Rotational effects thermodynamics

Under most circumstances the equations given in Table 10.4 accurately calculate the thermodynamic properties of the ideal gas. The most serious approximations involve the replacement of the summation with an integral [equations (10.94) and (10.95)] in calculating the partition function for the rigid rotator, and the approximation that the rotational and vibrational partition functions for a gas can be represented by those for a rigid rotator and harmonic oscillator. In general, the errors introduced by these approximations are most serious for the diatomic molecule." Fortunately, it is for the diatomic molecule that corrections are most easily calculated. It is also for these molecules that spectroscopic information is often available to make the corrections for anharmonicity and nonrigid rotator effects. We will summarize the relationships... 

This can lead to problems in NMR spectra. The magnitude of the energy barrier to the rotation determines what the effect on the spectrum will be. (For the thermodynamically-minded, we are talking about energy barriers of the order of 9-20 Kcal mol.)... 

The EfZ ratio of stilbenes obtained in the Rh2(OAc)4-catalyzed reaction was independent of catalyst concentration in the range given in Table 22 357). This fact differs from the copper-catalyzed decomposition of ethyl diazoacetate, where the ratio diethyl fumarate diethyl maleate was found to depend on the concentration of the catalyst, requiring two competing mechanistic pathways to be taken into account 365), The preference for the Z-stilbene upon C ClO -or rhodium-catalyzed decomposition of aryldiazomethanes may be explained by the mechanism given in Scheme 39. Nucleophilic attack of the diazoalkane at the presumed metal carbene leads to two epimeric diazonium intermediates 385, the sterically less encumbered of which yields the Z-stilbene after C/C rotation 357,358). Thus, steric effects, favoring 385a over 385 b, ultimately cause the preferred formation of the thermodynamically less stable cis-stilbene. 

The objective of this first part of the book is to explain in a chemically intelligible fashion the physical origin of microwave-matter interactions. After consideration of the history of microwaves, and their position in the electromagnetic spectrum, we will examine the notions of polarization and dielectric loss. The orienting effects of the electric field, and the physical origin of dielectric loss will be analyzed, as will transfers between rotational states and vibrational states within condensed phases. A brief overview of thermodynamic and athermal effects will also be given. 

Considering the small rotations involved with the effects we have observed and considering the thermodynamic instability of the poled configuration, one wonders about the factors which stabilize... 

In addition to the above effects, the intermolecular interaction may affect polymer dynamics through the thermodynamic force. This force makes chains align parallel with each other, and retards the chain rotational diffusion. This slowing down in the isotropic solution is referred to as the pretransition effect. The thermodynamic force also governs the unique rheological behavior of liquid-crystalline solutions as will be explained in Sect. 9. For rodlike polymer solutions, Doi [100] treated the thermodynamic force effects by adding a self-consistent mean field or a molecular field Vscf (a) to the external field potential h in Eq. (40b). Using the second virial approximation (cf. Sect. 2), he formulated Vscf(a), as follows [4] ... 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

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