Conformation jumps

There remains an interpretation of ta to be found, ta exhibits an activation energy of about 0.43 0.1 eV, about three times as high as the C-C torsional barrier of 0.13 eV. The discrepancy must reflect the influence of the interactions with the environment and therefore ta appears to correspond to relaxation times most likely involving several correlated jumps. The experimental activation energy is in the range of that for the NMR correlation time associated with correlated conformational jumps in bulk PIB [136] (0.46 eV) and one could tentatively relate ta to the mechanism underlying this process (see later). 

For the latter copolymer, in which MMA units are frequently next to MGI units, this result means that the internal rotation changes associated with a conformational jump involving a MMA unit occur similarly for either MMA or MGI backbones. 

For main-chain acrylic radicals, created in solution at room temperature and above, the presence of a superposition of conformations or Gaussian distributions is unlikely. Polymers undergo conformational jumps on the submicrosecond timescale, even in bulk at room temperamre. ° The first two theories above require that the radicals be fairly rigid with little (Gaussian distribution) or no (superposition of static conformations) movement around the Cp bond. The main-chain radical is sterically hindered but still quite flexible, and a dramatic change in the hybridization at Ca is unlikely. We have approached our simulations with the hyperfine modulation model. 

The dynamics of bulk polymers have been approached in two different ways. On one hand, models of localized conformational jumps have been proposed to interpret numerous NMR experiments (see e.g. Ref. or . These models, which are specific of a given polymer assume that a short chain sequence performs conforpia-tional jumps between a few number of sites, the rest of the chain being immobile. Such localized jumps would lead to a well separated elastic peak in neutron quasielastic scattering experiments, in contradiction with all the experimental data obtained from polymer meltsIndeed, these models can in some cases be invoked to describe secondary relaxations in glassy polymers, but they are not sufficient to account for the numerous liquid-like properties of polymer melts. 

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

Dejean et al. [7], proposed another conformation jump model (referred to as the DLM model), in which a librational motion of the jump axis was introduced as the third motion. This model will correspond to the 3t model described below but the derivation of G (t) was empirically made in this case. 

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. 

Fig. 5.25 The most likely conformational jumps of the butylene group in polyjbutylene terephthalate). Each jump requires rotation around the second and fourth bonds from the left. The middle two carbon atoms are deuterated In each case. (Adapted with permission from the American Chemical Society.)...

The normal case with a molten or dissolved polymer is that its conformational jumps are quite rapid, compared with the tumbling and looping motions of entire chains. A typical barrier to a conformational jump in a vinyl polymer chain without external constraints is only approximately 12-20 kJ mol and is therefore readily surmounted at room temperature, typically at least 10 times per second. In this case, the local motions will contribute to the NMR relaxation parameters of the polymer, such as T, T2 and NOE. Similar motions will occur in the gel state and in the flexible solid, above Tg. 

Among the various expressions that are based on a conformational jump model and have been proposed for the orientation autocorrelation function of a polymer chain, G t), the formula derived by Hall and Helfand (HH) [4] leads to a very good agreement with fluorescence anisotropy decay data. It is written as... 

The Dejean-Laupretre-Monnerie (DLM) orientation autocorrelation function is based on the above description. It takes into account independent damped conformational jumps, described by the Hall-Helfand autocorrelation function, and librations of the internuclear vectors represented, as proposed by Howarth [17] (see chapter 4) by a random anisotropic fast reorientation of the CH vector inside a cone of half-angle and axis the rest position of the internuclear vector. The resulting orientation autocorrelation function can be written as... 

The detailed analysis of carbon-13 spin-lattice relaxation times of a number of polymers either in solution or in bulk at temperatures well above the glass-transition temperature has led to a general picture involving several types of motions. The segmental reorientation can be interpreted in terms of correlated conformational jumps which induce a damped orientation diffusion along the chain. It is satisfactorily described by the well-known autocorrelation functions derived from models of conformational jumps in polymer chains [4,5] which have proven to be very powerful in representing fluor-... 

Another important result is the similarity of the temperature variation of the correlation time r, associated with conformational jumps, and observed for all the polymers considered except polyisobutylene, to the predictions of the Williams-Landel-Ferry equation for viscoelastic relaxation, which indicates that the segmental motions observed by NMR belong to the glass-transition phenomenon. Moreover, the frequency of these intramolecular motions is mainly controlled by the monomeric friction coefficient of the polymer matrix. 

Our data of T in the coil form in Figure 10 can nearly be put over the master curve for T of polystyrene in the organic solvents, as shown in Figure 11, with the vfflues of the scaling parameters p and q p = 1.305 and q = 0.045(K ), by which the data of T y P in the coil form (in Figure 10) can also be put over the master curve for T P of polystyrene in the organic solvents. Therefore, the molecular motion of (MA-St)p in the coil form may be described in terms of the conformationed jump model combined with isotropic rotational diffusion, when the ratio Xp/Xp seems to be nearly 0.07. 

Fig. 15. (a) The monomer unit of trans- and cis-1,4-butadiene. The alternating sequence of CH—CH2 groups, for which the magnetization-exchange process is treated, (b) The geometry of the CH—CH2 spin system. The shaded circles represent protons and the black circles carbon atoms. The conformational jumps of the methylene protons lead to an average CH—CH2 proton distance rcH—CH2 Reproduced from Ref 65, with permission from American Institute of Physics. 

An unusual feature of C Ti values in cir-polybuta-1,4-diene is that the ratio of methine to methylene is 1.4, much less than the value 2 expected if the CH and CHj experience identical motions. Gronski has explained this discrepancy in terms of specific conformational jumps involving transitions between skewed conformations of allylic C—C bonds. 

An approximate but efficient solution is achieved by assuming a time scale separation between the fast jiggering motions within the potential wells and the slow conformational jumps. Under this assumption, projection of the diffusion operator onto a set of site functions, in the same number of the potential minima, can be performed to convert the diffusion equation into a master equation for jumps between discrete sites ... 

Crystallographers have had some success in using normal mode descriptions of internal motion, with effective frequencies as adjustable parameters, and initial steps have been taken to incorporate similar ideas into NMR refinements. This model builds in important large-scale correlated motions, but not generally the effects of local conformational Jumps. 

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