Amorphous relaxation process

The WLF approach is a general extension of the VTF treatment to characterize relaxation processes in amorphous systems. Any temperature-dependent mechanical relaxation process, R, can be expressed in terms of a universal scaling law ... 

Molecular Motion in amorphous atactic polystyrene (PS) is more complicated and a number of relaxation processes, a through 5 have been detected by various techniques as reviewed recently by Sillescu74). Of course, motions above and below the glass transition temperature Tg have to be treated separately, as well as chain and side group mobility, respectively. Motion well above Tg as well as phenyl motion in the glassy state, involving rapid 180° jumps around their axes to the backbone has been discussed in detail in Ref.17). Here we will concentrate on chain mobility in the vicinity of the glass transition. 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

The lattice models provide useful interpretations of spin relaxation in dissolved polymers and rubbery or amorphous bulk polymers. Very large data bases are required to distinguish the interpretive ability of lattice models from other models, but as yet no important distinction between the lattice models is apparent. In solution, the spectral density at several frequencies can be determined by observing both carbon-13 and proton relaxation processes. However, all the frequencies are rather hl unless T2 data are also included which then involves the prospect of systematic errors. It should be mentioned that only effective rotational motions of either very local or very long range nature are required to account for solution observations. The local... 

These two inequalities can be proved for a more general model in which the film is assumed to consist of multiple parallel bands, each band containing an arbitrary fraction of amorphous phase which exhibits multiple relaxation processes. 

The analysis of the real and imaginary part of the complex dielectric permittivity allows one to distinguish between the two main relaxation processes (a and P). The a-process is correlated to the transition from the ferro to the paraelectric phase and the p-process is attributed to segmental motions in the amorphous phase. 

The high-temperature relaxation process is typical for amorphous polymers and can be assigned to the a-relaxation that appears in the whole frequency range and in the temperature interval from 50 to 100°C. This process is well observed for all samples. It corresponds to the glass-rubber transition of the amorphous phase. 

Fully deuterated linear poly(ethylene) (PE) has been investigated also via various 2H NMR techniques below Tm, i.e. in the semi crystalline state [83, 84]. The crystallinity ratio was measured as a function of temperature and it was shown that the motions are highly restricted in the amorphous regions of PE. It was shown that the onset of 3 and a transitions (at which mobility appears in the crystalline phase) may be observed by 2H NMR on raising the temperature. This onset of local motions in the crystalline phase is related to the chain relaxation process quoted previously. 

Clear evidence of L-L transitions has been found only in /-Si modeled by the SW potential [269]. Sastry and Angell [288] performed MD simulations of supercooled /-Si using the SW potential. After cooling at ambient pressure, the liquid (HDL) was transformed to LDL at 1060 K. The Nc in LDL is almost 4, and the diffusivity is low compared with that in HDL. The structural properties of LDL, such as g(r) and Nc, are very close to those of LDA, which indicates that this HDL-LDL transition is a manifestation of the multiple amorphous forms (LDA and HDA) of Si. McMillan et al. [264] and Morishita [289] have also found structural fluctuations between LDL-like and HDL-like forms in their MD calculations for /-Si at 1100 K. Morishita has demonstrated that such a structural fluctuation induces spatial and temporal dynamical heterogeneity, and this heterogeneity accounts for the non-Debye relaxation process that becomes noticeable in the supercooled state [289]. 

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

Another example of an application of Eq. (145) is on microcomposite polymer materials. We have performed dielectric measurements of the glass transition relaxation process in a nylon-6,6 sample quenched in amorphous (QN), a crystalline nylon-6,6 sample (CN), and a microcomposite sample (MCN), which is the same crystalline nylon-6,6 but with incorporated kevlar fibers [275,276],... 

The high-frequency (3, 7,. .. subsidiary peaks in amorphous polymers are characteristically very broad with a half-height width of several decades (compared with 1.14 decades for a single Debye relaxation process), although a good, linear Arrhenius plot is usually obtained, suggesting a non-co-operative mechanism. Figure 3.8 shows the Arrhenius plot for the /3-relaxation of poly(epichlorhydrin),... 

Given all these caveats, how fast are relaxation processes in amorphous polymers In low molecular weight liquids relaxations are very fast, occurring in time frames of the order of 10 10 secs. In a polymer melt (T > T)... 

In the preceding sections, we have looked at the various types of relaxation processes that occur in polymers, focusing predominantly on properties like stress relaxation and creep compliance in amorphous polymers. We have also seen that there is an equivalence between time (or frequency) and temperature behavior. In fact this relationship can be expressed formally in terms of a superposition principle. In the next few paragraphs we will consider this in more detail. First, keep in mind that there are a number of relaxation processes in polymers whose temperature dependence we should explore. These include ... 

Relaxation processes in amorphous polymers below the glass transition involve local... 

The relaxation behavior of selected semicrystalline ESI is depicted in Figure 26.3. It can be seen that the loss peak evident in the temperature range —50 to +50 °C shows increasing breadth of the relaxation process as the styrene content in ESI decreases. The relaxation processes associated with this loss peak are complex in nature. The relaxation behavior of semicrystalline polymers is fundamentally different from that of amorphous polymers. The long-range segmental motions associated with the Tg process become hindered owing to the restrictions imposed by the crystallites. 

The a relaxation in both isotactic and syndiotactic PS is broader than that in atactic PS and the actual location of the peak is slightly shifted to higher temperature. The broadening effect was attributed to restrictions imposed by crystallites on the amorphous phases [12,24,25], Nakatani et al. [26] showed how the broadness of a syndiotactic PS sample can be represented by the overlapping of two glass relaxation processes arising from one purely amorphous component and the other amorphous component, which is under restrain owing to the proximity of crystallites. 

The effect of diluents on the viscoelastic behavior of amorphous polymers is more complex at temperatures below T, i.e., in the range of secondary relaxation processes. Mechanical, dielectric and NMR measurements have been performed to study the molecular mobility of polymer-diluent systems in this temperature range (see e.g. From extensive studies on polymers such as polycarbonate, polysulfone and polyvinylchloride, it is well known that diluents may suppress secondary relaxation processes. Because of the resulting increase in stiffness, these diluents are called antiplasticizers . Jackson and Caldwell have discussed characteristic properties... 

---