Chain increment method

Spyriouni, T. Economou, I.G. Theodorou, D.N. Thermodynamics of chain fluids from atomistic simulation a test of the chain increment method for chemical potential. Macromolecules 1997, 30, 4744—4755. 

Carnahan-Starling fluid 67 Cavitation 38 Chain contraction 21 Chain increment method 16 Chemical potential 202 Chi parameter 236, 242 Closure 220-225, 236 atomic 220... 

Table 4.1 lists values of as well as AH and ASf per mole of repeat units for several polymers. A variety of experiments and methods of analysis have been used to evaluate these data, and because of an assortment of experimental and theoretical approximations, the values should be regarded as approximate. We assume s T . In general, both AH and ASf may be broken into contributions Ho and So which are independent of molecular weight and increments AHf and ASf for each repeat unit in the chain. Therefore AHf = Hq + n AHf j, where n is the degree of polymerization. In the limit of n AHf = n AHf j and ASf = n ASf j, so T = AHf j/ASf j. The values of AHf j and ASf j in Table 4.1 are expressed per mole of repeat units on this basis. Since no simple trends exist within these data, the entries in Table 4.1 appear in numbered sets, and some observations concerning these sets are listed here ... 

If the poorer solvent is added incrementally to a system which is poly-disperse with respect to molecular weight, the phase separation affects molecules of larger n, while shorter chains are more uniformly distributed. These ideas constitute the basis for one method of polymer fractionation. We shall develop this topic in more detail in the next section. 

Using these assumptions the computer then calculates the sequential results of a large number of exposure increments on a chain 200 nucleotides long. The result is called a case history. Several hundred case histories are then averaged, and the cumulated number of hydrates and dimers and unreacted sites per chain are averaged as functions of exposure. Several comparisons of experimental results with expectations calculated by this method will be given below. 

Figure 48-5 Chimney construction-Jump-form technique. The jump-form technique of concrete chimney construction has been in use since the turn of the century and has been refined to a remarkably efficient construction method. Specially designed steel forms are raised in regular increments for each pour. The forms are raised by the crew using chain falls connected to overhead beams on the derrick—a structure that incorporates a work deck and is hung by cables from the inside of the concrete chimney. For each new pour, the derrick is raised using chain falls and reattached by cables to the concrete structure. Then the outside forms are raised, as one piece. Reinforcing steel is secured and the Inside forms are raised, again as one piece. After alignment and plumb are checked, the concrete is poured. Taper and wall thickness are adjusted by changing the circumference of the forms.

H2 addition is different from other methods of chain termination. For example, when the reaction temperature is raised, the termination rate is multiplied by some factor, which is determined by the activation energy. If the responses of all the sites are approximately the same, the MW distribution is shifted intact to lower MW, without distortion. (To understand why, note that the GPC curve is plotted on a logarithmic MW scale, and the multiplication of the various termination rates by a constant factor amounts to an additive shift across the MW distribution.) However, when H2 is added to the reactor, a new termination pathway is opened, adding to the overall termination rate. If each site is affected equally, then a constant increment is added to the termination rate at each site, which means that the MW distribution should be distorted. High-MW sites should respond proportionately more than the others. 

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