Equilibrium Moisture Content Isotherms of Codfish (Gadus morhua)

Sorption: A Statistical Thermodynamic Fluctuation Theory

“…Here, we demonstrate that an isotherm model, which incorporates the Langmuir, BET, , and GAB − models as its special cases, can be derived without assuming adsorption sites and layers. Such a generalization will serve as the justification for the routine application of these models beyond planar multilayer adsorption − ,,− , with an additional benefit of increased freedom in the allowed range of parameters. Our foundation is the dependence of sorbate–sorbate interaction (quantified via G 22 / v ) on sorbate activity, a 2 .…”

“…The BET, , GAB, − and Frenkel–Halsey–Hill (FHH) − models were proposed to explain multilayer adsorption on planar surfaces. These models have been applied to fit sorption isotherms of far more complex systems (such as moisture on wood, , powders, aerosol, rock, and food − ,− ); difficulties have arisen when assuming that these complex sorption phenomena lead to multilayer adsorption onto a plane. Recognizing the nonplanar nature of sorbents at the core of these difficulties, the fractal nature of surfaces has been taken into account for the multilayer models such as the BET , and FHH models. − However, how the “fractal dimension” D has been introduced is different from one model to another, , and different values of D depending on the range of sorbate vapor pressure , and even the values of D exceeding those of the embedding environment (i.e., 3) have sometimes been reported. ,− Furthermore, doubts have been raised on the foundations of the BET–GAB and FHH models themselves.…”

“…The uptake of moisture or gas by liquids and solutions has been studied for a long time, ,, with important applications such as CO 2 capture and moisture sorption in liquid food and drinks. − ,,− However, difficulties have arisen whenever solvation in the solution phase was confused with adsorption onto a solid surface due to an apparent similarity between solvation and adsorption. ,, For example, the key contribution to the Norrish constant, presumed to represent the “water structure” in liquid food, turned out to contain significant contributions from solute–solute interaction . Moreover, the osmotic stress technique, , which was founded on an apparent analogy between preferential solvation and the Gibbs adsorption isotherm, misattributed the exclusion of osmolytes from the protein surface to protein hydration increase. ,, Such confusion stems from an apparent similarity between sorption and solvation, which has been invoked for a long time. , In this context, the extension of solution-phase fluctuation to adsorption by Zimm and Zimm and Lundberg, and its subsequent applications beyond liquid sorbents, − must be re-examined.…”

Understanding Sorption Mechanisms Directly from Isotherms

“…Various isotherm models have been developed to answer this question. , However, the difficulty comes from the diverse functional shapes that isotherms exhibit; − the six types of isotherms, according to the IUPAC classification, − have been analyzed using more than 100 isotherm models proposed so far. − Such a practice, unfortunately, has made this simple question even more complicated for the following reasons. First, multiple isotherm models, each assuming a different adsorption mechanism (or even none), are capable of fitting the same data with comparable R 2 values. − Second, the most popular isotherm models, such as the Brunauer–Emmett–Teller (BET) , and Guggenheim–Anderson–de Boer (GAB), − have been applied routinely to real systems (e.g., food samples − and construction materials) that do not satisfy their original assumptions (i.e., site-specific, planar, layer-by-layer adsorption). The conundrum has led to the pessimism that “isotherm’s shape alone does not contain enough information to uniquely identify and quantify the underlying sorption mechanisms” …”

“…First, multiple isotherm models, each assuming a different adsorption mechanism (or even none), are capable of fitting the same data with comparable R 2 values. 14 − 17 Second, the most popular isotherm models, such as the Brunauer–Emmett–Teller (BET) 18 , 19 and Guggenheim–Anderson–de Boer (GAB), 20 − 22 have been applied routinely to real systems (e.g., food samples 23 − 25 and construction materials 26 ) that do not satisfy their original assumptions (i.e., site-specific, planar, layer-by-layer adsorption). The conundrum has led to the pessimism that “isotherm’s shape alone does not contain enough information to uniquely identify and quantify the underlying sorption mechanisms”.…”