Entropy surfactant adsorption

The heat and entropy of adsorption calculated in the manner outlined above for do-decyl sulfonate adsorption on alumina show marked changes at particular concentrations and are in agreement with the hypothesis of lateral interaction of surfactants to form two-dimensional aggregates (Fig. 4.15). Most interestingly, the association was found to produce a net increase in entropy of the system, suggesting a decrease upon aggregation... 

Since yn is positive, then the energy required to expand the interface to form a large number of droplets is positive and this term can be reduced by reducing /i2, e.g. by surfactant adsorption. The entropy term, however, is positive and this favours the formation of the emulsion. With macroemulsions, lAAy l > and hence is positive. This means that the... 

This transition may j-.e. reducing the specific surface energy, f. The reduction of f to sufficiently small values was accounted for by Ruckenstein (15) in terms of the so called dilution effect". Accumulation of surfactant and cosurfactant at the interface not only causes significant reduction in the interfacial tension, but also results in reduction of the chemical potential of surfactant and cosurfactant in bulk solution. The latter reduction may exceed the positive free energy caused by the total interfacial tension and hence the overall Ag of the system may become negative. Further analysis by Ruckenstein and Krishnan (16) have showed that micelle formation encountered with water soluble surfactants reduces the dilution effect as a result of the association of the the surfactants molecules. However, if a cosurfactant is added, it can reduce the interfacial tension by further adsorption and introduces a dilution effect. The treatment of Ruckenstein and Krishnan (16) also highlighted the role of interfacial tension in the formation of microemulsions. When the contribution of surfactant and cosurfactant adsorption is taken into account, the entropy of the drops becomes negligible and the interfacial tension does not need to attain ultralow values before stable microemulsions form. 

This explanation for the entropy-dominated association of surfactant molecules is called the hydrophobic effect or, less precisely, hydrophobic bonding. Note that relatively little is said of any direct affinity between the associating species. It is more accurate to say that they are expelled from the water and —as far as the water is concerned —the effect is primarily entropic. The same hydrophobic effect is responsible for the adsorption behavior of amphi-pathic molecules and plays an important role in stabilizing a variety of other structures formed by surfactants in aqueous solutions. 

In spite of the fact that the concentration of surfactants in the outer solution is assumed to be smaller than the critical micelle concentration, inside the network, micelles are supposed to be formed. The reason for this assumption is, first of all, intensive adsorption of surfactants on the network as a result of the ion exchange reaction. Moreover, in Refs. [38, 39], it was shown that critical concentration of micelles formation c c" within a polyelectrolyte network is much less than that in the solution of surfactant c° . Indeed, when a micelle is formed in solution immobilization of counter ions of surfactant molecules takes place, because these counter ions tend to neutralize the charge of micelles (see Fig. 13), whereas there is no immobilization of counter ions when the micelles are formed in the network the charge of micelles is neutralized by initially immobilized network charges which do not contribute to the translational entropy (Fig. 13). 

Lin and Yang (1987) also calculated the thermodynamic parameters of diazepam for micellar solubilization in Pluronic surfactant solutions at different temperatures (Table 13.4). For all systems, AG was negative, indicating micellar solubilization was spontaneous. The sign of entropy has been associated with the location of solubilized molecules within the micelles. Positive values have been observed for molecules embedded in the micelle center and negative values for adsorption of the molecules on the micelle surface. The results in this paper indicate that in the F-108 and F-88 Pluronics, diazepam molecules can penetrate into the micelle interior, whereas for F-68 and lower concentrations of F-88, diazepam is adsorbed on the micelle surface without penetration into the micellar core. 

The dispersion of one phase into a second phase in the form of globules leads to an Increase in the entropy of the system and results in the adsorption of surfactant and cosurfactant on the large Inter-facial area thus created. This adsorption decreases the Interfacial tension from about 50 dyne/cm, characteristic of a water-oil interface devoid of surfactants, to some very low positive value. In addition, the concentrations of surfactant and cosurfactant in the continuous and dispersed phases are decreased as a result of the adsorption, thereby reducing their chemical potentials. This dilution of the bulk phases leads to a negative free energy change, which we call the dilution effect. Dispersions that are thermodynamically... 

Polymers are mixtures of macromolecules of different molecular weight, and most commercially available products have rather broad distribution of the molecular weight. Some studies were carried out with fractions of a narrow distribution of the molecular weight, separated from commercially available polymers. Adsorption leads to fractionation as discussed above for some types of surfactants. Larger polymer molecules have higher affinity to the surface than smaller molecules composed of the same type of monomeric units. The selectivity is chiefly driven by the difference in the entropy of mixing in solution. Polydispersity of polymers is also one of the factors responsible for hysteresis loops in the adsorption-desorption cycles. 

Perhaps the simplest type of a polymeric surfactant is a homopolymer, that is formed from the same repeating units, such as PEO or poly(vinyl pyrrolidone). These homopolymers have minimal surface activity at the O/W interface, as the homopolymer segments (e.g., ethylene oxide or vinylpyrroUdone) are highly water-soluble and have little affinity to the interface. However, such homopolymers may adsorb significantly at the solid/liquid (S/L) interface. Even if the adsorption energy per monomer segment to the surface is small (fraction of kT, where k is the Boltzmann constant and T is absolute temperature), the total adsorption energy per molecule may be sufficient to overcome the unfavourable entropy loss of the molecule at the S/L interface. 

A least square plot of log Ccsc as a function of number of carbon atoms in the alkyl chain is given in Fig. 4.13. obtained from the slope of this line is —0.95kT and is comparable to the free energy of micellization measured for similar surfactants in solution (Fig. 4.14). Heat and standard entropy changes associated with the adsorption process can be calculated by considering the adsorption of the long-chain molecules, X, as follows (Somasundaran and Fuerstenau, 1972). 

The last term is characteristic of the thermodynamics of irreversible processes. Its magnitude becomes positive if the system s processes are irreversible. Typical irreversible processes are the adsorption or desorption of surfactants at liquid interfaces. The derivative of the second term of Eq. (2C.2), as local entropy production is... 

Thus, deviations from the ideal Langmuir isotherm can be caused both by intermolecular interactions, which result in an enthalpy of mixing, and by area differences between molecules, which produce a non-ideal entropy of mixing [18]. For a simple case where the interactions are of the Frumkin type and the partial molar areas of solvent and surfactant are constant the entropic effect of area differences results in typical features of macromolecular adsorption, e.g., a steep initial increase of adsorption ( high affinity adsorption) and a very slow rise once the surface is approximately half filled [18]. 

In analogy to surfactant molecules able to reorient, we assume here that protein molecules can exist in a number of states with different molar areas and that the non-ideality of enthalpy for protein adsorption layers does not depend on the state of molecules at the surface, that is, the activity coefficients are given by Eqs. (2.72). Assuming an entropy non-ideality (the convention oio = coi) and enthalpic non-ideality contribution of the Frumkin type, and taking into account the contribution of the DEL, Eq. (2.59), one can transform the equation of state for the surface layer (2.26) into... 

Equation (2.182) is commonly used to calculate the standard enthalpy of adsorption [83, 160, 171, 186, 187]. The constant K usually exhibits a weak dependence on temperature. The value of AH° calculated from Eq. (2.182) was found to be in the range of +10 to -20 kJ/mol for various surfactants. As mentioned above AG lies in the range -20 to -60 kJ/mol, hence the standard free energy of adsorption is mainly controlled by the adsorption entropy, see Eq. (2.180), and the value of TAS can amount to 10 to 50kJ/mol. The most significant contribution of entropy was found for the water/oil interface [160]. The increase of AS due to adsorption can be ascribed mainly to the disorder of water structure in the solution bulk [83, 160]. In solution the hydrocarbon chains of the surfactant molecules are surrounded by a structured water shell, while during the adsorption these shells are destructed. This leads to an increase in entropy of the system. The entropy also increases due to the transfer of hydrocarbon chains from the water phase to the gas phase and, especially, to the oil phase where they become more flexible. 

The third paper in this subject that we were able to retrieve is due to Biswas et al. [145]. In their introduction to the paper they said that dynamic and mechanistic aspects of adsorption of surfactants at the solid-liquid interface, particularly silica surface, were rare and quoted six papers. The most recent among them was due to Tiberg [146] in 1996. Adsorption kinetics was studied by Biswas et al. [145] using classical batch experiments. They found that the adsorption follows a two-step first-order rate equation. From the calculated rate constants they obtained the activation energies and entropies concluding that both processes are entropy controlled. 

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