Weights and Molecular Weight Determinations

Another way to express the molecular weight average is as a weight average. Each molecule in such an average contributes according to the ratio of its particular weight to that of the total, 

The above can be illustrated quite readily by imagining that a sample consists of five molecules of molecular weights 2, 4, 6, 8, and 10, respectively. To calculate the number average molecular weight, all the weights of the individual molecules are added. The sum is then divided by the total number of molecules in the sample (in this case 5)  

To calculate the weight average molecular weight of the above sample, the squares of each individual weight are divided by the total sum of molecular weights, in this case 30  

In solutions of polymers, the viscosities are more affected by the long chains than by the short ones. A correlation of the viscosity of the solution to the size of the chains or to the molecular weight of the solute allows an expression of a viscosity average molecular weight  

Solution viscosities of linear polymers relate empirically to their molecular weights. This is used in various ways to designate the size of polymers. The efflux time / of a polymer solution through a capillary is measured. This is related to the efflux time to of the pure solvent. Typical viscometers, like those designed by Ubbelohde, Cannon-Fenske, and other similar ones, are used in a constant temperature bath. The following relationships are used  

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The analyses which follow are arranged in the order in which they would be applied to a newly discovered substance, the estimation of the elements present and molecular weight deter-minations(f.e., determination of empirical and molecular formulae respectively) coming first, then the estimation of particular groups in the molecule, and finally the estimation of special classes of organic compounds. It should be noted, however, that this systematic order differs considerably from the order of experimental difficulty of the individual analyses. Consequently many of the later macro-analyses, such as the estimation of hydroxyl groups, acetyl groups, urea, etc. may well be undertaken by elementary students, while the earlier analyses, such as estimation of elements present in the molecule, should be reserved for more senior students. 

This method of Molecular Weight determination should be used only with solvents in which the particular substance is freely soluble, since it is essential that, on cooling, the solvent, and hot the solute, should crystallise out. 

Molecular weight determinations by depression of the freezrng-point are more accurate and far less troublesome than those by the elevation of the boiling-point (p. 440), and the former method should always be preferentially employed if the solubility of the organic compound in the soh ent is sufficiently high. 

Benzene. Pure benzene (free in particular from toluene) must be used, otherwise the freezing-point is too low, and crystallisation may not occur with ice-water cooling alone. On the other hand, this benzene should not be specially dried immediately before use, as it then becomes slightly hygroscopic and does not give a steady freezing-point until it has been exposed to the air for 2-3 hours. Many compounds (particularly the carboxylic acids) associate in benzene, and molecular weights determined in this solvent should therefore be otherwise confirmed. 

Condensation polymers such as polyesters and polyamides are especially well suited to this method of molecular weight determination. For one thing, the molecular weight of these polymers is usually less than for addition polymers. Even more pertinent to the method is the fact that the chain ends in these molecules consist of unreacted functional groups. Using polyamides as an example, we can readily account for the following possibilities ... 

This expression is consistent with the analysis of each of the lines in Table 5.1 as presented above and provides a general answer to one of the questions posed there. It is often a relatively easy matter to monitor the concentration of functional groups in a reaction mixture as we saw in discussing end group analysis as a method for molecular weight determination in Sec. 1.7. Equation (5.4) is... 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

In molecular weight determinations it is conventional to dissolve a measured mass of polymer m2 into a volumetric flask and dilute to the mark with an appropriate solvent. We shall use the symbol Cj to designate concentrations in mass per volume units. In practice, 100-ml volumetric flasks are often used, in which case C2 is expressed in grams per 100 ml or grams per deciliter. Even though these are not SI units, they are encountered often enough in the literature to be regarded as conventional solution units in polymer chemistry. 

This chapter contains one of the more diverse assortments of topics of any chapter in the volume. In it we discuss the viscosity of polymer solutions, especially the intrinsic viscosity the diffusion and sedimentation behavior of polymers, including the equilibrium between the two and the analysis of polymers by gel permeation chromatography (GPC). At first glance these seem to be rather unrelated topics, but features they all share are a dependence on the spatial extension of the molecules in solution and applicability to molecular weight determination. 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

To use GPC for molecular weight determination, we must measure the volume of solvent that passes through the column before a polymer of particular molecular weight is eluted. This quantity is called the retention volume Vj. Figure 9.14 shows schematically the relationship between M and Vj it is an... 

The molecular weight of SAN can be easily determined by either intrinsic viscosity or size-exclusion chromatography (sec). Relationships for both multipoint and single point viscosity methods are available (18,19). Two intrinsic viscosity and molecular weight relationships for azeotropic copolymers have been given (20,21) ... 

Melt Viscosity. Viscosities of resins at standard temperatures yield information about molecular weight and molecular weight distribution, as weU as valuable information with respect to appHcation logistics. Some customers prefer to receive resins in molten form. Melt viscosities help to determine the required temperature for a resin to be pumpable. Temperature—viscosity profiles are routinely suppHed to customers by resin manufacturers. In general, a molten viscosity of 1—1.1 Pa-s (1000—1100 cP) or less at process temperatures is convenient for the pumping and handling of molten resin. 

The nature of the alkyl group from the esterifying alcohol, the molecular weight, and the tacticity determine the physical and chemical properties of methacrylate ester polymers. 

Mass Spectrometry. Field desorption mass spectrometry has been used to analy2e PPO (179). Average molecular weight parameters (M and could be determined using either protonated (MH + ) or cation attachment (MNa + ) ions. Good agreement was found between fdms and data supphed by the manufacturer, usually less than 5% difference in all cases up to about 3000 amu. Laser desorption Fourier transform mass spectrometry was used to measure PPG ion and it was claimed that ions up to m/2 9700 (PEG) can be analy2ed by this method (180). 

Hydroxyl number and molecular weight are normally determined by end-group analysis, by titration with acetic, phthaUc, or pyromellitic anhydride (264). Eor lower molecular weights (higher hydroxyl numbers), E- and C-nmr methods have been developed (265). Molecular weight deterrninations based on coUigative properties, eg, vapor-phase osmometry, or on molecular size, eg, size exclusion chromatography, are less useful because they do not measure the hydroxyl content. 

Skin. The skin may become contaminated accidentally or, in some cases, materials may be deHberately appHed. Skin is a principal route of exposure in the industrial environment. Local effects that are produced include acute or chronic inflammation, allergic reactions, and neoplasia. The skin may also act as a significant route for the absorption of systemicaHy toxic materials. Eactors influencing the amount of material absorbed include the site of contamination, integrity of the skin, temperature, formulation of the material, and physicochemical characteristics, including charge, molecular weight, and hydrophilic and lipophilic characteristics. Determinants of percutaneous absorption and toxicity have been reviewed (32—35,42,43,46—49). 

The bulk viscosity control parameter for CSM, as with other elastomers, is molecular weight M and molecular-weight distribution (MWD). Mooney viscosity for CSM is determined by selection of the polyethylene precursor. 

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