Diffusion trapping times and dynamic percolation in an Ising system

We address the problem of diffusion through dynamic Ising network structures using random walkers (RWs) whose net displacements are partitioned into two contributions, arising from (1) transport through neighboring "conducting" clusters and (2) self-diffusion of the site on which the RW finds itself, respectively. At finite temperatures, the conducting clusters in the network exhibit correlated dynamic behavior, making our model system different to most prior published work, which has largely been at the random percolation limit. We also present a novel heuristic scaling analysis for this system that utilizes a new scaling exponent theta(z) for representing RW trapping time as a function of "distance" from the dynamic percolation transition. Simulation results in two-dimensional networks show that when theta(z) = 2, a value found from independent physical arguments, our scaling equations appear to capture universal behavior in the system, at both the random percolation (infinite temperature) and finite temperature conditions studied. This study suggests that the model and the scaling approach given here should prove useful for studying transport in physical systems showing dynamic disorder.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Kinetic lattice Monte Carlo simulation of viscoelastic subdiffusion

We propose a kinetic Monte Carlo method for the simulation of subdiffusive random walks on a Cartesian lattice. The random walkers are subject to viscoelastic forces which we compute from their individual trajectories via the fractional Langevin equation. At every step the walkers move by one lattice unit, which makes them differ essentially from continuous time random walks, where the subdiffusive behavior is induced by random waiting. To enable computationally inexpensive simulations with n-step memories, we use an approximation of the memory and the memory kernel functions with a complexity O(log?n). Eventual discretization and approximation artifacts are compensated with numerical adjustments of the memory kernel functions. We verify with a number of analyses that this new method provides binary fractional random walks that are fully consistent with the theory of fractional Brownian motion.     

On the number of benzenoid hydrocarbons

We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b(h) with h hexagons. We obtain b(h) up to h = 35. We prove that b(h) approximately const.kappa(h), prove the rigorous bounds 4.789 < or = kappa < or = 5.905, and estimate that kappa = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function summation operator b(h)z(h) approximately A(z) log(1 - kappa z), estimate A(1/kappa) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration (h) of benzenoids of size h grows as h(2 nu), with nu = 0.64115(5).     

Calculating the hopping times of confined fluids: two hard disks in a box

The dynamical transition between the anomalous single file diffusion of highly confined fluids and bulk normal diffusion can be described by a phenomenological model involving a particle hopping time tau(hop). We suggest a theoretical formalism that will be useful for the calculation of tau(hop) for a variety of systems and test it using a simple model consisting of two hard disks confined to a rectangular box with hard walls. In the case where the particles are moving diffusively, we find the hopping time diverges as a power law in the threshold region with an exponent of -(3/2). Under conditions where the particles move inertially, transition state theory predicts a power law behavior with an exponent of -2. Molecular dynamics simulations confirm the transition state theory result for inertial dynamics, while Brownian dynamics simulations suggest the scaling exponent is highly sensitive to the details of the algorithm.     

Ideal mixing behavior of the debye process in supercooled monohydroxy alcohols

Glass-forming monohydroxy alcohols exhibit two dielectric relaxation signals with super-Arrhenius temperature dependence: a Debye peak and an asymmetrically broadened alpha-process. We explore the behavior of these distinct relaxation features in mixtures of such liquids by dielectric measurements. The study focuses on the viscous regime of two binary systems: 2-methyl-1-butanol with 2-ethyl-1-hexanol and 1-propanol with 3,7-dimethyl-1-octanol. We find that the logarithmic relaxation time, log(tau), of the Debye peak follows an ideal mixing law (linear change with mole fraction), even in the case of mixing structurally dissimilar components. By contrast, the log(tau) versus mole fraction curve for the alpha-process is nonlinear, indicative of slower structural relaxation relative to the expectation on the basis of ideal mixing behavior. The latter observation is analogous to the effect of composition on viscosity, heat of mixing, and glass-transition temperature, whereas the ideal mixing of log(tau) seen for the Debye peak is the exception. We conclude that the unusual ideal mixing behavior of dielectric relaxation in monohydroxy alcohols is not a result of structural similarity, but rather yet more evidence of the Debye process being decoupled from other dynamic and thermodynamic properties.     

非晶氮化铁薄膜的生长机制——传统动力学生长标度方法的适用性

采用动力学标度方法研究了磁控溅射沉积的非晶氮化铁薄膜的动力学生长机制, 结果表明, 具有连续类柱状岛形貌的非晶氮化铁薄膜具有标度不变的自仿射分形特点, 其粗糙度指数α=0.82±0.21, 生长指数β=0.44±0.07, 动力学标度指数1/z=0.54±0.07. 薄膜生长符合提出的热重新发射生长模型.     

Two-dimensional colloidal aggregation: concentration effects

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration phi, following the law: d(f)=d(fo)+aphi(c). For the on-lattice simulations the fractal dimension in the zero concentration limit, d(fo), was 1.451+/-0.002, while for the off-lattice simulations the same quantity took the value 1.445+/-0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633+/-0.021 and 1.046+/-0.032, while for the off-lattice simulations they were 1.005+/-0.059 and 0.999+/-0.045, respectively. For the exponents z and z', defining the increase of the weight-average (S(w)(t)) and number-average (S(n)(t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z=z(o)+bphi(d) and z'=z'(o)+b'phi(d'). For the on-lattice simulations, z(o), b, and d were equal to 0.593+/-0.008, 0.696+/-0.068, and 0.485+/-0.048, respectively, while for the off-lattice simulations they were 0.595+/-0.005, 0.807+/-0.093, and 0.599+/-0.051. In the case of the exponent z', the quantities z'(o), b', and d' were, for the on-lattice simulations, equal to 0.615+/-0.004, 0.814+/-0.081, and 0.620+/-0.043, respectively, while for the off-lattice algorithm they took the values 0.598+/-0.002, 0.855+/-0.035, and 0.610+/-0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d(f)=d(fo)+aphi(c), with d(fo)=1.560+/-0.004, a=0.342+/-0.039, and c=1.000+/-0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S(w)(t) and S(n)(t) in the aggregation regime considered, and no exponents z and z' were defined. We argue however that for sufficiently long periods of time the cluster averages should tend to those for DLCA and, therefore, their exponents should coincide with z and z' of the DLCA case. Finally, we present the bell-shaped master curves for the scaling of the cluster size distribution function and their evolution when the concentration increases, for both the DLCA and RLCA cases.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Fractal to classical crossover of chemical reactions

Computer simulations on binary reactions of random walkers (A + A → A) on two- and three-dimensional percolation clusters bear out the recent superuniversality conjecture (integrated reaction rate α t²¹³). Moreover, the fractal-to-euclidean crossover (t²¹³ to t dependence) parallels that of the single walker.     

Density and energy relaxation in an open one-dimensional system

A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically. In this model, the random walkers interact through excluded volume interaction (single-file system); and the total number of walkers in the lattice can fluctuate because of exchange with a bath. In addition, the movement of the random walkers is biased by an external perturbation. Two models for the latter are considered: (1) an inverse potential (V proportional, variant 1/r), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential (V proportional, 1/r6). The calculated density of the walkers and the total energy show interesting dynamics. When the size of the system is comparable to the range of the perturbing field, the energy relaxation is found to be highly nonexponential. In this range, the system can show stretched exponential (e-(t/taus)beta) and even logarithmic time dependence of energy relaxation over a limited range of time. Introduction of density exchange in the lattice markedly weakens this nonexponentiality of the relaxation function, irrespective of the nature of perturbation.     

Interpretation of light-scattering spectra in terms of particle displacements

Quasielastic light-scattering spectroscopy is regularly used to examine the dynamics of dilute solutions of diffusing mesoscopic probe particles in fluids. For probes in a simple liquid, the light-scattering spectrum is a simple exponential; the field correlation function g(1)(q,tau) of the scattering particles is related to their mean-square displacements X2 identical with [(delta x(tau))2] during tau via g(1)(q,tau) = exp(-1/2 q2X2). However, demonstrations of this expression refer only to identical Brownian particles in simple liquids and show that if the form is correct then it is also true for all tau that g(1)(q,tau) = exp(-gamma tau), a pure exponential in tau. In general, g(1)(q,tau) is not a single exponential in time. A correct general form for g(1)(q,tau) in terms of the X(2n), replacing the incorrect exp(-1/2 q2X2), is obtained. A simple experimental diagnostic determining when the field correlation function gives the mean-square displacement is identified, namely, g(1)(q,tau) only reveals X2 if g(1)(q,tau) is a single exponential in tau. Contrariwise, if g(1)(q,tau) is not a single exponential, then g(1)(q,tau) depends not only on X2 but on all higher moments X(2n). Corrections to the crude approximation g(1)(q,tau) = exp(-1/2 q2X2) closely resemble the higher spectral cumulants from a cumulant expansion of g(1)(q,tau).     

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.     

Hopping time of a hard disk fluid in a narrow channel

We use Monte Carlo (MC) and molecular dynamics (MD) methods to study the self-diffusion of hard disk fluids, confined within a narrow channel. The channels have a pore radius of Rp, above the passing limit of hard disk diameter (sigma(hd)). We focus on the average time (tau(hop)) needed for a hard disk to hop past a nearest neighbor in the longitudinal direction. This parameter plays a key role in a recent theory of the crossover from single-file diffusion to the bulk limit. For narrow channels near the hopping threshold (Rp=1 in units of sigma(hd)), both MC and MD results for tau(hop) diverge as approximately (Rp-1)(-2). Our results indicate that the scaling law exponent does not appear to be dependent on the differences between the two dynamics. This exponent is consistent with the prediction of an approximate transition state theory.     

Physical insights from a penetration depth model of optically pumped NMR

A model of optically pumped NMR (OPNMR) behavior in GaAs that connects the photon energy dependence of the OPNMR signal intensity for (69)Ga with different polarizations of light has been developed. Inputs to this model include experimental conditions--external magnetic field (B(0)), temperature (T), and optical pumping parameters (tau(L), laser helicity)--as well as parameters that arise from sample-specific characteristics--electron spin lifetime (T(1e)), electron lifetime (tau(e)), electron-nuclear correlation time (tau(c)), and sample thickness (z). These various inputs affect the profile of the OPNMR signal intensity as a function of photon energy (E) in a predictable manner. Therefore, the profile can serve as a composite fingerprint by which individual parameters can be inferred when not known. Characteristics of the profile include the photon energy for maximum OPNMR signal intensity and the intensity ratio between sigma(+) and sigma(-) light.     

Kinetics of polymer translocation through a pore

We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1) proportional to t(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t) proportional to 1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1) proportional to t(5/8) and tau(t) proportional to n(8/5).     

Relationship between the nonexponentiality of relaxation and relaxation time in the problem of glass transition

By analyzing the experimental data for various glass-forming liquids and polymers, we find that the nonexponentiality, beta, and the relaxation time, tau, are commonly related: log(tau) is an approximately linear function of 1/beta, followed in most cases by a crossover to a higher linear slope. We rationalize this relationship in the recently developed elastic approach to the glass transition. The key to the observed common relationship between beta and tau is that the two quantities are governed by the same parameter, the liquid elasticity length, d el. The increase of d el on lowering temperature increases tau and decreases beta, resulting in the observed common relationship between beta and tau. In this picture, we also discuss the crossovers of beta and tau at low temperature.     

Critical behavior of trifunctional randomly branched polycyanurates

The behavior near the gelation threshold of trifunctional randomly branched polycyanurates is studied by static and dynamic light scattering. By static measurements the critical exponents γ, σ and η were obtained, which describe the divergence of the weight average (M_w) and the cutoff (M*) molecular weights and the radius of gyration (R_g) respectively. All these independently measured exponents together with τ, characterizing the power law behavior of the molecular weight distribution and measured by size exclusion chromatography coupled with light scattering, confirm the predictions of the three-dimensional percolation theory. With the help of size exclusion chromatography coupled with a light scattering and a viscosity detector, a fractal dimension D = 2.24 is obtained. On the other side, from the corresponding exponent for the whole unfractionated samples a fractal dimension D = 2.21 results, using a theory of Daoud. This suggests that the fractal dimension of the polycyanurates in dilute solution lies between the theoretical predictions D = 2.5 for the unswollen and D = 2.0 for the completely swollen state. Furthermore, it is shown by dynamic light scattering that the power law behavior over some decades in time of the time autocorrelation function and the divergence of the mean relaxation time are characteristics of the gelpoint. The development with increasing reaction time of the time correlation function of the gelling system from the pregel through the gelpoint into the gel state is analyzed quantitatively by a hybrid of a stretched exponential and a power law function.