Methods Of Statistical Thermodynamics Research Articles

Thermodynamic-like transformations in information theory

This article explores the application of thermodynamic and statistical thermodynamic formalism to information theory problems. In particular, the applicability of the transformation theory of thermodynamics is investigated. After a brief tutorial discussion of thermodynamic and statistical thermodynamic methods and concepts, their information theory analogues are developed. Besides information theory entropy, the information theory counterparts of temperature, chemical potential, Helmholtz free energy, etc., are developed and related to conventional information theory concepts such as channel capacity, matching of source and channel, etc. Information theory theorems are proved via the statistical thermodynamic analogue method; and, finally, several problems are formulated and solved using thermodynamic-like transformations. This article is aimed chiefly at bridging the interface between the two disciplines, and is intended to be provocative. Therefore, no attempt has been made to have it be all inclusive.

Thermodynamics of polymerization. Part IV. Free energy changes of binary copolymerization systems

AbstractUsing a statistical thermodynamic method we discuss the general shape of a free energy change versus composition curve for a binary copolymerization system. This simple theoretical approach gives reasonable agreement with the experimental results.

Thermochemistry of polymerization part III. Thermochemical aspects of propagation of polymerization

AbstractA statistical thermodynamic method of treating propagation of polymerization is developed. The effect of temperature on the sequence distribution of syndiotactic and isotactic units in free‐radical polymerization is discussed. This theory applies to the problem of probabilities of various possible modes of addition, namely head‐to‐head and head‐to‐tail addition, 1–2 and 1–4 addition, and formation of cis and trans configurations.

The thermodynamic characteristics of structural changes in water connected with the hydration of polyatomic and complex ions

On the basis of previously developed ideas [1] we have considered the thermodynamic characteristics of structural changes in water connected with the hydration of polyatomic and complex ions. We have shown that during the hydration of these ions, due to their rotation in the solution, there is an additional change in the structure of water compared with the case of monatornic ions of the same size and charge. It follows from the obtained data that for a large number of the ions considered there is negative hydration, ideas on which were developed by O. Ya. Samoilov. Previously [1] we studied the thermodynamic characteristics of strnctural changes in water connected with the hydration of rnonatomic ions. We showed that these changes could be characterized quantitatively by the quantity S AShydr is the change in entropy, during the hydration of monatomic ions; AS I is the change in entropy of an ion on transition from the gaseous state to solution. ASII characterizes the structural chan~es in water durinE the hydration of monatomic ions, due to their potential in solution. From this point of view it is of interest to consider the thermodynamic characteristics of structural changes in water connected with the hydration of polyatornic and complex ions. Polyatomic and complex ions exhibit other motions besides translational motion: rotational, vibrational, intraionie, etc. The entropy of the studied gaseous ions is made up of three components: translational (St), rotational (Sr) and vibrational (Sv). The electronic component of entropy can be taken equal to zero, since for most polyatomie gases the multiplet electron levels are absent. Providing there are sufficient data, each of these components can be calculated by methods of statistical thermodynamics [2-4]. Consequently, to solve the problem it is essential to find the peculiarities in the behavior of polyatomic and complex ions compared with monatomic ions in solution and their effect on the structure of water. In a previous communication [1], as the "true" entropy of a monatomic ion in an aqueous solution we took the entropy of an inert gas which had the same atomic weight and which was isoelectronic with it. This fact makes it possible to determine the quantity &SII, characterizing the structural changes in water during the hydration of monatomic ions, which is connected with the presence of an ion potential. The appearance of a charge on a particle in solution does not change its "true" entropy, since the electron component of entropy does not change. For polyatomie and complex ions in solution,the solution of the problem is somewhat more difficult. As for monatomie ions, the entropy of a polyatomic or complex ion in solution is conveniently taken to be the entropy of a neutral particle in solution, isoelectronic and isostructural to the considered ion,with the same molecular weight. This choice also makes it possible to separate the change in entropy connected with the structural changes in water during the hydration of polyatomic or complex ions from thatconneeted with the potential of the ions under consideration. Some of the features compared with monatomic ions, which are available here, will be considered later. We can therefore use equation (1) to calculate the change in entropy connected with structural changes in water during the hydration of polyatomic and complex ions,and that caused by their potential. The values of AShydr

Spectrophotometric and Partition Methods of Determining Association Constants of 1 :1 Charge-Transfer Complexes

The spectrophotometric method of determining the association constant of a complex AB when A, B, and the solvent have appreciable optical absorption is discussed, and the influence of the ratio of the concentrations of A and B examined. The formation of termolecular complexes such as A2B and of self-complexes such as A2 is found to affect the spectrophotometric method but not the partition method of determining association constants, whereas nonideality of the solutions affects both methods. The significance of the spectrophotometric method when applied to a completely general system including contact charge-transfer absorption is examined by means of Hill's statistical thermodynamic method of treating solutions. The results obtained are applied to three simple quasi-crystalline models. The experimental fact that spectrophotometric association constants are usually smaller than those determined by the partition method is shown to indicate that the attractive forces causing the formation of 1:1 complexes are probably not completely saturated in these complexes. In particular, for the extreme case in which the tendency of one side of an aromatic compound to complex formation is not affected by complex formation on its other side, it is shown that the spectrophotometric association constant would have only half the value found by the partition method. The experimental values in the literature for the association constants of a number of alkyl naphthalene-picric acid complexes are in good agreement with this view.

Thermodynamische Funktionen des gasförmigen 7Li19F

The values of free enthalpy, enthalpy, entropy, and heat content (calculated by the method of statistical thermodynamics for the state of an ideal gas at atmospheric pressure) are tabulated for temperatures from 273.16 to 3500 deg K. (J.S.R.)

Frenkel type defects and the melting of silver halide crystals

The author assumes that the melting of the crystals is connected with the passage of ions into interstitial positions. He introduces the assumption about the dependence of the energy of the crystal on the degree of order and from the above by the method of statistical thermodynamics he calculates the free energy of the crystal as a function of the temperature and a parameter characterizing the degree of order. By a discussion of the isotherms of the free energy he then obtains the melting temperature at which the degree of order changes suddenly. From this discontinuity the latent heat and the entropy can be determined. The calculated values are in good agreement with experiment.

On the Spin Wave Theory of Magnetic Susceptibility and Resonance Absorption in Antiferromagnetics

A theory of resonance absorption in antiferromagnetics based on the spin wave theory developed by Anderson and Kubo is presented The obtained resonance frequencies are given by two sharp ones, which are compared with the results of the classical theory by Nagamiya. In both cases the anisotropy energy has uniaxial symmetry. The absorption coefficient is also computed. Our calculations of the resonance frequencies are then extended to the antiferromagnetics having the anisotropy energy of ortho· rhombic symmetry. In the course of these calculations we obtained expressions for the magnetic susceptibility, using the obtained energy levels of the spin system which is subjected to a static magnetic field. They are in agreement with those which Kubo has dready given by use of the method of statistical thermodynamics.

On the Spin Wave Theory of Magnetic Susceptibility and Resonance Absorption in Antiferromagnetics

A theory of resonance absorption in antiferromagnetics based on the spin wave theory developed by Anderson and Kubo is presented. The obtained resonance frequencies are given by two sharp ones, which are compared with the results of the classical theory by Nagamiya. In both cases the anisotropy energy has uniaxial symmetry. The absorption coefficient is also computed. Our calculations of the resonance frequencies are then extended to the antiferromagnetic having the anisotropy energy of ortho-rhombic symmetry. In the course of these calculations we obtained expressions for the magnetic susceptibility, using the obtained energy levels of the spin system which is subjected to a static magnetic field. They are in agreement with those which Kubo has already given by use of the method of statistical thermodynamics.

Mechanisms of Sound Absorption in Fluids. II

A great many seemingly independent approaches to the problem of relaxation absorption in fluids have been made in the last thirty years. The purpose of this paper is to group similar methods together and to indicate the relations between the various approaches to the problems. The following four classifications may be helpful: (1) method of kinetic theory, (2) method of statistical thermodynamics, (3) method of irreversible thermodynamics, and (4) the phenomenological approach. Groupings similar to these appear in other problems in the field of chemical physics. The various methods, of course, do not compete, but complement each other. For some problems, the simultaneous use of various approaches brings fruitful results.

Mechanisms of Sound Absorption in Fluids

A survey has been made of the various mechanisms that have been suggested for the absorption of sound in fluids. These can be classified into two groups, viz., (1) viscosity absorption and (2) relaxation absorption. In the second group are included the effects of heat radiation, heat conduction, thermal relaxation, structural relaxation, and a more general type of relaxation proposed here. This last mechanism includes both thermal and structural relaxation as special cases. For mechanisms of the second group the expression relating the absorption coefficient and the velocity with the frequency can be derived by starting with the first law of thermodynamics and arriving at an acoustical equation of state. This transformation can be made without any special assumption as to the nature of the substance. The equation of state permits one to make a simple comparison of the various approaches to the problem. A study of the velocity and absorption as a function of frequency shows important differences between the two classifications. Thus the assumptions that the additional absorption in water (beyond the classical viscosity contribution) is due to structural relaxation (Hall) or dilatation viscosity (Eckart and Liebermann) are not precisely equivalent.

On the Retarding Field Current in Diodes

In a previous paper the authors have shown how the space charge distribution in plane and cylindrical diodes under retarding field conditions can be calculated by well-known methods of statistical thermodynamics, and have derived expressions for the upper limit of current for which this condition holds. In the present paper certain inaccuracies in the previous treatment are rectified, the argument is completed, and certain erroneous views, expressed in a recent paper by D. A. Bell, are criticized.

Distribution of Phases in Two-Phase Solids

The quasi-equilibrium distribution of a disperse phase, B, within a polycrystalline second phase, A, is investigated by methods of statistical thermodynamics. Phase B is assumed to consist of spherical particles of uniform size within the A crystals, and of lenticular particles of uniform size at the boundaries between two A crystals. The concentration (Mf) of B at the grain boundaries of A is found to be related to the sizes (r1 and r2) of the B particles at and away from grain boundaries, in terms of the interfacial energies (γaa and γba), the temperature (T), the over-all concentration (M), and the size of the A crystals (R), by (Mf1−Mf)(Mw1−Mw)−r13/r23=exp{−γaar12kT[9πZ−(9π/2)13(3Z3+2π)(r1/r2)3Z3−4π]},where w=1−2.66fr1R(Z−(π/3)Z−2)where Z=[2π(4(γba/γaa)+1)3(2(γba/γaa)−1]12. Temperature will significantly affect the distribution only if γaar12 is of the order of kT, or if γba/γaa∼½.

The caloric and thermal equation of state in quantum statistical mechanics

It is shown that in classical as well as in quantum mechanics the “dynamic” expressions for the caloric and thermal equations of state obtained with the method of quantum statistical mechanics are identical with the expressions obtained by the partition function method of statistical thermodynamics.