Capillary hysteresis

These results allows us to connect the observed hysteresis to the conformational changes in the NA molecule and consider it not as a macroscopic phenomenon like capillary hysteresis, but as natural property of the NA-water system. Our experimental and numerical results are in agreement with the data of other authors [13], [12], [14]. 

Figure 2. Capillary hysteresis of nitrogen in cylindrical pores at 77 K. Equilibrium desorption (black squares) and spinodal condensation (open squares) pressures predicted by the NLDFT in comparison with the results of Cohan s equation (the BJH method) for spherical (crosses and line) and cylindrical (line) meniscus.

Figure 87. Capillary Hysteresis Determined for Two Materials by Haines Apparatus.

Neimark, A.V. Percolation theory of capillary hysteresis phenomena and its application for characterization of porous solids. In Characterization of Solids II Rodrigues-Reinoso, F., et al., Ed. Elsevier Science Publishers Amsterdam, 1991 67-75. 

The adsorption and desorption isotherms have been calculated for the Nj sorption at 77K in cylindrical pores of MCM-41 materials in the range 1-12 nm. The points of spinodal and equilibrium transitions are plotted in Fig. 2. There are several features worth noticing. As the pore size increases, the line of spinodal desorption saturates at the value corresponding to the spinodal decomposition of the bulk liquid. The line of equilibrium capillary condensation asymptotically approaches the Kelvin equation for the spherical meniscus and the line of spontaneous capillary condensation asymptotically approaches the Kelvin equation for the cylindrical meniscus. This asymptotic behavior is in agreement with the classical scenario of capillary hysteresis [12] capillary condensation occurs spontaneously after the formation of the cylindrical adsorption film on the pore walls while evaporation occurs after the formation of the equilibrium meniscus at the pore end. Most interestingly, the NLDFT predictions of equilibrium and spontaneous capillary condensation transitions for pores wider than 6 nm are approximated by the semi-empirical equations of the Deijaguin-Broekhoff-de Boer theory [13]. 

Ravikovitch, P., DomhnaiU, S., Neimark, A., et al. (1995). Capillary hysteresis in nanopores theoretical and experimental studies of nitrogen adsorption on MCM-41. Langmuir, 11, 4765-72. 

Ioannidis, M.A., and I. Chatzis. 1993. A mixed-percolation model of capillary hysteresis and entrapment in mercury porosimetry. J. Colloid Interface Sci. 161 278-291. 

Figure 9.4 Comparison of pore diameters obtained from capillary hysteresis of nitrogen in cylindrical pores at 77.4 K. Equilibrium desorption and spinodal condensation pressures predicted by the NLDFT method in comparison with the resuits of the BJH method. (Reprinted with permission from A. V. Neimark and P. 1. Ravikovitch., Microporous Mesoporous Mater. 2001, 44-45, 697. Copyright 2(X)1 Elsevier.)...

De Boer [149] classified the capillary hysteresis loops according to their shapes, relating the latter to the occurence of pores of given types. He... 

PERCOLATIOH THEORY OF CAPILLARY HYSTERESIS PHEMOMEMA AMO ITS APPLICATIOM FOR CHARACTERIZATION OF POROUS SOLIDS... 

A statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space network models. New methods for computation of porous structure parameters are proposed as application. The main results are ... 

The presence of adsorption hysteresis is the special feature of all adsorbents with a mesopore structure. The adsorption and desorption isotherms differ appreciably from one another and form a closed hysteresis loop. According to the lUPAC classification four main types of hysteresis loops can be distinguished HI, H2, H3 and H4 (ref. l). Experimental adsorption and desorption isotherms in the hysteresis region provide information for calculating the structural characteristics of porous materials-porosity, surface area and pore size distribution. Traditional methods for such calculations are based on the assumption of an unrelated system of pores of simple form, as a rule, cylindrical capillaries. The calculations are based on either the adsorption or the desorption isotherm, ignoring the existence of hysteresis in the adsorption process. This leads to two different pore size distributions. The question of which of these is to be preferred has been the subject of unending discussion. In this report a statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space networks models, which are widely used for the modeling of such processes by many authors (refs. 2-10). The new percolation methods for porous structure parameters computation are also proposed. 

The influence of interconnection effects is diagrammatically illustrated on the example of a simple system consisting of one wide capillary of radius pj and two capillaries of radius pj (see Fig. 1). Capillary condensation in cylindrical capillary of radius p occurs at one value of relative pressure x+ (X=P/Ps) and desorption at another value of relative pressure x- The values x+ and X- depend on pore radius p, moreover X-(p)>x+(P) In this inequality the capillary hysteresis on the level of one capillary is displayed. It is conditioned by the difference of the mechanisms of capillary condensation and desorption. Capillary condensation occurs by means of spontaneous filling at the moment of the loss of adsorption film stability on the internal surface of capillary. This process is not reversible. Desorption occurs at the moment of equilibrium meniscus formation on the open end of capillary. 

A.V. Neimark, The theory of capillary hysteresis phenomena and methods of calculation of mesoporous structure characteristics, D.Sc. Thesis. Moscow State University (1987). 

The liquid cannot move beyond those places where the meniscus in the pore becomes flat, i.e, where the effective pore radius is equal to infinity. In particular, the latter phenomenon is one of the reasons of the capillary hysteresis in porous bodies and the presence of trapped air. 

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