Polymer degree of polymerization

Let us first consider two identical polymers, one deuterated and the other not, in a melt or a glassy state. The two polymers (degree of polymerization d) differ from each other only by scadermg lengths and b. If the total number of molecules is N, x is the volume fraction of the deuterated species x = N- / N, with Aq -t = A). According to equation (B1.9.116), we obtain... 

The other highly important feature of the polymerizations of this monomer is that they proceed with little if any termination and, perhaps more importantly, with little transfer. As a result, polymer degrees of polymerization approach closely to the theoretical value dictated by the molar ratio of monomer to catalyst and encourage the idea that by suitable substitution of the monomer it may yet be possible to arrive at a truly living carbocationic polymerization of an olefin. 

One final area for discussion is the use of NMR for the determination of polymer number average molecular weights. End group resonances were clearly visible in the 13c NMR spectrum of the ethylene-l-hexene copolymer in Figure 3. An opportunity to determine polymer degrees of polymerization or number average molecular weights should not be overlooked. 

Construct a graph of the molar entropy of mixing AS IR vs. volume fraction for a polymer solution where the polymer degree of polymerization Zj = 10 and 1000. You should do this by plotting AS IR values starting... 

In addition to the effect of the pack itself, there is the pattern of behavior experienced in spinning operations. At times in industry, high pack pressure occurs without a related change in polymer degree of polymerization, inhomo-... 

Initially the name and general information for a given fiber is set forth followed by an outline of the stmctural properties, including information about chemical structure of the polymer, degree of polymerization, and arrangement of molecular chains within the fiber. Physical properties... 

CHR) , formed, e g. from the reaction of diazomethane and alcohols or hydroxylamine derivatives in the presence of boron compounds or with metal compounds. Poly-methylene is formally the same as polyethene and the properties of the various polymers depend upon the degree of polymerization and the stereochemistry. 

The second category of polymerization reactions does not involve a chain reaction and is divided into two groups poly addition and poly condensation [4]. In botli reactions, tire growth of a polymer chains proceeds by reactions between molecules of all degrees of polymerization. In polycondensations a low-molecular-weight product L is eliminated, while polyadditions occur witliout elimination ... 

The reaction conditions can be varied so that only one of those monomers is formed. 1-Hydroxy-methylurea and l,3-bis(hydroxymethyl)urea condense in the presence of an acid catalyst to produce urea formaldehyde resins. A wide variety of resins can be obtained by careful selection of the pH, reaction temperature, reactant ratio, amino monomer, and degree of polymerization. If the reaction is carried far enough, an infusible polymer network is produced. 

The degree of polymerization of a polymer is simply the number of repeat units in a molecule. The degree of polymerization n is given by the ratio of the molecular weight of the polymer to the molecular weight of the repeat unit ... 

We began this section with an inquiry into how to define the size of a polymer molecule. In addition to the molecular weight or the degree of polymerization, some linear dimension which characterizes the molecule could also be used for this purpose. For purposes of orientation, let us again consider a hydrocarbon molecule stretched out to its full length but without any bond distortion. There are several features to note about this situation ... 

The high molecular weight of a polymer is one of the most immediate consequences of the chain structure of these molecules. As indicated in Sec. 1.2, it is also the basis for describing the size of the polymer molecule, either directly or through the degree of polymerization. Most methods for the determination... 

For polymers in which the degree of polymerization is large-a condition already assumed by the use of Eq. (1.48)-the remaining summations may be replaced by integrals... 

Figure 2.10 shows a plot of viscosity versus degree of polymerization for several polymers. Several things should be observed about this graph ... 

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 ... 

By line 5, the reaction has reached 80% completion and the number average value of the degree of polymerization is 5. Although we have considered this slowly evolving polymer in terms of the extent of reaction, another question starts to be worrisome How long is this going to take ... 

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