Affinity theory

Durrans in 1919 attempted to develop a theory based on the examination of the odours of substances considered class by class, and expressed the opinion that, from a chemical point of view, odour is caused primarily by the presence of unsatisfied or residual afiinity, but that the possession or otherwise of an odour by a body depends on physiological and physical as well as chemical properties. This theory, which is named the Residual Affinity Theory of Odour, demands that if a substance has an odour, it must answer to the following requirements — ... 

The second of the premises of the residual affinity theory has already been dealt with here, the third is obvious, it remains therefore onlj to consider the first. 

The effect of a particular element on the odour of its compound seems also to lend support to the residual affinity theory, for it is only the elements which possess residual affinity in certain of their compounds, which function as osmophores. Oxygen, nitrogen, sulphur, phosphorous, halogens, arsenic, antimony, bismuth, etc., whose valencies vary under certain conditions are powerfully osmophoric whereas carbon, hydrogen, and many others which have a constant valency are practically non-osmophoric, and it is very instructive to note that the element is osmophoric when it is not employing its full number of valencies and therefore has free affinity. 

Comparison with Statistical Theory, Small-strain Behaviour. Calculations of theoretical moduli, using the phantom theory and the affine theory as limiting cases, were carried out in order to compare the theoretical predictions with values found experimentally (Table IV). 

Our results tend to approach the affine theory with increasing z. That means, that the fluctuationsof crosslinks are more and more restricted, the reason for this being the change in microstructure. (This is quite different from the strain dependent restriction of fluctuations as predicted by Flory s recent theory.)... 

Comparison with Statistical Theory at Moderate Strains. So far we have shown, that a transition between the two limiting classical theories, i.e. affine theory and phantom theory, is possible by a suitable choice of the network microstructure. This argument goes beyond the revised theory by Ronca and Allegra and by Flory, which predicts such a transition as a result of increasing strain, thus explaining the experimentally observed strain dependence of the reduced stress. 

For chemists, the problem of affinity, or what Meyer called variable valence, was the central problem of chemistry, one in which, Ostwald claimed, chemists made no progress while seeking to measure chemical "forces." Meyer, who often is identified with the tradition of physical chemistry and theoretical chemistry, as noted in chapter 3, was confident that the answer to affinity lay in theories of motion, not in species or types, just as Nemst later was to identify the end of affinity theory with its reduction to physical causes. 

Figure 1. Stress relaxation curves for three different extension ratios. Uncross-linked high-vinyl polybutadiene with a weight average molecular weight of 2 million and a reference temperature of 283 K. G is the apparent rubber elasticity modulus calculated from classical affine theory. (Solid line is data from Ref. 1).

By this means the theory of the underlying space may be reduced to the simultaneous affine geometry of this set of affine spaces. The tensors provide a suitable aid for treatment of this simultaneous-affine theory. As first example we take contravariant vectors or contravariant tensors of first rank. That is a geometrical object that contains four components in each coordinate system... 

Correspondingly, the same law and formulae, as in affine theory, also serve for the projective differentiation of a completely general tensor. There are admittedly still further laws, not available in affine theory because they depend on the speciaf nature of a gauge transformation. We shall develop such laws only when we need them. 

We now have to show that the integrability conditions are in fact met in the case of projective geometry. The functions II have the form (7). From that one infers the existence of (12). The condition (13) can be verified by an elementary calculation based on (7). The considerations are however exactly the same as in affine theory so that we know immediately that the integrability conditions are necessary. 

It follows from the five-dimensional affine theory that (4) is invariant against particular transformations and from that also follows the invariance of the four-dimensional equations (6). These equations only depend on the functions n and on the curve in the parameter presentation (2) and not on (3). 

As in affine theory it is seen how to define the projective displacement of a hyperplane i aA" = 0 by the differential equations... 

As in affine theory one can also define a curvature tensor for the connection r. By contraction one obtains an analog of the Ricci tensor ... 

There is some debate about the affinity of proteins to hydrophobic surfaces. Some authors sustain the hydrophobic affinity theory [36], while others prefer the hydrophilic affinity theory [37]. The results obtained from studies carried out with culture medium supplemented with 10% fetal calf serum (PCS) suggested that the complex mixture of proteins present in PCS presented a higher affinity for the hydrophiUc surfaces. Furthermore, the Wa values suggested that the mixture of proteins adsorbed better on hydrophiUc surfaces, though the type of protein and their adsorption speed onto the surfaces is still unknown. However, the use of dynamic contact angle techniques (as has been confirmed with other materials) could help identify the velocity of adsorption and the munber of steps of adsorption, desorption, and/or ad-sorption/desorption that lead to the final interaction between the substrate and the proteins in the culture medium (Fig. 4). The contact angles obtained for the two different fluids are shown in Table 5. 

Fig. 6.4 (a) Width of the recovery window [63], and (b) relaxed creep modulus at 92.3°C. Also shown (dashed line) is the relaxed modulus predicted by the affine theory of rubber elasticity. Symbols are as in Fig. 6.3 [63, 377]... 

Fig. 6.4(b) shows the results of these calculations plotted versus crosslink density, together with the classical prediction from the affine theory of rubber elasticity = iNcksT where Nc is the number density of chains. It is clear there is approximate agreement with the theory (to within a factor 2), but there is also significant influence of chemical composition. In particular it is interesting to note the order of stiffness for polymers based on the three DIs MDI>DBDI>TDI. This reflects the relative intrinsic stiffness of the DI groups. 

What Taylor s accoimt reveals, in contrast to mainstream historical interpretations, is that affinity theory constimted the fundamental core of 18th century chemistry, thus standing as a definitive theory in its own right. Taylor relates this claim to the widespread presence of affinity tables and their indispensable role as... 

On the other hand, the generative power of affinity tables is evident in the fact that they were constantly amended and refined, often in light of empirical, tacit and extra-theoretical assumptions. The flexibility of affinity theory, evidenced by the variations upon affinity tables and their diverse uses, was the key to its success. More importantly, this supports the role of affinity theory in the disciplinary development of chemistry as a whole. Affinity had both explanatory and heuristic power, and its pedagogical applications through affinity tables allowed it to be used as an undisputed instmment of the greatest utility, as well as an object of scientific inquiry in its own right. 

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