The Hysteresis Loop in Adsorption Isotherms on Porous Vycor Glass and Associated Dimensional Changes of the Adsorbent. Ii

Quinn, H. W.; McIntosh, R.

doi:10.1139/v57-106

Cited by 24 publications

(27 citation statements)

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“…5 (water at 18.75 o C) together with those of Ref. 22 (butane at −6.2 o C), we find that along the reversible region at the top of the hysteresis loop, the relationship (∆l/l) vs ln(P/P 0 ) is practically linear but the slope is only 1.9 times higher for water than for butane. This leads to an embarrassing result: the K value is found to depend markedly on the adsorbate: it is 3 times higher for water than for butane.…”

Section: Ii-hysteresis Regionsupporting

confidence: 65%

“…(4), contrary to what has been assumed in all the papers where the deformation of the solid has been taken into account. 21,22,23 Actually, as is shown below, the shift (µ σ − µ v ) is small, but even small it cannot be ignored if we want to treat consistently the influence of the elastic deformation on adsorption. Then, for isothermal conditions, F σ can be written as…”

Section: I-reversible Adsorptionmentioning

confidence: 99%

“…Now, compare the elastic energy stored in the porous matrix to the corresponding variation of the surface free energy. Equations (22) and (32) show that the ratio F el so /γA is of the order of (∆l/l). More precisely, in Fig.…”

Section: I-reversible Adsorptionmentioning

confidence: 99%

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Influence of elastic deformation of porous materials in adsorption-desorption process: A thermodynamic approach

Grosman

Ortega

2008

Phys. Rev. B

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It has been known for a long time that the adsorption and condensation of gas cause elastic deformation of the porous matrix. The reversible formation of an adsorbed film, which precedes capillary condensation, results in an extension of the porous material while, in the hysteresis region, the negative liquid pressures under the concave menisci contract the porous matrix. The elastic deformation exhibits an hysteresis loop in the same pressure region as the adsorption phenomenon. These deformations have been neglected in practically all the theoretical treatments of adsorption. There are two reasons for this. First, the deformations are small in magnitude and were supposed to have small effects on the adsorption process, and second, no experiment has contradicted the existing model according to which, in systems where the pores interact, the source of interactions is pore-pore intersections. They are the experimental results obtained in SBA-15 and p + -type porous silicon, systems in which the pores interact whereas they are not connected, which lead us to question these models and consider the elastic deformation of the pore walls as a possible coupling parameter. Based on the experimental work of C. H. Amberg and R. McIntosh [Can. J. Chem. 30, 1012(1952] who measured both the linear deformation of a porous glass rod and the adsorbed amount during isothermal adsorption of water, we develop a thermodynamic approach which includes the elastic energy of the solid. This approach is generic to all porous materials. In the region of reversible adsorption preceding the capillary condensation where the variation of the surface free energy can be deduced from adsorption data, the linear extension of the solid is proportional to the variation of the surface free energy and to the elastic constant of the solid. This is the crucial point of the paper: thermodynamics of adsorption is directly connected to the elastic properties of the porous solid. In the hysteresis region, this linear relation can be used to deduce the variation of the surface free energy from the deformation measurements, a calculation which cannot be done from adsorption data. We find that the surface free energy related to the elastic deformation is an important component of the total free energy. It is shown that the condensation branch represents the more stable states and that an energy barrier exists to evaporation which depends essentially on the elastic deformation. The pores interact through the deformation of the walls. Based on this interaction mechanism and on the shape of the scanning curves which are common to materials with interconnected pores such as porous glass or noninterconnected pores such as p + -type porous silicon and SBA-15, we propose a scenario for the filling and emptying of these porous materials.

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Section: Ii-hysteresis Regionsupporting

confidence: 65%

Section: I-reversible Adsorptionmentioning

confidence: 99%

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Influence of elastic deformation of porous materials in adsorption-desorption process: A thermodynamic approach

Grosman

Ortega

2008

Phys. Rev. B

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“…Secondly, the solid matrix has to oppose the forces produced by the negative pressure and will be compressed. This latter contraction was measured by Quinn & McIntosh (1957) and is typically quite small (less than 0.2%). Schechter et at.…”

Section: Maximum Amount Adsorbedmentioning

confidence: 81%

Determination of the pore-size distributions and pore-space interconnectivity of Vycor porous glass from adsorption-desorption hysteresis capillary condensation isotherms

Mason

1988

Proc. R. Soc. Lond. A

143

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A model of a chaotic pore space in which cavities are randomly connected together by constrictions or windows is given. The behaviour of the system is described in terms of the cavity-size distribution, the window-size distribution, and the number of windows per cavity. A Bethe tree is used as the network of pore connections. The analysis of capillary condensation adsorption and desorption scanning curves is described, and the conclusion is drawn that desorption scanning curves are the more valuable in terms of the information that can be derived from them. This model is applied to the large number of scanning isotherms obtained by A. J. Brown (Ph. D. thesis, University of Bristol (1963)) for xenon on Vycor porous glass at 151 K. A method of correlating the results is given in which there is no need to separate the amount of capillary condensation from the amount of surface adsorption. The family of adsorption isotherms confirms the theory but some systematic differences remain. The family of desorption isotherms is used in a simple method that gives an estimate of the cavity-size distribution in terms of the Kelvin radius. The same isotherms are used in a more complicated method to give an estimate of the number of windows per cavity, together with a more precise cavity-size distribution and a window-size distribution. These results are then used to calculate the thickness of the surface adsorption. This enables the geometric pore sizes to be obtained from the Kelvin pore sizes. The cavity-size distribution thus obtained is in agreement with published values.

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“…Despite this, direct measurements of adsorptive deformation essentially are not conducted nowadays. Only measurements of structural characteristics of clay minerals [2][3][4][5][6][7][8], polymeric materials [9][10][11][12][13][14][15][16][17], carbons [1,[18][19][20][21][22][23][24][25][26], zeolites [27,28], and porous glasses [29,30] are performed. Moreover, no calculations of thermodynamic characteristics of a noninert adsorbent in the process of its deformation are performed (rare exceptions are [31,32].…”

Section: Introductionmentioning

confidence: 99%

Adsorption and deformation phenomena at interaction of N2 and microporous carbon adsorbent

Yakovlev

Фомкин

Tvardovski

2004

Journal of Colloid and Interface Science

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Deformation of activated carbon adsorbent ACC (adsorbent obtained by removing Si from SiC) upon N(2) adsorption has been studied. To solve this problem, a dilatometer was used. Its main part was a line differential transformer, the core of which was connected to the adsorbent by means of a rod. Any changes in the adsorbent height caused a change in the core position in the transformer, which influenced the signal recorded from its secondary winding. These results were compared with the adsorption isotherms. High sensitivity of the dilatometric method has been shown. The dilatometer used allowed the measurement of absolute deformations in the range 1 x 10(-4) to 3 mm.

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The Hysteresis Loop in Adsorption Isotherms on Porous Vycor Glass and Associated Dimensional Changes of the Adsorbent. Ii

Cited by 24 publications

References 0 publications

Influence of elastic deformation of porous materials in adsorption-desorption process: A thermodynamic approach

Influence of elastic deformation of porous materials in adsorption-desorption process: A thermodynamic approach

Determination of the pore-size distributions and pore-space interconnectivity of Vycor porous glass from adsorption-desorption hysteresis capillary condensation isotherms

Adsorption and deformation phenomena at interaction of N2 and microporous carbon adsorbent

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