Surface Diffusion Coefficient Research Articles

Green synthesis of Cu/Cu2O/CuO nanostructures and the analysis of their electrochemical properties

Heterogeneous Cu/Cu2O/CuO nanoparticles were synthesised via polyphenols of pomegranate for various application. X-ray diffraction and high resolution-scanning electron microscopy confirmed Cu/Cu2O/CuO NPs crystallinity and the particle size which ranged from 5 to 20 nm. The electrochemical band gap energies of Cu/Cu2O/CuO NPs were calculated to be between 0.9 and 2.1 eV. EIS measurements were used to calculate the capacitance and specific capacitance of the nanoparticles which were found to be 11.2 F and 69 F g−1. Surface diffusion coefficient obtained from cyclic voltammetry was found to be 1.54 × 10−6 cm2 s −1 with r2 of 0.99 suggesting a fast electron movement. The calculated surface coverage was 1.38 × 10−3 mol cm−2 suggesting the formation of monolayer at the electrode interface. The results confirmed the electroactivity of Cu/Cu2O/CuO electrode towards the volatile organic compound- ethanol. Cu/Cu2O/CuO exhibited good electrochemical performance towards ethanol with higher current density and most negative onset potential − 0.3 V, meaning that it requires lower energy for ethanol activity to occur at the electrode interface. EIS profiles confirmed the kinetics of Cu/Cu2O/CuO at the electrode surface with characteristic small circular curvature signifying that the polarisation resistance (Rp) is prominent, proposing a faster electron shuttling process for ethanol activity. Further, the amperometric response with long time test for the Cu/Cu2O/CuO based electrode system estimated a lower limit of detection to be 0.09 µM at a signal to noise ratio of 3 with sensitivity of 0.049 µA µM−1 at steady state. Raman and FTIR highlighted mechanism of coordination.

Application of concentration-dependent HSDM to the lithium adsorption from brine in fixed bed columns

Adsorption of lithium ions from simulated brine using layered lithium-aluminum hydroxides was investigated at 303 K in fixed-bed columns. The lithium adsorption isotherms in simulated brine were conducted using batch system, and the Langmuir isotherm model was found to fit the equilibrium data well. The effects of initial lithium concentration (C0, 200–400 mg/L), bed height (H, 30–200 cm), and feed flow rate (Q, 6–18 mL/min) on lithium breakthrough curves in packed bed columns were investigated systematically. In order to simulate the practical operation process, the breakthrough time was defined when the lithium recovery rate dropped down to 0.6. The column adsorption performance was improved with the increasing of bed height and the decreasing of the initial lithium concentration, feed flow rate. Furthermore, the Homogeneous Surface Diffusion Model (HSDM) with concentration-dependent surface diffusion coefficient was developed to simulate and predict the lithium adsorption curves. The numerical model results showed good agreement with the experimental data in simulated brine and factual brine circumstance, which proved that the model could successfully simulate the column adsorption process of lithium recovery. These results provided important information to design, optimize and scale-up the column adsorption process for lithium recovery from brine.

Synergic and competitive adsorption of Li–Na–MgCl2 onto lithium–aluminum hydroxides

Layered lithium–aluminum hydroxides have been used for the lithium adsorption for its high selectivity and cyclic stability. The adsorption performances of lithium and sodium in the mixing solution with abundant magnesium chloride were investigated using batch system at 303 K. The lithium adsorption capacity was increased from 5.02 to 5.69 mg/g (initial lithium concentration is 350 mg/L) with the increasing of initial chloride ions concentration from 200 to 350 mg/L, while the sodium decreased. Both the adsorption capacities of lithium and sodium were lower in Li–Na–MgCl2 system than that’s in Li–MgCl2 and Na–MgCl2 system, which indicated the competitive effects between lithium and sodium ions. In addition, the Langmuir model could describe the isotherms of lithium and sodium well. Then, the homogeneous surface diffusion model (HSDM) was applied to represent the lithium adsorption kinetics. The surface diffusion coefficients of lithium were dependent on the initial concentration and affected by sodium ions. The Biot numbers were ranged from 25 to 40 confirming that the intraparticle diffusion is the limiting step. Breakthrough curves of lithium and sodium demonstrated the lithium could be enriched and obtained with fixed bed adsorption process, and verified the competitive adsorption phenomenon.

Biopolyelectrolyte Surface Diffusion Within a Planar Slit Geometry

The effective surface diffusion of biopolyelectrolytes within nanoscale confinement is integral to biosensing, biocatalysis, bioseparations (such as chromatography columns utilizing nanoporous media), as well as biophysical processes. Confinement influences the surface-mediated diffusion of biopolyelectrolyte chains due to the presence of electric double layers and the increased frequency of transient polymer/surface interactions. Here, the diffusion of poly-L-lysine (PLL) in a nanoslit was studied using Convex Lens-induced Confinement (CLiC) single-molecule tracking microscopy. Three surface chemistries were employed to understand and compare the effects of electrostatic and short-range interactions, respectively. In all cases, the effective surface diffusion coefficient increased rapidly with slit height until it saturated at its value for a semi-infinite interface for slit heights <30 nm. The evolution of the diffusion coefficient with slit height was faster for amine-functionalized surfaces with which PLL exhibited stronger short-range interactions. These hydrogen-bonding interactions influenced the intermittent random walk behavior by increasing the waiting times between flights and the re-adsorption probability (a.k.a. sticking coefficient) during flights. Intermittent random walks were simulated within a planar slit geometry, using the appropriate adsorption probabilities and waiting time distributions (obtained from diffusion at a single interface) to account for the characteristic short-range interactions between PLL and each type of surface chemistry. The simulated step-size distributions were in good agreement with experimental measurements, indicating that the fine details of diffusion in nanoscale confinement can be quantitatively described by a model that combines confined Brownian motion with transient surface adsorption and desorption, using parameters obtained only from the behavior at a single interface in a semi-infinite geometry. These results highlight the importance of short-range biopolyelectrolyte/surface interactions on diffusion within confined environments and moreover, demonstrate the complex relationship between electrostatics, confinement, and local polymer and surface chemistry on biopolyelectrolyte surface diffusion within a nanoslit.

Monte Carlo simulation of thermophysical properties of liquid Ni-15%X (Co, Cu, Yb) alloys

In this paper, the embedded-atom method was used to study the influence of different solute elements (Co, Cu, Yb) on the thermophysical properties of liquid Ni-based alloys. By exploring the relationship between surface tension, viscosity, diffusion coefficient and temperature of liquid Ni-based alloys with three solutes in the range of 1500 ~ 1900 K, we found that under certain components the surface tension of liquid Ni-based alloys with three solutes decreased as temperature increased. Except the case that the atomic radius of the same period decreased with the increase of the atomic number and influence of lanthanide and actinide contraction, the surface tension of liquid Ni-based alloys decreased with the increase of atomic number. The viscosity of liquid alloy showed a downward trend with increasing temperature, and the viscosity decreased exponentially with the temperature increasing under certain components. The variation trend of diffusion coefficient of the three kinds of atoms was similar to that of the temperature, which increased with the increase of temperature under the same component. Especially, the diffusion coefficient increases exponentially with the increase of temperature under certain components. These simulated data provided necessary thermophysical parameters for non-equilibrium dynamics analysis of liquid-phase alloys and also supplied a sound theoretical basis for exploring the internal physical mechanism of “liquid microstructures–thermophysical properties–preferred phase of nucleation”.

Removal of Cr (VI) from an aqueous solution using an activated carbon obtained from teakwood sawdust: Kinetics, equilibrium, and density functional theory calculations

Because of its acute toxicity and high mobility, the hexavalent chromium [Cr (VI)] found in wastewater is a risk to the environment. In this study, activated carbon was produced from teakwood sawdust, which was chemically modified using ZnCl2 (AT) as an efficient adsorbent for Cr (VI) removal from aqueous systems. Batch experiments were conducted to identify kinetic, diffusional, and equilibrium parameters. In addition, to better understand the adsorption process, computer calculations were conducted based on the density functional theory (DFT). A maximum adsorption capacity of 72.46 mg g−1 was achieved by adapting experimental data to the Langmuir isotherm model. Intraparticle diffusion was further identified through a three-dimensional diffusion model, which revealed that it was ruled by intraparticular diffusion based on surface diffusion, with surface diffusion coefficient (Ds) values ranging from 1.29 × 10−10 to 0.78 × 10−10 cm2 s−1. Finally, computational chemistry calculations and an FTIR analysis determined that oxygenated functional groups, lactone, semiquinone, phenols, and carboxylic acids were involved in the process of Cr (VI) adsorption on AT. Moreover, the main adsorption mechanisms were found to be complexation, electrostatic interaction, and reduction of Cr (VI) to Cr (III).

EVOLUCIÓN TEMPORAL DE UNA DEPRESIÓN SOBRE LA SUPERFICIE DEL HIELO MONOCRISTALINO

The surface of a monocrystalline ice sample was observed at −5 ◦C (268 K). For which it was superficially polished and allowed to evolve in the presence of activated silica gel for three hours. The evolution of a depression was studied using three-dimensional micrographs obtained with an Olympus OLS4000 LEXT confocal microscope. A predominance of surface diffusion transport was found in the evolution of the depression. This is based both on the value obtained for the surface diffusion coefficient, as well as on the values found for the exponents corresponding to the evolution of the depth of the well and its width.

A New Slip Length Model for Enhanced Water Flow Coupling Molecular Interaction, Pore Dimension, Wall Roughness, and Temperature

In this paper, a slip length model is proposed to analyze the enhanced flow based on the Hagen–Poiseuille equation. The model considers the multimechanisms including wall-water molecular interactions, pore dimensions, fractal roughness, and temperature. The increasing wall-water interactions result in the greater slip length and flow enhancement factor. The increased temperature enhances the kinetic energy of water molecules that leads to great surface diffusion coefficient and small work of adhesion. The wall roughness can decrease the slip length and flow enhancement factor in hydrophilic nanopores. This work studies the effects of multimechanisms on slip length and flow enhancement factor theoretically, which can accurately describe the liquid flow in nanopores.

Gas Diffusion in Coal Powders is a Multi-rate Process

Gas migration in coal is strongly controlled by surface diffusion of adsorbed gas within the coal matrix. Surface diffusion coefficients are obtained by inverse modelling of transient gas desorption data from powdered coals. The diffusion coefficient is frequently considered to be dependent on time and initial pressure. In this article, it is shown that the pressure dependence can be eliminated by performing a joint inversion of both the diffusion coefficient and adsorption isotherm. A study of the log–log slope of desorbed gas production rate against time reveals that diffusion within the individual coal particles is a multi-rate process. The application of a power-law probability density function of diffusion rates enables the determination of a single gas diffusion coefficient that is constant in both time and initial pressure.

Effect of surface preparation on corrosion of steel rebars coated with cement-polymer-composites (CPC) and embedded in concrete

Nowadays, Cement-Polymer-Composites are widely used to coat steel rebars to delay the initiation of corrosion in reinforced concrete (RC) structures. However, Cement-Polymer-Composite (CPC) coating is sometimes inadequately applied on rusted steel and can lead to premature under film/crevice corrosion. This paper investigates the effect of such inadequate applications of CPC coating and premature corrosion on the service life of RC structures. For this, maximum surface chloride concentrations, diffusion coefficients, and chloride thresholds were determined by a one-year-long laboratory study on the specimens obtained from a 6-year-old bridge and prepared in the laboratory. Studies found that the chloride threshold of inadequately coated steel rebar (i.e., coating on ‘as received’ surface) is significantly lower than that of the adequately coated steel rebars (i.e., coating on ‘sandblasted’ surface). Also, the corrosion initiation time for systems with inadequately coated steel rebar was about 50% less than that of the systems with adequately coated steel rebars. The corrosion mechanisms were justified with micrographs. It is recommended not to use CPC coated steel rebars if adequate surface preparation (say, cleaning/sandblasting) is not implemented.

Role of surface exchange kinetics in coated zirconia dual-phase membrane with high oxygen permeability

In order to comprehend the enhancement mechanism of oxygen permeability by surface coating in the zirconia-based dual-phase membrane, it is necessary to comprehend surface exchange reactions in coated-membrane. Surface exchange reactions significantly contribute to oxygen permeability in a thin membrane with a thickness lower than characteristic thickness; thus, it is extremely important to define the correlation of surface exchange kinetics between the membrane and coating material. The permeation fluxes of zirconia-rich composite membrane [70 vol% Zr0.79Sc0.2Ce0.01O2-δ (ScSZ): 30 vol% La0.7Sr0.3MnO3±δ (LSM), LSM30] in the thickness range of 40–340 μm have been investigated as a function of oxygen partial pressure on the feed and permeate sides to elucidate the enhancement in the permeation flux by a Nd2NiO4+δ (NNO)-coating layer. The oxygen permeation resistances were estimated from oxygen fluxes as a function of PO2 through the oxygen permeation model. The surface exchange (k' and k'') and diffusion (D) coefficients are obtained from the resistances. The diffusion coefficient of the coated membrane is similar to that of ScSZ, which corresponds to the main element of the membrane as the ionic conductor. Additionally, the surface exchange coefficient of the coated membrane is similar to that of NNO as the coating material. The surface exchange reaction on the feed side is faster than that on the permeate side under the operating condition. In order to ensure a more detailed elucidation, the k values obtained from the permeation model are compared with those obtained from the electrical conductivity relaxation method and characteristic length (LC). Despite differences in the experimental conditions such as morphologies, the surface exchange coefficients exhibited similar values and trend in the temperature range of 750–900 °C, irrespective of the experimental method.

Surface Diffusion in Gaseous Monolayers of an Insoluble Surfactant.

Surface diffusion is an important mass transfer mechanism of surfactant molecules within adsorbed layers, which has to be taken into account in many fluid dynamics problems. Although considerable research has been devoted to studying the thermodynamic and rheological properties of surface films, rather less attention has been paid to surface diffusivity measurements. Current measurement methods, which are based on marking part of surfactant molecules in uniform motionless layers with the radiotracer or fluorescence technique, are well suited for use in quite condensed layers, but they do not work in rarefied layers due to increasing contribution of density fluctuations at an interface. In this study, we propose a method for measuring the surface diffusion coefficient in gaseous monolayers of an insoluble surfactant under dynamic conditions, i.e., in the presence of a flow at an interface. Our approach is based on measuring the velocity of thermocapillary flow on the water surface, which contains molecules of an insoluble surfactant. We show that under conditions of the balance between thermo- and solutocapillary tangential stresses the convective motion exists at an interface, which is caused by a blurring of the surface concentration gradient of surfactant molecules due to the surface diffusion mechanism. For calculations of the surface diffusion coefficient, we use the equation proposed earlier in the theoretical study [ Homsy , G. M. ; et al. J. Fluid Mech. 1984 139 , 443 - 459 ]. The surface diffusion coefficient measured by us in gaseous layers is 2-3 orders of magnitude larger than the results for liquid-expanded and liquid-condensed layers obtained by other researchers. Finally, we compare the obtained results with the known measurements of surface diffusion and discuss the limitations of the proposed method.

New theoretical model to calculate the apparent permeability of shale gas in the real state

Although many studies have been conducted to investigate the mechanisms of shale gas transport through a single nanopore, the mechanisms are not yet well understood. In this study, a theoretical model was developed to calculate the apparent permeability of shale gas in a real state through a single nanopore, and the apparent permeability of a bundle of nanopores was derived. Second, to improve the reliability of the newly developed model, two models for gas deviation factor and viscosity were selected based on 278 data points, and the models for surface diffusion coefficient were also discussed. Third, the validity of the developed model was investigated using two sets of experimental data from the literature. Finally, the effects of gas state, pore radius, temperature, adsorption parameters and pore radius distribution on apparent permeability were systematically analyzed. The results show that the developed model is capable of determining the apparent permeability of shale gas transport through a single nanopore and describing the migration process of shale gas. The Chen & Yang model, Dranchuk & Abou-Kassem model and Sutton model are selected to calculate the surface diffusion coefficient, gas deviation factor and viscosity, respectively. The effects of pore radius, temperature, and adsorption parameters are more remarkable at low pressures than at high pressures. In addition, the surface diffusion of shale gas in a single nanopore cannot be ignored, but it can be ignored in a shale core with large pores under reservoir conditions. Large pores in the shale core control the apparent permeability.

Oxygen isotope exchange in proton-conducting oxides based on lanthanum scandates

A method of the oxygen isotope exchange with equilibration of the gas phase was used in order to obtain the temperature dependences of the oxygen surface exchange and diffusion coefficients of the proton-conducting oxides La1–xSrxScO3–δ (x = 0; 0.04; 0.09) in the temperature range of 600–900 °C and oxygen pressure of 1.01 kPa. The diffusion and oxygen surface exchange coefficients increase with the strontium content in oxides. The rates of the individual stages of the oxygen exchange process on the surface of the oxides were determined. The oxygen incorporation was revealed to be rate-determining for the undoped LaScO3 oxide. However, for the strontium-doped oxides La1–xSrxScO3–δ (x = 0.04; 0.09), the difference between the rates of oxygen dissociative adsorption and oxygen incorporation decreases with increasing the strontium concentration, in a way that for the La0.91Sr0.09ScO3−δ oxide these stages become competing. The possible reasons for these differences in oxygen surface exchange kinetics were analyzed in this paper. Using the obtained oxygen diffusion coefficients, the oxygen-ionic conductivities in accordance with the Nernst-Einstein equation, and the contributions of the oxygen-ion and proton components of the total conductivity of the La1–xSrxScO3–δ (x = 0.04; 0.09) oxides in the wet reducing atmosphere (pH2O = 2.35 kPa, pO2 = 10−15 Pa) were calculated. The proton transference numbers were found to be close to unit at the wet reducing atmospheres in the temperature range of 500–600°С.

Analysis of gas transport behavior in organic and inorganic nanopores based on a unified apparent gas permeability model

Different from the conventional gas reservoirs, gas transport in nanoporous shales is complicated due to multiple transport mechanisms and reservoir characteristics. In this work, we presented a unified apparent gas permeability model for real gas transport in organic and inorganic nanopores, considering real gas effect, organic matter (OM) porosity, Knudsen diffusion, surface diffusion, and stress dependence. Meanwhile, the effects of monolayer and multilayer adsorption on gas transport are included. Then, we validated the model by experimental results. The influences of pore radius, pore pressure, OM porosity, temperature, and stress dependence on gas transport behavior and their contributions to the total apparent gas permeability (AGP) were analyzed. The results show that the adsorption effect causes Kn(OM) > Kn(IM) when the pore pressure is larger than 1 MPa and the pore radius is less than 100 nm. The ratio of the AGP over the intrinsic permeability decreases with an increase in pore radius or pore pressure. For nanopores with a radius of less than 10 nm, the effects of the OM porosity, surface diffusion coefficient, and temperature on gas transport cannot be negligible. Moreover, the surface diffusion almost dominates in nanopores with a radius less than 2 nm under high OM porosity conditions. For the small-radius and low-pressure conditions, gas transport is governed by the Knudsen diffusion in nanopores. This study focuses on revealing gas transport behavior in nanoporous shales.

Insight into mass transfer during ultrasound-enhanced adsorption/desorption of blueberry anthocyanins on macroporous resins by numerical simulation considering ultrasonic influence on resin properties

The mass transfer mechanism about ultrasonic enhancement of blueberry anthocyanin adsorption and desorption on macroporous resins were investigated. Ultrasound treatment led to the decrease of resin size, whereas average pore diameter, specific surface area, total pore volume were less affected. Then, the pore volume and surface diffusion model considering ultrasound-induced changes of particle size and surface area was employed to model anthocyanin adsorption process numerically. Generally, sonication enhanced external mass transfer coefficient (kL) and surface diffusion coefficient (Ds) during adsorption. The values of kL and Ds under sonication at 279 W/L and 20 °C were 7.578 × 10−2 cm/s and 2.000 × 10−9 cm2/s, which were 2.0% and 140.1% higher than the kL and Ds values under orbital agitation at 20 °C. Accordingly, anthocyanins penetrated into the interior of macroporous resins faster under sonication. The overall intraparticle diffusion for anthocyanin adsorption was dominated by pore volume diffusion with the contribution percentage higher than 50%. Sonication enhanced the contribution of surface diffusion to the overall diffusion, which was consistent with the increase of Ds with ultrasound energy. Moreover, a general diffusion model also incorporating the variations of particle size and surface area was utilized to model anthocyanin desorption process. The overall anthocyanin diffusivity increased with both ultrasound energy level and temperature. Anthocyanins distributed more homogenously inside resins under sonication at 279 W/L than under other treatments. This work could be a reference for the valorization of anthocyanins in food industry, especially juice and wine industries.

Interplay of adsorption and surface mobility in tracer diffusion in porous media.

We model the diffusion of a tracer that interacts with the internal surface of a porous medium formed by a packing of solid spheres. The tracer executes a lattice random walk in which hops from surface to bulk sites and hops on the surface have small probabilities compared to hops from bulk sites; those probabilities are related to bulk and surface diffusion coefficients and to a desorption rate. A scaling approach distinguishes three regimes of steady state diffusion, which are confirmed by numerical simulations. If the product of desorption rate and sphere diameter is large, dominant bulk residence is observed and the diffusion coefficient is close to the bulk value. If that product is small and the surface mobility is low, the tracers are adsorbed most of the time but most hops are executed in the bulk. However, for high surface mobility, there is a nontrivial regime of dominant surface displacement, since the connectivity of solid walls allows the tracers to migrate to long distances while they are adsorbed. In this regime, we observe rounded tracer paths on the sphere walls, which are qualitatively similar to those of a recent experiment on polystyrene particle diffusion. The calculated average residence times are proportional to the bulk and surface densities of an equilibrium ensemble of noninteracting tracers, and the relation between those densities sets the adsorption isotherm. Simulations performed with initially uniform (nonequilibrium) distribution of tracers in the pores show other nontrivial results in cases of dominant surface residence: slow increase of the mean-square displacement at short times, since the tracer has not explored a homogeneous medium, and a remarkable slowdown between the first encounter with a solid wall and the first hop from that point. Relations between our results and other models of diffusion and adsorption in porous media are discussed.

Synthesis and surface activity of phenylselenide-1-undecyl trimthylamonium bromide

Selenium-containing surfactant has aroused considerable attention due to its unique chemical properties, especially environmental sensitivity. Here we synthesized a Se-containing cationic surfactant, phenylselenide-1-undecyl trimethylammonium bromide (PSeTAB), and studied its Krafft temperature (TK), equilibrium/dynamic surface tension, and foam properties. The results showed that with the addition of H2O2, the hydrophobic selenide group in PSeTAB was oxidized to a hydrophilic selenoxide structure, providing another polar head, and thus producing a larger geometry. As a result, PSeTAB-Ox exhibited a stronger affinity to water, lowering the TK, tendency toward micellization and adsorption (higher cmc, less negative and ), dynamic surface activity (smaller ) and diffusion coefficients, compared to PSeTAB. Macroscopically, PSeTAB showed relatively good foaming properties, while PSeTAB-Ox has hardly any foaming ability.

A novel numerical model of gas transport in multiscale shale gas reservoirs with considering surface diffusion and Langmuir slip conditions

AbstractMultiflow mechanisms coexist in shale gas reservoirs (SGRs) due to the abundant nanopores and the organic matter as a medium of gas souring and storage. The gas transport mechanisms in nanopores including bulk gas transfer and adsorption‐gas surface diffusion were already investigated in pore‐scale models, but their effects on actual gas production of multistage fractured horizontal wells in SGRs are not clearly understood, which are crucial for the economic development of unconventional resources. Therefore, a comprehensive apparent permeability (AP) model which couples the surface diffusion of adsorbed gas, slippage flow considering the additional flux generated by surface diffusion based on Langmuir's theory, and Knudsen diffusion is established. The presented model is validated with the experimental data and lattice Boltzmann method (LBM) simulation results. Then, we propose a numerical model which combines multiflow mechanisms in microscale pores and a multistage fractured horizontal well (MSFHW) in macroscale shale gas reservoirs together. The effects of different transport mechanisms on both AP of nanopores and gas production are analyzed thoroughly. The results show that the effect of surface diffusion on the apparent permeability of nanopores is much greater than that on the actual gas production of MSFHW, and the influence of high‐pressure condition must be considered when calculating the surface diffusion coefficient. The presented numerical model has important implications for accurate numerical simulation and efficient development of shale gas reservoirs.

Nonlinear Frequency Response Analysis as a Tool for Identification of Adsorption Kinetics: Case Study—Pore-Surface Diffusion Control

In the present paper, the Nonlinear Frequency Response (NFR) analysis is applied for theoretical study of kinetics of adsorption governed by pore-surface diffusion. The concept of higher-order frequency response functions (FRFs) is used. Based on a nonlinear mathematical model for adsorption of pure gas and spherical adsorbent particles, the theoretical first- and second-order FRFs, which relate the adsorbate concentration in the particle to the surrounding pressure (F1(ω) and F2(ω,ω)), have been derived. The obtained FRFs have been simulated for different steady-state pressures and different ratios (between zero and one) of surface to pore diffusion coefficients. The results show that, unlike F1(ω), F2(ω,ω) exhibits features which unambiguously distinguish the pore-surface diffusion model from pure pore diffusion and micropore diffusion. Based on the characteristic features of F1(ω) and F2(ω,ω), a new methodology for direct estimation of the separate values of the pore and surface diffusion coefficients has been established.