Condensation adsorption isotherms of type IV (or V) according to BDDT classification on porous adsorbents composed of one or two groups of adsorption sites are derived statistically. When beta(c1) (or beta(c2)) is less than unity, the isotherm becomes type IV, and when it is greater than unity, the isotherm becomes type V. it is understood that the negative sign(-) of the additional adsorption energy, q, in the nth layer in deriving those theoretical isotherms plays a decisive role on the horizontally flat approach to the axis of the isotherm near the saturation vapor pressure. The values of the surface area can be calculated easily. The pore radii of all the adsorbents which we have obtained by using the derived isotherms with respect to the appropriately selected experimental data agree with those obtained by using the Kelvin equation. Many surface mono-layer adsorption isotherms are obtained in the process of deriving the various adsorption isotherms. From them we can learn that the surface sites are not adsorbed completely even near the saturated vapor pressure, and we can find the range of error by comparing them with v(m)s of the BET equation. We could mention through judging the results of a great deal of the experimental isotherm data of types IV and V that "the cause of hysteresis phenomena of the condensation adsorption-desorption of gases is originated from the deviation from the thermodynamically reversible adsorption-desorption process in the condensation adsorption-desorption of gases".

Pore Condensation Adsorption Isotherms Surface Mono-layer Adsorption Isotherms Hysteresis Phenomena

Barrer RM, Macleod DM, Trans. Faraday Soc., 50, 980 (1954) 
Brunauer S, Deming LS, Deming WE, Teller E, J. Am. Chem. Soc., 62, 1723 (1940) 
Brunauer S, Emmett PH, Teller E, J. Am. Chem. Soc., 60, 309 (1938) 
Chuikina VK, Kiselev AV, Mineyeva LV, Muttik GG, J. Chem. Soc.-Faraday Trans., 1, 1345 (1972)
Culver RU, Heath NS, Trans. Faraday Soc., 51, 1569 (1955) 
Culver RU, Heath NS, Chapter 4, in the below reference (Gregg and Sing, 1969)
Darcey JR, Clunie JC, Thomas DG, Trans. Faraday Soc., 54, 250 (1958) 
de Boer JH, Lippens BC, J. Catal., 3, 38 (1965) 
Emmett PH, Cines M, J. Phys. Chem., 51, 1248 (1947) 
Gregg SJ, Sing KSW, "Adsorption, Surface Area and Porosity," Academic Press Inc. (London) Ltd., Second Printing (1969)
Harris MR, Whitaker G, J. Appl. Chem., 13, 348 (1963)
Hill TL, J. Chem. Phys., 14, 263 (1946) 
Hill TL, J. Chem. Phys., 14, 268 (1946) 
Homes JM, Beebe RA, Canadian J. Chem., 35, 1542 (1957) 
Katz SM, J. Phys. Chem., 53, 1166 (1949) 
Kim D, Korean J. Chem. Eng., 17(2), 156 (2000)
Kipling JJ, Wilson RB, Trans. Faraday Soc., 56, 562 (1960) 
Langmuir I, J. Am. Chem. Soc., 40, 1361 (1918) 
Mason G, Proc. R. Soc. Lond., A415, 453 (1988)
McQuarrie DA, "Statistical Thermodynamics," Harper & Row Publisher (1979)
Pickett G, J. Am. Chem. Soc., 67, 1958 (1945) 
Pierce C, Smith RN, Wiley JW, Cordes H, J. Am. Chem. Soc., 73, 4551 (1951) 
Prenzlow CF, Halsey GD, J. Phys. Chem., 61, 1158 (1957) 
Rao KS, J. Phys. Chem., 45, 506 (1941) 
Rudzinski W, Everett DH, "Adsorption of Gases on Heterogeneous Surfaces," Academic Press Ltd. (1992)
Salby ML, "Fundamentals of Atmospheric Physics," Academic Press, Chapter 9 (Fig. 9.14) (1996)
Sears FW, Salinger GL, "Thermodynamics, Kinetic Theory and Statistical Thermodynamics," Addison-Wesley Publishing Company, 3rd ed. (1975)
Shull CG, J. Am. Chem. Soc., 70, 1405 (1948) 
Wig EO, Juhola AJ, J. Am. Chem. Soc., 71, 561 (1949) 
Wooton LA, Brown C, J. Am. Chem. Soc., 65, 113 (1943)