Polar and dispersion interactions at carbon surfaces: further development of the XPS-based model

Enthalpy of immersion (ΔH_i) in water has been measured for a series of ozone oxidised non-porous carbon blacks and, as in our previous studies been found to correlate directly with the total surface oxygen level [O]_T measured by X-ray photoelectron spectroscopy. An equation that allows calculation of either parameter from the other is given and shown to describe behaviour for a wide range of carbon black surfaces which contain ozone-generated or native oxygen functional groups. Using this approach, the surface polarity and the relative hydrophilic character of such surfaces can be predicted. A molar enthalpy for the polar interaction between water and surface oxygen atoms of 17 kJ mol⁻¹ is obtained by assuming a 1:1 co-ordination between water molecules and carbon surface oxygen atoms. The data lead to a predicted value of 37.5 mJ m⁻² for the immersion of oxygen-free carbon black external surface into water. This equates to a value of 2.5 kJ mol⁻¹ for the non-specific dispersion interaction between water and an oxygen-free carbon black surface when a molecular area of 10.5×10⁻²⁰ m² for water is assumed. The same carbon black when oxidised using nitric acid gives a different enthalpy of immersion to the ozone-treated and native oxide materials, this is attributed to differing chemistry of the two surface types, this aspect is discussed. The nitric acid treated carbons do, however, give the same value as the ozonated and native oxide carbons (37.5 mJ m⁻²) for the immersion of an oxygen-free carbon surface into water. A correlation between the point of zero charge (pH_PZC) of the carbons and ΔH_i or [O]_T is also presented. The results from these measurements show extremely good agreement with data from other groups who have used TPD to assess surface oxygen concentration. This gives a firm basis for confident prediction of the thermodynamic properties of carbon surfaces from single measurement techniques.     

Electrochemical enhancement of adsorption capacity of activated carbon fibers and their surface physicochemical characterizations

The adsorption of activated carbon fibers (ACFs) and their surface characteristics were investigated before and after electrochemical polarization. The adsorption kinetics of m-cresol showed the dependence on polarized potential, and the adsorption rate constant increased by 77.1%, from 6.38 × 10⁻³ min⁻¹ at open-circuit (OC) to 1.13 × 10⁻² min⁻¹ at polarization of 600 mV. The adsorption isotherms at different potentials were in good agreement with Langmuir isotherm model, and the maximum adsorption capacity increased from 2.28 mmol g⁻¹ at OC to 3.67 mmol g⁻¹ at polarized potential of 600 mV. These indicated that electrochemical polarization could effectively improve the adsorption rate and capacity of ACFs. The surface characteristics of ACFs before and after electrochemical polarization were evaluated by N₂ adsorption-desorption isotherms, scanning electron microscope (SEM), zeta potential and Fourier transform infrared spectroscopy (FTIR). The results showed that the BET specific surface area and pore size increased as the potential rose. However, the surface chemical properties of ACFs hardly changed under electrochemical polarization of less than 600 mV. This study was beneficial to understand the mechanism of electrochemically enhanced adsorption.     

A study of electrochemically treated PAN based carbon fibres by IGC and XPS

Inverse gas chromatography (IGC) has been used with conventional and novel probes in conjunction with X-ray photoelectron spectroscopy (XPS) to assess the surface chemistry of a range of aged polyacrylonitrile carbon fibres. Using conventional probes the thermodynamic surface properties were investigated at 100 °C. The dispersive component of the surface free energy, , was determined and ranged from 73.1 mJ m⁻² to 92.2 mJ m⁻². Unconventional probes, chosen as analogues of the functionalities present in a potential matrix material, were also eluted through the IGC columns. Surface compositions and peak fitting of C 1s spectra from XPS analysis helped identify groups on the fibre surface. Using these results, mechanisms of interactions occurring at the interface of a carbon fibre reinforced polymer composite have been proposed. Hydrogen bonding and stronger acid-base interactions are the main mechanisms of interactions. Although, the carbon fibres are aged, oxygen and nitrogen functionalities introduced from surface treatment have remained active.     

Kinetics of dissociative adsorption of ethylene glycol on Pt(1 0 0) electrode surface in sulfuric acid solutions

The dissociative adsorption of ethylene glycol (EG) on Pt(1 0 0) electrode surface cooled in air after flame annealing was investigated by using programmed potential step technique and in situ FTIR spectroscopy. The stable adsorbates derived from EG dissociative adsorption on Pt(1 0 0) were determined by in situ FTIR spectroscopy as linear- and bridge-bonded CO. The quantitative results demonstrated that the average rate of dissociative adsorption of EG on Pt(1 0 0) surface varies with electrode potential, yielding a volcano-type distribution with a maximum value located near 0.10 V versus SCE. From the variation of the quantity of CO adsorbates generated in EG dissociative adsorption with the adsorption time t_ad, the initial rate (ν_i) of this surface reaction was evaluated quantitatively. The maximum value of ν_i has been determined to be 2.64 × 10⁻¹¹ mol cm⁻² s⁻¹ in a solution containing 2 × 10⁻³ mol L⁻¹ EG. The influence of the surface structure of Pt(1 0 0) electrode obtained by different pretreatment as well as of the specific adsorption of (bi)sulfate anions on the kinetics of EG dissociative adsorption has been also investigated and discussed. In comparison with a Pt(1 0 0) surface cooled in air atmosphere after flame treatment, the Pt(1 0 0) surface cooled in an Ar-H₂ stream or subjected to a treatment of fast potential cycling decreased significantly the initial rate ν_i of EG dissociative adsorption. Similar effect was also observed for the specific adsorption of (bi)sulfate anions. However, the maximum attainable coverage () of adsorbates derived from EG dissociative adsorption is not affected either by the surface structure of Pt(1 0 0) or by (bi)sulfate anions adsorption.     

On the determination of surface areas in activated carbons

The paper examines the validity of two approaches frequently used to determine surface areas in activated carbons, namely the BET method and the use of immersion calorimetry. The study is based on 21 well characterized carbons, whose external and microporous surface areas, S_e and S_mi, have been determined by a variety of independent techniques. It appears clearly that S_BET and the real surface area S_mi + S_e are in agreement only for carbons with average pore widths L_o around 0.8-1.1 nm. Beyond, S_BET increases rapidly and S_BET − S_e is practically the monolayer equivalent of the micropore volume W_o. This confirms that a characterization of surface properties based on S_BET is, a priori, not reliable. The study of the enthalpy of immersion of the carbons into benzene at 293 K, based on Dubinin’s theory, shows that Δ_iH consists of three contributions, namely from the interactions with the micropore walls (−0.136 J m⁻²), the external surface (−0.114 J m⁻²), and from the volume of liquid found between the surface layers in the micropores (−141 J cm⁻³). It appears that for carbons where L_o > 1 nm, the real surface area cannot be determined in a reliable way from the enthalpy of immersion and a specific heat of wetting alone.     

Adsorption of asparagine on the gold electrode and air/solution interface

The adsorption of asparagine (Asn) on a gold electrode from 0.1 M LiClO₄ aqueous solutions was investigated. The experimental data obtained from ac impedance measurements were analyzed to determine the dependence of adsorption parameters, i.e. the standard Gibbs energy of adsorption (ΔG⁰), maximal value of surface excess concentration (Γ_max) of Asn and parameter of interactions in the adsorbed layer (A) on the electrode potential. The relatively large value of Gibbs energy of adsorption (∼ −47 kJ mol⁻¹) gives the evidence of a very strong adsorption of Asn at the polycrystalline Au electrode. The comparison of the adsorption behavior of Asn at the air/solution and the Au/solution interfaces points out to the significant electronic interactions of adsorbate molecules with the Au electrode, since the adsorption of Asn on a free surface (from the same solutions) is very week. The analysis of the electrochemical data as well as the infrared reflection absorption spectroscopy (IRAS) results reveal that Asn molecules are anchored to the Au surface through oxygen atoms of the carboxylate group COO⁻ and through the amide carbonyl group.     

Microporosity of carbon deposits collected in the Tore Supra tokamak probed by nitrogen and carbon dioxide adsorption

Nitrogen and carbon dioxide adsorption experiments have been used to investigate the porosity of carbon deposits formed in the Tore Supra tokamak as a consequence of the erosion of the plasma-facing components. We compare BET, α_s-, and Dubinin-Raduskevich methods to distinguish between micropore volume (∼0.04 cm³ g⁻¹) and external surface (∼90 m² g⁻¹). Consistent results have been obtained for nitrogen and carbon dioxide, and the smallest pores are shown to be reversibly closed and opened under air exposure and outgassing at 600 °C, respectively, probably due to blocking of pore entrances by surface oxides. Pore size distribution is calculated using the non-local density functional theory: a novel and straightforward method is used to fit the experimental isotherms by Lorentzian distributions of pores centered in some relevant pore size regions. We thus show that the tokamak sample micropores are mainly ultra-micropores (∼75%) whose widths are centered at 0.6 nm. This latter result is in good qualitative agreement with the outgassing effect and in good quantitative agreement with what is deduced from α_s-plot.     

Electrochemical characterization of cetyltrimethyl ammonium bromide modified carbon paste electrode and the application in the immobilization of DNA

A cetyltrimethyl ammonium bromide modified carbon paste electrode (CTAB/CPE) was developed in this work based on the surface modification method. The improved electrochemical response of K₄Fe(CN)₆ at this electrode indicated that CTAB could change the surface property of carbon paste electrodes (CPEs), which was demonstrated by the electrochemical impedance spectroscopy (EIS). In 0.1 mM [Fe(CN)₆]^3−/4−, a low exchange current (i₀) of 2.72×10⁻⁷ A at bare CPE was observed while that at CTAB/CPE was 6.79×10⁻⁵ A. The effect of CTAB concentration on the electrode quality revealed that CTAB formed a compact monolayer on the electrode surface with high density of positive charges directed outside the electrode. This electrode showed strong accumulation ability toward Fe(CN)₆⁴⁻ and can also accumulate Co(phen)₃²⁺ by the adsorption of the organic ligands in the hydrophobic area of the monolayer. The electrode was applied to the immobilization of DNA, which was characterized by the isotherm adsorption of Co(phen)₃²⁺.     

XPS and flow-cell EQCM study of albumin adsorption on passivated chromium surfaces: Influence of potential and pH

The adsorption of albumin (BSA: bovine serum albumin) on passivated chromium surfaces was studied in deaerated sulphate solutions as a function of potential (in the passive state) and pH (from 4 to 10). In situ switch-flow cell EQCM measurements were coupled to ex situ XPS analyses. EQCM results showed that (i) the initial adsorption rate is about 3.3 ng cm⁻² s⁻¹ which corresponds to 3 × 10¹⁰ molecules cm⁻² s⁻¹, irrespective of the passive potential and pH, and (ii) the passive potential as well as the pH have no influence on the amount of adsorbed BSA (Δm = 440 ± 70 ng cm⁻² on the adsorption plateau). From the XPS N 1s and C 1s signals, which provide a fingerprint for the protein, it can be concluded that BSA is adsorbed on the Cr surface and is chemically intact. The XPS results show that (i) when increasing the passive potential, the oxide layer thickness increases (mean value: d_ox = 2.2 ± 0.2 nm), and (ii) the passive film is not modified by the adsorption of protein. From combined EQCM and XPS data, a full coverage of the Cr surface by the adsorbed proteins (γ = 1) is demonstrated at pH 4 (whatever the passive potential). The thickness of the continuous BSA layer (h_BSA) is 3.3 ± 0.3 nm, which corresponds to one monolayer “side-on”, i.e. oriented parallel to the surface. At pH 5.5 and 10, the adsorbed proteins form islands. The surface coverage is much lower (γ ∼ 0.5), and the height of the protein islands is significantly higher (h_BSA ∼ 6.5 nm). The results suggest a strong interaction (partially covalent) between the protein and the passivated chromium surface.     

Investigation of adsorption and inhibitive effect of 2-mercaptothiazoline on corrosion of mild steel in hydrochloric acid media

The inhibition effect of 2-mercaptothiazoline (2MT) on the corrosion behavior of mild steel (MS) in 0.5 M HCl solution was studied in both short and long immersion times (120 h) using potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and linear polarization resistance (LPR) techniques. For long-term tests, hydrogen gas evolution (VH₂−t) and the change of the open circuit potential with immersion time (E_ocp − t) were also measured in addition to the former three techniques. The surface morphology of the MS after its exposure to 0.5 M HCl solution with and without 1.0 × 10⁻² M 2MT with the different immersion times was examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The thermal stability of the inhibitor film was investigated by thermogravimetric analysis (TGA). The value of activation energy (E_a) for the MS corrosion and the thermodynamic parameters such as adsorption equilibrium constant (K_ads), free energy of adsorption (ΔG_ads), adsorption heat (ΔH_ads) and adsorption entropy (ΔS_ads) values were calculated and discussed. The potential of zero charge (PZC) of the MS in inhibited solution was studied by the EIS method, and a mechanism for the adsorption process was proposed. The results showed that 2MT performed excellent inhibiting effect for the corrosion of the MS. Finally, the high inhibition efficiency was discussed in terms of adsorption of inhibitor molecules and protective film formation on the metal surface. TGA results also indicated that the inhibitor film on the surface had a relatively good thermal stability.     

Determination of the kinetic parameters of oxygen reduction on copper using a rotating ring single crystal disk assembly (RRDCu(h k l)E)

The kinetics of the oxygen reduction reaction (orr) on Cu(h k l) surfaces are investigated in perchloric acid and sulfuric acid solutions using rotating ring disk electrode (RRD_Cu(h k l)E). Parameters, such as reaction order, kinetic current, rate constant, Tafel slopes as well as the number of electrons transferred are determined. The variation in the activity and reaction pathway with the crystal faces in different electrolytes is related to the surface characteristics of Cu(h k l) and the structure-sensitive inhibiting effect of the adsorbed anions on their surfaces. In 0.1 M HClO₄, the difference in activity is clearly observed on Cu(h k l) surfaces (Cu(1 0 0) > Cu(1 1 1) although it is relatively small). The higher activity of Cu(1 0 0) arises from its more open characteristics which may facilitate the co-adsorption of O₂. On the other hand, the adsorption of oxygenated species on Cu(1 1 1) at E > −0.35 V induces a 2 e⁻ pathway; while a 4 e⁻ reduction is observed on Cu(1 0 0) in the entire potential region (−0.70 V < E < −0.10 V). In 0.5 M H₂SO₄, the sequence in activity between Cu(1 1 1) and Cu(1 0 0) varies with the potentials, i.e., Cu(1 0 0) is initially more active than Cu(1 1 1) at −0.35 V < E < −0.15 V, however, the reversal in the activity between Cu(1 1 1) and Cu(1 0 0) is observed at more negative potentials (−0.45 V < E < −0.35 V). The desorption of strongly adsorbed (bi)sulfate anions on Cu(1 1 1) induces the 2 e⁻ reduction via peroxide formation, however, a 4 e⁻ reduction is dominant on the Cu(1 0 0) surfaces. The major effect of (bi)sulfate anions and oxygenated species on the orr kinetics and reaction pathway on Cu(h k l) surfaces is the blocking of active copper sites for the adsorption of O₂ molecules.     

Surface chemistry of phosphorus-containing carbons of lignocellulosic origin

Activated carbon adsorbents were prepared by phosphoric acid activation of fruit stones in an argon atmosphere at various temperatures in the 400-1000 °C range and at different acid/precursor impregnation ratios (0.63-1.02). The surface chemistry of the carbons was investigated by elemental analysis, cation exchange capacity (CEC, measured by neutralization of NaOH with acidic surface groups), infrared spectroscopy and potentiometric titration. Porous structure was derived from adsorption isotherms (N₂ at −196 °C and CO₂ at 0 °C). It was demonstrated that all carbons show considerable cation exchange capacity, the maximum (CEC = 2.2 mmol g⁻¹) being attained at 800 °C, which coincides with the maximum contents of phosphorus and oxygen. The cation exchange properties of phosphoric acid activated carbons from fruit stones are chemically stable in very acidic and basic solutions. Proton affinity distributions of all carbons show the presence of three types of surface groups with pK at 2.0-3.3, 4.6-5.9 and 7.6-9.1. These pK ranges were ascribed primarily to: (a) phosphorus-containing and carboxylic groups; (b) lactonic groups, and (c) phenolic groups, respectively. Phosphoric acid activated carbons are microporous with a relatively small contribution of mesopores. A maximum BET surface area of 1740 m² g⁻¹ was attained at 400 °C.     

Correlation between heats of immersion and limiting capacitances in porous carbons

Based on more than 80 carbons, the paper shows that immersion calorimetry into benzene, water and carbon tetrachloride can be used to assess with a good accuracy the limiting capacitance C_o at low current densities in both acidic (2 M H₂SO₄) and aprotic (1 M tetraethyl ammonium tetrafluoroborate in acetonitrile) electrolytic solutions. The enthalpies of immersion Δ_iH(C₆H₆) and Δ_iH(H₂O) provide information on C_o-acidic, where both the surface area and the oxygen content play a role. On the other hand, in the case of the organic electrolyte the oxygen content has only a small influence and C_o-aprotic is directly related to Δ_iH(C₆H₆) and Δ_iH(CCl₄). Carbon tetrachloride has a critical dimension (0.65 nm), which is close to the size of the (C₂H₅)₄N⁺ ion (0.68 nm) and therefore Δ_iH(CCl₄) provides better information in the case of carbons with small micropores. The advantage of this approach lies in the fact that immersion calorimetry, in itself a useful tool for the structural and the chemical characterization of carbons, can also be used to evaluate directly the gravimetric capacitances of these solids at low current densities.     

Properties of electrolytes in the micropores of activated carbon

The dependence of the composition of aqueous electrolytes in the pore system of activated carbon on the potential has been determined by monitoring the amount of ions exchanged with the external electrolyte upon immersion and upon changing the electrode potential. From the investigation with KF solutions, a quantity δ/√? = 4 × 10⁻¹⁰ m is evaluated where δ is half the width of the micropores, and ? the (relative) permittivity. This is in accordance with δ ≈ 1 nm and ? ≈ 7 applying to essentially immobilized water and fits into the results with the other electrolytes. Anions are adsorbed in the cases of sodium perchlorate and potassium hydroxide, while protons are adsorbed in the case of acids (HCl, H₂SO₄). The adsorption of ClO₄⁻ seems to result from electrostatic interaction with the solid, while H⁺ and OH⁻ are strongly chemisorbed, probably at surface groups like >CO. Ionic mobilities of ions in the micropores have been determined from conductance measurements concerning the pore electrolyte of a single spherical particle of activated carbon. Mobilities are more than one order of magnitude lower than those in bulk electrolyte, probably due to an increased viscosity of the liquid in the narrow pores and/or to the coulombic interaction with charged domains of the solid. The rate of charging of the capacitor (solid/micropore electrolyte) is assisted by macropores distributing ions throughout the carbon material.     

Oxygen and phosphorus enriched carbons from lignocellulosic material

Activated carbons were prepared by phosphoric acid activation of fruit stones in air at temperatures 400-1000 °C. The surface chemistry was investigated by elemental analysis, cation exchange capacity, infrared spectroscopy and potentiometric titration. The porous structure was analyzed from adsorption isotherms (N₂ at 77 K and CO₂ at 273 K). It was demonstrated that all carbons show considerable cation exchange capacity, the maximum (2.2 mmol g⁻¹) being attained at 700 °C, which coincides with the maximum contents of phosphorus and oxygen. The use of air instead of argon during thermal treatment increased the amount of cation exchangeable surface groups for carbons obtained at 400-700 °C. Proton affinity distributions of all carbons show the presence of three types of surface groups with pK 1.8-3.1 (carboxylic and polyphosphates), 4.8-6.3 (second dissociation of carboxylic, weak acid in polyphosphates and enol structures) and 8.1-9.7 (phenols and enol structures). Carbons obtained in air at 400-600 °C show enhanced copper adsorption from 0.001 mol L⁻¹ Cu(NO₃)₂ in acidic solutions as compared to carbons obtained in argon. Carbons obtained in air show well-developed porous structure that is equivalent or higher as compared with carbons obtained in argon; the difference being progressively increased with increasing treatment temperature.     

Adsorption equilibrium of organic vapors on single-walled carbon nanotubes

Gravimetric techniques were employed to determine the adsorption capacities of commercially available purified electric arc and HiPco single-walled carbon nanotubes (SWNTs) for organic compounds (toluene, methyl ethyl ketone (MEK), hexane and cyclohexane) at relative pressures, p/p₀, ranging from 1 × 10⁻⁴ to 0.95 and at isothermal conditions of 25, 37 and 50 °C. The isotherms displayed both type I and type II characteristics. Adsorption isotherm modeling showed that SWNTs are heterogeneous adsorbents, and the Freundlich equation best describes the interaction between organic molecules and SWNTs. The heats of adsorption were 1-4 times the heats of vaporization, which is typical for physical adsorption of organic vapors on porous carbons.     

Relationship between pore surface areas and electric double layer capacitance in non-aqueous electrolytes for air-oxidized carbon spheres

To investigate the relationship between pore structure and specific capacitance of electric double layer capacitors with non-aqueous electrolytes, phenol resin based carbon spheres were modified by oxidation in dry air, giving a wide range of pore structure. Surface area due to the presence of different pores was characterized through α_s plots of adsorption isotherms of N₂ gas at 77 K as microporous surface area (S_micro.) due to micropores and external surface area (S_ext.) mainly due to the mesopores. A simple model can be presented by recognizing the different contributions of S_micro. and S_ext. in forming electric-double layers. The capacitance per unit external surface area was larger by one order of magnitude than that per unit surface area of micropores (0.187 F/m² versus 0.017 F/m² at charge-discharge current of 4 mA/g), revealing greater contribution of external surface to specific capacitance for electric-double layers than surface of micropores. With the increase in charge-discharge current to 40 mA/g, the relative contribution of external surface became more significant, which was supposed to be due to large sizes of electrolyte ions, Et₃MeN⁺ and BF₄⁻.     

Preparation, characterization and Methylene Blue adsorption of phosphoric acid activated carbons from globe artichoke leaves

Activated carbons were prepared by the pyrolysis of artichoke leaves impregnated with phosphoric acid at 500 °C for different impregnation ratios: 100, 200, 300 wt.%. Materials were characterized for their surface chemistry by elemental analysis, “Boehm titrations”, point of zero charge measurements, infrared spectroscopy, as well as for their porous and morphological structure by Scanning Electron Microscopy and nitrogen adsorption at 77 K. The impregnation ratio was found to govern the porous structure of the prepared activated carbons. Low impregnation ratios (~ 100 wt.%) led to essentially microporous and acidic activated carbons whereas high impregnation ratios (> 100 wt.%) gave essentially microporous-mesoporous carbons with specific surface areas as high as 2038 m²·g^− 1, pore volume as large as 2.47 cm³·g^− 1, and a slightly acidic surface. The prepared activated carbons were studied for their adsorption isotherms of Methylene Blue at pH = 3 and pH = 9. The supermicroporous structure of the material produced at 200 wt.% H₃PO₄ ratio was found to be appropriate for an efficient adsorption of this dye controlled by dispersive and electrostatic interactions depending on the amount of oxygen at the surface.     

Adsorption of methimazole on the mercury electrode

The electrosorption behaviour of methimazole (vetranal) at the mercury/1 M NaClO₄ interface was determined from a double layer differential capacity measurements extrapolated to zero frequency. Methimazole is the thiourea derivative, which is used as a drug in the overactivity of the thyroid gland. The values of zero charge potential were shifted to negative potentials ca. 230 mV with an increasing methimazole concentration from 10⁻⁴ M to 10⁻¹ M. The relative surface excesses Γ′ of methimazole were calculated from surface pressure at the density of surface charge σ = constant. The values of Γ′ increase with the increase of σ. Adsorption of methimazole was analyzed on the basis of the constants obtained from the Frumkin and virial isotherms. The values of the standard Gibbs energy of adsorption ΔG° increase with the increase of σ while the values of interaction parameters A and B decrease.     

Dynamic aspects of cerium dioxide sintering: HT-ESEM study of grain growth and pore elimination

Sintering of CeO₂ is studied in situ by high temperature scanning environmental microscopy (HT-ESEM) at T = 1400 °C. The morphological modifications of a single grains population are recorded for 6 h. Kinetic parameters are extracted from image series. The local grain growth determined from the single population studied in situ is compared to the general grain growth obtained by classical ex situ technique. Using HT-ESEM for sintering study is validated. The grain boundary velocities range between 0 and 5 μm h⁻¹, with a mean value of about 1 μm h⁻¹. The migration of the intragranular surface pores is described. Their velocities range between 0.4 and 1.2 μm h⁻¹ and depend on pore diameters: the smaller the pore, the faster the pore velocity. The time required to fill a pore that arises at the sample surface is determined as a function of pore diameter. The time for pore elimination dependence with the pore diameters is also established.