Crankshaft relaxation

Fig. 8.2. Rotation of carbon atoms in a chain molecule (crankshaft relaxation, af-ter [79])...

In crystalline regions, relaxation processes may also occur. Many of the mechanisms described above, for example the crankshaft relaxation, are not possible in crystalline regions due to the larger packing density. Instead, the mobility of free chain ends or rearrangements of faults in the lattice may provide relaxation mechanisms. 

It is usually considered that the y relaxation arises from crankshaft and kink movements of polymethylenic sequences, but the clear maximum of tanS and loss modulus for the three polybibenzoates here reported leads to the conclusion that the motion responsible of this relaxation also takes place when one of the methylenic... 

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. 

Dyn ic mechanical analysis was discussed in terms of the nodular morphology concept in crossllnked structures. Beta relaxations in all the cured resins were bimodal in appearance. But, vAiile MPD-cured resins shewed a maximum at 25 C with a smaller shoulder at -40 C, TDA and DAEB-cured resins had maxima at -40 C with a less significant peak at 25 C. For DAIPB and DATBB-cured resins the two peaks were approximately equal in magnitude. The two overlapping peaks at -40 and 25 C were attributed to crankshaft motions in the matrix and nodules. 

The mechanical dispersion peaks in low-Tg epoxies such as Bisphenol-A based resin (Epon 828, products from Shell Development Company) have been the subject of numerous studies 143,145148,152 "155, l59>. The alpha-dispersion peak related to the glass transition can undoubtly be attributed to the large-scale cooperative segmental motion of the macromolecules. The eta-relaxation near —55 °C, however, has been the subject of much controversy 146,153). One postulated origin of the dispersion peak is the crankshaft mechanism at the junction point of the network epoxies (Fig. 17). The crankshaft motion for linear macromolecules was first propos-ed 163 166> as the molecular origin for secondary relaxations which involved restricted motion of the main chain requiring at least 5 and as many as 7 bonds 167>. This kind of... 

Fig. 3.9 Diagrams of molecular relaxation mechanisms (a) conformational flip of chlorohexane, (b) crankshaft rotation in polyethylene.

These results seem Incompatible with the assumption of a "crankshaft-like motion". We believe that they can be understood if we asstime that the transition from the cis to the trans form does not take place In a single step but rather by a large number of oscillations around the bond angle by which the transition state Is approached. If we then Impede these oscillations by Incorporating the azobenzene group into a polymer chain, we reduce equally the rate at which the transition state Is approached and the rate at which a strained bond relaxes to its initial shape. 

Fig. 1 Free volume, v, in polymers (A) the relationship of free volume to transitions, and (B) a schematic example of free volume and the crankshaft model. Below the Tg in (A) various paths with different free volumes exist depending on heat history and processing of the polymer, where the path with the least free volume is the most relaxed. (B) shows the various motions of a polymer chain. Unless enough free volume exists, the motions cannot occur. (From Menard K. Dynamic Mechanical Analysis A Practical Introduction, CRC Press Boca Raton, 1999).

In crystalline polymers, the principal relaxation process is associated with melting. In polyethylene, a (1-. and 7-transit ions have been identified and, particularly in higb-tlensity polyethylene, the a-transition has been sub-divided into a and a. In ethylene-based polymers, the y-transitions at —120°C is generally associated with the amorphous phase, in particular, with crankshaft motion of methylene sequences. " However, based upon studies of solution grown lamellae, it has also been suggested that this may llien be associated with... 

First is the crankshaft mechanism of Schatzki.16 It has been observed for many polymers containing linear (CH2) sequences with n = 4 or greater, that a secondary relaxation occurs at about -120 °C at 1 Hz. This seems to be true regardless of whether the CH2 sequences occur in the main chain or in the side groups. Thus both polyethylene and poly-n-butyl methacrylate exhibit this relaxation. The mechanism proposed by Schatzki is shown in Figure 5-14. 

The motion responsible for the relaxation is a rotation about the two co-linear bonds 1 and 7 such that the carbon atoms between bonds 1 and 7 move in the manner of a crankshaft. The co-linearity of the two terminal bonds is achievable if there are four intervening carbon atoms on the assumption of tetrahedral valence angles and a rotational isomeric state model. Support is to be found for the crankshaft mechanism in the fact that the activation energy estimated for the model, 54 kJ/mol, is close to the experimental results, 50-63 kJ/mol, and in the fact that the predicted free volume of activation, about four times the molar volume of a CH2 unit, is also in good agreement with experimental estimates based on pressure studies. 

The y-transition is a broad relaxation in the temperature- or frequency-domain, interpreted as a localized crankshaft-like motion of the backbone of the chain. This interpretation of the DMA result [51] agrees well with the calorimetry. The calorimetric results were interpreted already in 1962 based on an energy estimation as a local relaxation of gauche conformations in the amorphous phase [53,54]. The broad increases in the heat capacity beyond the vibrational Cp of amorphous PE seen in Fig. 2.46 were interpreted as a gradual, local unfreezing of the gauche-trans equilibrium. 

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