Relaxations in the Glassy State

In contrast to other Tg methods, dynamic measurements easily detect glassy state relaxations and have been extensively applied to their study. These include dynamic mechanical methods, dielectric relaxation, and nuclear magnetic resonance (NMR). Since we are primarily concerned with viscoelastic response at this point, we shall confine the discussion to the dynamic mechanical technique and delay our consideration of dielectric and NMR methods until Chapter 7. 

As should be apparent, it is possible to detect secondary relaxations by performing measurements over a frequency range at constant temperature or over a temperature range at constant frequency. The latter technique is usually employed, largely because extended mechanical frequency ranges are difficult 

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 time-temperature or frequency-temperature superposition scheme discussed in Chapter 4, Section B, is applicable to secondary relaxations as well as to the glass transition, assuming that the observed secondary relaxation peaks are well resolved. When the shift factors are obtained for these secondary relaxations, it is found that their temperature dependencies do not obey the WLF equation but follow an equation of the Arrhenius form, that is , 

Thus plots of log aT versus l/T for a secondary relaxation will yield straight lines, not curves as in the WLF case. This fact has been used to distinguish the main glass transition from other relaxations occurring in semicrystalline polymers.  

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Polycarbonate (PC) serves as a convenient example for both, the direct determination of the distribution of correlation times and the close connection of localized motions and mechanical properties. This material shows a pronounced P-relaxation in the glassy state, but the nature of the corresponding motional mechanism was not clear 76 80> before the advent of advanced NMR techniques. Meanwhile it has been shown both from 2H NMR 17) and later from 13C NMRSI) that only the phenyl groups exhibit major mobility, consisting in 180° flips augmented by substantial small angle fluctuations about the same axis, reaching an rms amplitude of 35° at 380 K, for details see Ref. 17). 

The stimulated-echo technique is well suited not only to investigate the primary relaxation of glass forming liquids above Tg, but also the secondary relaxation in the glassy state. In 2H NMR studies on the -process, it is advisable to measure the correlation function rather than Fsin(tm p)- In the former experiment, the... 

This study is the first step towards a quantitative prediction of chain flexibility based on conformational analysis. Torsional relaxation of the adjacent bonds is very important. The present approach differentiates between the polymer relaxations in the glassy state and in the melt state. It provides insight into the crystallinity of a system and succeeds in explaining the isomorphic transformations of PDES. Chain flexibility is influenced by at least two types of factors the number of isomeric states available and the torsional freedom in a given state, which is determined by the shape of the potential well. 

The JG y9-relaxation in the glassy state, like the a -relaxation, is sensitive to thermal history, physical aging, and the particular thermod5mamic (TyP) path used to arrive at the glassy state. 

Figure 6. Activation energy of the JG relaxation in the glassy state for different isobaric measurements plotted versus the related Tg(P). QN in tristyrene (5% and 10% wt. are indicated by open circles and solid squares, respectively), 5% wt. QN in PS800 (solid triangles), PPGE (solid stars), 5% wt CNBz in tristyrene (open stars), 17% ClBz in decalin from reff ] (solid down triangles). Dashed lines are the predictions according toEq. (3).

Cp° is the conhgurational heat capacity, i.e. the difference in Cp between the liquid (glass) and crystal states, and T2 is the temperature at which the conhgurational entropy reaches zero, T k- A modihed Adam-Gibbs model describes non-equilibrium relaxation in the glassy state. A hctive temperature is introduced, which represents the... 

Robertson, R. E., Free volume theory and its applications to polymer relaxation in the glassy state, in Computational Modeling of Polymers, Bicerano, J., Ed., Marcel Dekker, New York, 1992, pp. 297-361. 

Robertson, R. E., Effect of free volume fluctuations on polymer relaxation in the glassy state J. Polym. Sci. Polym. Phys. Ed, 17, 597-613 (1979). 

Jain, S. C., and Simha, R., Relaxation in the glassy state volume, enthalpy and thermal density fluctuations. Macromolecules, 15, 1522-1525 (1982). 

Intermediate - Temperature Relaxations. Secondary relaxations in the glassy state at temperatures intermediate between those of the a- and P- relaxations have been reported, but workers disagree as to their nature, location and origin. Confusion arises in part from a failure to recognize the existence of two separate processes. Krum and MUller [19] observed an intermediate relaxation only for injection-moulded or cold-drawn polycarbonate samples. Since the magnitude was diminished by annealing and the loss was not detected in fully annealed samples, they concluded that the intermediate process is a non-equilibrium effect associated with residual stresses. 

Proper choice of material effects are minimal for polymers with a high Tg and a minor P relaxation in the glassy state. Addition of inorganic filler particles further reduces the effects by reducing the relative density change of the material [22]. 

Another DMA analysis is shown in Fig. 4.170 for poly(vinyl chloride), [-CHCl-CHjlx- The data for G, G", and tan 6 are given as a function of temperature for one frequency. The glass transition occurs at about 300 K, as indicated by the drop in G and the peaks in G" and tan 6. In addition, there is a broad peak in G" and in tan 6, indicating a secondary, local relaxation in the glassy state. Semicrystalline... 

POSS-Epoxy Epoxy-POSS diglycidyl ether of bisphenol A Pendants Tg increases and broadens the shape of viscoelastic spectrum not affected slowing down of the chain relaxation in the glassy state [39,46]... 

A sharp step or peak in a DSC curve requires a ACp such as occurs at Tg. Here ACp arises from hole formation, as elaborated by Kauzmann. jjirai and Eyring, and Wunderlich. 5 O Reilly and Karasz noted that there was no observed ACp associated with secondary relaxations in the glassy state of polymers. These secondary relaxations were usually accompanied by a relatively small discontinuity in the thermal expansion coefficient, Aa, reported by Heydemann and Guicklingi for PVC and PMMA, and by Simha and his colleagues for many polymers. It seems possible that the ACp to be expected with such small Acs might be too weak to be observed by DSC. However, we propose here an alternate explanation. 

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