Amorphous dynamical relaxation

Next we note that there are two physieally different sources of temperature and pressure dependence of the elastic constants of polymers. One, in common with that exhibited by all inorganic crystals, arises from anharmonic effects in the interatomic or intermolecular interactions. The second is due to the temperature-assisted reversible shear and volumetric relaxations under stress that are particularly prominent in glassy polymers or in the amorphous components of semi-crystalline polymers. The latter are characterized by dynamic relaxation spectra incorporating specific features for different polymers that play a central role in their linear viscoelastic response, which we discuss in more detail in Chapter 5. 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

Transitions. Samples containing 50 mol % tetrafluoroethylene with ca 92% alternation were quenched in ice water or cooled slowly from the melt to minimise or maximize crystallinity, respectively (19). Internal motions were studied by dynamic mechanical and dielectric measurements, and by nuclear magnetic resonance. The dynamic mechanical behavior showed that the CC relaxation occurs at 110°C in the quenched sample in the slowly cooled sample it is shifted to 135°C. The P relaxation appears near —25°C. The y relaxation at — 120°C in the quenched sample is reduced in peak height in the slowly cooled sample and shifted to a slightly higher temperature. The CC and y relaxations reflect motions in the amorphous regions, whereas the P relaxation occurs in the crystalline regions. The y relaxation at — 120°C in dynamic mechanical measurements at 1 H2 appears at —35°C in dielectric measurements at 10 H2. The temperature of the CC relaxation varies from 145°C at 100 H2 to 170°C at 10 H2. In the mechanical measurement, it is 110°C. There is no evidence for relaxation in the dielectric data. 

To understand the global mechanical and statistical properties of polymeric systems as well as studying the conformational relaxation of melts and amorphous systems, it is important to go beyond the atomistic level. One of the central questions of the physics of polymer melts and networks throughout the last 20 years or so dealt with the role of chain topology for melt dynamics and the elastic modulus of polymer networks. The fact that the different polymer strands cannot cut through each other in the... 

The Fourier transform of this quantity, the dynamic structure factor S(q, ffi), is measured directly by experiment. The structural relaxation time, or a-relaxation time, of a liquid is generally defined as the time required for the intermediate coherent scattering function at the momentum transfer of the amorphous halo to decay to about 30% i.e., S( ah,xa) = 0.3. 

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

According to a dynamic mechanical study by Saba, Sauer, and Woodward (1963) for PPO and a dilatometric study by Daane and Barker (1964) for cellulose acetate, the high-temperature relaxations of PPO, CDA, and CTA are primary relaxations which arise from segmental motion in the amorphous phase and the low-temperature relaxations are presumably ascribed to a more local motion in the amorphous phase. 

The sensitivity of the three relaxation times to the molecular dynamics and structure will be discussed in a subsequent section. The general temperature dependence of Tj, T1 and T2 for a typical linear amorphous polymer with one side group attached to a backbone is shown in Fig. 4. 

DSC measurements showed that the crystallization ability of this interphase region was reduced by the silane modification of the glass beads. Despite an increase in the amount of amorphous material with increasing number of silane layers, a decrease in the intensity of the fourth lifetime was observed. This decrease in the free volume is in accordance with the earlier observed reduced mobility in the interphase region measured by dynamic-mechanical spectroscopy in the melt state [9,10] and creep and stress relaxation measurements in the solid state [12]. 

The quasi-static modelling of the dynamics of the ester group flip in an amorphous cell of atactic PMMA has yielded information complementary to that derived from dynamic mechanical analysis, dielectric relaxation and, mainly, multidimensional 13C and 2H solid-state NMR. The main results are ... 

The approach developed in this paper, combining on the one side experimental techniques (dynamic mechanical analysis, dielectric relaxation, solid-state 1H, 2H and 13C NMR on nuclei at natural abundance or through specific labelling), and on the other side atomistic modelling, allows one to reach quite a detailed description of the motions involved in the solid-state transitions of amorphous polymers. Bisphenol A polycarbonate, poly(methyl methacrylate) and its maleimide and glutarimide copolymers give perfect illustrations of the level of detail that can be achieved. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

Rather recently, we have studied the solid-state structure of various polymers, such as polyethylene crystallized under different conditions [17-21], poly (tetramethylene oxide) [22], polyvinyl alcohol [23], isotactic and syndiotactic polypropylene [24,25],cellulose [26-30],and amylose [31] with solid-state high-resolution X3C NMR with supplementary use of other methods, such as X-ray diffraction and IR spectroscopy. Through these studies, the high resolution solid-state X3C NMR has proved very powerful for elucidating the solid-state structure of polymers in order of molecules, that is, in terms of molecular chain conformation and dynamics, not only on the crystalline component but also on the noncrystalline components via the chemical shift and magnetic relaxation. In this chapter we will review briefly these studies, focusing particular attention on the molecular chain conformation and dynamics in the crystalline-amorphous interfacial region. 

Hardy, L., Stevenson, I., Boiteux, G., Seytre, G., and Schonhals, A. (2001). Dielectric and dynamic mechanical relaxation behaviour of poly(ethylene 2,6 naphthalene dicarboxyl-ate). I. Amorphous films. Polymer 42(13), 5679-5687. 

---