Modeling of the Psychophysical Response Curves Using the Grand Canonical Ensemble in Statistical Physics

Abstract

This paper aims to investigate the peripheral mechanism of taste perception by the use of the grand canonical ensemble in statistical physics. It allows a better understanding of this process and its interpretation at a microscopic level. The experimental part allowed us to obtain psychophysical curves relative to four nutritive sweeteners (sucrose, fructose, glucose, and maltitol). These curves represent the intensity of sweetness as a function of sugar concentration in water. A Sensory Measuring Unit for Recording Flux (SMURF) device is used to obtain intensity-time curves for each of the studied sweeteners. To model these curves we have established the expressions of some models using grand canonical ensemble formalism in statistical physics and applying some simplification approaches. The fitting of the psychophysical data with statistical models by numerical simulation demonstrates a good correlation between the models and the experimental curves. Some physicochemical parameters interfere in the expression of the established models. These parameters are classified in two categories: on one hand, the steric aspect, which is manifested by the density of taste receptor site, and the number of molecules per receptor site and on the other hand, an energetic aspect illustrated by the concentration at half saturation, which gives indirectly the sweet molecule-receptor site energy of interaction.

Modeling of adsorption isotherms of dye N719 on titanium oxide using the grand canonical ensemble in statistical physics for dye sensitized solar cells

“…Secondly the rotational degree of freedom is neglected, since it is freezed in the solution. Also, the freedom degree of vibration can be neglected in comparison with the translation degree (Ben Lamine and Bouazra, 1997; Knani et al, 2007) We consider that a variable number of dye molecules are adsorbed onto N m receptor sites located on a unit mass of the adsorbent. The adsorption reaction of a dissolved dye molecule (D) onto a receptor site (R) should include astoichiometric coefficient n as the following equation:…”

“…If n is greater than 1, it represents the number of anchored molecules on one site and is called a multi-molecular adsorption. If n is less than 1, it would represent the fraction of molecule per site (Knani et al, 2007;Khalfaoui et al, 2002). Then we take the inverse of this number (n 0 = 1/n) which would represent the number of sites that adsorbed dye molecule is linked to.…”

“…The process is called a multi-anchorage adsorption. A multi-anchorage adsorption cannot be performed without considering a parallel position of the molecule to the adsorbent surface (Knani et al, 2007;Khalfaoui et al, 2002). So a multi-anchorage adsorption is also called a parallel adsorption.…”

“…In addition to its stoichiometric aspect, 1/n represents the average number of anchorages per dye molecule and gives information about the molecule position with n (or n 0 ) as a stereographic coefficient. (Knani et al, 2007;Khalfaoui et al, 2002).…”

On the use of the Hill’s model as local isotherm in the interpretation of the behaviour of the adsorption energy distributions

“…The local isotherm provides an explicit relationship between the adsorbed quantity on each homogeneous patch with equilibrium pressure and the adsorption energy on the patch [20,22,23,25]. To obtain the integral equation we have use the following reasoning: It is usual to consider a model with two energies or three energies of adsorption [21]. For example for two energies E 1 and E 2 the adsorbed quantity is:…”