Molar mass and degree of polymerization

Many properties of polymers show a strong dependence upon the size of the polymer chains, so that it is essential to characterize their dimensions. This normally is done by measuring the molar mass (Af) of a polymer which is simply the mass of 1 mole of the polymer and usually is quoted in units of g mol or kg moP The term molecular weight is still often used instead of molar mass, but is not preferred because it can be somewhat misleading. It is really a dimensionless quantity, the relative molecular mass, rather than the weight of an individual molecule which is of course 

For network polymers the only meaningful molar mass is that of the polymer chains existing between junction points (i.e. network chains), since the molar mass of the network itself essentially is infinite. 

The molar mass of a homopolymer is related to the degree of polymerization (jc), which is the number of repeat units in the polymer chain, by the simple relation 

With very few exceptions, polymers consist of macromolecules (or network chains) with a range of molar masses. Since the molar mass changes in intervals of Mq, the distribution of molar mass is discontinuous. However, for most polymers these intervals are extremely small in comparison to the total range of molar mass and the distribution can be assumed to be continuous, as exemplified in Fig. 1.3. 

Whilst a knowledge of the complete molar mass distribution is essential in many uses of polymers, it is convenient to characterize the distribution in terms of molar mass averages. These usually are defined by considering the discontinuous nature of the distribution in which the macromolecules exist in discrete fractions i containing Ni molecules of molar mass M/. 

A normal polymer sample contains molecules with a variety of lengths and it is only possible to quote an average value of the molar mass. A typical distribution of molar mass is shown in Fig. 1.3. Often the exact form of the distribution is not known and it is conventional to describe it in terms of either a number average molar mass, M or a weight average molar mass, My. Both of these parameters can be measured experimentally. In the definition of M and M , it is envisaged that the distribution of molar mass 

It is often more convenient to deal in terms of mass fractions w, rather than the numbers of molecules, the mass fraction w, being defined as the mass of molecules of length i divided by the total mass of all molecules. 

Combining Equations (1.3) and (1.5) gives M in terms of mass fractions as 

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Specification with regard to mass fractions, mole fractions, molar masses and degrees of polymerization... 

Properties of polyolefins primarily depend on the type of monomers and route of polymerization, resulting in various molar mass and degree of crystallinity. They can be simply modified by introducing various functional groups or mixed with other polymers and fillers to get tailored properties for required applications. 

The molar mass, relative molecular mass or degree of polymerization may be included in the seheme of Rules 8.1 and 8.2 by adding the eorresponding figures, followed by the symbol M, Mr or DP, respeetively. 

All potentially molar-mass-dependent quantities have been labelled with a summation index k in Eq. (30), which, in this form, also holds for dilute solutions of mixtures of chemically different species or copolymers with heterogeneity of both chemical composition and degree of polymerization. 

Long-time reproducibility of elution profiles broad standard calibration with dextran T-500 transformation of a scb-type calibration function into nb/Icb-type via universal calibration dp of synthetic glucans in the presence of significant amounts of monomer mass and molar degree of polymerization of Triticale (hybride) starch... 

Differences between molar and mass degree of polymerization distribution of a partially hydrolized starch... 

On-line changing of solvent from DMSO to H2O for a starch glucan establishing an absolute calibration function characteristics of mass and molar degree of polymerization distribution for a broad distributed starch sample... 

Statistical and block copolymers based on ethylene oxide (EO) and propylene oxide (PO) are important precursors of polyurethanes. Their detailed chemical structure, that is, the chemical composition, block length, and molar mass of the individual blocks may be decisive for the properties of the final product. For triblock copolymers HO (EO) (PO)m(EO) OH, the detailed analysis relates to the determination of the total molar mass and the degrees of polymerization of the inner PPO block (m) and the outer PEO blocks (n). 

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-...

In 1994, we reported the dispersion polymerization of MM A in supercritical C02 [103]. This work represents the first successful dispersion polymerization of a lipophilic monomer in a supercritical fluid continuous phase. In these experiments, we took advantage of the amphiphilic nature of the homopolymer PFOA to effect the polymerization of MMA to high conversions (>90%) and high degrees of polymerization (> 3000) in supercritical C02. These polymerizations were conducted in C02 at 65 °C and 207 bar, and AIBN or a fluorinated derivative of AIBN were employed as the initiators. The results from the AIBN initiated polymerizations are shown in Table 3. The spherical polymer particles which resulted from these dispersion polymerizations were isolated by simply venting the C02 from the reaction mixture. Scanning electron microscopy showed that the product consisted of spheres in the pm size range with a narrow particle size distribution (see Fig. 7). In contrast, reactions which were performed in the absence of PFOA resulted in relatively low conversion and molar masses. Moreover, the polymer which resulted from these precipitation... 

A further remark has to be made when the stars contain polydisperse arms. The radius of gyration is now based on the z-average of the mean square radius of gyration over the molar mass distribution while the degree of polymerization is the weight average Also for this case the molar mass dependence of this radius could be calculated and was found to be [83]... 

The molar mass distribution of branched materials differ most significantly from those known for Hnear chains. To make this evident the well known types of (i) Schulz-Flory, or most probable distribution, (ii) Poisson, and (iii) Schulz-Zimm distributions are reproduced. Let x denote the degree of polymerization of an x-mer. Then we have as follows. 

Whereas subscripts placed immediately after the formula of the monomeric unit or the block designate the degree of polymerization or repetition, mass and mole fractions and molar masses - which in most cases are average quantities - may be expressed by placing corresponding figures after the complete name or symbol of the copolymer. The order of citation is the same as for the monomer species in the name or symbol of the copolymer. Unknown quantities can be designated by a, b, etc. 

As already shown, conventional macromolecules (or polymers) consist of a minimum of a several hundred covalently linked atoms and have molar masses clearly above 10 g/mol. The degree of polymerization, P, and the molecular weight, M, are the most important characteristics of macromolecular substances because nearly all properties in solution and in bulk depend on them. The degree of polymerization indicates how many monomer units are linked to form the polymer chain. The molecular weight of a homopolymer is given by Eq. 1.1. 

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