Nonequilibrium glassy state

The nonequilibrium glassy state, 5(t) = f(t) -f, is determined by solving the kinetic equations which describe the local motion of holes in response to molecular fluctuations during vitrification and physical aging. The solution is (11)... 

Where p defines the shape of the hole energy spectrum. The relaxation time x in Equation 3 is treated as a function of temperature, nonequilibrium glassy state (5), crosslink density and applied stresses instead of as an experimental constant in the Kohlrausch-Williams-Watts function. The macroscopic (global) relaxation time x is related to that of the local state (A) by x = x = i a which results in (11)... 

In this section, the composite system with the properties given by Eq. (58) will be used. Since glassy polymers are not in thermodynamic equilibrium, the change in the nonequilibrium glassy state and its relaxation define the viscoelastic response. The relaxation modulus is given by Eq. (40). 

Equations for structural relaxation are presented. At the same time, a theoretical justification of extending Doolittle s equation from the equilibrium liquid to nonequilibrium glassy states is discussed. 

By including the effect of volume relaxation below Tg, calculations of the PVT properties of amorphous polymer have been extended from the equilibrium liquid to nonequilibrium glassy states. The study reveals the effects of kinetic, pressure, and stresses on Tg, which depends on relaxation time. 

In general, the prediction of the asymmetric volumetric relaxation processes in glassy materials requires that expressions such as (4-6) and (4-10) that describe the dependence of the characteristic relaxation time on free volume or entropy be extended so that they can describe the nonequilibrium state. Several different expressions for in the nonequilibrium glassy state have been proposed (Scherer 1992). One simple expression is obtained by applying the free volume expression (4-6) to the nonequilibrium state. Then... 

Amorphous polymers heats of dissolution studies were performed often enough. It is supposed, that the heat effect of system transition from metastable (nonequilibrium) glassy state in quasiequilibrium solution give the dominant contribution in the heat of dissolution value. In addition, the... 

When PLLA is quenched from the melt and vitrifies, a nonequilibrium glassy state is reached. Even in the glass, short-range mobility produces molecular rearrangements that drive the thermodynamic variables closer to their equilibrium values. The mobility of the polymer chains, that is, the ability to eliminate excess free volume, is directly related to temperature. 

Food materials (ingredients or whole systems) can be composed of matter in one, two, or all three physical states solid (crystalline or amorphous or a combination of both), liquid, and gas. The crystalline state is an equilibrium solid state, whereas the amorphous glassy state is nonequilibrium solid state. The main transitions that occur between the physical states of materials of importance to foods are summarized by Roos and Karel (1991) and Roos (2002). The most important parameters affecting the physical state of foods, as well as their physicochemical properties and transition temperatures, are temperature, time, and water content (Slade and Levine, 1988 Roos, 1995). Pressure is not included in this list, as food materials usually exist under constant pressure conditions. 

Through the understanding of the nonequilibrium changes in the glassy state of miscible blends, the excess volume of mixture is analyzed, and is related to the nonequilibrium enthalpy of mixing. In contrast to the multi-phase systems, the presence of a maximum yield stress in a miscible glassy blend at a critical concentration is predicted as a function of the nonequilibrium interaction. In accordance with Eq. (59), the total volume of a compatible blend is written as... 

When both components of a binary mixture have high molecular weights normal for commercial polymers, the entropy of mixing is negligible in the free energy of mixing expression [48]. The nonequilibrium interaction parameter for binary compatible mixtures in the glassy state is related to the parameter for volume interaction by [49]... 

For a fixed strain rate, a comparison of Eq. (74) and experimental data [51, 52] of miscible blends is shown in Fig. 32. Curves 1 and 2 represent, respectively, the PPO/PS blends in compression, and the PPO/PS-pCIS blends in tension.Table 2 lists the three parameters fjf2, CK, and A/f2 used in curves 1 and 2. The unique feature here is the presence of a maximum yield (or strength) for 0 <

nonequilibrium interaction (A < 0). Such phenomenon does not occur in incompatible blends or composite systems. Table 2 also reveals that the frozen-in free volume fractions which are equal to 0.0243 and 0.0211 for polystyrene and for PPO, respectively. These are reasonable values for polymers in the glassy state. In the search for strong blends, we prefer to have —A/f2 > 1, and a larger difference between the yield stresses of blending polymers. 

The glassy state of materials refers to a nonequilibrium, solid state, such as is typical of inorganic glasses, synthetic noncrystalline polymers and food components. Characteristics of the glassy state include transparency, solid appearance and brittleness (White and Cakebread 1966 Sperling 1992). In such systems, molecules have no ordered structure and the volume of the system is larger than that of crystalline systems with the same composition. These systems are often referred to as amorphous (i.e., disordered) solids (e.g., glass) or supercooled liquids (e.g., rubber, leather, syrup) (Slade and Levine 1991 Roos 1995 Slade and Levine 1995). 

Owing to the fact that the glassy state is a nonequilibrium or metastable state, the thermodynamic properties of a glassy system (volume, enthalpy, etc.) in isothermal conditions will evolve toward thermodynamic equilibrium. The evolution of the volume is usually expressed in terms of = p — Ve)/Ve, where v and are, respectively, the specific volume at time t and at equilibrium. After a T-jump cooling experiment, the variation of 8 with time, in isothermal conditions, follows trends similar to those shown (18) in Figure 12.16. This process is known as structural recovery. 

From a conceptual viewpoint the primary theoretiotl problem yet to be solved is the stress transfer mechanism in polymer solids. As noted earlier, polymers have statistical structures v4ien in the glassy state and a rather broad spectrum of order-disorder when in the crystalline state. Detailed analysis of stress transfer throi a glassy structure requires comprehensive analysis of chain conformation in the (nonequilibrium) glass which in turn requires an imderstanding of both the intramolecular and intermolecular energetics. 

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