Chain theory

Appropriately, this was called the Folded Chain Theory and is illustrated in Fig. A.ll. There are several proposals to account for the co-existence of crystalline and amorphous regions in the latter theory. In one case, the structure is considered to be a totally crystalline phase with defects. These defects which include such features as dislocations, loose chain ends, imperfect folds, chain entanglements etc, are regarded as the diffuse (amorphous) regions viewed in X-ray diffraction studies. As an alternative it has been suggested that crystalline... 

Blomstrand-Jorgensen chain theory, 1, 6 Blood coagulation calcium, 6,591 Blood/brain barrier brain imaging techniques technetium complexes, 6, 991 technetium complexes, 6,985 Blood plasma... 

Chemists were convinced that all the chlorine atoms had to be bonded to the cobalt in some way, and since ammonia is a gas at room temperature they could not understand why the ammonia molecules did not evaporate away. One of the first proposed explanations was the chain theory, in which the ammonia... 

Similarly, Wei et al. [18] made analogous predictions of C < 0 using hypernetted-chain theory and incorporating molecular polarizability. However, the discussion was again restricted to the plausibility of negative C under -control. 

If we assume that those peculiarities of the toxin which cause their distribution are localized in a special group of the toxin molecules and the power of the organs and tissues to react with the toxin are localized in a special group of the protoplasm, we arrive at the basis of my side chain theory. The distributive groups of the toxin I call the haptophore group and the corresponding chemical organs of the protoplasm the receptor. . .. Toxic actions can only occur when receptors fitted to anchor the toxins are present. 

Bech-Larsen T and Grunert K G (1998), Integrating the theory of planned behaviour with means-end chain theory - A study of possible improvements in predictive ability , in Andersson P, Proceedings of the 27th EMAC Conference, Stockholm, 20-23 May, 305-314. 

The phenomenon of chemical induction was intensively studied by Jorissen [33-37]. He discovered that indigo was not oxidized by dioxygen but was simultaneously oxidized in the presence of oxidized triethylphosphine or benzaldehyde. He measured the factor of chemical induction in these reactions as equal to unity. Later, he proved that the oxidation product of benzaldehyde, benzoic peracid, did not oxidize indigo under conditions of experiment. This shows that a very active intermediate was formed during the oxidation of benzaldehyde and that it was not perbenzoic acid. Engler assumed peroxide to be in two forms, namely, an active moloxide A02 and a more stable peroxide. A new correct interpretation of chemical induction in oxidation reactions was provided later by the chain theory of oxidation of organic compounds (see later). 

The same structure was proposed later by Hock and Schrader [40]. It became clear only in 1939 when Criegee et al. [41] proved that peroxide formed by cyclohexene oxidation has the structure of hydroperoxide. Later studies, performed by Farmer and Sutton [42], greatly extended the number of hydroperoxides as products of olefin oxidation. Beginning from the later part of the 20th century, the chain theory of organic compound oxidation became the theoretical ground for the experimental study in this field. The main events of the development of oxidation chemistry before the chain theory of oxidation are presented in Table 1.1. 

Main Discoveries and Concepts in the Field of Oxidation by Dioxygen, Which Appeared before the Chain Theory [43-46]... 

DEVELOPMENT OF THE CHAIN THEORY OF OXIDATION OF ORGANIC COMPOUNDS... 

Chronological Table of the Main Concepts and Experimental Findings of Chain Theory of Hydrocarbon Oxidation... 

Cyclisation of polymer chains. Theory and experiment 64 Entropy changes for cyclisation reactions in solution 74... 

Markov chains theory provides a powerful tool for modeling several important processes in electrochemistry and electrochemical engineering, including electrode kinetics, anodic deposit formation and deposit dissolution processes, electrolyzer and electrochemical reactors performance and even reliability of warning devices and repair of failed cells. The way this can be done using the elegant Markov chains theory is described in lucid manner by Professor Thomas Fahidy in a concise chapter which gives to the reader only the absolutely necessary mathematics and is rich in practical examples. 

Grotthus chain theory phys chem An early theory used to explain the conductivity of an electrolyte. In which it was assumed that the cathode and anode attract hydrogen and oxygen respectively, and the molecules of the electrolyte are stretched out In chains between the electrodes, with decomposition occurring in molecules closest to the electrodes. grot-hus chan, the-3-re group CHEM I.Afamllyofelementswithsimilarchemical properties. 2. Acombina-tlon of bonded atoms that behave as a unit under certain conditions, for example. 

In some cases the main portion of the final products is formed by decomposition of peroxides. This is the current aspect of the classic Bach-Engler peroxide theory with respect to the chain theory of oxidation processes. 

Including mixed systems among the research on the mechanism of liquid-phase oxidation reactions aids subsequent development of the chain theory and undoubtedly contributes to practical chemistry. 

An alluring field of research is the mechanism of action of oxidation inhibitors. This research will undoubtedly yield in the near future a theory for inhibition of undesirable oxidation processes. The relatively stable free radicals observed on such inhibition display extremely interesting properties. Of great interest are the effects of synergism, of inhibitor mixtures, and of mixtures of inhibitors with catalysts. A strictly quantitative and elegant description of all these phenomena may be made within the scope of the chain theory for slow oxidation. 

Chain theory of reaction was applied to explain the reason for the extremely high number of molecules (up to 10 ) caused to react photochemically by only one quantum,... 

Explosion Limits Determination from a Unified Thermal and Chain Theory, In the paper of... 

Gray fit Yang (Ref 1), a mathematical model was proposed to unity the chain and thermal mechanisms of explosion. It was shown that the trajectories in the phase plane of the coupled energy and radical concentration equations of an explosive system will oive the time-dependent behavior of the system when the initial temperature and radical concentration are given. In the 2nd paper of the same investigators (Ref 2), a general equation for explosion limits (P—T relation) is derived from a unified thermal and chain theory and from chis equation, the criteria of explosion limits for either the pure chain or pure thermal theory can be deduced. For detailed discussion see Refs... 

Expln limits determination from a unified thermal and chain theory 6 E377... 

Figure 2. Types of constraint in the molecular theories. In the earliest such constraint theoiy (uppermost portion of the figure) the total effects of the constraints were placed on the cross-links themselves. In the subsequent constrained-chains theory, they were placed at the mass centers of the network chains and, in the diffused-constraints theory, along the entire network chains. The lowermost portion of the figure shows how additional experimental information could suggest a more refined placement of the constraints.

As already described, the upper three portions of Figure 2 summarize the differences in the way the constraints are applied in the constrained-junction theory, constrained-chain theory, and the diffused-constraints theory, respectively [4], Additional comparisons between theory and experiment for a variety of elastomeric properties should be very helpful [20], Also, neutron-scattering measurements conducted on series of networks having different values of the junction functionality , which is the number of chains emanating from a junction (cross-link), would be extremely useful in suggesting how to position the constraints along a chain in refining such models, since should have a pronounced effect on the... 

See, e.g., J.G. Kemeny and J.L. Snell, Finite Markov Chains (Van Nostrand, Princeton 1960) D.L. Isaacson and R.W. Madsen, Markov Chains, Theory and Applications (Wiley, New York 1976). 

We shall return to the discussion of this assumption in Chapter VI, which deals in detail with chain reactions. It may be stated here that it proves to be a not unreasonable one. Nevertheless the chain theory does not appear to be the general explanation of unimolecular changes. 

The chain theory can obviously provide a rate of activation great enough to account for any observed rate of reaction. With Lindemann s theory it is necessary that the normal rate of production of activated molecules by collision should be at least equal to and indeed considerably greater than the number of molecules undergoing chemical transformation in unit time. 

The chain theory is not possible for endothermic changes and indeed is only probable for exothermic reactions in which the heat of reaction is moderately great. Further, some rather marked effect of foreign gases on a chain reaction is rather to be expected, although it is by no means absolutely inevitable. 

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