Chain length maximum possible

The generated polysulfide dianions of different chain-lengths then establish a complex equilibrium mixture with all members up to the octasulfide at least see Eqs. (5) and (6). For this reason, it is not possible to separate the polysulfide dianions by ion chromatography [6]. The maximum possible chain-length can be estimated from the preparation of salts with these anions in various solvents (see above). However, since the reactions at Eqs. (22) and (23) are reversible and Sg precipitates from such solutions if the pH is lowered below a value of 6, the nonasulfide ion must be present also to generate the Sg molecules by the reverse of the reaction at Eq. (22). The latter reaction (precipitation of Sg on acidification) may be used for the gravimetric determination of polysulfides [11]. There is no evidence for the presence of monoprotonated polysulfide ions HS - in aqueous solutions [67, 72]. 

Aside from chemical composition and chain length the properties of macromo-lecular substances are substantially determined by the conformation and configuration of the individual macromolecules. Isolated macromolecules do not take up a precisely defined three-dimensional shape they rather assume a statistically most probable form which approximates to the state of maximum possible entropy. This is neither a compact sphere nor an extended rigid chain, but rather a more or less loose statistical coil (Fig. 1.7). 

Applying the phase rule, it is found that, in the two component system NaP03 + H20, a maximum of four phases is possible at the quadruple points 199,302). In addition to, at the most, two crystalline substances and water vapor, an amorphous glass-like phase is always present. This phase consists of mixtures of polyphosphates, the chain length of which rises with increasing temperature. Only Na2H2P207, Maddrell s salt (h) and trimetaphosphate occur as stable solid phases in addition to NaH2P04. 

We now have accurate values for the ratio kp2/2kt for a number of hydrocarbons, which fixes a maximum possible chain length (defined as the relative rates of Reactions 1 and 2)... 

With a number of assumptions regarding the enthalpy of this reaction and the maximum chain-length of the polymer another mathematical equation was derived which is applicable at all temperatures but yields a polymer concentration of only 10 % at 120 C in contradiction to all analytical data available at the time. In a supplementary publication by Gee et al. [66] the enthalpy of the ring addition reaction was reduced to 13.3 kJ mor and the reaction entropy assumed as 31 J mol K but novel results were not obtained. The authors discussed however the possibility that the sulfur melt may contain rings larger than Ss and that the polymer So present at temperatures below 159 °C may consist of very large rings rather than chains. 

The independence of the maximum adsorption (or the lowest possible area per molecule in the dense adsorption layer. smin = 5,) of the surfactant chain length can only be explained if we assume that as the adsorption values reach Tmax, the surfactant molecules are closely packed and oriented normal to the surface. Estimates of the limiting values of adsorption, Tmax b / R T, from the experimental a(c) dependencies, with the successive evaluation of minimum area per molecule, s, = 1/NA Tmax, for carboxylic acids, are -0.21 nm2, which agrees with the values established by other methods, e.g. by X- ray diffraction on surfactant crystals. 

Almost every other residue in this sequence is Gly and between them lie either Ala or Ser residues. This alternation allows the sheets to fit together and pack on top of one another in the manner shown in Figure 6.12. The arrangement results in a fiber that is strong and relatively inextensible, because the covalently bonded chains are stretched to nearly their maximum possible length. Yet the fibers are very flexible, because bonding between the sheets involves only the weak van der Waals interactions between the side chains, which provide little resistance to bending. 

---