Polymerization, degree of, defined

This term refers to the number of repeating units in the 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, represent this DP. The relation between degree of polymerization and molecular weight M of the same macromolecule is... 

When the degree of polymerization, defined by n in the above structure, is large, the bisphenol A epoxide is solid and is used as a polymer in its own... 

The onset of the collapse transition (which corresponds, e.g., to vanishing second virial coefScient of interactions between the stars) is shifted with respect to that for linear polymer of the same degree of polymerization (defined by eqn [54]) toward poor solvent strength conditions. This shift is explained by larger intramolecular concentration in the star polymer close to the 6 point, r=0. 

As we have seen, mean field theory predicts that the phase behavior of conformationaly symmetric diblocks can be described in terms of just two quantities, /Ac and/A. A general result of the NSCFT is that, as long as each microphase can be described by a single independent lattice parameter, then the entire microphase diagram of a system of diblock copolymers depends on three parameters, which are / Aeff, the compositional asymmetry /a, and the conformational asymmetry e. Aeff is an effective degree of polymerization, defined by... 

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... 

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 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. 

The chapter is organized in a spiral fashion. First, we examine how the degree of polymerization and its distribution vary with the progress of the polymerization reaction, with the latter defined both in terms of stoichiometry and time. In the first round, we consider these topics for simple reaction... 

In homogeneous media acrylamide is terminated by bimolecular termination [51-53]. In this case the degree of polymerization (DP ), as defined by Chapiro [51] is ... 

The weight average degree of polymerization Xw may be derived as follows, where it is assumed that a ac. We begin by defining... 

Polymer products synthesized in laboratories and in industry represent a set of individual chemical compounds whose number is practically infinite. Macro-molecules of such products can differ in their degree of polymerization, tactici-ty, number of branchings and the lengths that connect their polymer chains, as well as in other characteristics which describe the configuration of the macromolecule. In the case of copolymers their macromolecules are known to also vary in composition and the character of the alternation of monomeric units of different types. As a rule, it is impossible to provide an exhaustive quantitative description of such a polymer system, i.e. to indicate concentrations of all individual compounds with a particular chemical (primary) structure. However, for many practical purposes it is often enough to define a polymer specimen only in terms of partial distributions of molecules for some of their main characteristics (such as, for instance, molecular weight or composition) avoiding completely a... 

Basic definitions Let X be some property of a polymer chain such as the degree of polymerization, molar mass, radius of gyration, or comonomer content of a copolymer, etc. In general, the polymer is heterogeneous with respect to X, which can assume discrete values X,. We now define for molecules with X = X,-. 

Figure 1.2. A number molecular mass distribution N (M) of an ideal chain polymer. N (M) is defined for integer multiples of Mm, the monomer mass. The integer factor, P, is called the degree of polymerization... 

It should be noted that the product of a step polymerization is a mixture of polymer molecules of different molecular weights. The molecular weight distribution is characterized by the number-average and weight-average degrees of polymerization, X and Xw> respectively, defined by... 

Figure 8. Part of a tetrafunctional network formed from an RA t and RBi polymerization corresponding to Mc°, the molar mass between junction points of the perfect network (a). Detail of the chain structure defining Mc° for HDl reacting with an OPPE, n is the number-average degree of polymerization of each arm with respect to oxypropylene units, (b). Part of the chain structure defining v, the number of bonds in the chain forming the smallest ring structure (C), for the reaction system in (b) (29). Reproduced, with permission, from Ref. 21. Copyright 1980, Stein-...

Higher-order averages are also important for network formation the number average value of functional groups per weight-average degree of polymerization is defined by... 

The polystyrene data were collected from a steady state, continuous, well-mixed reactor. The initiator was n-butylli-thlum for data of Figure 2 and was azobisisobutylnitrile for data of Figure 3. Toluene was used as a solvent. The former polymerizatl n y ields an exponential population density distribution ( ), M /M = 1.5 the latter yields a molar distribution defined as th product of degree of polymerization and an exponential ( ), M /M = 2.0. Standards utilized in calibration of both instrumen s ftere polystyrene supplied by Pressure Chemical Company. 

Quantitative characteristics of a macromolecule or an assembly of macromolecules, such as mass and mole fractions or percentages as well as the degrees of polymerization and molar masses, may be expressed by placing corresponding figures after the complete name. The order of citation is the same as for the monomer species in the name. Some characteristics cannot be defined for all types of macromolecules and assemblies dealt with in this document, e.g. molar mass of a network. 

The residue from each diol and each diacid (separately, not together) in the polymer chain is termed a structural unit (or a monomer unit). The repeating unit of the chain consists of two structural units, one each of the diol and diacid. The total number of structural units in any particular system equals the total number of bifunctional monomers initially present. The number-average degree of polymerization X is defined as the average number of structural units per polymer chain. (The symbols P and DP are also employed to signify... 

---