Critical chain length

We saw in Sec. 2.9 that the viscosity of a bulk polymer is proportional to M, where a is either 1.0 or 3.4, depending on whether the polymer is below or above, respectively, the critical chain length for entanglement. For solutions, a similar result is obtained, only it is [r ] rather than r itself which is proportional to M ... 

This step is termed nucleation and leads to the formation of primary particles. The nuclei, the smallest particles formed in the nucleation step, are considered to be formed by aggregation of growing polymer chains precipitating from solution as they exceed their critical chain length. 

Coran and Patel [33] selected a series of TPEs based on different rubbers and thermoplastics. Three types of rubbers EPDM, ethylene vinyl acetate (EVA), and nitrile (NBR) were selected and the plastics include PP, PS, styrene acrylonitrile (SAN), and PA. It was shown that the ultimate mechanical properties such as stress at break, elongation, and the elastic recovery of these dynamically cured blends increased with the similarity of the rubber and plastic in respect to the critical surface tension for wetting and with the crystallinity of the plastic phase. Critical chain length of the rubber molecule, crystallinity of the hard phase (plastic), and the surface energy are a few of the parameters used in the analysis. Better results are obtained with a crystalline plastic material when the entanglement molecular length of the... 

In applying equation (l) Cardenas and 0 Driscoll use Xq as the critical chain length for chain entanglement and permit Xq to decrease as ( )p increases during the polymerization according to equation (l). Therefore, during the course of polymerization they note three kinds of termination reactions ... 

Applying the heUx coil theory to computational studies of the mPE backbone suggests that above a critical chain length of seven or eight repeat units the backbone can adopt a helical structure. The attachment of additional monomer units would further stabihze the helical structure and increase the cooperativity of the folding reaction [23]. 

Fig. 38 General mechanism of the nucleation and elongation stages of polymerization generating a helical structure (the arrows represent the interactions among repeating units). Secondary interactions light arrows), absent in the first turn of the helix, are the molecular origins of a less favorable nucleation event (i.e.,the critical chain length) beyond which propagation becomes more favorable...

Above the critical chain length, where both the friction and entanglement are important, the relationship is ... 

The critical chain length is often the onset of strength -related properties and is generally considered the lower end for useful mechanical properties. The Z value for polymers varies but is typically between 200 and 1000 units in length. For instance, the Z value for PS is about 700 for PIB about 600 for poly(decamethylene sebacate) about 300 for PMMA about 200 and for poly(dimethyl siloxane) about 1000. 

PEGs also showed enhanced stability similar to that of ph-PEG. PEG containing hydroquinone substitutions showed a decrease in critical chain length but again not as drastically as the naph-PEG because the bulky hydrophobic group on the hydroquinone is in the middle of the chain while that of the 1-naphthol is on the end of the chain. Thus the effects of hydrophobic interactions have been shown to be a universal stabilizing factor in interpolymer complexation. 

They said that a comb polymer with very short branches would not fulfil condition 1, and a star polymer would not fulfil condition 2 unless the branches were very much longer than the critical chain length but polymers having relatively few but long branches, especially ramified or tree-like structures, should fulfil these conditions. Subsequent work, summarised in Section 5, has largely borne out their predictions, though no quantitative treatment is yet available. 

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. 

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