Molecular weight determinations

For characterisation of macromolecules the first step is to determine the degree of polymerisation (DP) or the molecular weight (M) of the polymeric compounds. The methods usually employed for this purpose are, without exception, based on the physical chemistry of polymer solutions (Table 5.1) and have been popularised quickly and widely owing to the recent remarkable development of automatic apparatus. 

Method Detecting physical quantity Average MW Measurable upper limit of MW range (approx.) 

End-group assay Number of end groups in polymeric chains 2x 10  

Vapour-pressure osmometry Temperature difference between solution and solvent drops in saturated solvent vapour Mn 4x 10  

Light-scattering including SAXS and SANS Intensity of scattered visible light, X-rays and neutrons 1 X lO  

The secondary methods, such as solution viscosity and gel permeation chromatography, require prior establishment of empirical relationships that relate the molecular weight to the viscosity of the polymer solution or to the retention times in a gel-permeation column. Once such calibration has been done, the secondary methods provide a fast, simple, and accurate way to obtain molecular weights. The solution viscosity and gel permeation chromatography methods are described in a later part of this chapter. 

The secondary methods, such as solution viscosity and gel permeation chromatography, require prior establishment of empirical relationships that relate the molecular weight to the viscosity of the polymer solution or to the retention times 

Size exclusion chromatography (which is also kno vn as gel permeation chromatography) is based on the premise that a polymer molecule in solution adopts a random coil configuration, which encompasses a volume (known as its hydrodynamic volume) that is proportional to its molecular weight. We fractionate polymers according to their hydrodynamic volumes to generate a molecular weight distribution plot. 

The viscosity of a dilute solution of polymer depends on the molecular weight of the polymer. This gives us a simple method for measuring molecular weight based on viscosity, which is readily measured. 

To perform this analysis, we first prepare a dilute solution of polymer with an accurately known concentration. We then inject an aliquot of this solution into a viscometer that is maintained at a precisely controlled temperature, typically well above room temperature. We calculate the solution s viscosity from the time that it takes a given volume of the solution to flow through a capillary. Replicate measurements are made for several different concentrations, from which the viscosity at infinite dilution is obtained by extrapolation. We calculate the viscosity average molecular weight from the Mark-Homvink-Sakurada equation (Eq. 5.5). 

Largest molecules flow through directly, smaller molecules are trapped in pores 

Smaller molecules are absorbed into more pores and thus take longer to elute 

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Measurements on copper) I) chloride show the vapour to be the dimer of formula CU2CI2, but molecular weight determinations in certain solvents such as pyridine show it to be present in solution as single molecules, probably because coordination compounds such as py -> CuCl (py = pyridine) are formed. 

Molecular Weight Determinations by Physical Methods. Vapour Density. Victor Meyer s Method. 

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. 

The cryoscopic constant Kj gives the depression of the melting point AT (in degrees Celsius) produced when 1 mol of solute is dissolved in 1000 g of a solvent. It is applicable only to dilute solutions for which the number of moles of solute is negligible in comparison with the number of moles of solvent. It is often used for molecular weight determinations. 

The method of end group analysis for molecular weight determination is not only simple to understand, but can also be done with ordinary laboratory equipment in many instances. 

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... 

Titanium Complexes of Unsaturated Alcohols. TetraaHyl titanate can be prepared by reaction of TYZOR TPT with aHyl alcohol, followed by removal of the by-product isopropyl alcohol. EbuUioscopic molecular weight determinations support its being the dimeric product, octaaHoxydititanium. A vinyloxy titanate derivative can be formed by reaction of TYZOR TPT with vinyl alcohol formed by enolization of acetaldehyde (11) ... 

Molecular weight determinations of ECH—EO, ECH—AGE, ECH—EO—AGE, ECH—PO—AGE, and PO—AGE have not been reported. Some solution studies have been done on poly(propylene oxide), and these may approximate solution behavior of the PO—AGE copolymer (33,34). 

Sepharose (e.g. Sepharose CL and Bio-Gel A) is a bead form of agarose gel which is useful for the fractionation of high molecular weight substances, for molecular weight determinations of large molecules (molecular weight > 5000), and for the immobilisation of enzymes, antibodies, hormones and receptors usually for affinity chromatography applications. 

Such data can provide a calibration curve and allow the constants (E) and F ) in equation (20) to be determined. The value of the molecular weight of an unknown solute can then be obtained from its (H) value by reading the value directly from the curve or by calculation using the predetermined constants (E) and (F ) in equation (20). It should be pointed out that an error of up to 30% may not appear to be very useful but, in fact, such precision can be extremely valuable in the preliminary examination of many biochemical substances where only very small quantities of material are available. It is also an ideal method for molecular weight determination before more accurate, labor-intensive and time-consuming methods are considered. 

Molecular weight assignments for such resins will be dependent on the method used for measurement. Each manufacturer has his own relative scale. In practice, absolute molecular weight determination is not important. The method used must discriminate between resins with sufficient resolution to allow prediction of resin performance in the applications of interest. 

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