Crystals melting entropy

Cured polymers of butadiene with low cross-link density do not tend to cold flow and are useful elastomers. These vulcanized elastomers crystallize when stretched, but when the stress is removed, the restoring force is largely entropy and most of the crystals melt and the chains return to the random conformation.The tensile strength is increased dramatically when large amounts of carbon black or amorphous silica are added. 

No general rules about the entropy of transitions, as were found for liquid and plastic crystal transitions, can be set up for condis crystals. Two typical examples may illustrate this point. Polytetrafluoroethylene has a relatively small room-temperature transition-entropy on its change to the condis state and a larger transition entropy for final melting. Polyethylene has, in contrast, a higher condis crystal transition entropy than melting entropy (see Sect. 5.3.2). 

AS is the entropy difference between crystal and liquid and is related to the increase in disorder when a crystal melts, or with the probabilities of the chain conditions in both phases. This follows from ... 

At this temperature, the entropy change for dissolution of liquid hydrocarbons in water is zero. However, the entropy of protein denaturation is far from zero at this temperature but amounts to 17.6 J - K l per mole of amino acid residues (Privalov, 1979), a value that corresponds to an 8-fold increase of the number of possible configurations and is close to the value expected for the helix-coil transition of polypeptides (Schellman, 1955). This difference shows that an oil drop is an inadequate model for a globular protein. A more suitable model resembles that of a small crystal with a quite definite positive melting entropy (see also Bellow, 1977, 1978). 

Liquids are neither characterised by the random chaotic motion of molecules, which one find in gases, nor by the perfect order of moleculars arrangement in solids. They occupy an intermediary position where molecules are more disorderly than those of a solid, but much less disorderly than those of gases. Because of this fact the enthalpy change when a crystal melts is always positive and the corresponding entropy change is also positive. This implies that there is less of order when a crystal melts. The liquid is thus intermediate between the complete order of the crystalline state and the complete disorder of the gaseous state. Because of this fact, the development of a molecular theory for liquids has posed formidable difficulties. 

A simple method to determine is based on the dependence of the melting temperature on the crystallization temperature, T. (14). Tm increases linearly with T. as Figure 2.16 shows (15). Since can never be lower than F., the line F = F represents the limit, i.e., the situation of perfect reversibility in which melting and crystallization occur at the same temperature. The extrapolation of F to F = F provides T%. This procedure is the one most widely used because it is applicable to all samples, not just to single crystals. Table 2.2 shows the values of 7%, melting enthalpy, and melting entropy of some polymers (16). The values of which... 

The heat capacity between the melting point and 1836 K was determined from the enthalpy measurement by King et al. (1.). The heat capacity was assumed constant above and below the measured range. At 1000 K, a glass transition was assumed below which the heat capacity was assumed to be that of the crystal. The entropy at 298.15 K is calculated in a manner analogous to that used for the enthalpy of formation. 

Crystals containing polyatomic units of structure which are effectively non-spherical usually exhibit some increase in disorder in the mutual orientation of these units when the crystal melts. For such crystal lattices, the total entropy of fusion, Sf, may be written as the sum of two terms Sf = Spos. + 5or.-... 

The entropy change on crystal-melting, ASm, may be taken to represent Sc at the melting point T, hence Equation (7) may be written as... 

Table 2.1.1. Melting entropy of molecular crystals (in entropy units,...

Fig.1 Illustration of the crystallization/melting process of globular small molecules and long polymeric molecules. The latent entropy of the latter transition (AStr) consists of two major contributions the configurational term and the volume-dependent term (ASv) (see text)...

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