Franz model

A number of basic studies in the area of donor solvent liquefaction have been reported (2 -9). Franz (10J reported on the interaction of a subbituminous coal with deuterium-labelled tetra-lin, Cronauer, et al. (11) examined the interaction of deuterium-labelled Tetralin with coal model compounds and Benjamin, et al. (12) examined the pyrolysis of Tetralin-l-13C and the formation of tetralin from naphthalene with and without vitrinite and hydrogen. Other related studies have been conducted on the thermal stability of Tetralin, 1,2-dihydronaphthalene, cis-oecalin and 2-methylin-dene (13,14). 

Franz TJ (1978) The finite dose technique as a valid in vitro model for the study of percutaneous absorption in man. Curr Probl Dermatol 7 58-68. 

Baner, A., Brandsch J. Franz, R. and Pringer, O. (1996). The application of a predictive migration model for evaluating the compliance of plastic materials with European food regulations. Food Addit. Contain., 13, 5, 587-601. 

For in vitro testing the Organisation for Economic Cooperation and Development (OECD) approved in 2004 test guideline 428 [37], which currently advocates the use of human, rat, and pig skin to measure cutaneous absorption by a vertical diffusion system (Franz cell). Dmg concentrations are followed in an acceptor fluid separated by the skin from the donor vehicle, which is applied to the external surface of the skin. Instead of human or animal skin, human skin models could be used as soon as the equivalence of their results are proven. Comparative studies indicate a correlation of penetration data in vitro and in humans [38]. 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

S. Franz and J. Hertz, Glassy transition and aging in a model without disorder. Phys. Rev. Lett. 74, 2114-2117 (1995). 

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

To describe the transport through a molecular system having HOMO and LUMO energy levels, one of the applicable models is the Franz two-band model.75-81 This model provides a non-parabolic energy-momentum E(k) dispersion relationship by considering... 

J. M. Franz, I. P. Vondescher, and R. Voges. Quantitative mechanistic studies in simultaneous fluid flow and intestinal absorption using steroids as model solutes. 

Procedure B has been developed and proposed by Fraunhofer IW (Franz et al. 1994) without incorporating model contaminants. It is a black-box approach which monitors inherently present recycling-related substances and is applicable to a ready-to-use food contact article. In this way, the procedure meets not only the R D and quality assurance requirements of the manufacturer but also offers a test possibility for enforcement labs. Essentially, procedure B consists of two experimental key steps ... 

Franz R, Huber M and Piringer OG, 1997, Presentation and experimental verification of a physico-mathematical model describing the migration across functional barrier layers into foodstuffs. Food Additiv. Contam. 14 (6-7), 627-640. 

S. Franz and F. Ritort, Dynamical solution of a model without energy barriers. Europhys. Lett. 31, 507 (1995). 

BEGLEY T, CASTLE L, FEIGENBAUM A, FRANZ R, HINRICHS K, LICKLY T, MERCEA P, MILANA M, O BRIEN A, REBRE s, RIJK R and PiRiNGER o (2005), Evaluation of migration models that might be used in support of regulations for food contact plastics . Food Additives and Contaminants, 22(1), 73-90. 

Franz, R.M. Browne, J. Lewis, A. Experimental design, modeling, and optimization strategies for product and process development. In Pharmaceutical Dosage Forms Disperse Systems, 2nd Ed. Lieberman, H.L., Rieger, M., Banker, G., Eds. Marcel Dekker, Inc. New York, 1996 1, 427-514. 

As discussed above, surface fields do not play as important a role in the photochemistry of these systems. The electric field gradients are not generally sufficient to completely separate the electron and hole wavefunctions. In the event of surface charging, the field effects are better treated as a perturbation on the wavefunctions and can be modelled as a first-order Stark effect. The effect is similar to a Franz-Keldysh effect for bulk semiconductors except that there is still significant hole and electron wavefunction overlap. The oscillator strength remains similar in magnitude, albeit the frequency shifts to the red as the electron-hole pair is more... 

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