turtousity on the heat and mass transport within the extracellular space are found to be significant. The results presented in this work play an important role in producing more effective imaging techniques for brain injury based on the apparent diffusion coefficient.