Gurvitsch rule

The section cd can be regarded as due to relatively large cone-shaped pores that would fill and empty without hysteresis. At the end of section cd, then, all pores should be filled, and the adsorbent should hold the same volume of any adsorbate. See Ref. 200 for a discussion of this conclusion, sometimes known as the Gurvitsch rule. 

If the region FGH of the isotherm represents the filling of all the pores with liquid adsorbate, then the amount adsorbed along to plateau FGH, when expressed as a volume of liquid (by use of the normal liquid density) should be the same for all adsorptives on a given porous solid. This prediction is embodied in a generalization put forward many years ago by Gurvitsch and usually known as the Gurvitsch rule. 

This widespread conformity to the Gurvitsch rule constitutes powerful support for the capillary condensation hypothesis in relation to Type IV isotherms. It is perhaps hardly necessary to stress that in order to test data for conformity to the rule it is essential that the stage which corresponds to the complete filling of the pores shall be clearly identifiable—as in the... 

Evidence of a different kind is furnished by the fact that the Gurvitsch rule (p. 113) is often obeyed by systems showing Type I isotherms " the amounts of different adsorptives taken up by a given adsorbent, when expressed as a volume of liquid, agree within a few per cent. The order of agreement is illustrated by the typical examples in Table 4.1 for the adsorption of n-alkanes on ammonium phosphomolybdate, and in Table 4.2 which refers to a variety of adsorptives on a silica gel. It must be admitted, however, that there are cases where considerable deviations from the Gurvitsch mle are found, even though the isotherms are of Type 1. Thus, in Table 4.3 the variation in values of the saturation uptake is far outside... 

The Gurvitsch rule for ammonium phosphomolyb-date - . Quantity adsorbed at a relative pressure of 0-9t, calculated as a volume of liquid... 

Comparison of the pore volume obtained (a) by the Gurvitsch rule and (b) from the densities in mercury and in another fluid... 

If the adsorbent contains micropores, the uptake is enhanced in the low pressure region and the isotherm is correspondingly distorted. In the t-plot, extrapolation of the curve gives a positive intercept which is equivalent to the micropore volume by means of the Gurvitsch rule. 

Textural characterization was performed by N2 adsorption-desorption at 77 K using a Micromeritics ASAP 2010 analyzer. The samples were preheated under vacuum in three steps of Ih at 423 K, Ih at 513 K, and finally 4 h at 623 K. BET specific surface area, Sbet, was calculated using adsorption data in the relative pressure range, P/Po, from 0.05 to 0.2. Total pore volume, Vp , was estimated by Gurvitsch rule on the basis of the amount adsorbed at P/Po of about 0.95. The primary mesopore diameter, Dp, was evaluated using the BJH method from the desorption data of the isotherm. The primary mesopore volume, Vp, and the external surface area, Sext were determined using the t-plot method with the statistical film thickness curve of a macroporous silica gel [5]. 

The specific surface area (Sbet) was evaluated by full 3-parameters BET equation and by 2-parameters linear BET plot in the range p/p° 0.01-0.2. The total pore volume (Vt) was evaluated by Gurvitsch rule. BJH method was applied on the desorption isotherm branch only for mesoporous materials, in order to evaluate the mesopore width. Mean pore size (doFi) was calculated using DFT method (Micromeritics DFT Plus software) for all materials with the cylindrical pores in oxide surface model. 

Pore Volume (Ml/G) of Several Polymer Carbons Calculated from Adsorption at Relative Vapor Pressure (0.98) (Gurvitsch Rule)... 

Nitrogen adsorption isotherms were measured at 77K, using an automated instrument (Omnisorp lOOcx, Beckman Coulter Electronics Ltd). Adsorbent samples (approximately O.lg) were out-gassed at 200"C to a residual pressure of 10" mbar for at least 6 hours prior to the measurement of isotherms. Specific surface areas were derived from the isotherms using the BET equation [2]. Total pore volumes were obtained using the Gurvitsch Rule and the micropore volumes were determined using the Og method [2]. Mesopore volumes were subsequently determined by subtraction. 

Application of the Gurvitsch rule leads to the values of pore volume, v, ... 

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