Chemical potential of mixing

The excess quantities in each equation represent the corresponding temperature and pressure derivatives of the excess chemical potential of mixing. When the values of the temperature and pressure derivatives of Apfx for the reference state or Ap x for the standard state are defined, then all quantities in Equations (8.77)—(8.80) are also defined. 

Figure 8.3. Chemical potentials of mixing in a binary system for reference state as the pure component.

In the summations, the stoichiometrical coefficient v, is negative for the reactants and positive for the products. In Eq. 6.2 the first term on the right hand side is the unitary affinity A, which comprises of the stoichiometrical sum of the unitary chemical potentials of the reactants and products, and the second term is the affinity of mixing AM, which comprises of the stoichiometrical sum of the chemical potentials of mixing for the reactants and products. By substituting the unitary affinity A for the first term on the right hand side of Eq. 6.2 and defining this to be equal to RT In K(T, p we obtain Eq. 6.3 ... 

Problem 2.5(a) (Worked Example) From the Flory-Huggins free energy per unit volume, Eq. (2-33), show that the excess chemical potential of mixing of the solvent, — yLig, in a polymer... 

By definition, the chemical potential of mixing jUb — /Cg is obtained by taking the derivative of AF with respect to g, holding constant. Thus,... 

If we compare this with (7.52) we see that the standard chemical potential is the same as before, but the chemical potential of mixing is altered the activity ai—Xiyi replaces the mole fraction Xi, This may be generalized to other thermodynamic quantities. The standard properties of a non-ideal system are the same as those of the corresponding ideal reference system. It is only the quantities dependent upon composition that are altered by the introduction of activity coefficients. This is illustrated by table 7.2 which is to be compared with table 7.1. 

At an equilibrium degree of swelling, the chemical potentials of mixing and of elastic deformation of the network balance, so that ... 

The condition of swelling equilibrium can be calculated by means of two theoretical approaches. It is assumed that the chemical potential of mixing for a network is the same as the chemical potential of mixing an uncross-linked polymer of high molecular weight and of the same structure as the network polymer. The mixing term can be described by means of the Flory-Huggins (FH) equation. The calculation of the elastic deformation term is based on the rubber elasticity theory (RET). 

From this equation, the chemical potential of mixing per moles of component f(A/r, ) can be calculated [48]. For a binary mixture. 

In the 1970s a new theory of polymers, taking account of correlations between monomers, was developed based on the analogy found between polymer statistics and critical phenomena [105]. For the chemical potential of mixing in the semidilute region scaling theory yields... 

If we introduce the chemical potential of mixing of the first component according to... 

Figure 1.5. Concentration dependence of the chemical potential of mixing Ap,f RT (a), the molar Gibbs potential of mixing AGm/RT (6) for regular mixtures with ajRT (the digits at the curves) = 3, 2, 2,1 (endothermic mixtures), 0 (ideal mixture), —I (exothermic mixture). stands for dApifdxj. State diagram (c) bi—binodal, sp—spinodal, C—critical point. ajRTc = 2 at T = Tc...

Figure 3.2. Chemical potential of mixing of LMW component ( ) 2ind that of polymer (6) in HT units against the volume fraction of polymer U2, 3 = 1,000 (the values of are specified near the curves) (Tompa, 1956) [H.Tompa Polymer Solutions. Copyright 19.56 by Academic Press]...

The chemical potential of mixing of LMWL relates to its vapour pressure by the relationship (Equation 1.1.3-5)... 

If Ap] is riK asured in a certain concentration range, Gibbs-Durgham s equation enables the polymer chemical potential of mixing to be determined by numerical or graphical integration... 

If in the system P+LMWI< at some temperature 1 the chemical potential of mixing of the polymer in solution per mole of monomeric units A//2 at some concentration I i = rj proves to be equal to the difference of the chemical potentials of polymer in the crystal and amorphous phases then there will be two phases in equilibrium, namely, polymer... 

The second virial coefficient is then proportional to the excess chemical potential of mixing when ... 

Using the combinatorial entropy of mixing taken from the Flory-Huggins theory the chemical potential of mixing is calculated as... 

Figure 3.13 shows the way of how the residual chemical potential of mixing depends on temperature is determined by the nature of an oligomer component of a mixture and the relaxation state of a matrix. Mixtures, containing any of investigated -methylene-dimetacrylates and the first two representatives of -oxymethylene-dimetacrylates, demonstrate that only as a function T varies at transition from a glass state to a rubber state, therefore it s just the rate of ordering that varies. However, mixtures of PVC with n-... 

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