Pore Size distribution: relation desorption

Another property of importance is the pore volume. It can be measured indirectly from the adsorption and/or desorption isotherms of equilibrium quantities of gas absorbed or desorbed over a range of relative pressures. Pore volume can also be measured by mercury intrusion techniques, whereby a hydrostatic pressure is used to force mercury into the pores to generate a plot of penetration volume versus pres- sure. Since the size of the pore openings is related to the pressure, mercury intrusion techniques provide information on the pore size distribution and the total pore volume. 

N2 adsorption-desorption isotherms and pore size distribution of sample II-IV are shown in Fig. 4. Its isotherm in Fig. 4a corresponds to a reversible type IV isotherm which is typical for mesoporous solids. Two definite steps occur at p/po = 0.18, and 0.3, which indicates the filling of the bimodal mesopores. Using the BJH procedure with the desorption isotherm, the pore diameter in Fig. 4a is approximately 1.74, and 2.5 nm. Furthermore, with the increasing of synthesis time, the isotherm in Fig. 4c presents the silicalite-1 material related to a reversible type I isotherm and mesoporous solids related to type IV isotherm, simultaneously. These isotherms reveals the gradual transition from type IV to type I. In addition, with the increase of microwave irradiation time, Fig. 4c shows a hysteresis loop indicating a partial disintegration of the mesopore structure. These results seem to show a gradual transformation... 

Based on the above general principles, quite a number of models have been developed to estimate pore size distributions.29,30,31-32,33 They are based on different pore models (cylindrical, ink bottle, packed sphere,. ..). Even the so-called modelless calculation methods do need a pore model in the end to convert the results into an actual pore size distribution. Very often, the exact pore shape is not known, or the pores are very irregular, which makes the choice of the model rather arbitrary. The model of Barett, Joyner and Halenda34 (BJH model) is based on calculation methods for cylindrical pores. The method uses the desorption branch of the isotherm. The desorbed amount of gas is due either to the evaporation of the liquid core, or to the desorption of a multilayer. Both phenomena are related to the relative pressure, by means of the Kelvin and the Halsey equation. The exact computer algorithms35 are not discussed here. The calculations are rather tedious, but straightforward. 

The relation between pore volume and pore dimensions is presented graphically either in the form of a cumulative plot of pore volume against mean pore size (i.e. d up versus fp) or ideally as a distribution (or frequency curve), dv /drp versus rp (or J wp). Since the computation is usually based on the notional removal of the con-J densate by a step-wise lowering of p/p°, in practice the pore size distribution is J expressed in the form of 8vJSrp versus f p. The computation is somewhat complkj cated because allowance must be made at each desorption step for the thinning of the adsorbed multilayer in pores from which the capillary condensate has already been removed. Jj... 

Nitrogen adsorption/condensation measurements were performed using an Autosorb-1 analyzer to calculate sample surface area and pore size distribution. BET analysis at 77 K was applied for extracting the monolayer capacity from the adsorption isotherm and a N molecular cross-sectional area of 0.162 nm2 was used to relate tne monolayer capacity to surface area. PSD s were calculated from the desorption branches of the isotherms using a modified form of the BJH method [18]. Mercury intrusion measurements were performed using an Autoscan-33 continuous scanning mercury porosimeter (12-33000 psia) and a contact angle of 140°. 

Now, an important question is How, those parameters Sp, Vp, (Dmax/2c), c, and x are affected by the gradual narrowing of pores due to some kind of surface functionalization A second question is which of, and how, the parameters t, c and (Dmax/2o) are interrelated. The question becomes more interesting, and perhaps intriguing, since all the above quantities are calculated just from one kind of measurement, namely the N2 adsorption/desorption data. A partly answer to the above question was attempted in a previous work [10] in which sixteen mesoporous vanado-phoshoro-aluminates solids were tested and some relationships between c and (Dmax/2o) were established. A first target of this paper is to extend the search for such possible inter-relations to a class of mesoporous silicas, with a random pore size distribution whose porosity has been systematically and gradually modified by surface fiinctionalization... 

The gas adsorption-desorption technique relates to the adsorption of nitrogen (or, less commonly, carbon dioxide, argon, xenon, and krypton), at cryogenic temperatures, via adsorption and capillary condensation from the gas phase, with subsequent desorption occurring after complete pore filling. An adsorption-desorption isotherm is constructed based upon the relationship between the pressure of the adsorbate gas and the volume of gas adsorbed/desorbed. Computational analysis of the isotherms based on the BET (Brunauer-Emmett-Teller) (Brunauer et al. 1938) and/or BJH (Barrett-Joyner-Halenda) (Barrett et al. 1951) methods, underpinned by the classical Kelvin equation, facilitates the calculation of surface area, pore volume, average pore size, and pore size distribution. 

Porosity can be used to describe the pore distribution and pores size associated with an LDH. Pore distribution is related to the method of LDH formation (383) and ions associated with the material, whereas pore size is related more to the method of preparation and interconnection of LDH platelets. The porosity of a material is commonly analyzed by N2 adsorption/desorption and pore size distribution analysis. N2 adsorption/desorption isotherms are a plot of the volume of N2 adsorbed versus relative pressures. Pore size distributions are calculated using the Barrett, Joyner, and Halenda method based on the isotham data (385). 

Recent progress in the theory of adsorption on porous solids, in general, and in the adsorption methods of pore structure characterization, in particular, has been related, to a large extent, to the application of the density functional theory (DFT) of Inhomogeneous fluids [1]. DFT has helped qualitatively describe and classify the specifics of adsorption and capillary condensation in pores of different geometries [2-4]. Moreover, it has been shown that the non-local density functional theory (NLDFT) with suitably chosen parameters of fluid-fluid and fluid-solid interactions quantitatively predicts the positions of capillary condensation and desorption transitions of argon and nitrogen in cylindrical pores of ordered mesoporous molecular sieves of MCM-41 and SBA-15 types [5,6]. NLDFT methods have been already commercialized by the producers of adsorption equipment for the interpretation of experimental data and the calculation of pore size distributions from adsorption isotherms [7-9]. 

Quantitatively establishing the relation between the size of the pores that are compressed and the pressure of densification is obviously essential in order to determine pore volume distribution as a function of pore size. This relation has been established by Pirard et al. (Pirard, 1995) from the analysis of nitrogen adsorption-desorption isotherms of aerogels that were partially densified by mercury porosimetry at increasing pressures. Two types of aerogels were analyzed silica-zirconia aerogels, whose densification is completely... 

Both nitrogen adsorption and mercury penetration provide a direct measure of pore size distribution and pore volume. However, these direct measures do not permit a determination of the morphology of the materials from pressure-volume relationships. DeBoer (ref. 1) was among the first to relate the shape of the nitrogen adsorption/desorption isotherms and the location and shape of the hysteresis loop to the type of pores associated with the material. Much attention has been paid to better define the relation between morphology of the pores of a material and the adsorption/desorption isotherms (ref. 2). Much less attention has been paid to the relationship of morphology to mercury penetration data (ref. 3). 

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