Frozen lattice model

A comparison of the critical field, calculated within the frozen lattice model, in terms of the microscopic crystal field and magnetoelastic coefficients gives... 

Free volume frozen fraction, FF 131-132,137,187 Free volume lattice model 128-132,138-142... 

Tang and DilP have attempted a theoretical investigation of this question. Using an HP lattice model, they find a low-temperature point below which large fluctuations are frozen out. They also conclude that proteins having greater stability tend to have fewer large fluctuations, and hence lower overall flexibilities. 

The memory-lattice model has the same structure here as for the isotropic material. The potential is changed. Consider a chain in an uncrosslinked polymer which is at a minimum potential energy before stretching at R = Ro. The sample is stretched so that Ro changes to Rc where X = Xo. The sample is frozen, crosslinked at this elongation, and then reheated to the rubbery state. The potential associated with an arbitrary deformation is given by... 

Fig. 2. The molecular description which suggested the use ctf the lattice model The random coil has to form a turn of a-helix (A). Favorable intnactions stabilizing the helix occur only when the rotations about six bonds are frozen (B. The tozm rotations are shown with one rf tte bvorable interactions is the NH—OC hydrogen bond, indicated with a dashed line when it occurs.) Subsequent freezing of the rotations about only two bonds will produce the same favorable contacts upon goii from B to C (cf. Pauling and Cor (56% for the stmcture of the a-helix). TIk equilibrium constant for the reaaion coil A is much less than unity, while that for the reactions At B and B C is near unity...

In chemical shift calculations for acylium ions, it was not necessary to model the ionic lattice to obtain accurate values. These ions have tetravalent carbons with no formally empty orbitals, as verified by natural bond orbital calculations (89). Shift calculations for simple carbenium ions with formally empty orbitals may require treatment of the medium. We prepared the isopropyl cation by the adsorption of 2-bromopropane-2-13C onto frozen SbF5 at 223 K and obtained a 13C CP/MAS spectrum at 83 K (53). Analysis of the spinning sidebands yielded experimental values of = 497 ppm, 822 = 385 ppm, and (%3 = 77 ppm. The isotropic 13C shift, 320 ppm, is within 1 ppm of the value in magic acid solution (17). Other NMR evidence includes dipolar dephasing experiments and observation at higher temperature of a scalar doublet ( c-h = 165 Hz) for the cation center. 

A variety of different models of the interface between water and a solid phase have been used in computer simulations. As far as the solid is concerned, a basic distinction can be made between smooth solid phases without atomic structure on the one hand and corrugated surfaces on the other. The latter surfaces have been modeled as rigid (frozen) or flexible atomic lattices representing the solid phase [47-51] or as a corrugated external potential that describes the effect of the solid phase by a more or less elaborate potential function F(x,y,z) [52-56]. The generic metallic features are modeled by treating the metal phase as a medium of infinite dielectric constant or by using the jellium model (e.g.. Ref. 57-59). In several cases, the results of semi-empirical and ab initio quantum chemical calculations have been parametrized [40, 48, 55]. 

---