Zeta Adsorption Isotherm Research Articles

Experimental examination of the phase transition of water on silica at 298 K.

The objective of this study was to investigate the prediction of the wetting characteristics obtained from the equilibrium adsorption analysis using the Zeta adsorption isotherm approach with an experimental study. Water vapor's adsorption and wetting characteristics on a hydroxylated and nano-polished silica substrate were studied in near-equilibrium conditions at temperatures near 298K. Using a UV-visible interferometer, water vapor adsorbate film thicknesses were measured and converted into amount adsorbed per unit area. The current results show that the wetting transition occurred at an average subcooling value of 0.39K, less than the predicted value of 0.49K. All the different experimental observations showed growth of film thickness as a function of subcooling value with a maximum film thickness of 12.6nm. The analysis of the results further showed that the maximum stable film was in a metastable state that then condensed in a dropwise manner, if perturbed by increasing the subcooling. The study further revealed that the adsorbate is unstable after transitioning. The solid surface energy calculated by including the near-equilibrium observations was comparable and close to that of the equilibrium studies, thus supporting solid surface energy as a material property.

Determination of the surface properties and adsorption states of nanoporous materials using the zeta adsorption isotherm.

The adsorption process of porous materials has always been a popular field of research in interfacial physics, and the surface physical parameters of materials can be obtained from their adsorption characteristics, which has a great influence on the performance of materials. Based on the zeta adsorption isotherm, we propose a method based on the zeta adsorption isotherm to predict the entire adsorption process of porous materials and determine material surface properties from the measured isotherm data in the heterogeneity-free range. We applied the zeta constants of the silica adsorption system to the corresponding adsorption isotherm of the porous material. The results showed that the predicted adsorption isotherms are in good agreement with the experimental measurements before pore filling and can effectively identify the pressure ratios at the beginning and end of pore filling. In the region of high-pressure ratios, the Kelvin equation was utilized to calculate the pressure ratio at a contact angle of 0°. The surface parameters of the materials were determined by geometrically calculating the variation of the adsorption amount and the desorption isotherms in the high-pressure ratio range were calculated from these surface parameters. The predicted desorption isotherms can well reflect the adsorption process of silica porous materials in the region of a high-pressure ratio. In addition, for the surface parameters of the materials, the specific surface area calculated from the adsorption and desorption isotherms, respectively, differed by less than 7.9%, and the reliability of the method was verified by comparing the results with those of the argon adsorption systems.

Specific Surface Area of Nanopowders from Argon Adsorption at 77 and 87 K: Zeta Adsorption Isotherm Approach

The surface characterization of nanopowders is widely attempted by both N2 and Ar vapor adsorption methods. They are used as complementary probe molecules because of their similarities and certain differences. However, the respective reported analyses, using the Brunauer–Emmett–Teller method, suffer from inconsistencies between the determined values of the specific surface areas, As. We examine this issue by using the zeta adsorption isotherm approach on the reported data for both vapors on two different samples from the same batch of a nanopowder material. By assuming the equivalence of the As determined by both of the vapors, we obtain the average occupied area of an adsorbed argon atom, σA(Ar), on silica and carbon black at the solid- and liquid-state temperatures of 77 and 87 K, respectively. We then examine the determined value of σA(Ar) by obtaining As for other samples of the same material with varying specific areas. By transforming the adsorption data from mass-specific to area-specific, the respective thermodynamic isotherms, nSV, of Ar vapor adsorbing on silica and carbon black are obtained. The determined nSV are then used with the Gibbs adsorption equation to determine the solid surface energy, γS0, and solid–vapor interface energy, γSV, for both substrates. The obtained γSV(xV) on both substrates is used to interpret the phase transition state of the Ar adsorbate at 77 K. The determined thermodynamic isotherms for Ar and N2 vapors are further used in a comparative study to show that the Ar vapor adsorption is negligibly affected by the change in silanol concentration on the silica surface in contrast with N2 vapor adsorption.

Thermodynamic N2 Vapor Isotherms of Materials: Zeta Adsorption Isotherm Approach

For N2 vapor adsorbing on a nanopowder at 77 K, we use a multicomponent canonical ensemble to determine the conditions for equilibrium between a contacting vapor phase and the adsorbed molecular clusters. Provided the substrate variations (heterogeneities) do not cause a phase transition, such as wetting or capillary condensation, we show that the equilibrium conditions allow an expression for an adsorption isotherm to be formed. The isotherm expression contains four constants that are to be obtained empirically from mass-specific adsorption measurements. The specific surface area of a substrate is expressed in terms of the specific number of adsorption sites and the cross-sectional area of an adsorbed N2 molecule on materials. This procedure is investigated by using the respective specific surface areas of different samples of a given material to transform the data into an area-specific basis. We pooled data sets from multiple samples with possibly different specific surface areas to form a single data set. The thermodynamic (zeta adsorption) isotherm is formulated after a regression analysis is performed on the pooled data set. This isotherm is used with the Gibbs adsorption equation to obtain the solid surface energy of a material as a function of the amount adsorbed. Five materials are examined: silica, α-alumina, γ-alumina, carbon black, and graphitized carbon. Their respective solid surface energies are each shown to be a material property.

Area Occupied by a Water Molecule Adsorbed on Silica at 298 K: Zeta Adsorption Isotherm Approach

The zeta adsorption isotherm, ZAI, is used with heterogeneity-free adsorption measurements, reported by Baker and Sing, to determine the area of a water molecule adsorbed on TK800 silica at 298 K. ...

Molecular insight into the formation of adsorption clusters based on the zeta isotherm.

This work presents a series of molecular dynamics simulations of argon adsorption on a silicon substrate with different lattice orientations. From the simulation results, the density profiles are discussed and the amount of adsorbed particles is obtained at different pressures. It is found that the solid surface orientation has a great influence on the density distributions and atomic arrangements near the surface. With the collected data, the thermal constants derived from the expression of zeta adsorption isotherms are determined. The calculated isotherms agree well with the simulation results. Also, from a microscopic point of view, the molecular insights show that the structures of the adsorbates are present as clusters with different numbers of particles. The size of the clusters changes with pressure. At a relatively small pressure ratio, most of the clusters consist of a single molecule. As the pressure ratio increases, larger sized clusters appear, forming various cluster-types. The molecular cluster distributions are closely consistent with the basic approximation of the zeta adsorption isotherm. Furthermore, the surface adsorption sites determined from molecular dynamics simulation show good agreement with that predicted by the zeta isotherm model, which reaffirms the effectiveness of the theoretical model. When the isotherm is extended to a pressure ratio greater than unity, a finite amount of adsorption is predicted and the wetting conditions are obtained. Affected by the solid surface orientations, the pressure ratio at wetting for the silicon substrate with the (111) surface plane is larger than those of the (100) and (110) surfaces, indicating that a higher subcooling is required for the wetting transition.

Initiation of condensation of toluene and octane vapours on a Si surface.

The adsorption of toluene and octane vapours on a homogenous silicon surface was measured under steady, thermal disequilibrium conditions where a vapour at a temperature TV is exposed to a solid surface at a lower temperature, TS. Zeta adsorption isotherm theory was used along with Gibbsian thermodynamics to examine the adsorption results analytically and to investigate the wetting conditions for these vapours. Further, from the prediction of the cluster distribution in the adsorbate, the conditions for the initiation of a liquid phase are predicted. Finally, the mechanism that determines the condensation mode of hydrocarbons on a silicon surface is investigated.

Specific Surface Area from Nitrogen Adsorption Data at 77 K Using the Zeta Adsorption Isotherm

The determination of the specific surface area (SSA) of solid powders has been a long-standing problem in surface science. We use the zeta adsorption isotherm and propose a method for determining the SSA of powders using the N2 adsorption measurements at 77 K. The consistency of the results obtained is demonstrated using two α-alumina samples that have different total surface areas. When the proposed method is applied to convert the amount adsorbed per unit mass to the amount adsorbed per unit area, we show that there is no measurable difference between their adsorption isotherms. Also, we show the proposed method can be applied to six different powders having a variation in their specific surface areas of two orders of magnitude. The corresponding error can be obtained from a single equilibrium adsorption measurement, and the maximum standard deviation in the mean value of the SSA among six cases is less than 7%.

Vapour adsorption kinetics: statistical rate theory and zeta adsorption isotherm approach.

The equilibrium zeta adsorption isotherm for vapours indicates the amount adsorbed is finite for vapour-phase pressures approaching the saturation value, and is strongly supported by experimental measurements for a number of different vapour-solid surface systems. This isotherm assumes the adsorbate consists of differently sized molecular clusters in local equilibrium rather than the adsorbate being in layers. We use the local-equilibrium approximation and develop a method to determine the expression for chemical potential of the adsorbate in terms of the amount adsorbed, nA(t). This allows us to apply statistical rate theory to calculate nA(t) at five different vapour-phase pressures, xV (≡PV/Psat), in terms of a parameter, re. Statistical rate theory indicates that re describes the dynamics of a given isolated system under equilibrium conditions. We consider two methods for determining the value of re that give the best agreement with the measurements performed at each of five values of xV. In one method, we assume, re, is a function of both temperature, T, and pressure, xV, and determine the five best-fit values of re. In the experiments, xV changes by a factor of more than two, but the standard deviation in the re values is 6%. In the second method, we assume re is a function only of T; and find that the value of re is not changed significantly. In all cases, the calculated nA(t) agree with the measurements.

Characterization of the Pore Structure and Surface Properties of Shale Using the Zeta Adsorption Isotherm Approach

The determination of the specific surface area and pore structure parameters of natural materials have been a long-standing issue. We propose a method for determining the specific surface area and pore size distribution that is based on the zeta adsorption isotherm and apply that method for each of two hydrocarbon vapors, octane and heptane, adsorbing on two types of shale, as-received and milled shale. We determined the specific surface areas of both materials, approximate the pores as cylindrical, and determine the average pore mouth radius. The standard deviation in the mean values of the specific surface areas and average pore radius determined with each of the two vapors is less than 3%. The experimental isotherms on the as-received shale indicate the existence of a pronounced adsorption–desorption hysteresis loop that results from the mesoporous structure of the material. We previously showed that liquid forms in the pores because of coalescence of molecular clusters inside the pores. In this study, we show that the pore emptying in the as-received shale is delayed because of the pore blocking effect. The zeta isotherm theory and the necessary conditions for thermodynamic equilibrium along with the measured amount adsorbed are used to determine the distribution in the pore mouth radii.

Prediction of the wetting condition from the Zeta adsorption isotherm.

We use the Zeta adsorption isotherm and propose a method for determining the conditions at which an adsorbed vapour becomes an adsorbed liquid. This isotherm does not have a singularity when vapour phase pressure, P(V), is equal to the saturation-vapour pressure, Ps, and is empirically supported by earlier studies for P(V) < Ps. We illustrate the method using water and three hydrocarbon vapours adsorbing on silica. When the Zeta isotherm is combined with Gibbsian thermodynamics, an expression for γ(SV), the surface tension of the solid-vapour interface as a function of x(V)(≡P(V)/Ps) is obtained, and it is predicted that adsorption lowers γ(SV) from the surface tension of the substrate in the absence of adsorption, γ(S0), to that at the wetting condition. The wetting hypothesis indicates that γ(SV) at wetting, x, is equal γ(LV), the surface tension of the liquid-vapour interface. For water vapour adsorbing on silica, adsorption lowers γ(SV) to γ(LV) at xVW equal unity, but for the hydrocarbons heptane, octane and toluene adsorbing on silica xVW is found to be 1.40, 1.30 and 1.32 respectively.

Clusters in the adsorbates of vapours and gases: zeta isotherm approach.

A procedure for determining the structure of vapour and gas adsorbates that is based on the Zeta adsorption isotherm is reported. For vapours and for gases, this isotherm supposes that an adsorbate consists of particle clusters with the number of particles in a cluster denoted ζ, where ζ can be 1, 2, 3… up to a maximum of ζm, and predicts the isotherm constants are independent of pressure. For vapours, this allows the isotherm constants to be determined from isotherm measurements made at pressures less than the saturation-vapour pressure, Ps, but applied at pressures greater than Ps. Since ζ has an upper limit, we show that there are no singularities in the vapour or gas adsorption isotherms for any pressure. This allows the adsorption of vapours at pressures greater than Ps to be investigated: clusters with ζm molecules are predicted to increase in number as P(V) is increased, until they form an adsorbed film with each adsorption site occupied by a ζm-cluster. We apply the same procedure to determine the value of ζm for gas adsorption. For CO adsorbing on Ni(100), ζm is predicted to be unity for all the cases considered, indicating that the adsorbate consists of adsorbed molecules without any clustering. For H2 adsorption on the three different materials, ζm is found to be two: indicating the adsorbate consists of both adsorbed molecules and atoms. For each material considered, a pressure is predicted where the mole fractions of both are equal, and at higher pressure, the mole fraction of adsorbed molecules exceeds that of the adsorbed atoms.

Effect of pyrogallol-poly(ethylene glycol) on stabilization, structure, and interparticle potential of concentrated nickel nanoparticle suspensions

Nickel nanoparticles with an average diameter of 90 nm have been dispersed in de-ionized water with addition of pyrogallol-poly(ethylene glycol) polymers, hereafter termed Gallol-PEG, of different molecular weights as a surfactant. Measurement of zeta potential, infrared spectrum, and adsorption isotherm confirms the preferential anchoring from polar end of the surfactant molecules on the particle surface, forming a Langmuir-typed adsorption layer (adlayer) to provide an electrosteric stabilization. Concentrated nanoparticle suspensions with a solids loading up to 40 vol.% and an apparent viscosity lower than 10 Pa s at a shear rate of 100 s−1 have been obtained, indicating that the Gallol-PEG adsorption is effective in facilitating the suspension flow under stress. The suspensions are yet fractal in structure with an experimentally determined fractal dimension of 2.1, revealing that a reaction-limited cluster–cluster aggregation is operative. This weakly coagulated fractal structure stems primarily from the shallow interparticle attraction operative over a moderate interparticle separation (~5–10 nm), and is prone to the adlayer thickness and the molecular conformation of the surfactant.