Chains with correlated rotations

V. Galiatsatos and W. L. Mattice, Polym, Prepr. ACS, Div. Polym. Chem., 31f2), 586 (1990). The Correlation between H and for Chains with Symmetric Rotation Potential. 

The problem of conformational analysis of a chain is, therefore, that of calculating C. The approximation of the freely jointed chain, with no correlation between successive bonds, 69, gives a value of = 1. If one introduces into the model a constant value for the bond angles, but permits free rotation around the bonds (in the formula 70 all points of the base circumferences of the... 

A more direct method of studying rotation is to look for variation in the g or hyperfine (Section III,A,2) tensors as the temperature is changed. For certain peroxy radicals in polymers, considerable changes in the g tensor occur which can be correlated with both the onset of rotation of the polymer chain and also rotation about the C—O bond with increasing temperature (58, 59). Similar changes in the g tensor have been observed for ions formed by irradiation in frozen alcohols (60). Kazusaka et al. (61) have observed changes from an orthorhombic g tensor gt = 2.0266, g2 = 2.0097, g3 = 2.0042 at 77 K to an axial g tensor with gl = 2.007 and g = 2.018 at... 

For POM, a matrix algorithm for the statistical mechanical treatment of an unperturbed -A-B-A-B- polymer chain with energy correlation between first-neighboring skeletal rotations is described. The results of the unperturbed dimensions are in satisfactory agreement with experimental data. In addition, if the same energy data are used, the results are rather close to those obtained by the RIS scheme usually adopted. The RIS scheme is shown to be also adequate for the calculation of the average intramolecular conformational energy, if the torsional oscillation about skeletal bonds is taken into account in the harmonic approximation. 

Figure 9 Coupling of mobility with the glass transition in a polymer system. Mobility is the reciprocal of the correlation time for the type of motion indicated. Correlation times were evaluated from D-NMR relaxation data. (A) Reorientation or fluctuation of the chain axis. (O) Rotation about the chain axis. ( ) the 180° ring flips of side chain aromatic rings. Open and closed symbols refer to different degrees of deuteration. (Reproduced with permission from [4], Original data from [52].)...

Spin-lattice relaxation is most sensitive to fast segmental fluctuations such as side-chain rotation and backbone oscillations with correlation times of around 10 s < Tc < lO s. A combination of different relaxation measurements makes it possible to discriminate among the different spectral densities [2, 15]. For a complete description of the frequency dependence, however, a series of measurements needs to be carried out at several different field strengths. 

The fact that the rotation correlation times of probes attached to PMAA chains with substantially different molar masses (starting at ca. 20 x lO g/mol) obey the same dependence on pH confirms the assumption that all the chains form different numbers of globules of the same size, each of them formed by parts of the chain roughly corresponding to 20 x 10" g/mol. The formation of the pearl necklace structure is further supported by high residual anisotropy at low pH the globules... 

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