Frank’s model

Fig. 3.16a-c. a A series of fluctuations which are allowed in Frank s model, that is, attachments and detachments are both allowed but the chain is not permitted to fold until it has reached the lamellar thickness, b and c show a series of events which may also be expected to occur... 

However, subsequent detailed studies [33,55,56] have shown that the curvature of 100 faces in polyethylene can be explained quantitatively by applying Frank s model of initiation and movement of steps [57]. Curvature occurs when the average step- propagation distance is no more than about two orders of magnitude larger than the stem width. 

Illustrated in Fig. 15, Frank s model suggests a crystal imperfection of the type that would result if a cut were made part way through the crystal and the two sides skewed a distance of one layer at the edge of the crystal. Growth normal to the step occurs by filling of the Kossel... 

In order to explain the optical activity of living matter, Frank [19] has proposed a kinetic model which describes the accumulation of one enantiomer due to spontaneous symmetry breaking and autocatalytic enhancement of its concentration. Although the energy difference between D- and L-enantiomers is extremely small, Frank s model has been extended in order to discuss whether a very small systematic chiral perturbation rather than an accidental event can determine which enantiomer is formed [20]-[23]. For example, Kondepudi and Nelson [23] considered the reaction scheme... 

To date, this reaction remains the best investigated and most successful example of an asynunetric autocatalytic reaction in full accord with Frank s model. While its sensitivity to water and hmitation to special substrates excludes any involvement in prebiotic chemistry, it clearly shows the practical possibihty of spontaneous asynunetric synthesis, and ongoing research might provide us with new discoveries in the futiue. 

At an MEK concentration greater than 1 M, both the dynamic and the static quenching mechanisms have to be taken into account. Therefore, Frank and Vavilov s model of combined static and dynamic quenching model (28),... 

Recapitulating the foregoing discussion, it is clearly not our opinion that solution experiments appear to be inadequate for the purpose of comparison with molecular theories. However, we want to point out that due to the evident shortcomings of present theoretical and computational facilities a distinct scepticism is necessary in order to avoid the production of meaningless data. Of course, the solution experiments remain the main source of information, the data of which must be explained by theory. At the present stage of knowledge it is only possible to pick out selected properties of solutions which can be described satisfactorily on a molecular basis. For instance, referring to Frank and Wen s model of solvation shells W, the structure of the inner shell should not be modified too much by... 

Frank HS, Quist AS (1961) Pauling s model and the thermodynamic properties of water. J Chem Phys 34 604-611... 

Burton-Cabrera-Frank (BCF) Model. The models discussed in the previous section all require two-dimensional nucleation events for a new layer to start. These models fail to account for observed crystal growth rates at low supersaturations and are unsatisfying in the sense that they make crystal growth a noncontinuous process with the formation of a critical size two-dimensional nucleus the rate-determining step. A basis for a model in which the steps are self-perpetrating was put forward by Frank (1949). Frank s idea was that dislocations in the crystal are the source of new steps and that a type of dislocation known as a screw dislocation could... 

Wadsack. C., Hrzenjak, A., Hanner, A., Hirschmugl, B., Levak-Frank, S., Desoye, G., Sattler, W., and Malle, E. (2003), Trophoblast-like human choriocarcinoma cells serve as a suitable in vitro model for selective cholestcryi ester uptake from high density lipoproteins. Eur. J. Biochem. 270,451-462. 

Frank, H. S. Quist, A. S. (1961). Pauling s model and the thermodynamic properties of water. X Chem. Phys. 34, 604-11. [84] Frank, H. S. Wen, W-Y. (1957). Structural aspects of ion-solvent interaction in aqueous solutions a suggested picture of water structure. Disc. Faraday Soc. 24, 133-40. [78, 85]... 

Figure 12 Comparison of the parabolic Hansch model (left curve) and Franke s protein binding model (right curve). Log P, is the lipophilicity limit, where steric hindrance or other unfavorable interactions cause a change of the linear lipophilicity-activity relationship to a parabola (reproduced from Figure 9 of ref. [175] with permission from Birkhauser Verlag AG, Basel, Switzerland).

H. S. Frank and W.-Y. Wen, Structural aspects of ion-solvent interactions in aqueous solutions A suggested picture of water structure, Disc. Faraday Soc. 24 133 (1957). The earliest studies of ion hydration in relation to the Frank-Wen model have been summarized in B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, An terdam, 1981. More recent work is reviewed in J. E. Enderby and G. W. Neilson, The structure of electrolyte solutions. Rep. Prog. Phys. 44 593 (1981). 

Near the A-N transition, the present theory leads to the same conclusions as de Gennes s model discussed in 5.5.2 the divergent contributions to and in the nematic phase are given by (5.5.18) and (5.5.19). Near the C N transition, all three Frank constants diverge ... 

Palladino, J.L., Ribeiro, L.C., and Noordergraaf, A. 2000. Human circulatory system model based on Frank s mechanism. In Mathematical Modelling in Medicine, J.T. Ottesen and M. Danielsen, Eds., lOS Press, Amsterdam, pp. 29-39. 

Ml04 H. S. Frank, Solvent Models and the Interpretation of Ionization and Solvation Phenomena, in Chemical Physics of Ionic Solutions, Chapter 4 (B. E. Conway and R. G. Barradas, eds.), Wiley, New York (1966)... 

Frank, S., Bommer, J. J., Bungum, H., Cotton, F., Abrahamson, N. A. (2005). Composite Ground-Motion Models and Logic Trees Methodology, Sensitivities, and Uncertainties. Bulletin of the Seismological Society of America, 95(5), 1575-1593. doi 10.1785/0120040229... 

The interstitial model has a serious drawback, however, which is similar to the shortcomings of applying a lattice model to a fluid in general. It is therefore important to make a clear-cut distinction between results that pertain strictly to the model and results that have more general validity. In this section, we shall describe a simplified version of Pauling s model and briefly outline some of the results. The details are left as an exercise for the reader. A partial theoretical treatment of Pauling s model was carried out by Frank and Quist (1961). 

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