Branched molecules/polymers

In this model, derived originally for star-shaped branched molecules, polymer molecules are represented by beads connected by identical Hookean springs, and the decrease in viscosity with branching is expressed by the g1/2 rule. 

The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has v branches, it has v 2 chain ends if the branching is relatively low. Branched molecules are sometimes described as either combs or... 

The molecules used in the study described in Fig. 2.15 were model compounds characterized by a high degree of uniformity. When branching is encountered, it is generally in a far less uniform way. As a matter of fact, traces of impurities or random chain transfer during polymer preparation may result in a small amount of unsuspected branching in samples of ostensibly linear molecules. Such adventitious branched molecules can have an effect on viscosity which far exceeds their numerical abundance. It is quite possible that anomalous experimental results may be due to such effects. 

As the length and frequency of branches increase, they may ultimately reach from chain to chain. If all the chains are coimected together, a cross-linked or network polymer is formed. Cross-links may be built in during the polymerisation reaction by incorporation of sufficient tri- or higher functional monomers, or may be created chemically or by radiation between previously formed linear or branched molecules (curing or vulcanisation). Eor example, a Hquid epoxy (Table 1) oligomer (low molecular weight polymer) with a 6-8 is cured to a cross-linked soHd by reaction of the hydroxyl and... 

The UF-resin itself is formed in the acid condensation step, where the same high molar ratio as in the alkaline methylolation step is used (F/U = 1.8 to 2.5) the methylolureas, urea and the residual free formaldehyde react to form linear and partly branched molecules with medium and even higher molar masses, forming polydispersed UF-resins composed of oligomers and polymers of different molar m.asses. Molar ratios lower than approx. 1.7-1.8 during this acid condensation step might cause resin precipitation. 

The porous materials that offer the narrowest possible pore size distribution are those that have cylindrical pores of uniform diameter penetrating the entire medium without branching. Branching gives polymer molecules in the junctions extra conformational entropy. An agglomerate of tiny pieces of these porous materials, interlaced with larger voids (much larger than the pore size), should also be chosen. 

Dendrimers have distinctive properties, such as the ability to entrap small molecules in their core region and very low intrinsic viscosities in solution. Such properties require molecules to have achieved a particular size, and not all molecules with branches radiating from a core are large enough to develop the characteristic properties of true dendrimers. Branched molecules below this critical size are called dendrons and are the equivalent in dendrimer chemistry of oligomers in polymer chemistry. 

Percolation is widely observed in chemical systems. It was first recognized as a method to describe how small, branched molecules react to form polymers,... 

To examine the significance of this approximation further, it should be noted that a highly branched condensation polymer molecule, such as the one shown in Fig. 61, retains many unreacted functional groups which offer a number of opportunities for reaction between pairs on the same molecule. That intramolecular reaction between them proceeds to an appreciable degree in competition with intermolecular condensa-... 

A branched molecule obviously will extend over a smaller volume than would a linear one of the same molecular weight, or number of units. In other words, will be smaller for the nonlinear polymer of the same number n of equivalent elements. Hence it is convenient to write for a nonlinear polymer ... 

Theoretically, if each molecule in a polymer sample were to be linked to two of its neighbors, a single highly branched molecule would form that would encompass the whole sample. In practice, due to the statistical distribution of chain lengths and the random incorporation of crosslinks, the situation is far more complex. 

At the liquid nitrogen temperature, a lower molecular weight branched-chain polymer is obtained, which is believed to be produced in an additive ion-molecule chain reaction of the type... 

Star-shaped polymer molecules with long branches not only increase the viscosity in the molten state and the steady-state compliance, but the star polymers also decrease the rate of stress relaxation (and creep) compared to a linear polymer (169). The decrease in creep and relaxation rate of star-shaped molecules can be due to extra entanglements because of the many long branches, or the effect can be due to the suppression of reptation of the branches. Linear polymers can reptate, but the bulky center of the star and the different directions of the branch chains from the center make reptation difficult. 

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