Effective chemical potential

The antinucleon distribution functions follow by changing the sign of the effective chemical potential [11], Since we are interested in the low density region the contribution of the antinucleons can be neglected. Then, in mean-field approximation the chemical potential is related to the nucleon number density according to... 

An alternative theory, first proposed by Rettori and Villain (1988). takes the point of view which corresponds to the variation depicted in Fig. 1 (a), in which case the excess chemical potential of the top terrace is much lower than Eq. (6) suggests. In fact, in their treatment, the shrinkage of the top terrace is drivrii by the pressure from the step trains on either side, which has its origin in the repulsive interaction (of elastic or entropic origin) of like steps. This yields an effective chemical potential for the top terrace,... 

We recognize that z < 0 hence, we have introduced the absolute value, z. Second, there is no possibility of separately determining either a+ or a. For, by definition, /i+ (3G/dn+)T p n that is, the determination of /i+ requires addition of just positive ions to the solution, while holding the concentration of anions fixed. However, this step cannot be carried out operationally because it involves a violation of the Law of Electroneutrality. Consequently, one should not attempt to deal with individual ionic activities rather, as Eq. (4.1.3b) shows, the ionic activities occur in such a manner that only their product or their logarithmic sum is involved. Third, since thermodynamic descriptions must be confined to measurable properties we may regard the quantity n + RT in a on the left of Eq. (4.1.3a) as an effective chemical potential that is to be used to represent the behavior of the electrolytes. On the other hand, one does not wish to ignore the ionic nature of the solution hence it is customary to set... 

This can be explained by the fact that for very small nanodroplets, the effective chemical potential of silicon in the wire becomes higher than for the vapour phase. 

Equations (2) and (3) force the conclusion upon us that all extensive terms can be absorbed into an effective chemical potential, pjl = -fitx -I- - In X, and all intensive ones into an effective... 

Using Eq. (58), we may define the effective chemical potential of the particles in solution p ... 

In practice, the potential theory of single-component adsorption is used in the form of the homogeneous approximation (51). The value of is interpreted as an effective chemical potential jig of the adsorbate and as an effective adsorbate density. Thus, in addition to the dependence e(h), a correlation is required for ng(iig) [more generally T)]. In many cases, only the temperature dependence of itg is taken into account However, as shown in Ref. 101, at extremely high effective pressures developed close to a surface, neglecting the pressure compressibility may lead to errors around 10%. 

Instead of the MC and MD methods using explicit particles, another method, that is, polymeric self-consistent field theory (SCFT) proposed by Edwards, is often used to study the phase separation of block copolymers. In SCFT, a polymer chain is treated as a Gaussian string, which is exposed to a set of effective chemical potentials ( ). The chemical potentials are used instead of the actual interactions between different components. Importantly, the relation between the external potentials and the concentration field ((/>) is bijective. 

Figure 6.10 The stable ol-AIFj (0112) surfaces, including terminations derived from the (1x1) and ( 2 x 2) 3F terminations, as a function ofHF and H2O effective chemical potential (defined in Equation (6.9)) and partial pressure and temperature. The terminations derived om the (1 x I) 3F termination are denoted by an asteric. The area within the small rectangle is the accessible region of the phase diagram at 300 K and the region within the large rectangle is the accessible region at 600 K (see text for details)...

To estimate the total free energy of the reactive ternary system (Section 8.3.2), we first write the effective free energy potential of the binary blend that takes into account not only the free energy defined in Eq. (8.5) but also the reactive contribution on the right-hand side of Eq. (8.4). Hence, we define the effective chemical potential, jx = (6F(cp, t[)))/6(p, that accounts for the reactive term in Eq. (8.4), and rewrite this equation as (see References [10, 56]) ... 

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