Na型斜发沸石上Na+-Cu2+离子交换过程动力学

用静态离子交换法研究了Ｎａ型斜发沸石上２Ｎａ＝Ｃｕ＾２＋离子交换动力学，分别测定了液膜扩散常数Ｒ，粒内扩散系数Ｄ和滞留时间Ｔｄ，实验发现，离子交换起始为液膜扩散控制，随后在交换的大部分时间内为粒内扩散控制，并就温度、浓度对离子交换过程速率，Ｃｕ＾２＋平衡交换数量以及滞留时间的影响进行了讨论。     

Dependence of growth of the phases of multiphase binary systems on the diffusion parameters

A mathematical model of the diffusion interaction of a binary system with several phases on the equilibrium phase diagram is presented. The theoretical and calculated dependences of the layer thickness of each phase in the multiphase diffusion zone on the isothermal annealing time and the ratio of the diffusion parameters in the neighboring phases with an unlimited supply of both components were constructed. The phase formation and growth in the diffusion zone during “reactive” diffusion corresponds to the equilibrium state diagram for two components, and the order of their appearance in the diffusion zone depends only on the ratio of the diffusion parameters in the phases themselves and on the duration of the incubation periods. The dependence of phase appearance on the incubation periods, annealing time, and difference in the movement rates of the components across the interface boundaries was obtained. An example of the application of the model for processing the experimental data on phase growth in a two-component three-phase system was given.     

The effect of a carrier on the residence time of atoms in an arc discharge plasma

The residence time of impurity atoms in an arc discharge has been calculated using the solution of both steady state and non-steady state equations which describe four different mass transport models; conventional diffusion by itself; conventional diffusion together with the movement of ions in an electric field; conventional diffusion together with ambipolar diffusion and conventional diffusion together with both ambipolar diffusion and the movements of ions in an electric field. The best agreement between measured and calculated results is obtained using the model which considers only conventional and ambipolar diffusion. This model also adequately explains the effect of a carrier on the residence time of atoms in the arc discharge.     

Modeling the kinetics of gas adsorption in multilayer porphyrin films

A kinetic model is proposed to describe the diffusion and adsorption behavior of gas in multilayer films. Numerical solutions are attained on time scales of seconds using a finite differencing approximation to the kinetic equations. Predictions of this model are compared to experimental data for the case of NO2 diffusing through a porphyrin film. The model predicts a binding energy for the NO2 porphyrin interaction of 0.72 eV. It also predicts that for this system diffusion is the limiting factor for the adsorption response time of the film, although the recovery time is determined by both the diffusion coefficient and NO2 binding energy. Comparison with experiment gives a predicted diffusion coefficient of approximately 10(-14) m2.s-1.     

The significance of the surface condition in solutions to the diffusion equation: explaining “anomalous” sigmoidal, Case II, and Super Case II absorption behavior

Absorption into polymers is frequently described by the terms Fickian, sigmoidal (S-shaped), Case II, or Super Case II. This terminology is used to describe absorption that is respectively, linear with the square root of time, has a slight delay or S-shape with the square root of time, is linear with linear time, or increases more rapidly than with linear time. Solutions to the diffusion equation, Fick’s second law, that include a potentially significant surface condition are shown to reproduce all of these. Sigmoidal absorption results when the surface condition is moderately significant for either a constant diffusion coefficient or exponential diffusion coefficients. Exponential diffusion coefficients and a lower surface mass transfer coefficient result in Case II type behavior, with Super Case II behavior resulting when the surface condition becomes still more significant. The results reported here are supported by extensive experimental data with reasonable and verifiable values for the diffusion coefficients and surface mass transfer coefficients.     

Application of holographic interferometric microscopy to the study of diffusion in the polyvinylpyrrolidone–iodine system

Interferometric studies of the diffusion of molecular iodine into polyvinylpyrrolidone (PVP) are described. The diffusion process is observed by means of a holographic microscope which, with a camera, permits holograms to be recorded during the polymer–iodine interaction. The holograms are subsequently used to produce interferograms that monitor the diffusion process as a function of time. Measurements taken from the interferograms indicate that the diffusion mechanism is not purely Fickian and that the diffusing boundary of iodine is characteristic of case II diffusion. The interferograms yield values for average diffusion coefficients as a function of sample thicknesses that range from 2.32 to 9.53 × 10^?10 cm²/sec.     

Influence of potential and time on the dissolution of Sn-In, Sn-Zn, and In-Zn alloys with a low content of the second component in chloride media

The dissolution of low-melting alloys with low contents of the more negative component is investigated as a function of time and potential. It is shown, by taking potentiostatic measurements, that several time intervals exist where steady-state and non-steady-state diffusion coefficients are realized. The main dissolution parameters are potential-dependent, and two ranges exist where the steady-state diffusion coefficient varies with the potential.     

Kinetics of the initial steps of G protein-coupled receptor-mediated cellular signaling revealed by single-molecule imaging.

We report on an in vivo single-molecule study of the signaling kinetics of G protein-coupled receptors (GPCR) performed using the neurokinin 1 receptor (NK1R) as a representative member. The NK1R signaling cascade is triggered by the specific binding of a fluorescently labeled agonist, substance P (SP). The diffusion of single receptor-ligand complexes in plasma membrane of living HEK 293 cells is imaged using fast single-molecule wide-field fluorescence microscopy at 100 ms time resolution. Diffusion trajectories are obtained which show intra- and intertrace heterogeneity in the diffusion mode. To investigate universal patterns in the diffusion trajectories we take the ligand-binding event as the common starting point. This synchronization allows us to observe changes in the character of the ligand-receptor-complex diffusion. Specifically, we find that the diffusion of ligand-receptor complexes is slowed down significantly and becomes more constrained as a function of time during the first 1000 ms. The decelerated and more constrained diffusion is attributed to an increasing interaction of the GPCR with cellular structures after the ligand-receptor complex is formed.     

Pulsed Photoacoustic Study of the Diffusion of Chromophores in Human Skin

The technique of pulsed photoacoustic spectroscopy was used to investigate the diffusion of chromophores in human skin. The kinetic of diffusion has been studied for five solutions at different concentrations in a mixture of chromophores, as used in commercial sunscreens. In addition to the classical macroscopic interpretation of the diffusion process, a new method is shown to give more detailed information on chromophore presence at different depths in skin. For the first time, results are expressed in the frequency domain by means of the Fourier transform applied to the photoacoustic signal. The spectra are discussed versus the depth in skin samples and the time of diffusion kinetics. This new method of data analysis is shown to be very useful for understanding the influence of the internal structure of a medium on the penetration rate of chromophores into skin.     

Excitation transfer induced spectral diffusion and the influence of structural spectral diffusion

The theory of vibrational excitation transfer, which causes spectral diffusion and is also influenced by structural spectral diffusion, is developed and applied to systems consisting of vibrational chromophores. Excitation transfer induced spectral diffusion is the time-dependent change in vibrational frequency induced by an excitation on an initially excited molecule jumping to other molecules that have different vibrational frequencies within the inhomogeneously broadened vibrational absorption line. The excitation transfer process is modeled as Fo?rster resonant transfer, which depends on the overlap of the homogeneous spectra of the donating and accepting vibrational chromophores. Because the absorption line is inhomogeneously broadened, two molecules in close proximity can have overlaps of their homogeneous lines that range from substantial to very little. In the absence of structural dynamics, the overlap of the homogeneous lines of the donating and accepting vibrational chromophores would be fixed. However, dynamics of the medium that contains the vibrational chromophores, e.g., a liquid solvent or a surrounding protein, produce spectral diffusion. Spectral diffusion causes the position of a molecule's homogeneous line within the inhomogeneous spectrum to change with time. Therefore, the overlap of donating and accepting molecules' homogeneous lines is time dependent, which must be taken into account in the excitation transfer theory. The excitation transfer problem is solved for inhomogeneous lines with fluctuating homogeneous line frequencies. The method allows the simultaneous treatment of both excitation transfer induced spectral diffusion and structural fluctuation induced spectral diffusion. It is found that the excitation transfer process is enhanced by the stochastic fluctuations in frequencies. It is shown how a measurement of spectral diffusion can be separated into the two types of spectral diffusion, which permits the structural spectral diffusion to be determined in the presence of excitation transfer spectral diffusion. Various approximations and computational methodologies are explored.     

Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: molecular dynamics simulation

Brownian diffusion of rod-like polymers in the presence of randomly distributed spherical obstacles is studied using molecular dynamics simulations. It is observed that dependence of the reduced diffusion coefficient of these macromolecules on the available volume fraction can be described reasonably by a power law function. Despite the case of obstructed diffusion of flexible polymers in which reduced diffusion coefficient has a weak dependence on the polymer length, this dependence is noticeably strong in the case of rod-like polymers. Diffusion of these macromolecules in the presence of obstacles is observed that is anomalous at short time scales and normal at long times. Duration time of the anomalous diffusion regime is found that increases very rapidly with increasing both the polymer length and the obstructed volume fraction. Dynamics of diffusion of these polymers is observed that crosses over from Rouse to reptation type with increasing the density of obstacles.     

Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient

A general formalism for treating lateral diffusion in a multilayer medium is developed. The formalism is based on the relation between the lateral diffusion and the distribution of the cumulative residence time, which the diffusing particle spends in different layers. We exploit this fact to derive general expressions which give the global and local time-dependent diffusion coefficients in terms of the average cumulative times spent by the particle in different layers and the probabilities of finding the particle in different layers, respectively. These expressions are used to generalize two recently obtained results: (a) A solution for the short-time behavior of the lateral diffusion coefficient in two layers separated by a permeable membrane obtained by a perturbation theory is extended to the entire range of time. (b) A solution for the time-dependent diffusion coefficient of a ligand, which repeatedly dissociates and rebinds to sites on a planar surface, obtained under the assumption that the medium above the surface is infinite, is generalized to allow for the medium layer of finite thickness. For the latter problem we derive an expression for the Fourier-Laplace transform of the propagator in terms of the double Laplace transform of the probability density of the cumulative residence time spent by the ligand in the medium layer.     

Diffusion study of a polymer–diluent system using the optical mass transport method

Thermotropic polymers and low-molecular-weight mesogens share many common textural features. This circumstance is exploited to determine diffusion coefficents in a system consisting of a cholesteric polymer and a low-molecular-weight nematogen using the recently developed optical mass transport method. The self-diffusion coefficient and its concentration dependence were determined by using a distance–time approach, whereas the time dependence of the mutual diffusion coefficient was evaluated by a conventional concentration–distance analysis of the diffusion profile. Comparison with literature data indicates satisfactory agreement. The coefficient of the scaling law relating the self-diffusion coefficient and concentration is in accord with the value predicted by de Gennes for semidilute polymer solutions.     

Diffusion in the presence of periodically spaced permeable membranes

The diffusion of molecules in biological tissues and some other microheterogeneous systems is affected by the presence of permeable barriers. This leads to the slowdown of diffusion at long times as compared to barrier-free diffusion. At short times the effect of barriers is weak. In consequence, the diffusion coefficient D(t) decreases as a function of time. We derive an exact solution for the Laplace transform of D(t) for diffusion in a space separated into layers by equally spaced, parallel identical planes of arbitrary permeability. Additionally, we give an approximation to D(t) which is reasonably accurate over the whole range of the partition permeability from zero (the case of isolated layers) to infinity (the case of no barriers).     

Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.     

Calculation of the diffusion coefficient in a liquid based on the force covariance function

Methods of optimal use of statistical information on the Brownian motion of molecules in a liquid for calculating the diffusion coefficient are considered. Relationships between covariance functions for the displacement of a molecule, its velocity, and the force acting on the molecule are established. It is proposed the method of calculation of the diffusion coefficient estimates should be made using the force covariance function, which enables to reduce the time of simulation of the molecular motion. The proposed method is used for callculating diffusion coefficients for some systems.     

Diffusion at the liquid-vapor interface

Recently, the intrinsic sampling method has been developed in order to obtain, from molecular simulations, the intrinsic structure of the liquid-vapor interface that is presupposed in the classical capillary wave theory. Our purpose here is to study dynamical processes at the liquid-vapor interface, since this method allows tracking down and analyzing the movement of surface molecules, thus providing, with great accuracy, dynamical information on molecules that are "at" the interface. We present results for the coefficients for diffusion parallel and perpendicular to the liquid-vapor interface of the Lennard-Jones fluid, as well as other time and length parameters that characterize the diffusion process in this system. We also obtain statistics of permanence and residence time. The generality of our results is tested by varying the system size and the temperature; for the latter case, an existing model for alkali metals is also considered. Our main conclusion is that, even if diffusion coefficients can still be computed, the turnover processes, by which molecules enter and leave the intrinsic surface, are as important as diffusion. For example, the typical time required for a molecule to traverse a molecular diameter is very similar to its residence time at the surface.     

Diffusion of gas molecules in the polystyrene matrix

We have studied the diffusion of gas molecules inside an amorphous polystyrene matrix. The diffusion constant of several gases at T = 450 K in polystyrene was computed. Particular attention was given to CO₂ for temperatures between 300 and 800 K. The temperature dependence of the diffusion constant and the relationship between the diffusion constant and the diameter of the gas molecule were analysed. We further examined the motion of the gas molecules on the short time scale not readily accessible to experimental observation. Here we used the cage overlap function which gives information on the typical cage sizes and distribution times. On the short time scale the gas molecules show a hopping behaviour. The distribution of the time period between hopping events, the distance between the cages and the size of the cages in the polystyrene matrix in the presence of guest molecules were calculated. Through the analyzing, we get a clearer picture from the behaviour of gas molecules on short time scale in the polymer matrix.     

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.