Jump model

As one would expect, the rate of orientational relaxation in the jump model is activated, and the higher the libration barrier U0, the lower the rate. However, the Hubbard relation obtained as a result of Eq. (1.123) used in Eq. (2.96) does not involve this characteristic parameter of the solid-like model ... 

It is well known [11] that the reorientation rate in the jump model... 

This identifies the time between jumps t and the time of a jump t and breaks the initial assumption of the model, which considers jumps as instantaneous x [Pg.219]

As the translational energy of the impacting ion increases, the G-S cross section will rapidly fall off until at energies above 10 e.v., the electron jump model for the reaction will predominate. That mechanism does not seem to depend strongly on translational energy. 

The Bind and Jump Model for Lectin-Mucin Interactions 155... 

The diffusion-jump model for SBA and VML binding to Tn-PSM and the other PSM analogues can be envisioned as occurring with one subunit of SBA or VML bound to one aGalNAc residue of Tn-PSM at a time (Fig. 3A). (Two subunits of individual SBA or VML molecules simultaneously binding to a single Tn-PSM chain is not supported by the enhanced affinities of both lectins to 38/40-mer Tn-PSM relative to aGalNAcl-G-Ser (Table I). If two subunits of an SBA tetramer were bound to 38/40-mer Tn-PSM, the... 

Due to the tetrahedral arrangement of the windows within the cage, tetrahedral jumps of the cations are feasible. This jump model is confirmed by the averaged parameters obtained by lineshape simulations of the broad lines at 295 and 813 K. Cq is reduced at 813 K to about half of its original value at 295 K, and the averaged asymmetry parameter, (77), is 1. Especially (77) is a very sensitive parameter on jump angle due to the steepness of the curve in Fig. 8a. 

The temperature dependent T data are shown in Fig. 9. 7j values decrease from 28 ms at 21°C with increasing temperature, and show a minimum of 6.4 ms at 80° C. These results indicate the presence of the motion with a Larmor frequency of 30 MHz at this temperature. This minimum was found to be attributed to the flipping motion of a phenyl ring from the result of our other experiments discussed in later section.13 The jump rates of the flipping motion were estimated with a two-site jump model that a C-2H bond jumps between two equivalent sites separated by 180°, and that the angle made by the C-2H bond and the rotational axis is 60°. The quadrupole coupling constant of 180 kHz and the asymmetry parameter approximated to zero were used in the calculation. The calculated values for fitting with the... 

The line shapes were calculated for the flipping motion with the two-site jump model described above, and the calculated spectra are shown in Fig. 11 for the higher temperature region. The experimental line shapes at 20 and 30° C are well reproduced showing the motional mode and rates obtained by T analysis are reasonable at least around these temperatures. Above 40°C the calculated line shapes are invariable and remain in the powder pattern undergoing a rapid flipping motion, while the experimental ones... 

Fig. 20. (a) Allowed side chain conformations, (b) Distribution of CK-2H bond vectors, (c) Three-site jump model as an approximation of multi-site jumps. Reproduced with permission from the Society of Polymer Science, Japan. 

At temperatures around 50-60°C the three-site jump model is not a good approximation to the multi-site jump model, because the motion is not sufficiently rapid to be in the fast motion limit. However, the calculated spectra are fairly fitted with the observed ones. This is because the calculated spectrum is a superposition of constituent spectra whose rates are spread over several orders, so that the resultant spectrum is governed by the constituent spectra in the fast and slow motion limits having greater intensity than that in the intermediate exchange regime. 

The temperature dependent 7j for both samples was calculated by the three-site jump model with the parameters derived from the line shape and the result is shown in Fig. 18. The calculated 7j values for both samples are in good agreement with the experimental ones around the minimum, showing the validity of the parameters concerning with the jump rates and polar... 

There are experimental results that show the anisotropic nature of diffusion of methane in silicalite (24, 77). From a stochastic jump model of the diffusion process, Karger et al. (24) found that the ratio of the rate of diffusion in the direction of the two channel systems should not be less than 4.4 times that in the orthogonal direction ... 

Fig. 1. Line shape for the two-state-jump model. The frequencies are in units of being the frequencies of the two states. The numbers on curves indicate the modulation rate, a = y/toj.

As another simplification, we assume that the modulation 2 takes only two values co,. This is a generalization of the two-state jump model mentioned in Section 111. The basic space for Eq. (63) is then 2x2 dimension. It is convenient to write Eq. (63) as... 

Recently, the stochastic models for the Mossbauer line shape problem have been discussed by several investigators.20 Such models can be treated in a systematic way as we have described in the above. For example, in a 57Fe nucleus, the spin in the excited state is / = and that in the ground state is / = i, so that the Hamiltonian is a 6 x 6 matrix. If a two-state-jump model is adopted, the dimension of the matrix equation, Eq. (63), is 6 x 2 = 12. If the stochastic operator is of the type (26), then the equation is a set of six differential equations. These equations can be solved, if necessary, by computers to yield the line shape functions for various values of parameters. 

Note that this primitive single-jump model neglects the diffuse nature of the crystal/liquid interface. 

It also seems appropriate to discuss briefly the jump model of diffusion and its effect on linewidth. In this model, the resonant atoms are described as jumping from one lattice site to another by a function h(r), where this function (the correlation function) is the probability of finding the atom at r after a jump from the origin. The average residence time on each site is t,. Since the distance between lattice sites is of the order of the y-ray wavelength, an estimate for the linewidth broadening is... 

First, it is worth noting that the activation energy value derived from the 22.6 MHz data strongly depends on the motional model considered. Thus, with a two-site jr-flip jump model, leading to a single exponential correla-... 

The experimental multifield relaxation data (T T2, n.O.e.) for amylose were nicely reproduced by using these two models.11 However, the wobbling-in-a-cone model is favored for two reasons first, it requires fewer adjustable parameters than the bistable jump model to fit the data second, the jump model requires /32 = 48.9°... 

Fig. 15.—Bistable (two-state) jump model. [Reproduced with permission from Fig. 3 of P. Dais, Carbohydr. Res., 160 (1987) 73-93 and Elsevier Science B.V.]...

The parameter t is given in Eq. A-9 in the Appendix, as a function of the correlation time, t associated with internal motion. One of the input parameters is the angle j3, formed between the relaxation vector (C—H bond) and the internal axis of rotation (or jump axis), namely the C-5—C-6 bond. The others are correlation times t0 and r, of the HWH model, obtained from the fit of the data for the backbone carbons. The fitting parameters for the two-state jump model are lifetimes ta and tb, and for the restricted-diffusion model, the correlation time t- for internal rotation. The allowed range of motion (or the jump range) is defined by 2x for both models (Eqs. A-4 and A-9). 

Two-State Jump Model (Isotropic Overall Motion)58... 

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