By J.Z. Wu (auth.), Xiaohua Lu, Ying Hu (eds.)
With the improvement of technology and technology,more and extra complicated fabrics corresponding to porous fabrics, ion liquid, liquid crystals, skinny ?lms and colloids and so forth. are being built in laboratories. even if, it really is dif?cult to organize those complicated fabrics and use them on a wide scale with no a few adventure. accordingly, mo- cular thermodynamics, a mode that laid emphasis on correlating and examining the thermodynamic homes of a number of ?uids some time past, has been lately hired to review the equilibrium houses of advanced fabrics and determine thermodynamic types to examine the evolution means of their elements, - crostructures and services in the course of the training procedure. during this quantity, a few very important development during this ?eld, from basic points to functional functions, is reviewed. within the ?rst bankruptcy of this quantity, Prof. Jianzhong Wu provides the applying of Density sensible conception (DFT) for the learn of the constitution and thermodynamic homes of either bulk and inhomogeneous ?uids. This bankruptcy offers a tut- ial review of the elemental techniques of DFT for classical structures, the mathematical kinfolk linking the microstructure and correlation services to measurable th- modynamic amounts, and the connections of DFT with traditional liquid-state theories. whereas for pedagogythe dialogue is restricted to one-componentsimple - ids, related principles and ideas are at once appropriate to combos and polymeric platforms of sensible obstacle. This bankruptcy additionally covers a couple of theoretical techniques to formulate the thermodynamic functional.
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Additional info for Molecular Thermodynamics of Complex Systems
To decouple these two factors, Density Functional Theory for Liquid Structure and Thermodynamics 47 we may use a functional Taylor expansion of ρ (2) (Γλ , r1 , r2 ) with respect to the perturbation potential ∆Γ(r1 , r2 ): (2) ρ (2) (Γλ , r1 , r2 ) = ρ0 (r1 , r2 ) + λ + λ2 2! dr3 dr4 δ ρ (2) (Γλ , r1 , r2 ) δ λ ∆Γ(r3 , r4 ) dr3 dr4 dr5 dr6 ∆Γ(r3 , r4 )∆Γ(r5 , r6 ) + · · · . ∆Γ(r3 , r4 ) λ =0 δ 2 ρ (2) (Γλ , r1 , r2 ) δ λ ∆Γ(r3 , r4 )δ λ ∆Γ(r5 , r6 ) λ =0 (160) A ﬁrst-order perturbation theory retains only the ﬁrst term on the right side of Eq.
87: c(1) (ρ0 ; r) = ln[ρ0 Λ3 ] − β µ . (102) Substitution of Eq. 102 into Eq. 101 gives: ln[ρ (r)/ρ0 ] = −β ν (r) + dr c(2) (ρ0 ; r, r )∆ρ (r ) + · · · . (103) Equation 103 is exact provided that the direct correlation functions of the reference system are known. , the magnitude and range of ∆ρ (r). If the direct correlation function is short-ranged and ∆ρ (r) is small, Eq. 103 converges rapidly. In that case, the functional Taylor expansion may be truncated after the second-order direct correlation function: ρ (r)/ρ0 ≈ exp[−β ν (r) + dr c(2) (ρ0 ; r, r )∆ρ (r )].
131) Substituting Eq. 129 into 128 gives: − < p2i /m >=< ri · Fitotal >, (132) where pi = mr˙i is the molecular momentum. The left side of Eq. 132 is equal to 3kB T according to the average kinetic energy. From Eq. 132, we obtain the virial theorem by a summation of overall molecules: −3NkB T = ∑ < ri · Fitotal > . Z. 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.
Molecular Thermodynamics of Complex Systems by J.Z. Wu (auth.), Xiaohua Lu, Ying Hu (eds.)