Schatzki crankshaft motion

Davis and Eby support the -30°C value on the basis of volume-time measurements Stehling and Mandelkern (127) favor the -128°C value based on mechanical measurements, lllers (128) and Boyer (9) support the value of -80°C based on extrapolations of completely amorphous ethylene-vinyl acetate copolymer data with copolymer-T relationships. Boyer (9) supports the position that -80° is Tg L) and -30°C represents Tg(U). Tlie transition at -128°C is thought to be related to the Schatzki crankshaft motion (Section 8.4.1), although the situation apparently is more complicated (128). Tobolsky (129) obtained -81 °C for amorphous polyethylene based on a Fox plot [see equation (8.73)] of statistical copolymers of ethylene and propylene, it-polypropylene having a Tg of -18°C. 

Define the following terms free volume loss modulus tan 5 stress relaxation plasticizer Schatzki crankshaft motions A, WLF equation compressibility Young s modulus. 

Figure 8.16 Schatzki s crankshaft motion (41) requires at least four—CH2— groups in succession. As illustrated, for eight —CHj— groups, bonds 1 and 7 are collinear and intervening —CH2— units can rotate in the manner of a crankshaft (44).

Extensive theoretical and experimental works were carried out on local dynamics of polymers in solution and bulk to elucidate the mechanism of conformational transitions [106]. Formerly, it was believed that the most reasonable mechanism for the conformational transitions was a crankshaft-like motion such as the Schatzki crankshaft [117] or three-bond motions [118,119] in which two bonds in a main chain rotate simultaneously. However, recent computer simulations [ 120-128] have revealed many interesting features of conformational transitions of a polymer chain in solutions and melts. 

A crankshaft motion has been proposed in the solid state for molecular fragments consisting of three or more rotors linked by single bonds, whereby the two terminal rotors are static and the internal rotors experience circular motion (Schatzki 1962). 

Before embarking on a discussion of the results of these studies let us add one historical note. The difficulty with swinging the polymer tails in a conformational transition has been recognized for many years. A means of circumventing was proposed by Schatzki. Verdier and Stockmayer had earlier invoked a similar principle but used it only to produce Rouse modes. We know now that slow Rouse modes are insensitive to the details of the faster time-scale dynamics. The proposed motions are completely local, and involve going from one equilibrium rotational isomeric state to another by moving only a finite, small number of atoms. Mechanisms of this class have come to be known as crankshaft motions (a term applicable in the strictest sense only to the Schatzki proposal). Because of the limited amount of motion and the simplicity of the dynamics these models are easy to understand, analyze, and simulate. This probably contributes to the continued attention devoted to them. The crankshaft idea has helped to focus attention on the necessity to localize the motion associated with conformational transitions, but complete localization is too restrictive. There are theoretical objections that can be raised to the crankshaft mechanism, but the bottom line is that no signs of it are found in our simulations. 

Many polymers undergo second order transitions at temperatures below T, [224] the transitions are caused by rotations of side groups about an axis which is perpendicular to the chain, by the motion of sequences of 3 — 5 methylenic groups from the backbone or by motion of chain portions in polymers containing heteroatoms in the main chain [162, 226]. The second kind of motion, noted by Schatzki [226] in ethene copolymers and in many homopolymers, is referred to as the crankshaft effect and it occurs immediately below T,. Because it is almost insensitive to the... 

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