Flexible surface model

Another common theme in FP studies is the richness of possible surface phases -in some cases, dozens of structural isomers are computed to be thermodynamically accessible at room temperature. This has led to speculation that many oxide surfaces are more dynamic than previously thought, but definitive conclusions will only be possible once the processes of surface diffusion are identified and their activation energies are computed. This is perhaps the next frontier in FP oxide simulation. Meanwhile, the flexible surface model for active sites on metals [5] is finding some application in explaining the apparently facile diffusion of interstitial ions in non-stoichiometric oxides, despite the rigidity of the oxide lattice [26]. 

Figure 8 The flexible surface model can describe the important features of the thermodynamics of balanced microemulsions, (a, b) The calculated phase diagram of Daicic et al. [46]. (c) Experimental phase diagram of Strey [49]. fiE — microemulsion.

From these phase diagrams, one important conclusion must be emphasized A comparison of the water-rich side and the oil-rich side of the phase diagram shows similar properties in their phase behavior and structures. In each side as the alcohol concentration is varied, the system exhibits the sequence micelle (or vesicle)-lamellar-sponge. This reveals that although the experimental situation seems opposite, the physics is the same and can be described with the flexible surface model [19]. Symmetry properties of phase behavior were found also with nonionic surfactants systems [104]. 

The most lucid way of conceptually and quantitatively understanding the rich structural variation and structural transitions of microemulsions is to use the framework of the flexible surface model (35). The basic assumption in this model is to describe a surfactant monolayer or bilayer as a mathematical surface dividing space into two or more separate regions. With each configuration of the surface one associates a curvature (free) energy G. obtained as a surface integration of a local curvature free-energy density... 

Wennerstrom, H. and Olsson, U., On the flexible surface model of sponge phases and microemulsions, Langmuir, 9, 365-368 (1993). 

In theoretical analyses of the various self-assembly microstructures of nonionic surfactant-water-oil systems, the flexible surface model, using the curvature energy concept [6], has been found to be very useful [1, 2, 7-10]. Here, the relative stability of a given phase and microstructure results from an interplay of the curvature energy of the... 

A description of crazing with a cohesive surface appears appropriate for the crazes observed in glassy polymers, since the trends reported experimentally are quite well captured. The cohesive surface model distinguishes the three steps of crazing (initiation, thickening, and breakdown) and is flexible enough to incorporate more sophisticated formulations of one of these stages when available. 

Consideration of another major modification that has been applied to the flexible chain model seems pertinent at this point. It has long been appreciated that the velocity field of the solvent would be perturbed deep inside a coiled polymer molecule. It is clear that this effect is not considered in the above treatment because the viscous drag is given as psXi in equation (3-51) irrespective of whether Xi happens to be inside the coiled molecule or on its surface. Thus one might expect the Rouse formulation to be most applicable to polymer-solvent systems in which the elongated conformations of polymer chains predominate. For such conformations, there would be little shielding of one part of a molecule by another part of the same molecule. This is the case in... 

As well as being a widely studied model system, the chemistry of water on rutile Surfaces also imderpins many of the diverse uses of oxide materials, as first illustrated with the photoelectroysis of water on rutile [93]. Almost all photocatalytic applications take place in an aqueous environment. Even in UHV systems, water is a principal component of the residual gas. The recent applications of FP techniques to study this system illustrate the efficacy of using FP simulations as a complementary investigative tool alongside experimental techniques. However, the story also highlights clear requirements regarding the accuracy and flexibility of the surface model. 

The behavior near the Pt(lOO) surface (see Ref. 150, 151) is qualitatively similar to the one on the Hg(l 11) surface. It is only noted here that with the flexible BJH model used in Ref. 150 the bimodal character of the distribution function is not observed, apparently because the flexibility of the model allows for a wider range of low energy orientations within the adlayer hydrogen bond network. 

Other flexible isotherm models extending the Langmuir model are based on the theory of heterogeneous surfaces (Jaroniec and Madey, 1988) and on concepts provided by statistical thermodynamics (Hill, 1960). The latter approach allows deriving the following second-order isotherm model that is capable to describe inflection points in the isotherm courses ... 

Figure 11.1. Conolly surface plot of the oxygen atoms obtained from molecular dynamic simulation of the water/l,2-dichloroethane (DCE) junction (a). A flexible SPC model was employed for the 343 water molecules, while the 108 DCE molecules were described by a four-centre, simple charge, flexible model. A spherical probe was used with a radius of SA and the Gibbs dividing surface is located at z = 4A. Density variations of the water/vapour, water/DCE and DCE/vapour junction as obtained from the average of trajectories over 200 ps at 300 K (b). Reprinted with permission from ref.[6]. Copyright (1996) American Chemical Society.

This kind of perfect flexibility means that C3 may lie anywhere on the surface of the sphere. According to the model, it is not even excluded from Cj. This model of a perfectly flexible chain is not a realistic representation of an actual polymer molecule. The latter is subject to fixed bond angles and experiences some degree of hindrance to rotation around bonds. We shall consider the effect of these constraints, as well as the effect of solvent-polymer interactions, after we explore the properties of the perfectly flexible chain. Even in this revised model, we shall not correct for the volume excluded by the polymer chain itself. 

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