Chemical potential entropic component

A2 from equation (5.16) or the cross second virial coefficient from equation (5.17). In turn, this knowledge of the second virial coefficients and their temperature dependence allows calculation of the values of the chemical potentials of all components of the biopolymer solution or colloidal system, as well as enthalpic and entropic contributions to those chemical potentials. On the basis of this information, a full description and prediction of the thermodynamic behaviour can be realised (see chapter 3 and the first paragraph of this chapter for the details). 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

Similar attempts were made by Likhtman et al. [13] and Reiss [14]. Reference 13 employed the ideal mixture expression for the entropy and Ref. 14 an expression derived previously by Reiss in his nucleation theory These authors added the interfacial free energy contribution to the entropic contribution. However, the free energy expressions of Refs. 13 and 14 do not provide a radius for which the free energy is minimum. An improved thermodynamic treatment was developed by Ruckenstein [15,16] and Overbeek [17] that included the chemical potentials in the expression of the free energy, since those potentials depend on the distribution of the surfactant and cosurfactant among the continuous, dispersed, and interfacial regions of the microemulsion. Ruckenstein and Krishnan [18] could explain, on the basis of the treatment in Refs. 15 and 16, the phase behavior of a three-component oil-water-nonionic surfactant system reported by Shinoda and Saito [19],... 

Krukowski et al. [24] studied the effect of molecular shape in details by performing exact enumerations on lattice models of different molecular shapes. They calculated the entropic component of the chemical potential, i.e.,... 

The presence of such an additive will decrease or increase the miscibility of the two-component system. An attempt has also been made by Miller and Neogi (65) to explain the thermodynamic stability in terms of chemical potential of the two phases, the interparticle potentials, the entropic contribution and the interfacial free energy. 

Another technique to determine the vapor-liquid equilibrium of pure substances or mixtures, which has some similarities with what is described in [190, 204-206], is the grand equilibrium method [192]. It is a two-step procedure, where the coexisting phases are simulated independently and subsequently. In the first step, one NpT simulation of the liquid phase is performed to determine the chemical potentials p] and the partial molar volumes v of all components i. These entropic properties can be determined by Widom s test molecule method [207] or more advanced techniques, such as gradual inserticMi [208-210] (see below). On the basis of the chemical potentials and partial molar volumes at a specified pressure po, first order Taylor expansions can be made for the pressure dependence ... 

Phase equilibrium may be dealt with through the equality of chemical potentials of each component in all phases while phase stability may be studied through the appropriate spino-dal conditions and the conditions for the critical points(13). The present LF model uses an "entropic" correction term in the expression for the chemical potential entirely analogous to the corresponding correction term of the Equation-of-State theory of Flory and coworkers (14) and which is equal to -rj for a binary mixture i-j. The "entropic parameter q j is a unitless adjustable binary parameter.This correction term does not appear in the expressions for the excess volume and the excess enthalpy of the mixture. 

This chapter summarizes the potential of surface segregation in order to vary the surface chemical composition based on thermodynamical parameters. As a result, materials containing at least two constituents, one being of higher surface energy than the other will evolve towards a state where the interfacial tension is minimized. Minimization of the surface energy requires overcoming entropic forces and drives the movement of one of the components towards the material surface. So that, in principle, and as has been reviewed in this chapter one can tailor the surface properties of a polymer film. 

As already discussed in the Introduction (Section 4.1), molecular composites, as first envisioned by Flory, show phase separation based strictly on entropic effects. Those entropic effects arise from the differences in molecular conformation between the rigid rod and the random coil component in the mixture. Thus, in order to interrupt the phase separation, one possible approach is to enhance the potential for specific interactions through the incorporation of interacting chemical groups into the polymeric components of the mixture. 

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