Molecular dynamics simulation of solvent-polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.     

Local and average diffusion of nanosolutes in agarose gel: the effect of the gel/solution interface structure

Fluorescence correlation spectroscopy (FCS) has been used to study the diffusion of nanometric solutes in agarose gel, at microscopic and macroscopic scales. Agarose gel was prepared and put in contact with aqueous solution. Several factors were studied: (i) the role of gel relaxation after its preparation, (ii) the specific structure of the interfacial zone and its role on the local diffusion coefficient of solutes, and (iii) the comparison between the local diffusion coefficient and the average diffusion coefficient in the gel. Fluorescent dyes and labeled biomolecules were used to cover a size range of solutes of 1.5 to 15 nm. Their transport through the interface from the solution toward the gel was modeled by the first Fick's law based on either average diffusion coefficients or the knowledge of local diffusion coefficients in the system. Experimental results have shown that, at the liquid/gel interface, a gel layer with a thickness of 120 microm is formed with characteristics significantly different from the bulk gel. In particular, in this layer, the porosity of agarose fiber network is significantly lower than in the bulk gel. The diffusion coefficient of solutes in this layer is consequently decreased for steric reasons. Modeling of solute transport shows that, in the bulk gel, macroscopic diffusion satisfactorily follows the classical Fick's diffusion laws. For the tested solutes, the local diffusion coefficients in the bulk gel, measured at microscopic scale by FCS, were equal, within experimental errors, to the average diffusion coefficients applicable at macroscopic scales (>or=mm). This confirms that anomalous diffusion applies only to solutes with sizes close to the gel pore size and at short time (相似文献   

Interdiffusion of solvent into glassy polymer films: a molecular dynamics study

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t(1/2) in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick's model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.     

Specific Features in Measuring Particle Size Distributions in Highly Disperse Aerosol Systems

The distribution of highly dispersed aerosols is studied. Particular attention is given to the diffusion dynamic approach, as it is the best way to determine particle size distribution. It shown that the problem can be divided into two steps: directly measuring particle penetration through diffusion batteries and solving the inverse problem (obtaining a size distribution from the measured penetrations). No reliable way of solving the so-called inverse problem is found, but it can be done by introducing a parametrized size distribution (i.e., a gamma distribution). The integral equation is therefore reduced to a system of nonlinear equations that can be solved by elementary mathematical means. Further development of the method requires an increase in sensitivity (i.e., measuring the dimensions of molecular clusters with radioactive sources, along with the activity of diffusion battery screens).     

Gaussian model for localized translational motion: application to incoherent neutron scattering

A simple model based on Gaussian statistics, aimed at describing localized diffusive translational motion in one, two, and three dimensions is presented and used to calculate the corresponding incoherent neutron scattering laws. In the time domain, these laws are closed form mathematical functions. In the frequency domain, some of these laws can be expressed as an infinite series depending on one single index. Owing to this relative simplicity, such a model can advantageously replace previous models such as diffusion on a segment, inside a circle and inside a sphere with an impermeable surface, to analyze neutron quasielastic scattering data associated with molecular motions in confined media. It may also be more realistic when the confinement is defined by soft, ill-defined boundaries.     

Measuring the mutual diffusion coefficient for dodecyl acrylate in low molecular weight poly(dodecyl acrylate) with laser line deflection (Wiener's Method) and the fluorescence of pyrene

Diffusion of small molecules into glassy polymers is quite complicated and almost always non-Fickian. Little work has been done with the diffusion of low molecular weight polymers that are liquids at room temperature (such as poly(dodecyl acrylate)) into their miscible monomers. We have studied three molecular weights under 20 000 to determine if poly(dodecyl acrylate) diffusion into dodecyl acrylate could be treated with Fick's law and if so to determine the values of the diffusion coefficients. We compare two methods for measuring the diffusion of dodecyl acrylate into poly(dodecyl acrylate): We used laser line deflection (Wiener's method) and improved upon the method from published reports. We also used the dependence of pyrene's fluorescence on the viscosity to measure the concentration distribution, and thus to extract the diffusion coefficient. After an initial relaxation period, diffusion in all cases followed Fick's law with a single concentration-independent diffusion coefficient. Comparison of the diffusion coefficients obtained by both methods yielded the same order of magnitude for the diffusion coefficients (10(-7) cm2/s) and showed the same trend in the dependence on the average molecular weight of the polymer (a decrease in the diffusion coefficient with an increase in the molecular weight).     

Modelling of adsorption kinetics and calibration curves of gaseous volatile organic compounds with adsorptive solid-phase microextraction fibre: toluene and acetone for indoor air applications

Solid-phase microextraction (SPME) with adsorptive Carboxen/PDMS fibre is a powerful sampling device for volatile organic compounds (VOCs) at trace levels in air. However, owing to competitive adsorption, quantification remains a challenging task. In this area, a theoretical model, based on Fick's laws and an extended Langmuir equation, is proposed to deal with the adsorption kinetics of acetone/toluene mixture on SPME fibre under various static extraction conditions. The semipredictive model is first used to determine the axial diffusion coefficients of analytes in the sampling device. The model is then tested with a complex VOC mixture, showing good agreement with experimental data.     

微波辅助提取石蒜和虎杖中有效成分的动力学模型

基于微波辅助提取(MAE)中药材中化学成分的非稳态扩散过程, 根据Fick第二定律建立了石蒜中石蒜碱、力可拉敏和加兰他敏以及虎杖中白藜芦醇和大黄素微波辅助提取过程的动力学模型. 研究了提取时间、提取温度及药材粒度等因素对石蒜中石蒜碱、力可拉敏和加兰他敏以及虎杖中大黄素和白藜芦醇的提取率的影响, 采用Matlab软件编程对动力学模型进行回归分析, 拟合的动力学模型与实验结果吻合. 根据模型计算了石蒜中石蒜碱、力可拉敏和加兰他敏以及虎杖中大黄素和白藜芦醇在MAE提取过程中的扩散系数D, 与溶剂加热回流法(SRE)比较, 引入增强因子γ, 表征了微波对溶质分子扩散传质的影响及其对不同基质药材作用的差异.     

Radial Electrochemical Flow Cell for On‐Line Coupling with Mass Spectrometry: Theory and Electrooxidation of Dimethylaminomethyl Ferrocene

A new, radial, miniature, three‐electrode flow cell is introduced. The cell's configuration is most suitable for on‐line electrochemistry – mass spectrometry since it is characterized by low resistive losses, high conversion efficiency, and isolation of the counter electrode reaction by‐products from the product stream reaching the MS. A mathematical model describing convection diffusion in the radial cell is developed. Cell's performance can be predicted over a wide parametric range by a simple mathematical expression which converges to the Levich equation under low conversion conditions. The performance of the cell is demonstrated by studies of dimethylaminomethyl ferrocene (DMAMF) oxidation which is a simple single electron charge transfer reaction and allows validation of the mathematical model. The theoretical predictions of the model were in agreement with the results of on‐line electrochemistry – mass spectrometry studies of DMAMF.     

Simulation of Non-Linear Flow Density in Transition State from the Mathematical Model of the Diffusion of Metal Anions Through a Flat Sheet Supported Liquid Membrane

A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick's second law. From this model, and from Fick's first law, the flow density is derived as a non-linear concentration gradient. Both expressions, concentration and flow density, depend on the thickness of the membrane and on time. Since the rate constant plays an important role in the model, it is considered as the parameter that controls the system and an equation for it is obtained. This equation explains the velocity of the co-transport process. The proposed model takes into account the species co-transported together with the metal ions. An equation for the number of moles of this species is obtained as a function of the metal species. The concentration gradient of this species explains the behaviour of pH in the feed phase during the process. The model is tested against experimental data corresponding to the transport of metal anions in acidic solution and it is shown that the co-transport process is reproduced with high accuracy.     

A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts

In deriving a constitutive equation from a molecular model of polymers in concentrated solutions and melts, Doi and Edwards used a mathematical approximation, the “independent alignment approximation,” which has recently been shown to produce significant error in the particular case of stress relaxation following a double-step strain in opposite direction. In the present paper, in order to examine the approximation in general cases, we derive a new constitutive equation without using the independent alignment approximation. The new equation is a nonlinear integro-differential equation and is solved numerically for several cases, i.e., steady shear and elongational flows, and the transient flows after the start of shear and elongation. It is found that, in the cases examined here, the new constitutive equation gives nearly the same results as the old one: the rheological functions calculated from the two theories differ no more than 30%. This substantiates the expectation that the independent alignment approximation does not produce drastic error as long as the flow direction is not reversed.     

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT)

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)相似文献   

Non-steady-state diffusion in programmed heating

The utilization, for programmed heating, of Fick's second equation concerning non-steady-state diffusion is discussed. Methods for calculating the activation energy of the diffusion process and the factorD ₀ of the Arrhenius equation from a single non-isothermal experiment are suggested.     

The development of a new LDF mass transfer correlation for adsorption in fixed beds

In this study, a general LDF model has been introduced to predict mass transfer rate through adsorbents with the macropore diffusion as the controlling step. Using this relation eliminates the need for solving the time-consuming diffusion equation to find mass transfer rate through the porous adsorbent. The proposed relation was successfully applied in the general mathematical model for an adsorption fixed bed. This correlation was adjusted to be capable of predicting the mass transfer rate in a wide range of gas adsorption systems reported in the literature. This correlation was used in 21 different adsorbent and adsorbate systems. The results demonstrated an excellent agreement between the correlation results and those obtained using Fickian diffusion equation. By applying the developed LDF model instead of diffusion model, a great deal of CPU time can be saved. The latter characteristic will be very important when this model is employed in commercial software such as Aspen Adsorption or Prosim Dynamic Adsorption Column.     

A quasi-equilibrium theory of protein adsorption

A model is developed to describe the adsorption and desorption of proteins to and from a surface film under quasi-equilibrium conditions. Starting from Fick's first law of diffusion, an equation for the flux of molecules to a surface is derived assuming a gradient in the chemical potential from the bulk to the surface and a potential barrier due to an existing surface film. Protein molecules are modeled as components with varying surface areas to depict the different orientations of molecules with respect to the film. For concentrated solutions, formation of multilayer protein films is described by allowing components with small minimum surface areas. The thermodynamic analysis is based on Butler's equation for the chemical potentials of the components of a Gibbs surface layer and a first-order model for the nonideality of the surface layer enthalpy and entropy. The model assumes reversible adsorption, consistent with globular proteins that show little denaturation or flexible-chain proteins that reversibly denature at the interface. The model predicts the behavior of five different experiments measuring film properties of the serum protein albumin in quasi-equilibrium and equilibrium conditions at over 2 orders of magnitude in concentration using a single set of parameters. This provides a new framework for analyzing interactions and adsorption of protein films. The key new features of this model are an extension of the classical Smoluchowski analysis to calculate the adsorption and desorption rate, a model of multilayers with decreased molecular areas to allow effective densities greater than a close-packed monolayer, and a concentration-dependent layer thickness.     

Enhanced translational diffusion of rubrene in sucrose benzoate

The translational diffusion of rubrene in the fragile molecular glass former, sucrose benzoate (SB) (fragility index m approximately 94), has been studied from T(g)+6 K to T(g)+71 K(T(g)=337 K) by using the technique of holographic fluorescence recovery after photobleaching. In the temperature range of the measurements, the translational relaxation functions were observed to decay exponentially, indicating that Fick's law of diffusion governs the translational motion of rubrene in sucrose benzoate. The value of the translational diffusion coefficient D(T) obtained from the 1e time of the translational relaxation function varied from 5.3 x 10(-15) cm2 s(-1) at 343 K to 5.0x10(-9) cm2 s(-1) at 408 K. The temperature dependence of D(T) for diffusion of rubrene in SB is compared with that of the viscosity and the dielectric relaxation time tau(D) of SB. The temperature dependence of D(T) is weaker than that of Teta for T<1.2T(g) but tracks the reciprocal of the dielectric relaxation time 1tau(D) for 1.05T(g)相似文献   

Kinetics and Mechanism of the Sorption of Some Aromatic Amines onto Amberlite IRA-904 Anion-Exchange Resin

The kinetics of the sorption of aromatic amines such as o-aminophenol (o-AP), o-phenylenediamine (o-PDA), and p-phenylenediamine (p-PDA) onto Amberlite anion-exchange resin in chloride form was investigated in batch experiments spectrophotometrically at different temperatures. The sorption rate is zero order in all amines sorbed, increasing directly in the order: p-PDA相似文献   

The concentration dependence of the diffusion and permeability in a homogeneous membrane

For the sorption and diffusion coefficient dependence on the concentration of the penetrant the transport properties of a homogeneous medium are calculated. The diffusion current is assumed to be proportional to the negative gradient of the chemical potential. This is in contrast with the first Fick's law that assumes this current to be proportional to the negative gradient of the concentration of the penetrant. The difference between the two cases depends on the concentration dependence of the sorption coefficient. In a homogeneous membrane the chemical potential formulation leads to an equation which is very similar to the Fickian expression. The apparent diffusion coefficient, however, depends not onlly on the transport resistance but also on the deviation of the sorption coefficient from constancy.