The Glass Transition Phenomenon

Transition from liquid to solid state occurs, for well defined cooling rates, at a temperature Tg, known as the glass transition temperature. The variation of specific volume (see Fig. 7.8) and Young s modulus (see Fig. 7.9) with 

Glass transition temperatures usually refer to an experiment time of 1 s or a frequency of 1 Hz. 

In polymer chains, the motions associated with the glass transition are due to rotations about covalent bonds in the backbone. Although localised in a few bonds (about 10), as shown schematically in Fig. 7.11, combined motion over the complete length of the backbone allows a movement of the whole chain. Behaviour is no longer that of a solid, but rather resembles that of a viscous liquid at high temperature. 

Clearly, the chain can only move if there is enough space available in its neighbourhood to contain the new segment conformation. The increase with temperature of this free volume can be expressed as 

The variation described by this formula has been illustrated in Fig. 7.12. For polystyrene, dividing the experiment time by 10 (or mnltiplying the frequency by 10) shifts the occnrrence of the glass transition np by 5 or 6°C. For polyisoprene, the corresponding shift is between 8 and 10°C. 

At the time of development of free volume theory, two important empirical equations of viscosity were known. They are the Doolittle (1951) equation (3.01) and the Vogel, Tamman and Fulcher (VTF) equation (3.02) (Vogel, 1921, Fulcher, 1923, Tammann and Hesse, 1926), which are given below. 

In equation (3.01), A and B are empirical constants, Vocc is the volume occupied by the constituent particles and v/ is the free volume. In equation (3.02), T/o, C and To are constants. VTF equation implies that viscosities of glass forming supercooled liquids are non-Arrhenius and To is the temperature which linearizes the data of the non-Arrhenius plot. Cohen and Turnbull (Cohen and Turnbull, 1959 Turnbull and Cohen, 1961, 

Equation (3.06) suggests that as v/ decreases, q increases exponentially and the transport is severely curtailed. Correspondingly, the motion of the particle gets confined to the Voronoi polyhedron and as expected the motion becomes more and more oscillatory. The empirical VTF equation (3.02) may be recovered from equation (3.06) by a proper substitution of V/. One plausible assumption is that v/ = Vi - Vg s Aa(T-Tg) where Vi is the 

In the theory, z is later related to the total configurational entropy because s JS = z jN, where s is the entropy of the unit of minimum or critical size, z s cannot be less than k r 2). Further, the relaxation time. 

In general, volume V and entropy S of the supercooled liquid can be treated as functions of P and T. We may therefore write. 

In this section, we summarize the major relaxation phenomena observed when a molecular liquid is cooled from above its melting point down to the glass transition temperature, Tg, and further below into the glass. Since DS allows one to cover a very wide frequency range and to probe relaxation processes with weak relaxation strengths, we focus on discussing DS. More detailed information about this topic can be found in Refs. 17-24. 

At temperatures say, below 70 K further relaxation processes occur. There, the frequency dependence of (v) changes from a negative slope to a positive one. In this temperature range, thermally activated dynamics in asymmetric double-well potentials (ADWP) and, below 10 K, tunneling phenomena were discussed relating to the so-called low-temperature anomalies of glasses.27,30,31 

Regarding the line shape of s (v), numerous phenomenologic susceptibility functions have been proposed to describe the main relaxation peak, which deviates from 

The susceptibility contribution resulting from the /1-process can be often described by assuming a Gaussian distribution of activation enthalpies g(AHp). 19,52,53 Thus, one can write 

Triggered by predictions of the mode coupling theory (MCT see Chapter 4), the dynamics of super-cooled liquids was also studied by NS58 60 and LS61 65 revealing details of the susceptibility in the GHz regime. The spectra give evidence that a further fast-relaxation contribution has to be taken into account to explain in particular the shape of the susceptibility minimum, a feature also seen in the DS 

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It was found that Afi Tg and Aa Tg are not constant and therefore the SB equation has limited applicability. Hie results indicate an increase in Aa Te with increasing Tg. Therefore it is inadmissible to use the product A a Tg as a universal value in any theoretical discussion of the glass-transition phenomenon. At the same time, this conclusion in no way excludes the free-volume theory and the role of free-volume in the transition from the glassy to the liquid or rubberlike state. 

From a more fundamental point of view, the glass transition phenomenon has been explained using different types of physical models, as shown... 

The glass transition phenomenon has been presented in Chapter 4. Here, only structure-property relationships will be briefly examined. 

A comparative study of the kinetic and thermodynamic approaches to the glass transition phenomenon was made by Vijayakumar and Kothandaraman (1987). 

III. Some Comments on Theoretical Approaches to the Glass Transition Phenomenon... 

III. SOME COMMENTS ON THEORETICAL APPROACHES TO THE GLASS TRANSITION PHENOMENON... 

The glass transition phenomenon is an unsolved problem of condensed matter physics. Most approaches agree that the glass transition temperature Tg—though... 

Before we go into some details of MCT, we briefly mention that there exists another microscopic theory of the glass transition phenomenon, the replica theory [120,121], which is inspired by spin glass theory [122] and which lends some... 

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