Entropy surface coverage

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as... 

Figure 2. Variation of the integral net heat of sorption (—Qs), change of free energy (—AG), and change of the integral entropy (TaS) with surface coverage (6) of beechwood (39)...

AS°ads. .. standard entropy of adsorption at zero surface coverage, J/mol-K... 

The temperature dependent vapor pressure of pure elements or compounds is frequently used to define volatility. For the adsorbed state the relevant quantity is the desorption pressure, which depends on the temperature and on the surface coverage. The individual crystal lattices with their characteristic binding properties and thus, their standard entropy of the pure solid phase,... 

It is assumed that the binding energy of an adsorbed single molecule to the surface approximately equals its partial molar adsorption enthalpy at zero surface coverage. In the adsorbed state at zero surface coverage the individual variations of the entropy are partly but not completely suppressed. Hence, it is expected that this adsorption enthalpy is proportional to the standard sublimation enthalpy, which characterizes the volatility properties of pure solid phases as an integral value, ... 

Many systems give linear plots of pjn against p over a limited ranges of pressure, but such linearity does not by itself imply conformity with the Langmuir model. As already indicated, a second condition is that the energy of adsorption should be independent of surface coverage. Thirdly, the differential entropy of adsorption should vary in accordance with the ideal localized model (Everett, 1950). That no real system has been found to satisfy all these requirements is not surprising in view of the complexities noted here and in subsequent chapters. 

While a knowledge of surface mobility is of great interest in physical adsorption, it becomes essential in chemisorption phenomena. For instance in calorimetric work a curve of differential heats of adsorption versus surface coverage will be horizontal if adsorption is localized but shows the customary slope from high to low values of the heat of adsorption if the adsorbed layer is mobile Furthermore if a chemisorbed intermediate takes part in a surface reaction (crystal growth, corrosion, catalysis), it is essential to know whether, after adsorption anywhere on the surface, it can migrate to a locus of reaction (dislocation, etch pit, active center). Yet here again, while Innumerable adsorption data have been scrutinized for their heat values, very few calculations have been made of the entropies of chemisorbed layers. A few can be found in the review of Kemball (4) and in the book of Trapnell (11). 

Rigid molecule, entropy only at low surface coverage, (i.e., 6 < 0.2)... 

Rigid molecule, entropy only at high surface coverage... 

Practically all observations [241-243, 245,249, 261, 262,264] of the entropy driven brush stretching (see Eq. 59) have been performed for polystyrene brushes immersed in an identical, except for the isotopic status, PS matrix. The change in the conformational properties of the brush has been observed as a function of surface coverage o [241-243,245,249,261,262,264] and/or host matrix degree of polymerization P [241,243]. These studies were initiated in 1992 by us [241] and two other groups [249,262]. Here we resume the results of these reports focusing on the verification of the schematic conformation diagram (InP/ln N vs lno/ln N) predicted by theory [232, 239, 267] and presented in Fig. 35. 

Much of our information about the nature of the adsorbed gas layer comes from studies of the amount of gas adsorbed on a surface a (the surface coverage) as a function of gas pressure P at a given temperature. The o-P curves derived from these experiments are called adsorption isotherms. Adsorption isotherms are used primarily to determine thermodynamic parameters that characterize the adsorbed layer (heats of adsorption, and the entropy and heat capacity changes associated with the adsorption process) and to determine the surface area of the adsorbing solid. The latter measurement is of great technical importance because of the widespread use of porous solids of high surface area in various industrial processes. The effectiveness of participation by a porous solid in a surface reaction is often proportional to the surface area of the solid. The simplest adsorption isotherm at a constant temperature is obtained from Eq. 3.85, which we can rewrite as... 

We have measured A gH for plateau adsorption of HPA on different substrates (11,26,33) and for RNase on polystyrene (33) With both proteins, and under many conditions, A gH > 0, implying again that spontaneous adsorption occurs by virtue of an entropy increase A gS > 0. In section 2 the same conclusion has been drawn for the interaction between HPA and polystyrene latex at low surface coverage. 

The small complementary molecular building blocks used are relatively easy to synthesize. These nanoporous surfaces could be used to immobilize and host a large variety of guest species [23,24]. These research activities, however, have revealed a number of important aspects of monolayer formation, such as the role of concentration, surface coverage control, self-recognition, and self-selection [17]. Although directional supramolecular interactions, such as H-bonding, have proven to be quite predictable, other factors that play a role in the formation of the self-assembles, such as entropy and the influence of surface, are less understood and difficult to control. 

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