The Glass Transition and the Glassy State

When the polymer cools and the temperature lowers, the mobility in the amorphous regions of the polymer decreases. The lower the temperature, the stiffer the polymer becomes until a point of transition is reached. This transition is called glass transition or second-order transition [15]. The temperature at that transition is called the glass transition temperature, designated by Tg. Beyond stiffness, a change is manifested in specific volume, heat content, thermal conductivity, refractive index, and dielectric loss. Bueche illustrated glass transition as follows [16]. In measuring the force necessary to force a needle into a polymer, like polystyrene, at various temperatures, there is a relationship between the force required to insert the needle and the temperature [16]. As the temperature is being lowered, maximum resistance to penetration is reached at Tg. As stated, above Tg chains undergo cooperative localized motion. It is actually estimated that above Tg segmental motion of anywhere between 20 and 50 chain atoms is possible. Below the second-order transition temperature, however, there is insufficient energy available to enable whole segments of the polymeric chains to move. The structure is now stiff and brittle and resists deformation. When, however, sufficient amount of heat energy enters the material again and the temperature rises above Tg larger molecule motion involving coordinated movement returns. This requires more space, so the specific volume also increases and the polymer is in a rubbery or a plastic state. Above Tg, because large elastic deformations are possible, the polymer is actually both tougher and more pliable. Chemical structures of the polymers are the most important factors that affect the glass transition temperatures. Molecular weights also influence Tg, as it increases with the molecular weight. In addition, Tg also varies with the rate of cooling. Table 2.2. shows the structures of and lists relative Tg values of some common polymers. One way to obtain Tg is by studying thermal expansion of polymers. It is generally observed that the thermal coefficient of expansion is greater above the glass transition temperature than below it, though the magnitude of the change differs from one polymer to another. By plotting volume vs. temperature for a polymer, one can obtain Tg as shown in Fig. 2.3, which illustrates obtaining Tg from specific volume-cooling temperature curves [17]. Polymers with bulky, tightly held side groups or stiff bulky components in the backbone have high Tg values. This is due to the fact that such side groups or bulky components interfere with segmental motion. Such polymers require higher temperatures to acquire sufficient free volume for segmental motion. This can be observed in Table 2.2. which shows that the glass temperature of polystyrene with stiff benzene ring side groups is much higher than that of polyethylene. Also, polymers with high attractive forces between chains will require more heat energy to go from a glassy to a rubbery or a plastic state. On the other hand, polymeric chains with loose hanging side chains that tend to loosen the polymer structure and increase the free volume for segmental movement will have lower Tg. For instance, the glass transition temperature of poly (methyl methacrylate) is higher than that of poly (n-butyl methacrylate) as can be seen from Table 2.2. The transition to the glassy state from an equilibrium liquid results in changes in enthalpy, H, and volume, V. The specific heat is related to the enthalpy by definition:

The glassy state is nonequilibrium in nature and exhibits a tendency to undergo structural relaxation toward equilibrium. This tendency of the glassy state to relax structurally toward equilibrium is often referred to as structural recovery. It was observed, however, that the progress towards structural recovery with time varies significantly between a down-quench and an up-quench. This is referred to as asymmetry of structural recovery. The nonlinearity of the process is described by the following equation [16]:

where,  t is  the relaxation time and v is the specific volume . The value of Tg is also affected by other parameters, suchas molecular  weight,diluentconcentration,tacticity,externalpressure,crosslinking, chain stiffness, and mechanical deformation. For linear polymer, the Fox–Flory equation [18] described the relationship between Tg and the molecular weight:

Fig. 2.3 The relationship of the specific volume of a polymer to the temperature.

This equation, however, is limited in scope. It is actually neither valid for very high molecular weight polymers nor is it applicable to low molecular weight polymers. The transition in a polymer from a molten state to a glassy one actually occurs over a temperature range. This range also includes Tg. At the glass transition temperature, however, the change in viscosity is rapid, from very viscous to a glassy one. Polymeric materials that undergo rearrangements in response to outside stimulus, like light, are becoming increasingly important in various industrial application (see Chap. 10). Urban and coworkers [19] studied stimuli-responsive (TSR) transitions and correlated them to the glass transition temperatures (Tg). Based on their empirical data obtained from a copolymer, they concluded that the relationship between Tg and TSR is

where the V₁ and V₂ are the copolymer’s total volumes below and above the T_SR, respectively, T_g is the glass transition temperature of the copolymer, and P1 and P2 are the fraction of the free volume (f_free) at T_g (P₁) and (Tg, _midpoint-T_SR)_50/50 for each random copolymer (P2), respectively. They feel that this relationship can be utilized to predict the total volume changes as a function of TSR- Tg for different copolymer compositions.

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مواضيع ذات صلة

The Crystalline State

Rheology and Viscoelasticity of Polymeric Materials

Thermodynamics of Elasticity

Elasticity

Induction Forces in Polymers

Effects of Dipole Interactions

Structure and Property Relationship in Organic Polymers

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الأسموزية والديلزة Osmosis and dialysis

الحجم والشكل

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