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Table 2 Isotherm models used to describe the sorption behavior of karaya gum

From: Study on equilibrium moisture sorption characteristics and modeling of Karaya (Sterculia urens Roxb.) gum

Isotherm model Mathematical expression References
GAB (Guggenheun–Anderson–de-Boer) \(M = \frac{{M_{{\text{o}}} CKa_{{\text{w}}} }}{{\left( {1 - Ka_{{\text{w}}} } \right)\left( {1 - Ka_{{\text{w}}} + CKa_{{\text{w}}} } \right)}}\) Quirijns et al. (2005)
Hasley \(a_{{\text{w}}} = \exp \left( {\frac{ - a}{{M^{b} }}} \right)\) Halsey (1948)
Iglesias and Chirife \(M = a + b\left( {\frac{{a_{{\text{w}}} }}{{1 - a_{{\text{w}}} }}} \right)\) Iglesias and Chirife (1982)
Curie \(M = \exp \left( {a + ba_{{\text{w}}} } \right)\) Caurie (1970)
BET (Brunauer Emmett and Teller) \(M = \frac{{CM_{{\text{o}}} a_{{\text{w}}} }}{{\left[ {\left( {1 - a_{{\text{w}}} } \right) + \left( {C - 1} \right)\left( {1 - a_{{\text{w}}} } \right)a_{{\text{w}}} } \right]}}\) Brunauer (1938)
  1. M, EMC, % db; aw, water activity; a and b, constants; Mo, monolayer moisture content, % db; C Guggenheim constant; and K, factor correcting for properties of multilayer molecule with respect to the bulk liquid