Polymer molecule, number

N degree of polymerization of polymer molecules number of func-... 

Number of polymer molecules Number of lipid molecules... 

Begin by recognizing that a molecule containing x of the head-to-head links will be cleaved into x + 1 molecules upon reaction. Hence if N is the number of polymer molecules in a sample of mass w, the following relations apply before and after cleavage = (x l)Nj, or w/M = (x + l)(w/Mj,). Solving for x and... 

Dividing both sides of Eq. (6.58) by [M-], the total radical concentration, gives the number fraction of n-mer radicals in the total radical population. This ratio is the same as the number of n-mers in the sample containing a total of N (no subscript) polymer molecules ... 

Since the total number of polymer chains is proportional to [B"]o, the number of n-mers in a population of N polymer molecules is given b>... 

We assign an index number to each of the polymer molecules and pick up the analysis of the problem after i polymer molecules have already been placed on an otherwise empty lattice. Our first question, then, concerns the number of ways the (i + l)th polymer molecule can be placed in the lattice. The polymer is to be positioned one repeat unit at a time, so it is an easy matter to count the number of available positions for the first segment of the (i + l)th molecule. Since the total lattice consists of N sites and ni of these are already occupied, the first segment of the (i + l)th molecule can be placed on any one of the N - ni remaining sites. 

The total number of ways of placing N polymer molecules in the lattice is given by the product of factors like these, one for each molecule ... 

We are most often concerned with solutions which are dilute with respect to polymer. This means that nj Vj polymer molecule is so much greater than that of the solvent, the disparity in the number of moles is even more extreme than for the same approximation applied to compounds of comparably sized molecules. Since the approximation Xj = n2/(ni -I- n2) = nj/nj apphes to dilute solutions, we can write... 

A number of materials exist which neither attack the polymer molecule chemically nor dissolve it but which cannot be used because they cause cracking of fabricated parts. It is likely that the reason for this is that such media have sufficient solvent action to soften the surface of the part to such a degree that the frozen-in stresses tend to be released but with consequent cracking of the surface. 

A polymer is made up of a large number of small molecular units, called monomers, combined together chemically. A typical polymer molecule contains a chain of monomers several thousand units long. The monomer units of which a given polymer is composed may be the same or different. 

Only one polymer molecule is produced per mole of inhibitor. The inhibitor must be at least equimolar with the number of chains formed. Concentrations must be chosen (usually very low) to give the desired molecular weight. 

Even in the absence of flow, a polymer molecule in solution is in a state of continual motion set forth by the thermal energy of the system. Rotation around any single bond of the backbone in a flexible polymer chain will induce a change in conformation. For a polyethylene molecule having (n + 1) methylene groups connected by n C — C links, the total number of available conformations increases as 3°. With the number n encompassing the range of 105 and beyond, the number of accessible conformations becomes enormous and the shape of the polymers can only be usefully described statistically. 

The size of a polymer molecule may be defined either by its mass (see Chapter 6) or by the number of repeat units in the molecule. This latter indicator of size is called the degree of polymerisation, DP. The relative molar mass of the polymer is thus the product of the relative molar mass of the repeat unit and the DP. 

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