8.4 OTHER TRANSITIONS AND RELAXATIONS

As the temperature of a polymer is lowered continuously, the sample mayexhibit several second-order transitions. By custom, the glass transition is des-ignated the a transition, and successively lower temperature transitions arecalled the b, g, . . . transitions. One important second-order transition appearsabove Tg, designated the Tll (liquid–liquid) transition. Of course, if the polymeris semicrystalline, it will also melt at a temperature above Tg.

8.4.1 The Schatzki Crankshaft Mechanism

8.4.1.1 Main-Chain Motions There appear to be two major mechanismsfor transitions in the glassy state (45). For main-chain motions in hydrocar-bon-based polymers such as polyethylene, the Schatzki crankshaft mechanism(46), Figure 8.16 (47), is thought to play an important role. Schatzki showedthat eight —CH2— units could be lined up so that the 1–2 bonds and the 7–8bonds form a collinear axis. Then, given sufficient free volume, the interven-ing four —CH2— units rotate more or less independently in the manner of anold-time automobile crankshaft. It is thought that at least four —CH2— unitsin succession are required for this motion. The transition of polyethyleneoccurring near -120°C is thought to involve the Schatzki mechanism.

It is interesting to consider the basic motions possible for small hydrocar-bon molecules by way of comparison. At very low temperatures, the CH3—groups in ethane can only vibrate relative to the other. At about 90 K ethaneundergoes a second-order transition as detected by NMR absorption (48), andthe two CH3— units begin to rotate freely, relative to one another. For propaneand larger molecules, the number of motions becomes more complex (49), asnow three-dimensional rotations come into play. One might imagine that n-octane itself might have the motion illustrated in Figure 8.16 as one of its basicenergy absorbing modes.

8.4.1.2 Side-Chain Motions The above considers main-chain motions.Many polymers have considerable side-chain “foliage,” and these groups can,of course, have their own motions.

A major difference between main-chain and side-chain motions is thetoughness imparted to the polymer. Low-temperature main-chain motions act

8.4 OTHER TRANSITIONS AND RELAXATIONS 375

Figure 8.16 Schatzki’s crankshaft motion (41) requires at least four —CH2— groups in suc-

cession. As illustrated, for eight —CH2— groups, bonds 1 and 7 are collinear and intervening

—CH2— units can rotate in the manner of a crankshaft (44).

to absorb energy much better than the equivalent side-chain motions, in theface of impact blows.When the main-chain motions absorb energy under theseconditions, they tend to prevent main-chain rupture. (The temperature of the transition actually appears at or below ambient temperature, noting theequivalent “frequency” of the growing crack.The frequency dependence is dis-cussed in Section 8.5.) Toughness and fracture in polymers are discussed inChapter 11.

8.4.2 The Tll Transition

As illustrated in Figure 8.17 (50), the Tll transition occurs above the glass tran-sition and is thought to represent the onset of the ability of the entire polymermolecule to move as a unit (9,51,52). Above Tll, physical entanglements playa much smaller role, as the molecule becomes able to translate as a whole unit.

Although there is much evidence supporting the existence of a Tll (51–53),it is surrounded by much controversy (54–57). Reasons include the strongdependence of Tll on molecular weight and an analysis of the equivalent

376 GLASS–RUBBER TRANSITION BEHAVIOR

Figure 8.17 Thermomechanical spectra (relative rigidity and logarithmic decrement versus

temperature (K) of anionic polystyrene, Mn = 20,200 (50).

behavior of spring and dashpot models (see Section 10.1). The critics contendthat Tll is an instrumental artifact produced by the composite nature of thespecimen in torsional braid analysis (TBA), since TBA instrumentation is theprincipal method of studying this phenomenon (see Figure 8.17). The Tll tran-sition may be related to reptation.

Many polymers show evidence of several transitions besides Tg. Table 8.6summarizes the data for polystyrene, including the proposed molecular mech-anisms for the several transitions. The General Mechanisms column in Table8.6 follows the results described by Bershtein and Ergos (58) on a number ofamorphous polymers. Clearly, different polymers may have somewhat differ-ent mechanistic details for the various transitions, especially the lower tem-perature ones. However, the participating moieties become smaller in size atlower temperatures. The onset of de Gennes reptation is probably associatedwith Tg, the motions being experimentally identified at Tg + 20°C.

8.5 TIME AND FREQUENCY EFFECTS ON

RELAXATION PROCESSES

So far the discussion has implicitly assumed that the time (for static) or fre-quency (for dynamic) measurements of Tg were constant. In fact the observedglass transition temperature depends very much on the time allotted to theexperiment, becoming lower as the experiment is carried out slower.

For static or quasi-static experiments, the effect of time can be judged intwo ways: (a) by speeding up the heating or cooling rate, as in dilatometricexperiments, or (b) by allowing more time for the actual observation. Forexample, in measuring the shear modulus by Gehman instrumentation, the

8.5 TIME AND FREQUENCY EFFECTS ON RELAXATION PROCESSES 377

Table 8.6 Multiple transitions in polystyrene and other amorphous polymers

Temperature Transitions Polystyrene Mechanism General Mechanism

433 K (160°C) Tll Liquid1 to liquid2 Boundary between rubberelasticity and rubbery flow states

373 K (100°C) Tg Long-range chain Cooperative motion of motions, onset of several Kuhn segments,reptation onset of reptation

325 K (50°C) b Torsional vibrations of Single Kuhn segment phenyl groups motion

130 K g Motion due to four Small-angle torsional carbon backbone vibrations, 2–3 mersmoieties

38–48 K d Oscillation or wagging Small-angle vibrations,of phenyl groups single mer