Fick's Coefficient Research Articles

Stationary Mixture BGK Models with the Correct Fick Coefficients

Stationary Mixture BGK Models with the Correct Fick Coefficients

Enhanced Organic Thin-Film Transistor Stability by Preventing MoO3 Diffusion with Metal/MoO3/Organic Multilayered Interface Source-Drain Contact.

The source-drain electrode with a MoO3 interfacial modification layer (IML) is considered the most promising method to solve electrical contact issues impeding organic thin-film transistors (OTFTs) from commercialization. However, this method raises many concerns because MoO3 might diffuse into organic materials, which causes device instability. In this work, we observed a significant device stability degradation by damaging on/off switching performance caused by MoO3 diffusion. To prevent the MoO3 diffusion, a source-drain electrode with a multilayered interface contact (MIC) consisting of a top-down stack of metal, MoO3 IML, and organic buffer layer (OBL) is proposed. In the MIC device, the MoO3 IML serves well for its intended functions of reducing contact resistance and suppressing minority carrier injection to the OTFT channel. The inclusion of OBL to the MIC helps block MoO3 diffusion and thereby leads to better device stability and an increased on/off ratio. Through combinations with several organic compounds as a buffer layer, the MoO3 diffusion related electrical behaviors of OTFTs are systematically studied. Key parameters related to MoO3 diffusion such as the Fick coefficient and bias-stress stability such as carrier trapping time are extracted from numerical device analysis. Finally, we summarize a general rule of material selection for making robust source-drain contact.

Fick and Maxwell-Stefan Diffusion Coefficients in the Ternary Liquid Mixture of Acetone-Methanol-Chloroform

Fick diffusion coefficients are calculated by means of molecular simulation for liquid mixtures containing acetone, methanol and chloroform at 1 atm and 298 K for different compositions. For this means, Maxwell-Stefan (MS) diffusion coefficients were calculated using physical properties of the components and thermodynamic factors, Γ, using three different models of Wilson, NRTL and UNIQUAC. Because of the lack of experimental data for Fick diffusivities for ternary system, the validity of the model was tested by comparing Fick diffusivities obtained for binary subsystems with experimental data for acetone- chloroform system. The results were in good agreement. So the Fick coefficients, Maxwell-Stefan diffusion coefficient and the thermodynamic factors were predicted for the ternary mixture as well as its binary subsystems by molecular simulation in a consistent manner. The presented ternary diffusion data should facilitate the development of aggregated predictive models for diffusion coefficients of polar and hydrogen-bonding systems and allows for an efficient and consistent prediction of multicomponent Fick diffusion coefficients from molecular models.

Fick diffusion coefficients via molecular dynamics: An alternative approach in the Fourier domain

Mutual diffusion coefficient data are required for several systems of scientific and engineering interest to properly describe mass transport phenomena over a wide range of pressures, temperatures, and compositions. In this work, we calculated Fick diffusion coefficients for some CO2 and n-alkane mixtures at high pressures using a new method, which we derived by introducing modifications to the Fourier Correlation Method (FCM) originally proposed by Nichols and Wheeler [I&EC Research, 54, 12,156–12,164 (2015)]. The modified FCM (mFCM) results were validated through comparisons with experimental data and with Fick coefficients calculated by employing well-established Molecular Dynamics methodologies. The new approach has some interesting advantages, such as providing Fick coefficients for molecular systems directly through a single equilibrium calculation, in contrast to traditional methods in which an extra calculation is needed to obtain the so-called thermodynamic factor. It is shown that the new approach considerably reduces the finite-size effect of the simulation box on the calculated diffusion coefficients, which are thus obtained in the thermodynamic limit.

Mass transition and mass diffusion coefficients in a diffuse interface model

The purpose of this paper is to determine the mass transition and mass diffusion coefficients in the diffuse interface model. By means of the thermodynamic probabilities of molecules transiting (phase change) and shifting (diffusing), the rate of mass transition and the mass diffusion flux are derived first. By comparing them with the corresponding formulas in the diffuse interface model, the two coefficients are then obtained. The mass transition coefficient is proportional to the rate of molecular unidirectional transition under the mutual equilibrium of liquid and vapor species. The mass diffusion coefficient is proportional to the rate of molecular unidirectional travel through a unit surface under the condition that two local elements at two sides of the surface are in mutual equilibrium. This diffusion coefficient can finally be expressed as the product of the Fick concentration diffusion coefficient and the mixing density besides an energy (or temperature) factor. The Fick coefficient obtained at present is reduced to the self-diffusion coefficient at the gas boundary of the binary mixing layer and becomes the Fick diffusion coefficient of gas in pure liquid at the liquid boundary. The present coefficients (including Fick coefficient) are different from the existing ones in the literature.

Experimental measurement of the effective diffusion and thermodiffusion coefficients for binary gas mixture in porous media

Thermodiffusion or Soret effect, corresponding to a mass flux caused by a temperature gradient applied to fluid mixture, has been taken into account in many porous media applications, particularly in chemical engineering and geophysics. In the literature, the effective macro-scale diffusion coefficients are now well established, while uncertainty remains concerning the relationship between the effective thermodiffusion coefficient and micro-scale parameters (such as pore-scale geometry). Our previous study on theoretical model of effective thermodiffusion coefficient for a pure diffusion regime confirmed that the tortuosity factor acts in the same way on both Fick diffusion coefficient and on thermodiffusion coefficient. In this study, new experimental results obtained with a two bulb apparatus are presented. The diffusion and thermodiffusion of a helium–nitrogen and helium–carbon dioxide system through cylindrical samples filed with glass spheres of different diameter are measured at the atmospheric pressure. Concentrations are determined by analyzing the gas mixture composition in the bulbs with a katharometer device. A transient-state method for coupled evaluation of thermodiffusion and Fick coefficient in two bulbs system is proposed. The obtained results are in good agreement with theoretical results from previous study and emphasize the porosity of the medium influence on both diffusion and thermodiffusion process. The tortuosity of the medium calculated using both effective diffusion and effective thermodiffusion coefficients are the same.

Transient-state method for coupled evaluation of Soret and Fick coefficients, and related tortuosity factors, using free and porous packed thermodiffusion cells: Application to CuSO4 aqueous solution ( 0.25M)

The measurement of Soret coefficients in liquids is not easy and usually not very precise because the resulting concentration gradient is small and moreover can be perturbed by undesired convection currents. In order to suppress, or to drastically reduce these convection currents, the use of a porous medium is sometimes suggested. The question arises as to whether the Soret coefficient is the same in free fluid and in porous medium. This is the aim of this paper. To this end, for a given liquid mixture, the time evolution of the vertical concentration gradient is experimentally measured in the same thermodiffusion cell filled first with the free liquid and next with a porous medium followed by saturation by the liquid mixture. Both the isothermal diffusion (Fick) coefficient and the Soret coefficient can be deduced, providing that a correct working equation is used. The proposed equation results from integration of the general mass conservation equation with realistic boundary conditions (zero mass flux at the boundaries) and some simplifying assumptions rendering this equation more tractable than the one proposed some decades ago by Bierlein (J.A. Bierlein, J. Chem. Phys. 23, 10 (1955)). The method is applied here to an electrolytic solution (CuSO4, 0.25 M) at a mean temperature of 37 degrees C. The Soret coefficients in free and porous medium (zircon microspheres in the range of 250-315 x 10(-6) m) may be considered to be equal ( S(T) = 13.2+/-0.5 x 10(-3) K(-1)) and the tortuosity factors for the packed medium are the same relative to thermodiffusion and Fick coefficients (tau = 1.51+/-0.02).

Multicomponent surface diffusion of adsorbed species: a description based on the generalized Maxwell—Stefan equations

Surface diffusion of n sorbed species is described using the generalized Maxwell-Stefan (GMS) formulation of irreversible thermodynamics. The approach treats the vacant sites (V) as the ( n + 1)th component in the diffusing mixture. The diffusion coefficients defined in the GMS treatment are basically of two kinds: (i) the coefficient Đ; iV , signifying the facility for diffusive exchange between species i and the vacant sites; and (ii) the coefficients Đ; ij , describing the facility for counter-exchange between the sorbed species i and j. The GMS counter-sorption diffusivity is, in turn, relatable to the coefficients Đ; iV and Đ; jV ; the latter are estimated from single-sorbent diffusivity data. The direct influence of the fractional surface analyzed. For diffusion of a single sorbed species the Fick surface diffusivity D 1 V is related to the GMS diffusivity Đ; 1 V by D 1 V = Đ; 1 V /(1 − θ 1) a known result; the GMS coefficient Đ; 1 V is commonly referred to as the “intrinsic” or “corrected” diffusivity while the Fick coefficient D 1 V is usually termed the “apparent” diffusivity. The expression for the tracer diffusivity: ▪ derived from the GSM formulation is a convenient new result; its utility in interpretation of tracer diffusion data is demonstrated using the experiments of Pope (1967, Trans. Faraday Soc. 63, 734–742). Surface diffusion of multicomponent ( n⩾2) sorbed species is described by a matrix of Fick diffusivities [D] ≡ [B] −1 [Γ]. The elements of [B] are explicitly related to the GMS coefficients Đ; iV and Đ; if , while the matrix of thermodynamic factors [Γ], derivable from the adsorption isotherm, portrays the direct influence of the surface occupancies θ i on surface transport. The results of the prediction of [D] fo binary sorption are in broad agreement with the Monte Carlo simulations of Palekar and Rajadhyaksha (1986, Chem. Engng Sci. 41, 463–468). For constant value of the Fick matrix [D], analytical solutions for transient uptake of multicomponent mixtures are obtained as n-dimensonal matrix analogs of the corresponding solution for single-component sorpton. The application of the suggested solution technique is demonstrated by simulation of the transient uptake of n-heptane and benzene on NaX zeolite. The model is capable of reproducing the maximum in the n-heptane kinetic sorption curve, as experimentally observed by Kärger and Bülow (1975, Chem. Engng Sci. 30, 893–896). Analysis of binary counter-sorption using the GMS approach helps to explain the experimental observation that adsorption and desorption rates may be significantly different; the rationale is to be found in the dependence of the GMS counter-sorption diffusivity on surface composition. It is concluded that the GMS formulation provides the most convenient practical formulation on multicomponent surface diffusion.