Polymerization degree of

The size of a polymeric molecule can be described by its degree of polymerization, n, which is the number of monomeric units linked together in the polymer chain. The degree of polymerization relates to the molecular mass of the polymer and the monomer as follows  

What is the degree of polymerization of a PE sample with a molar mass of 280,000 daltons  

Molar mass of ethylene = 28 daltons (or g/mol) n = 280,000 daltons/28 daltons = 10,000 

Typical values of n for plastics are in the range of 4000-100,000 monomeric units. 

Calculate the molecular mass of a sample of poly(vlnyl chloride) (PVC) with degree of polymerization n = 1.5 x 104. 

This term refers to the number of repeating units that constitute a polymer molecule. We shall use the abbreviation DP for the degree of polymerization defined in this way. The subscript n used on the parentheses in the foregoing structural formulas for polymers represents this DP. The relation between degree of polymerization and molecular weight M of the same macromolecule is given by 

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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. 

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 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 mean monomer density decreases with the increasing degree of polymerization. 

It is not possible to apply (C2.1.1) down to the level of monomers and replace by the degree of polymerization N and f by the sum of the squares of the bond lengths in the monomer because the chemical constitution imposes some stiffness to the chain on the length scale of a few monomer units. This effect is accounted for by introducing the characteristic ratio defined as C- — The characteristic ratio can be detennined... 

In homopolymers all tire constituents (monomers) are identical, and hence tire interactions between tire monomers and between tire monomers and tire solvent have the same functional fonn. To describe tire shapes of a homopolymer (in the limit of large molecular weight) it is sufficient to model tire chain as a sequence of connected beads. Such a model can be used to describe tire shapes tliat a chain can adopt in various solvent conditions. A measure of shape is tire dimension of tire chain as a function of the degree of polymerization, N. If N is large tlien tire precise chemical details do not affect tire way tire size scales witli N [10]. In such a description a homopolymer is characterized in tenns of a single parameter tliat essentially characterizes tire effective interaction between tire beads, which is obtained by integrating over tire solvent coordinates. 

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 ... 

Note that the average weight per repeat unit could be used to evaluate the overall degree of polymerization of this terpolymer. For example, if the molecular weight were 43,000, the corresponding degree of polymerization would be... 

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... 

As should be expected, both (fg ) and r show the same dependence on the degree of polymerization or molecular weight. Since the radius of gyration can be determined experimentally through the measurement of viscosity or light scattering, it is through this quantity that we shall approach the evaluation of 1. 

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

Figure 2.10 is drawn on log-log coordinates more than two orders of magnitude in degree of polymerization are covered. 

The family of curves consist of two straight-line portions, with a change of slope occurring at a degree of polymerization in the range 10 -10. ... 

It should be noted that a log-log plot condenses the data considerably and that the transition between a first-power and a 3.4-power dependence occurs over a modest range rather than at a precise cutoff. Nevertheless, the transition is read from the intersection of two lines and is identified as occurring at a degree of polymerization or molecular weight designated n, or, respectively. 

By analogy with Eq. (2.47), we write the force of viscous resistance experienced by a molecule in an array of uniform molecules of degree of polymerization n as... 

This simple derivation gives us the desired result, a relationship between the relaxation time and the degree of polymerization ... 

Aside from the side chains, the movement of the backbone along the main reptation tube is still given by Eq. (2.67). With the side chains taken into account, the diffusion velocity must be decreased by multiplying by the probability of the side-chain relocation. Since the diffusion velocity is inversely proportional to r, Eq. (2.67) must be divided by Eq. (2.69) to give the relaxation time for a chain of degree of polymerization n carrying side chains of degree of polymerization n ... 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

Equation (1.41) gives the probability of finding one end of a chain with degree of polymerization n in a volume element dx dy dz located at x, y, and z if the other end of the chain is located at the origin. We can use this relationship to describe the unstretched chain shown in Fig. 3.2a all that is required is to replace n by n, the degree of polymerization of the subchain. Therefore for the unstretched chain (subscript u) we write... 

The degree of polymerization of the subchain is n. If the degree of polymerization of the molecule as a whole is n, then there are n/n subchains per molecule. We symbolize the number of subchains per molecule as N. Other properties of the subchain-which, incidentally, should not be confused with the chains between crosslink points in elastomers-will also have the subscript s as they emerge. 

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