By Rolando M.A. Roque-Malherbe, Rolando Roque-Malherbe
As nanomaterials get smaller, their houses more and more diverge from their bulk fabric opposite numbers. Written from a fabrics technological know-how standpoint, Adsorption and Diffusion in Nanoporous fabrics describes the method for utilizing single-component fuel adsorption and diffusion measurements to symbolize nanoporous solids. Concise, but complete, the e-book covers either equilibrium adsorption and adsorption kinetics in dynamic platforms in one resource. It offers the theoretical and mathematical instruments for examining microporosity, kinetics, thermodynamics, and delivery techniques of the adsorbent floor. Then it examines how those measurements elucidate structural and morphological features of the fabrics. special descriptions of the phenomena comprise diagrams, crucial equations, and completely derived, concrete examples in accordance with the author's personal study reports and perception. The ebook comprises chapters on statistical physics, dynamic adsorption in plug move mattress reactors, and the synthesis and amendment of significant nanoporous fabrics. the ultimate bankruptcy covers the foundations and functions of adsorption for multicomponent platforms within the liquid part. Connecting fresh advances in adsorption characterization with advancements within the delivery and diffusion of nanoporous fabrics, this booklet is perfect for scientists taken with the study, improvement, and functions of recent nanoporous fabrics.
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H. , New York, 1998. 2. , Physical Chemistry, Mc Graw Hill, New York, 2001. 3. H. A. Guggenheim, Statistical Thermodynamics (revised edition), Cambridge University Press, Cambridge, 1949. 4. , Statistical Mechanics (second edition), Cambridge University Press, Cambridge, 1955. 5. , An Introduction to Statistical Physics, J. Wiley & Sons, New York, 1949. 6. Landau, L. , Statistical Physics, Addison & Wesley, Reading, MA, 1959. fm Page 32 Wednesday, December 20, 2006 6:28 PM 32 Adsorption and Diffusion in Nanoporous Materials 7.
8 CANONICAL PARTITION FUNCTION FOR A SYSTEM OF NONINTERACTING PARTICLES Once the system’s canonical partition function, Z, has been calculated, by the summation of E exp − i , kT over all the possible Ω accessible quantum states of the system, then all the thermodynamic properties of the system are readily established. However, the existence of forces between the molecules composing the system in study make Z extremely difﬁcult to evaluate. Nevertheless, for a system with no intermolecular forces we can relatively easily evaluate Z.
M. , Phys. Rev. , 6A, 769, 1971. 34. , Phys. Rev. A, 7, 772, 1973. 35. Landau, L. , Mecanique, Mir, Moscou, 1966. 36. , Investigations on the Theory of Brownian Movement, Dower Publications, New York, 1956. 37. , Comptes Rendus de l’Academie de Sciences (Paris), 146, 530, 1908. 38. , Springer-Verlag, New York, 1996. 39. , Oxford University Press, Oxford, 1975. 1 33 LEGENDRE TRANSFORMATIONS The Legendre transformations  allow us to describe a function using a different set of variables. Given a function f(x,y), the total derivative of that function is given as: df = ∂f ∂f dx + dy ∂x ∂y The coefﬁcients for the partial derivatives are deﬁned as: u= ∂f ∂f , and v = ∂x ∂y To change to a new representation, the function, g(u,x) is deﬁned as: g(u,x) = f(x,y) – ux, implying that: dg = df − xdu − udx Using the total derivative of f(x,y) then: dg = − xdu + vdy where: x=− ∂g ∂g , and v = ∂y ∂u Consequently the Legendre transformation construct, from a function f = f(x,y), a function g = g(u,y), which by deﬁnition depends on u and y.
Adsorption and Diffusion in Nanoporous Materials by Rolando M.A. Roque-Malherbe, Rolando Roque-Malherbe