Elementary Molecular Theories

The statistical basis of diffusion requires arguments that may be familiar from kinetic molecular theory. Elementary concepts from the theory of random walks and its relation to diffusion form the third topic, which is covered in Section 2.6. As is well known, the random walk statistics can also be used for describing configurational statistics of macromolecules under some simplifying assumptions this is outlined in Section 2.7. 

This chapter treats the descriptions of the molecular events that lead to the kinetic phenomena that one observes in the laboratory. These events are referred to as the mechanism of the reaction. The chapter begins with definitions of the various terms that are basic to the concept of reaction mechanisms, indicates how elementary events may be combined to yield a description that is consistent with observed macroscopic phenomena, and discusses some of the techniques that may be used to elucidate the mechanism of a reaction. Finally, two basic molecular theories of chemical kinetics are discussed—the kinetic theory of gases and the transition state theory. The determination of a reaction mechanism is a much more complex problem than that of obtaining an accurate rate expression, and the well-educated chemical engineer should have a knowledge of and an appreciation for some of the techniques used in such studies. 

The cycle rank completely defines the connectivity of a network and is the only parameter that contributes to the elasticity of a network, as will be discussed further in the following section on elementary molecular theories. In several other studies, contributions from entanglements that are trapped during cross-linking are considered in addition to the chemical cross-links [23,24]. The trapped entanglement model is also discussed below. 

The basic postulate of elementary molecular theories of rubber elasticity states that the elastic free energy of a network is equal to the sum of the elastic free energies of the individual chains. In this section, the elasticity of the single chain is discussed first, followed by the elementary theory of elasticity of a network. Corrections to the theory coming from intermolecular correlations, which are not accounted for in the elementary theory, are discussed separately. 

The method by which this is done might ultimately be used to make a direct molecular theory for the forces on the elementary stress tetrahedron. 

Trimolecular reactions (also referred to as termolecular) involve elementary reactions where three distinct chemical entities combine to form an activated complex Trimolecular processes are usually third order, but the reverse relationship is not necessarily true. AU truly trior termolecular reactions studied so far have been gas-phase processes. Even so, these reactions are very rare in the gas-phase. They should be very unhkely in solution due, in part, to the relatively slow-rate of diffusion in solutions. See Molecularity Order Transition-State Theory Collision Theory Elementary Reactions... 

ELECTROSTATIO BOND ELECTROSTATIO SUREAOE POTENTIAL ELECTROSTRIOTION ELECTROTAXIS ELECTROVALENT BOND ELEMENTARY OHARGE ELEMENTARY REACTION Elementary reaction stoichiometry, MOLECULARITY CHEMICAL KINETICS UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION Element effect,... 

STOICHIOMETRIC NUMBER Stoichiometry of elementary reactions, CHEMICAL KINETICS MOLECULARITY UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION STOKE S SHIFT... 

It is noteworthy that Gibbs himself was acutely aware of the qualitative failures of 19th-century molecular theory (as revealed, for example, by erroneous classical predictions of heat capacities Sidebar 3.8). In the preface to his Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics (published in the last year of his life), Gibbs wrote ... 

The molecular theory of surface tension was dealt with by Laplace (1749-1827). But, as a result of the clarification of the nature, of intermolecular forces by quantum mechanics and of the more recent developments in the study of molecular distribution in liquids, the nature and value of surface tension have been better understood from a molecular viewpoint. Surface tension is closely associated with a sudden, but continuous change in the density from the value for bulk liquid to the value for die gaseous state in traversing the surface. See Fig. 2. As a result of this inhomogeneity, the stress across a strip parallel to the boundary—pu per unit area—is different from that across a strip perpendicular to die boundary—pr per unit area. This is in contrast with die case of homogeneous fluid in which the stress across any elementary plane has the same value regardless of the direction of die plane,... 

Although the material contained in this book concerns the theory of many-electron atoms and ions, its many ideas and methods (e.g., graphical methods, quasispin and isospin techniques, particle-hole formalism, etc.) are fairly universal and may be easily applied (or already are) to other domains of physics (nuclear theory, elementary particles, molecular, solid state physics, etc.). 

However, if it is known from kinetic or other evidence that a reaction M + N - Product is a simple elementary reaction, i.e., if it is known that its mechanism is simply the interaction between a molecule of M and a molecule of N, then the molecular theory of reaction rates predicts that the rate of this elementary step is proportional to the concentration of species M and the concentration of species N, i.e. it is second order overall. The reaction is also said to be bimolecular since two molecules are involved in the actual chemical transformation. 

Avogadro, A. 1811 Essay on a manner of determining the relative masses of the elementary molecules of bodies, and the proportions in which they enter into their compounds. J. de Physique 73, 58-76. (English edn Dalton, J. and others Foundations of the molecular theory. Edinburgh William Clay, Alembic Club Reprint no. 4 (1893).)... 

Sanchez I.C., R.H. Lacombe, "An Elementary Molecular Theory of Classical Fluids. Pure Fluids", J. Phvs. Chem.. 1976, 80(21),2352-2362. 

Lorenzo Romano Amadeo Carlo Avogadro, Essay on a Manner of Dermining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in Which They Enter Into These Compounds, Journal de Physique, de Chimie et d Histoire naturelle, vol. 73, (1811) 58. Translation from Alembic Club Reprints, No. 4, Foundations of the Molecular Theory Comprising Papers and Extracts by John Dalton, Joseph Louis Gay-Lussac, and Amadeo Avogadro, (1808-1811), available at dbhs.wvusd.kl2.ca.us/ webdocs/Chem-History/Avogadro.html. 

Sanchez, I.C. Lacombe, R.H. An elementary molecular theory of classical fluids. J. Phys. Chem. 1976, 80, 2352. 

The importance of the time parameter in the study of reactions is clear already in the early kinetic studies, where it takes the form of the inverse rate constant. From the point of view of fundamental chemical theory, elementary chemical reactions are simply the detailed dynamics of electrons and atomic nuclei that constitute the total molecular system of reacting species, which is governed by the time-dependent Schrddinger equation... 

The basic postulate of elementary molecular theories of rubber elasticity states that the elastic free energy of a network is equal to the sum of the elastic free... 

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