Entropy of clearing

The entropies of clearing of these polymers, ASj, also showed an even-odd relationship, but they demonstrated no particular trends Values for the entropy of clearing... 

The entropies of clearing of these three series of polymers were determined by DSC measurements and showed a remarkable even-odd relationship for the determined values as shown in Fig. 6. Polymers of the series 1 mesogen showed a very weak even-odd effect of values of approximately 3 cal mol K , while the other two... 

Fig. 6. Variation in the Entropy of Clearing with Spacer Length for Polymers 1,2and4inXable 1...

In similar work by Blumstein and Thomas, polymers of mesogenic structure 14 with high molecular weights were prepared, and these also showed the same relationships observed previously for transition temperatures and entropies of clearing In this case, a uniform increase was observed in the clearing entropies of both the odd and even series, and an additive value to AS of 0.36 cal mol could be calculated... 

The range of mesophase stability and melting temperature was greater for the polymer with a polymethylene spacer than that with a siloxane spacer however, the size of the entropy of clearing was reversed. In all such measurements, the properties of the copolymer fell between these two extremes, except for the case of the range of mesophase stability, which was greater for the copolymer than the two homopolymers. In all cases, the mesophases were identified as nematic from characterization by polari-zed-light microscopy. 

Table 4. Effect of Mesogenic Group and Flexible Spacer on Entropy of Clearing, AS , of LC Polyesters...

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

A great many liquids have entropies of vaporization at the normal boiling point in the vicinity of this value (see benzene above), a generalization known as Trouton s rule. Our interest is clearly not in evaporation, but in the elongation of elastomers. In the next section we shall apply Eq. (3.21) to the stretching process for a statistical—and therefore molecular—picture of elasticity. 

These equations clearly show that for an ideal gas U, H, Cp, and Cy are functions of temperature only and are independent of f and V The entropy of an ideal gas, however, is a func tion of both T and f or of both T and V... 

It is clear by comparing the uansition state theory with the collision model that the conesponding entropy of activation can be calculated from the value... 

A number of groups have criticized the ideas of Dauben and Noyce, especially the concept of PDC. Kamernitzsky and Akhrem, " in a thorough survey of the stereochemistry of addition reactions to carbonyl groups, accepted the existence of SAC but not of PDC. They point out that the reactions involve low energies of activation (10-13 kcal/mole) and suggest that differences in stereochemistry involve differences in entropies of activation. The effect favoring the equatorial alcohols is attributed to an electrostatic or polar factor (see also ref. 189) which may be determined by a difference in the electrostatic fields on the upper and lower sides of the carbonyl double bond, connected, for example, with the uncompensated dipole moments of the C—H bonds. The way this polar effect is supposed to influence the attack of the hydride is not made clear. 

Usually, only the Arrhenius energy of activation, E, is given in these papers it differs from the heat of activation,JH, by RT (about 0.6 kcal at ordinary temperatures). Only a few entropies of activa-tion, JS, were calculated the frequency factor, whose logarithm is tabulated, is proportional to this reaction parameter. It is clear that the rate, E, and JS determined for an 8jfAr2 reaction are for the overall, two-stage process. Both stages will contribute to the overall results when their free energies of activation are similar. 

The effect of temperature on the monomer reactivity ratio is fairly small. In those few cases examined with sufficient accuracy,the ratio nearly always changes toward unity as the temperature increases —a clear indication that a difference in activation energy is responsible, in part at least, for the difference in rate of the competing reactions. In fact, the difference in energy of activation seems to be the dominant factor in these reactions differences in entropy of activation usually are small, which suggests that steric effects ordinarily are of minor importance only. 

The processes that occur at a finite rate, with finite differences of temperature and pressure between parts of a system or between a system and its surroundings, are irreversible processes. It has been shown that the entropy of an isolated system increases in every natural (i.e., irreversible) process. It may be noted that this statement is restricted to isolated systems and that entropy in this case refers to the total entropy of the system. When natural processes occur in an isolated system, the entropy of some portions of the system may decrease and that of other portions may increase. The total increment, however, is always greater than the total decrement. The entropy of a nonisolated system may either increase or decrease, depending on whether heat is added to it or removed from it and whether irreversible processes occur within it. Considered all in all, it is necessary to define clearly the system under consideration when increases and decreases in entropy are discussed. 

If k is expressed in liters per mole per second, the standard state for the free energy and entropy of activation is 1 mole/liter. If the units of k are cubic centimeters per molecule per second, the corresponding standard state concentration is 1 molecule/cm3. The magnitudes of AG and AS reflect changes in the standard state, so it is not useful to say that a particular reaction is characterized by specific numerical values of these parameters unless the standard states associated with them are clearly identified. These standard states are automatically determined by the units chosen to describe the reactant concentrations in the phenomenological rate expressions. 

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