Amorphous liquid state

Melting is normally driven by an entropy gain, then AS > 0. With the decrease of temperatures from T, the integral at the right-hand side of (6.53) decays gradually from zero to —AS, as demonstrated in Fig. 6.16b. However, a linear extrapolation to AS = 0 reaches a finite temperature rather than zero absolute temperature, which can be defined as T. This result implies that below Ts, Si < Sc-Apparently, the amorphous liquid state could not be more ordered than the crystalline solid state, which is against the third law of thermodynamics. Early in 1931, Simon pointed out this problem (Simon 1931). In 1948, Kauzmann gave a detailed description, and proposed that there should exist a phase transition such as crystallization before extrapolation to to avoid this disaster (Kauzmann 1948). Therefore, this scenario is also called the Kauzmann paradox. 

The existence of pure amorphous bulk polymers has been a controversial issue since the beginning of polymer science. Natural rubber yields an X-ray pattern tiiat contains only amorphous halos, typical of any liquid. Nevertheless, it was difficult for many scientists to believe that molecules with a polymeric chain structure could pack in a truly amorphous way. There are still papers that are submitted for publication that assert that amorphous rubbery polymers are actually composed primarily of microcrystalline domains. This issue has been clarified by the incisive theoretical and experimental work of Flory. It is now understood that there are polymers that exhibit liquid crystalline phases upon melting of the crystals. The nature of the noncrystalline state of pure bulk polymers depends on tiie detailed local structure of the chain and the ratio of die persistence lengtii of die chain to the diameter of the mer. Molecules that are conformationally dexible enough to have a small persistence length can exist in the amorphous liquid state. 

Structure and properties of polymers in the pure amorphous liquid state... 

The detailed descriptions of the structures of calamitic phases allow us to classify the mesomorphic liquid crystal state, and to place this state in context with the crystalline and amorphous liquid states [3]. Table 1 describes the relationship between ordered crystals, disordered or soft crystals, liquid crystals and the isotropic liquid. 

He proposes chain folding for the amorphous liquid state which will give the random coil dimensions found by neutron scattering, i.e., a radius of gyration proportional to the square root of molecular weight. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

The thickness of amorphous alloys is dependent upon production methods. Rapid quenching from the liquid state, which is the most widely used method, produces generally thin amorphous alloy sheets of 10-30 tm thickness. This has been called melt spinning or the rotating wheel method. Amorphous alloy powder and wire are also produced by modifications of the melt spinning method. The corrosion behaviour of amorphous alloys has been studied mostly using melt-spun specimens. 

One of the most important areas of application of the solid-state NMR technique is the investigation of the structures of cross-linked amorphous materials in cases where X-ray diffraction technqiues are not applicable. Polymeric resins are one such important class of materials. A lot of work has been done in this area by several investigators 36,37 38 since the beginning of the 80. Some solid-state NMR data of phenolic resins are presented in Fig. 10. Comparison with liquid state data for... 

The number of defects is maximal in the amorphous and liquid states. The phase diagram in Figure 5 shows the volume-temperature relationships of the liquid, the crystalline form, and the glass (vitreous state or amorphous form) [14], The energy-temperature and enthalpy-temperature relationships are qualitatively similar. 

Two simple thermodynamic considerations are suggested upon examination of Fig. 8. The first is that at temperatures below Tml the free energy of the bulk mesophase G m is in general bound to be lower than Gl, the free energy of the amorphous. In the limit of Class II mesophases, since AHml = 0, we will have Gm = Gl at T = 0 K while Gm < Gl at temperatures 0 < T < Tml since it is Sm > Sl at temperatures low enough as compared to Tml (Sect. 3.1). In the case of Class I mesophases AHml > 0. he., mesophases are enthalpically stabilized with respect to the liquid state, while Sm < Sl, so it will be Gm < Gl at temperatures T, with 0 < T < Tml- Note that the above consideration will in... 

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. 

FIG. 31 Schematic diagram illustrating the transition between a supercooled liquid state (rubber) and an amorphous solid state (glass). The glass transition event is typically caused by a decrease in water content and/or temperature. The reversibility of the transition, as indicated by the dotted arrow, is material dependent (see text for further discussion of the reversibility of the transition). 

Once in the amorphous solid state, undesirable changes in the properties of amorphous ingredients and foods (e.g., stickiness, caking, collapse, loss of crispness) can occur via a reversal in the two events discussed earlier (1) an increase in moisture content (water plasticization) so that the Tg of a material is decreased to below room temperature and (2) an increase in temperature [thermal plasticization (Roos, 2003)] so that the temperature of the material rises above its Tg. In both cases and their combination, the once glassy material is now in a rubbery or liquid state and is undesirable and/or unfit for consumption. 

When an amorphous material exists in a glassy state, it is hard and brittle. In a rubbery state, the material is soft and pliable. An amorphous material, at solid state (also referred to as glass), does not flow, but the molecules are randomly distributed as if they were in liquid state. When this "glass" is heated, it softens and eventually becomes a fluid. However, this is not a first-order transition and therefore occurs over a range of temperatures called the glass transition temperature (Tg). The state... 

Contrary to a fluid in the gaseous state, a liquid has a surface, and is characterized by a surface tension. For water, the surface tension is 72 mN m" at 25°C [1,2]. Again, contrary to the fluid in the gaseous state, the volume of a liquid does not change appreciably under pressure it has a low compressibility and shares this property with matter in the solid (crystalline, glassy, or amorphous) state. For water, the compressibility is 0.452 (GPa)" at 25°C [1,2]. These are macroscopic, or bulk, properties that single out the liquid state from other states of aggregation of matter. 

Figure 9.3 Energy of a 64 atom supercell of InP during quenching from a liquid state into an amorphous state. The energy of crystalline InP is also shown. (Reprinted by permission from the source cited in Fig. 9.2.)...

Polymers can exist as liquids, as elastomers or as solids but can be transferred into the gaseous state only under very special conditions as are realized in, for example, MALDI mass spectrometry. This is because their molecular weight is so high that thermal degradation sets in before they start to evaporate. Only a few polymers are technically applied in the liquid state (silicon oils, specidty rubbers) but most polymers are applied either as elastomers, or as rigid amorphous or semicrystalline solids. 

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