Theory, association

Each author has provided an introduction that serves to initiate the reader into the topic. Where appropriate, a brief exposition of associated theory is presented, but the essence of each chapter lies in the practical examples used to illustrate each topic. It is anticipated that even though the range of presented examples is not necessarily comprehensive, sufficient information is given to allow the reader to understand the strengths, advantages, and limitations of each technique. It is important that workers in the field have a good feel for what a given method cannot yield, as well as what it can provide. 

In solution theory the specialized distribution functions of this kind should appear in the theory of ion pairs in ionic solutions, and a form of the Bjerrum-Fuoss ionic association theory adapted to a discrete lattice is generally used for the treatment of the complexes in ionic crystals mentioned above. In fact, the above equation is not used in this treatment. Comparison of the two procedures is made in Section VI-D. 

Fig. 9. Logarithm of the cation activity coefficient versus the square root of the concentration for the system of manganese ions and cation vacancies in sodium chloride at 500°C. Filled-in circles represent the association theory with Rq = 2a, and open circles the association theory with R = 6/2. Crosses represent the present theory with cycle diagrams plus diagrams of two vertices, and triangles represent the same but with triangle diagram contributions added.

Fig. 10. The degree of association into nearest- and next-nearest-neighbour complexes, p, versus concentration, c, at 500°C for manganese ions and cation vacancies in sodium chloride. Filled circles represent the simple association theory, open circles the Lidiard association theory, and crosses the present theory using Eq. (173) when the first term only has been retained in the virial appearing in the equation for the defect distribution function (Eq. (168)). The point of highest concentration represented by a cross may be in error due to the neglect of higher terms in the virial series, and the dotted curve has not been extended to include it.

In the terminology of association theory p is the degree of association into complexes which have been defined to include excited states up to a separation of < -th nearest neighbours (cf. Section VI-A). The result for nearest-neighbour association in the limit of zero concentration is similar to, but not quite identical with,... 

Each factor in square brackets arises from an exclusion factor, E, in the defining equation for the distribution function G, Eq. (170). The factor (1 — 1/ ) by which the result differs from the simple association theory arises from the term in square brackets in Eq. (172) and has already been commented on. 

For simplicity we consider only the continuum limit (i.e. Mayer ionic solution theory). The last equation allows us to calculate the value of p which the association theory should predict in order to be compatible with the true value, which we assume to be given by the Mayer theory in the range considered. It is... 

The trial-by-fire methods of science, however, sidetracked the linear development of high polymer theory, for the theory was swept up by the development of the association theory of collodal particles at about the turn of the century. The peculiar and hard to understand chemical and physical behavior of polymers had, on occasions, lead to the suggestion that unusual or special forces were involved in their formation. In order to explain the forces, workers turned to the work of Thomas Graham. 

Thus in 1899, Johannes Thiele extended his valence theory of double bonds to include colloids. Thiele suggested that in such materials as polystyrene the molecules of styrene were bound together merely by association of the double bonds. He referred to this association as "partial valence" (21). In 1901, Rohm concluded that the transformation of acrylic esters into polymers was from an "allotropic alteration" and not a chemical reaction (22). Schroeter, working with salicylides just as Kraut, Schiff, and Klepl before him, concluded that the tetrameric salicylide was formed by "external forces about the monomeric molecules", and that the chemical structures of the monomers were unaltered (23). Thus the association theory rapidly grew in popularity. 

In support of the association theory, colloid chemists cited non-reproduceable cryoscopic molecular weight determinations (which were eventually shown to be caused by errors in technique) and claimed that the ordinary laws of chemistry were not applicable to matter in the colloid state. The latter claim was based, not completely without merit, on the ascerta-tion that the colloid particles are large aggregates of molecules, and thus not accessible to chemical reactants. After all many natural colloids were shown to form double electrical layers and adsorb ions, thus they were "autoregulative" by action of their "surface field" (29). Furthermore, colloidal solutions were known to have abnormally high solution viscosities and abnormally low osmotic pressures. 

The rapid acceptance of the association theory was accompanied by an equally rapid dropping of the high molecular weight or polymer concept. Olby (31) has stated that three developments made the theory attractive as an explaination for the behavior of polymers. First, he sates, was Alfred Werner s introduction of the concept of two kinds of combining forces—Hauptvalenzen or primary valence forces, and Nebenvalenzen or secondary forces (32). When applied to cellulose, proteins, or rubber, the mole-... 

The third development was the seeming experimental support of the association theory by X-ray crystallography. This support was based on the then accepted idea that the molecular cannot be larger than the unit cell of the crystal. Although it is obvious to us that this is untrue, the idea was then "obviously true". 

Yet, even as the association theory was at the peak of its acceptance, the pieces to a generally accepted, high molecular weight model were being formed. (Unable to resist the temptation) the high molecular weight concept bounced back with the work of Carl Harries in 1904. 

Up until Staudinger entered the field most polymer preparations were isolated events. As examples, in 1872 Baumann described the preparation of an insoluble mass when vinyl chloride was exposed to sunlight (43) just as Simon had formed a jelly of styrene in 1839 (44). Staudinger, however, systematically prepared the materials and studied their preparation as well as properties. By 1920, he was convinced the association theory was incorrect. 

Fredga was doubtlessly referring to the conflict between the advocates of the association theory and those who supported the long chain concept. The conflict of ideas came to a head in the period 1925 to 1930. In this period the respective protagonists presented their ideas in two important conferences and several decisive papers. By the end of this period resistance to the macromolecular viewpoint was reduced to a few holdouts, but resolution of the facts, as Fredga indicated, did not come easily. 

At the same time K. H. Meyer and Mark (69) proposed an important structure for cellulose which is best described as a compromise between the aggregates of the association theory and Standinger s macromolecules. In an extensive paper, they carefully developed the idea of cellulose chains consisting of so called "primary valence chains". They further proposed that the primary valence chains were aggregated by molecular forces such as hydrogen bonding and van der Waal s forces. 

Even the champions of the long chain aspect did not agree with each other, as they easily could have done because instead of concentrating on the essential principle, they disagreed in specific details and, at certain occasions, they argued with each other more vigorously than with the defenders of the association theory. (48)... 

The symposium was held on September 23, 1926, in Dusseldorf. It was a classic showdown between association theory constituents, M. Bergmann and H. Pringsheim supported by E. Waldschmidt-Leitz, and Staudinger. Mark was invited by Chairman Willstaetter at the prompting of his close friend F. 

Their model is a compromise between the association theory and Staudinger s macromolecules. 

Staudinger disagreed with Meyer and Mark only on two points. He believed their estimate of the main chains was too short and denied the existence of micelles. These differences were slight, and as Priesner reports (27), there was interest on both sides for an extensive exchange of ideas. While differing on these points, both concepts were substantially different from those of the association theory advocates. 

Mixtures of diastereomers of 2,4,6-trlphenylheptane are epimerized. The mole fractions olisotactic, heterotactic, and syndiotactic isomers at equilibrium at 343 K are 0.217, 0.499, and 0.284, respectively. There results are interpreted according to the theory of stereochemical equilibrium. The theory of equilibria between isomers and the associated theory of the conformer populations for each isomer provide a mutually consistent interpretation of the two kinds of results, the same arbitrary parameters being used for both. Stereochemical equilibria and conformer population calculated for PS for the same parameters differ considerably from those for the oligomers. 

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