Distribution with Linear Chains

In the absence of LCB formation, r = t = 1/DP , and Equation 2.115 with i = 0 becomes Flory s most probable distribution for linear chains. 

A series of aliphatic polyesters, characterised by asymmetric oligomer distributions, heteroterminated linear chains, and cyclic oligomers, were studied using MALDI. Structural characterisation results were compared with those from fast atom bombardment mass spectrometry, electrospray ionisation mass spectrometry, NMR and end-group titration. MALDI molecular weight determination was contrasted with those from GPC and NMR. 23 refs. 

Because of the absence of chain limiter, the catalyst itself may initially act as the chain limiter (Fig. 8.22). The catalyst reacts with the olefinic regions of the polymer backbone and causes chain scission to occur, forming two new chains. The reactive carbene which is produced then moves from chain to chain, forming two new chains with each scission until the most probable molecular weight distribution is reached (Mw/Mn = 2), producing linear chains end capped with [Ru] catalyst residues. 

Table 1 shows the carbon chain distributions for several typical commercial alkylates. The carbon chain distributions for linear alkylbenzene (LAB) samples A, C, and E are determined by the distillation cut of n-paraffins used to make the LAB. LAB samples B and D represent blended alkylates made by mixing samples such as A and E in different ratios. This provides to the customer LAB products with a wide variety of molecular weights and improves the utilization of the fl-paraffin feedstocks. 

The Ziegler process produces linear alcohols with an even number of carbon atoms and is based on the polymerization of ethylene under catalytic conditions, generally with triethylaluminum as in the Alfol and the Ethyl processes. The distribution of alkyl chains depends on the version of the process employed but the alcohols obtained after fractionation can be equivalent to those obtained from fats and oils or have purpose-made distributions depending on the fractionation conditions. 

Figure 4. The solute-oxygen distribution function for a linear chain of cations in water (1 g/cm ) at 298 K, (a) single ion (b) chain of ions. Circles simulation solid lines polymer RISM. (Reproduced with permission from Ref. 8. Copyright 1987 North Holland Press.)...

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

---