Ensemble grand mixed isostress isostrain

Therefore, in the classic limit, thermal averages in the grand mixed isostress isostrain ensemble may be cast as... 

Figure 5.20 Shear modulus C44 as a function of shear strain asxo- (O) MC simulations in grand mixed isostress isostrain ensemble (—) representation of small-strain approximation C44 (asxo) = 00 + 02 (asxo) (see Eqs. (5.113) and (5.114)].

To obtain a more concise picture of thermodynamic stability of different film morphologies, we plot directly from Eq. (5.119) using the molecular expression for Tyy [see Eq. (5.85)], which does not contain any fluid substrate contribution between the fluid substrate... 

Figure 5.22 (a) Normal compressional stress (see Appendix E.3 for molecular expressions) as a function of substrate separation from GCEMC simulations (O) (o.Sxo = 0.0). Solid lines aie intended to guide the eye. (b) As (a) but for [see Eq. 5.119]. Intersections between the latter and the vertical lines demarcate (meta- or thermodynamically) stable states in the grand mixed isostress isostrain ensemble for = 0.0 (see text). 

Figure 5.25 (a) as a fimction of shear strain qSxO for mono- (O), bi- (A), and trilayer (-I-) morphologies calculated in grand mixed isostress isostrain ensemble... 

The demonstration of equivalence departs from the observation that partition functions in any statistical physical ensemble comply with the general form given in Eq. (B.52) with individual summands as given in Eq. (B.54). Thus, according to th( discussion in Appendix B.4, wo may approximate the grand mixed isostress isostrain ensemble partition functiou x b (2.70a) b> the maximum terms in the sums appearing on the right side of that equation... 

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