By J.Z. Wu (auth.), Xiaohua Lu, Ying Hu (eds.)

ISBN-10: 3540691146

ISBN-13: 9783540691143

ISBN-10: 3540691162

ISBN-13: 9783540691167

With the improvement of technological know-how and technology,more and extra advanced fabrics reminiscent of porous fabrics, ion liquid, liquid crystals, skinny ?lms and colloids and so forth. are being constructed in laboratories. even though, it truly is dif?cult to organize those complicated fabrics and use them on a wide scale with out a few event. as a result, mo- cular thermodynamics, a style that laid emphasis on correlating and studying the thermodynamic homes of quite a few ?uids some time past, has been lately hired to review the equilibrium houses of advanced fabrics and identify thermodynamic versions to examine the evolution means of their parts, - crostructures and capabilities through the guidance procedure. during this quantity, a few very important development during this ?eld, from primary features to functional purposes, is reviewed. within the ?rst bankruptcy of this quantity, Prof. Jianzhong Wu offers the applying of Density useful idea (DFT) for the research of the constitution and thermodynamic homes of either bulk and inhomogeneous ?uids. This bankruptcy provides a tut- ial evaluate of the fundamental options of DFT for classical platforms, the mathematical family members linking the microstructure and correlation capabilities to measurable th- modynamic amounts, and the connections of DFT with traditional liquid-state theories. whereas for pedagogythe dialogue is proscribed to one-componentsimple - ids, comparable principles and ideas are at once acceptable to combinations and polymeric structures of sensible situation. This bankruptcy additionally covers a number of theoretical ways to formulate the thermodynamic functional.

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**Sample text**

71) i In analogy to the one-body density distribution function, a two-body density distribution function is related to the probability of ﬁnding two molecules at positions r and r : ρˆ i, j (r1 , r2 ) = δ (r1 − ri )δ (r2 − r j ), (72) where subscripts i and j denote two labeled molecules, one at position r1 and the other at r2 . If there is only a single pair of labeled molecules in the system, integration of Eq. 72 is equal to one. For a system containing N identical spherical molecules, there are N(N − 1) undistinguishable molecular pairs at positions r1 and r2 .

Towards that end, we need to use the Hohenberg–Kohn theorem [27], which was established 4 A Legendre transform switches independent variables in the fundamental equation of thermodynamics. For example, F = E − T S is a Legendre transform that changes the fundamental equation of thermodynamics from E = E(S,V, N) to F = F(T,V, N). Here the thermodynamic variable is a function. Density Functional Theory for Liquid Structure and Thermodynamics 21 originally in the quantum mechanics of the ground-state energy of electrons at 0 K.

Wu Clausius deﬁned the right side of Eq. 133 as virial, which means force in its Latin origin. The pressure of a thermodynamic system can be identiﬁed from the force per unit area exerted on the system boundary. Near the system boundary, the total force on each molecule Fitotal includes a contribution due to all other molecules in the system Fi , and that due to the container Fi . The pressure can be calculated from the ensemble average of the total force exerted on the boundary per unit area. According to Gauss’ theorem, the contribution of the force due to the container to the viral is given by: ∑ < ri · Fi >= dr < δ (r − ri ) ri · Fi >= − r · nP dA = −P ∇ · rdV = −3PV, i (134) where dA represents a surface element with a normal in the direction of the unit vector n, r stands for the position of the surface element dA, and the negative sign indicates that the force from the container to a molecule is opposite to that from the molecular to the container.

### Molecular Thermodynamics of Complex Systems by J.Z. Wu (auth.), Xiaohua Lu, Ying Hu (eds.)

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