Three-bond jump model, motion

In the three bond jump model for segmental motion there are two parameters. The time scale is set by the harmonic average correlation time, Tjj and the effective distribution of correlation times is set by the number of coupled bonds m. The sharp cut off of coupling solution of the three bond jump model is employed here. The composite spectral density for internal rotation by jumps or stochastic diffusion plus segmental motion by three bond jump is... 

To apply the models to the interpretation of the data, the approach developed for the polycarbonates will be followed. The phenyl proton Tj s are interpreted first in terms of segmental motion. For these protons, the dipole-dipole interaction is parallel to the chain backbone and therefore relaxed only by segmental motion. In the three bond jump model the parameters tjj and m are adjusted to account for phenyl proton data, and in the Weber-Helfand model the parameters tq and tj are adjusted. Table II contains the three bond jump parameters, and Table III, the Weber-Helfand model parameters. Both models can simulate the data within 10% which is equivalent to the experimental error. 

Table II Phenyl Group Motion Simulation Parameters Three Bond Jump Model Using the...

As the first point, the dynamics of the phenyl group in the poly-formal can be considered. Motional descriptions from the two segmental models can be compared as they have been before for the polycarbonates ( 5). In the three bond jump model the primary parameter is the harmonic mean correlation time, and in the... 

Weber-Helfand model the primary parameter is the correlation time for cooperative backbone transitions, X]. At the lower temperatures studied, xq plays an increasing role in the Weber-Helfand model but xj is still the major factor. This is an interesting point in itself since cooperative transitions were also found to predominate when the Weber-Helfand model was applied to the polycarbonates. Here in the polyformal, single bond conformational transitions do play a larger role and this can be seen in the three bond jump model as well by the drop of m to 1 at lower temperatures. Since xj and x are both measures of the time scale for cooperative motions, it is interesting to note that the Arrhenius summaries of the two correlation times in Tables II and III are very similar. This similarity, taken together with the domination of cooperative transitions in the Interpretations, supports the utility of both models though the Weber-Helfand model is developed from a more detailed analysis of chain motion. 

Since none of the lattice models is now clearly superior, the choice for interpretation of spin relaxation in polymers is arbitrary. Familiarity leads us to select the Jones and Stockmayer model so we will now consider application of this model to several well studied polymer systems in order to compare dynamics from polymer to polymer. Also the equations required to consider anisotropic Internal rotation of substituent groups and overall molecular tumbling as independent motions in addition to backbone rearrangements caused by the three-bond jump are available for the Jones and Stockmayer model (13). 

In addition to determining the time scales for several local motions in polyformal, two different interpretational models for segmental motion will be employed. An older model by Jones and Stockmayer (7 ), based on the action of a three bond jump on a tetrahedral lattice is compared with a new model by Weber and Hel-fand (8), based on computer simulations of polyethylene type chains. These two models for segmental motion have been compared before (5 ) for two polycarbonates but somewhat different results are seen in the polyformal interpretation. 

The correlation time p characterizes three-bond jumps, and the correlation time B characterizes other processes. Bendler and Yaris have also reconsidered the diamond lattice model, and replaced the discrete jump kinetic formulation by a continuum with adjustable cut-offs in the frequency spectrum. The high cut-off arises from the finite size of the smallest displaceable unit, and the low cut-off from the fact that chain displacements will be damped out as they travel down the chain. Librational motions, hitherto neglected, have been considered by Howarth, with success in interpreting relaxation data on proteins. It is possible that this factor should also be taken into account for synthetic polymers. 

One of the most widely used tools to assess protein dynamics are different heteronuclear relaxation parameters. These are in intimate connection with internal dynamics on time scales ranging from picoseconds to milliseconds and there are many approaches to extract dynamical information from a wide range of relaxation data (for a thorough review see Ref. 1). Most commonly 15N relaxation is studied, but 13C and 2H relaxation are the prominent tools to characterize side-chain dynamics.70 Earliest applications utilized 15N Ti, T2 relaxation as well as heteronuclear H- N) NOE experiments to characterize N-H bond motions in the protein backbone.71 The vast majority of studies applied the so-called model-free approach to translate relaxation parameters into overall and internal mobility. Its name contrasts earlier methods where explicit motional models of the N-H vector were used, for example diffusion-in-a-cone or two- or three-site jump, etc. Unfortunately, we cannot obtain information about the actual type of motion of the bond. As reconciliation, the model-free approach yields motional parameters that can be interpreted in each of these motional models. There is a well-established protocol to determine the exact combination of parameters to invoke for each bond, starting from the simplest set to the most complex one until the one yielding satisfactory description is reached. The scheme, a manifestation of the principle of Occam s razor is shown in Table l.72... 

By comparison of observed and theoretically calculated spectra it can be shown that these carbons are involved in gauche-trans conformational jumps of the C-D bond through a dihedral angle of 103°, and from the correlation times as a function of temperature an activation energy of 5.8 kcal/mol is found. Several seemingly plausible motional models are excluded by these results, but the data agree with models proposed by Helfand (21,22) for motion about three bonds. 

The 2-site 120° jump motion for the basal molecules switches between these two hydrogen bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behaviour for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons were estimated to be 10 and 21 kj mol-1, respectively. This dynamic model was further supported by analysis of the dependence of the quadrupole echo 2H NMR lineshape on the echo delay and consideration of 2H NMR spin-lattice relaxation time data. 

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