Relaxation main chain

Ti values may occur with such native biopolymers as ribonuclease A, deoxyribonucleic acid, and collagen, whose molecular motions are restricted, but, as yet, high values have not been observed for polysaccharides in solution, or for gels, in which these motional-restriction effects may be equivalent, or less marked. However, an extensive relaxation-study by Levy and coworkers68 on poly(n-alkyl methacrylates) may serve as a model for future experiments on polysaccharides, as this type of molecule has a main chain and side chains, albeit more mobile than those in polysaccharides. 

Homopolymers such as poly[(V)-3,7-dimethyloctyl-2-methylpropylsilylene], 117, were initially studied, and the helix-helix transition was discussed in terms of an entropically driven phenomenon in which at temperatures below Tc the side chains of the helical polymer are in a very ordered state and enforce a particular screw sense, whereas above Tc, the side chains become disordered such that the main chain can relax into the opposite screw sense.314 This concept is expressed in Figure 47. 

Below Tg, in the glassy state the main dynamic process is the secondary relaxation or the )0-process, also called Johari-Goldstein relaxation [116]. Again, this process has been well known for many years in polymer physics [111], and its features have been estabhshed from studies using relaxation techniques. This relaxation occurs independently of the existence of side groups in the polymer. It has traditionally been attributed to local relaxation of flexible parts (e.g. side groups) and, in main chain polymers, to twisting or crankshaft motion in the main chain [116]. Two well-estabhshed features characterize the secondary relaxation. 

Fig. 4.15 Momentum transfer (Q)-dependence of the characteristic time r(Q) of the a-relaxation obtained from the slow decay of the incoherent intermediate scattering function of the main chain protons in PI (O) (MD-simulations). The solid lines through the points show the Q-dependencies of z(Q) indicated. The estimated error bars are shown for two Q-values. The Q-dependence of the value of the non-Gaussian parameter at r(Q) is also included (filled triangle) as well as the static structure factor S(Q) on the linear scale in arbitrary units. The horizontal shadowed area marks the range of the characteristic times t mr- The values of the structural relaxation time and are indicated by the dashed-dotted and dotted lines, respectively (see the text for the definitions of the timescales). The temperature is 363 K in all cases. (Reprinted with permission from [105]. Copyright 2002 The American Physical Society)...

An important first step in interpreting the C-13 spectra is to distinguish a-carbons from 3-carbons, i.e. methine from methylene. Observation of multiplicity when the proton decoupler is off is one way, but this is not always easy if the lines are broadened by chemical shift multiplicity. Measurement of has been used for this purpose since the 3-carbon with two bonded protons relaxes about twice as fast as the a-carbon with only one. A very positive way is by deuterium labelling. In Fig. 3 is shown the main-chain 25 MHz carbon spectrum of two styrene-S02 copolymers containing 58 mol% styrene, or a ratio of styrene to SO2 of 1.38 (7 ). In the bottom one, 3,3-d2-styrene has been used, cind all the 3-carbon resonances are distinguishable from the a-carbon resonances since the presence of deuterium has eliminated their nuclear Overhauser effect because of this eind the deuterium J coupling ( 20 Hz), they are markedly smaller eind broader than the a-carbon resonances. 

Schaefer and Natusch have shown that for many synthetic high polymers in solution the NOE factors and relaxation times of carbon atoms in or near the main chains eire similcir (.2. In such cases the relative peak areas in the spectra obtained by the noise-decoupled and fast pulsing technique can be used as a good approximation for quantitative microstructure euialysis. However for our investigation of the polymerization of cyclic ethers we are frequently interested in the quantitative measurements of monomers and oligomers as well as the concentrations of the continuously growing polymeric species. Therefore, the assumption of Schaefer and Natusch is not applicable. 

The nmr data for this type of motion are direct and the motion clearly involves rotation about bonds in the millisecond time scale range. However. less direct evidence for motion comes from other techniques such as fluorescence depolarization, 02 diffusion, hydrogen exchange kinetics, and nmr relaxation times (see Ref. 4). The extent of this motion is not yet easy to define, but this evidence points to motion in the nanosecond time scale range. It is tempting to see the motion in this time scale as bond oscillations rather than rotations. To put it in a different way, on this time scale the side chains have some freedom to move with respect to each other but not normally to undergo substantial bond rotation. Table IV summarizes some references for motion of different types. Additionally, nmr relaxation studies suggest that the backbone or main chain of a protein is more restricted than that of the side chains. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

Carbon-13 spin-lattice relaxation times TL (Section 3.3) are relatively insensitive to the chain length of polymers [531]. The influence of local segmental motions predominates, as shown for low-density polyethylenes in which Tx values are one to two seconds for the main chain but up to seven seconds for peripheral side-chain carbon nuclei at 120 C [532] due to segmental mobility (Section 3.3.3.4). To conclude, quantitative evaluation of polymer carbon-13 spectra as necessary for side-chain determination requires the knowledge of spin-lattice relaxation times. 

Dynamic mechanical measurements. Dynamic mechanical measurements 97) of the storage and loss components of the rigidity modulus (G G") at a single frequency are shown in Fig. 31. As is the case with all polyethers, there is a main relaxation region associated with the onset of microbrownian motion of the main chain. In the region of the melting temperature, a catastrophic drop in modulus appears. 

We turn to the relaxation processes observed in smectic polymers with different attachment of mesogenic groups to the macromolecular backbone and compare dielectric behaviour of smectic and nematic polymers having identical mesogenic groups but different main chain structure. 

This is the motion of short sections of main chains which seems to be virtually independent of the free volume (density) of polymers. Such a local residual mobility is the only possible cause of secondary relaxations of polymers without side chains12. It manifests... 

With the exception of local main-chain motions, the above-mentioned types of molecular motions have been investigated on a series of hydrophilic polymethacrylates and polyacrylates by means of dynamic mechanical measurements carried out with a torsional pendulum. For this purpose, the constitution of polymethacrylates was systematically altered and correlated with the dynamic mechanical response spectra. It was established for a series of copolymers of poly(2-hydroxyethyl methacrylate) that the temperature of the y relaxation (140 K 1 Hz), assigned to the motion of 2-hydroxyethyl... 

The temperature position of the secondary fi relaxation (about 290 K 1 Hz), generally attributed to partial rotations of the side chains COOR, is only slightly affected by the polarity and volume of the substituent R but decreases markedly (by 120 K) on removal of the a-methyl group on the main chain. The experimental data obtained contradict the assumption that there is a certain relationship between this temperature and the glass transition temperature. Nevertheless, we can infer that the pertinent molecular mechanism in polymethacrylates differs from that in polyacrylates, probably due to the different participation of the main chains. The values of the individual contributions to the activation energy were estimated by employing a procedure similar to that used in the y relaxation process, and their sum was found to agree approximately with the experimental values. 

The y Relaxation. In common with many other polymers (8) both PPO and PS display significant loss maxima below room temperature at the frequencies under consideration. Whereas the process responsible for the a loss is at least qualitatively understood in terms of a main chain relaxation associated with the glass transition, y losses can often only tentatively be attributed to specific mechanisms. In PPO, for example, it does not seem unreasonable to propose that the y loss is associated with librations in the two pendant methyl groups this view is somewhat reinforced by the observation that in the dielectric measurements the relaxational strengths of the y and a loss processes are comparable. As the latter can be well interpreted (6) in terms of a dipolar relaxation of the main chain in which the entire dipolar contributions arise from the methyl groupings, it seems plausible to assume that the same dipoles are responsible for the y loss mechanism. In polystyrene there is a similar... 

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