Molecular jumps

When a stress is applied to the bulk polymer melt, the mass flows in the direction that relieves the stress. At the molecular level, the probability of a molecular jump becomes higher in the direction of the stress than in any other direction and hence these stress-relieving motions predominate, leading to the observed pattern of flow. There is evidence that the molecular unit of flow is not the complete macromolecule but rather a segment of the molecule containing up to 50 carbon atoms. Viscous flow takes place by successive jumps of such segments until the entire macromolecule has shifted. 

The measurement of relaxation times 7j and T2 and the subsequent application of the theory formulated by Bloembergen et al. (236), and extended by Kubo and Tomita (272) and Torrey (288), leads to the determination of motional and thermodynamic parameters such as mean times between molecular jumps, diffusion coefficients, and activation enthalpies for translation. For example, Resing and Thompson (289, 290) used this... 

An analogous mechanism has been proposed in the molecular jump reaction in which the average molecular weight of cw-1,4-polybutadiene... 

If the applied strain rate is equal to the rate of molecular jumps, then... 

The take up of water or other liquids within the cell walls of wood involve the take up of a molecule at a time and its movement from one adsorption site to another (molecular jump phenomenon) under a concentration gradient. This is distinct from flow of bulk liquids into the coarse capillary structure under a capillary force or pressure gradient. 

KanomataN, Ochiai Y (2001) Stereocontrol of molecular jump-rope crystallization-induced asymmetric transformation of planar-chiral cyclophanes. Tetrahedron Lett 42 1045-1048... 

Local motions which occur in macromolecular systems can be probed from the diffusion process of small molecules in concentrated polymeric solutions. The translational diffusion is detected from NMR over a time scale which may vary from about 1 to 100 ms. Such a time interval corresponds to a very large number of elementary collisions and a long random path consequently, details about mechanisms of molecular jump are not disclosed from this NMR approach. However, the dynamical behaviour of small solvent molecules, immersed in a polymer melt and observed over a long time interval, permits the determination of characteristic parameters of the diffusion process. Applying the Langevin s equation, the self-diffusion coefficient Ds is defined as... 

The self-diffusion paths of guest molecules in an isotropic host lattice can be described by a sum of successive individual molecular jumps (5,9,25, 26,59,60),... 

The broadening values obtained for methane diffusion can be fitted to a molecular jump model with a Gaussian distribution of jump lengths (25,62). Thus, the scattering law becomes a Lorentzian,... 

A possible interpretation of the experimental results is a 90° flip motion of the 2-butyne molecules. In the fast limit, such a motion generates a pseudoaxially symmetric CSA tensor with the parameters Sy = 56 11 ppm and = 157 6 ppm (14). The corresponding lineshape is included in Fig. 4. Considering the ZSM-5 framework, this 90° flip can be a molecular jump from a straight into a sinusoidal pore segment or vice versa. From Eq. (20) it follows that the values of the correlation time must be much less than 10 /is. 

Simulations of C NMR lineshapes have shown that experimental spectra that appear to result from a superposition of two different lines (cf. Fig. 15) can be explained by the above-mentioned molecular jump model. Analogous conclusions were drawn from macroscopic sorption kinetic data (82). From the experimental C NMR lineshapes, a mean residence time tj of 20 and 150 p-s for a concentration of six molecules per u.c. at 250 and 200 K, respectively, was derived. Provided that these jumps detected in C NMR spectroscopy are accompanied by a translational motion of the molecules, it is possible to derive self-diffusivities D from the mean residence times. Assuming the diffusion path of a migrating molecule as a sum of individual activated jumps, for isotropic systems the relation (P) = 6Dtj is valid, where (P) denotes the mean square jump length. Following experimental and theoretical studies on the preferential sorption sites of benzene molecules in the MFI framework (83-90), in our estimate the mean distance between adjacent sorption sites is assumed to be 1 nm. 

These last two equations are derived on the basis of the Eyring theory of holes in liquids. The assumptions here, in contrast to those of the Stokes-Einstein equations, are that the diffusing molecules are of the same order of size as those of the solvent. The discontinuity of the liquid medium thus plays an essential part in the Eyring theory, the fundamental length X being the distance between successive positions of the diffusing solute or solvent molecule as it jumps between the molecules of the liquid. The quantities D and )/, however, refer to the diffusion constant and the viscosity of the system measured in the usual way. They represent the observed effect of very large numbers of such molecular jumps. 

Moving from structure to dynamics, we recall the NMR results, [Ty91, Ya91a] which indicate that the molecules in solid Ceo tumble rapidly at room temperature but freeze at lower temperatures. Considering the structural data reviewed above, one would expect a more-or-less continuous rotational diffusion in the room temperature fee phase, and either small oscillations or molecular jumps between favorable orientations in the low temperature phase. This difference was very clearly seen in the overall spin-lattice relaxation time near the orientational phase transition.[Ty91b] It was also found that the... 

This report presents a determination of the fluidity of water adsorbed to saturation in zeolite 13-X. As a measure of the fluidity, the time between molecular jumps or correlation time, r, is employed it has been derived from measurements of nuclear magnetic resonance (NMR) relaxation times via the theory of Bloembergen, Purcell, and Pound (BPP)... 

Figure 2. Median molecular jump rate (3T )-1 vs. reciprocal temperature for liquid water, water in charcoal pores, and water in zeolite 13-X...

In the process of identification of condis crystals it was observed that conformational mobility alone is not sufficient to prove the presence of a condis phase. Large amplitude molecular jump motion may be possible already in crystals without disorder if the symmetry is identical before and after the jump. The frequencies of these jumps can be surprisingly large and the moving parts of the molecules substantial. In the condis phase quick reptation can lead to extension of folded chain crystals, and is possibly also involved in rearrangements on mechanical deformation and membrane functions. 

D. Laage and J. T. Hynes, A molecular jump mechanism of water reorientation. Science, 311 (2006), 832-835. 

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