Critical sequence length

This relationship shows that the amount of information that can be maintained in the form of a specific stable sequence is limited by the copying fidelity q. Thus the price that is paid for the global nature of the organization via variation is a limitation on the discrimination of fitness. Typical variations in fitness can only be selected for up to the critical sequence length since the fidelity of copying the whole sequence decreases exponentially with increasing sequence length. 

Figure 7.30 illustrates the limits from equilibrium to cold crystallization. They are based on a computer calculation for three-dimensional cold crystallization. It is assumed in this case that sequences of less than three A-units do not crystallize, and that at least two out of the four neighboring chains must match the sequence of three repeating units to make the central sequence crystalline. If all four lateral neighbors are crystalline, the repeating unit is in the interior of the crystal, if only three are crystalline, it is on the surface, and if only two are crystalline, it is part of an edge. With this critical sequence length and two surface free energies, experimental data of poly(ethylene terephthalate-co-sebacate) can be discussed, as is shown in Fig. 7.31. The experimental phase diagram of the same copolymer, but after slower cooling, is displayed in Fig. 7.26.

Figure 5.25 Time dependence of the half-width and vibrational frequency of the amorphous infrared band, the integrated intensity of the regular helical bands with the different critical sequence length (m), and the intensity of the toluene band evaluated for the solvent-induced crystallization process of a glassy syndiotactic polystyrene sample. Immediately after the injection of toluene, the half-width of the amorphous band increased, indicating an enhancement of thermal motion in the amorphous chains. This results in the formation and growth of regular helical segments [116,117].

This relationship was applied to analyze the crystallization data of six different sets of ethylene statistical copolymers [96]. In all cases, a linear relationship between logA// and logX was observed. Furthermore, the values of m determined for ethylene-olefin copolymers were found to be in the range of 6-13, in good agreement with the critical sequence length proposed by Randall and Ruff based on NMR data and modeling considerations [97]. 

Fig. 10.15 Plot of critical sequence length, f for coherent unimolecular surface nucleation against mol percent branch points of hydrogenated poly(butadiene), or similar random type copolymers. Vertical bars represent temperature intervals for isothermal crystallization of each copolymer.(3)...

In analysis of homopolymers the critical interpretation problems are calibration of retention time for molecular weight and allowance for the imperfect re >lution of the GPC. In copolymer analysis these interpretation problems remain but are ven added dimensions by the simultaneous presence of molecular weight distribution, copolymer composition distribution and monomer sequence length distribution. Since, the GPC usu y separates on the basis of "molecular size" in solution and not on the basB of any one of these particular properties, this means that at any retention time there can be distributions of all three. The usual GPC chromatogram then represents a r onse to the concentration of some avera of e h of these properties at each retention time. 

First of all, for this phenomenon to occur, it is necessary for at to be smaller than a0. If this condition is obeyed, the end-to-end distance of a sequence of it residues diminishes when those residues are converted from random-coil to helix, insofar as n is smaller than rtc = (a0/al)2. For the values of a0 and chosen for Fig. 11, the critical chain length nc is 223. At initial stages of a transition where fN is small, only short sequences of helix units will be present. 

Crystallization will take place to such an extent as to reduce the initial distribution to the equilibrium distribution and it can only occur at such lengths for which the initial distribution exceeds the equilibrium distribution. There thus exists at each temperature a critical chain length, c, the shortest sequence length that can crystallize at this particular temperature. 

The extent of crystallization at any sequence length is then o>°f - the difference between the initial and equilibrium distributions. The critical chain length is then given by the condition ... 

The critical chain length for the four-parameter model can be found in a similar manner to that used above. In this case, as discussed earlier (Equation 1), the probability P+( ) that a given sequence of + s is exactly of length is given by ... 

---