Measurement of molecular weight

The intent here is not to give a complete description of each method including the necessary equations needed to convert a particular measurement into a molecular weight. Rather, the essential features of each technique will be discussed briefly. 

The end group analysis method relies on a knowledge of the nature and types of end groups present. In this method the number of molecules are simply counted. This is accomplished by using standard analytical techniques to determine the concentration of the end groups and thereby the number of polymer molecules. See Rosen, (1993) for a more complete description of this procedure. 

The vapor pressure method uses two thermistor probes to measure the temperature difference between a drop of solvent placed on one probe and a drop of a solution of solute and solvent on the other probe. The difference in rates of vaporization at the two probes leads to a difference in temperature at the two probes. This difference in temperature can be related to the number average molecular weight. For more insight into the method and the magnitude of the temperature differences encountered (see Kumar and Gupta (1998)). 

The membrane osmometry method depends upon finding a suitable membrane which will allow solvent to move through the membrane but not allow motion of the solute in the reverse direction. That is, if a solute and solvent are separated by a semipermiable membrane as shown below in Fig. 4.43, the motion of the solvent will create an increase in pressure in the solute which can be measured by the relative difference of the height of the two fluids in their respective capillaries. This pressure differential can be related to the number average molecular weight. 

Typical glassware viscometers which are used for viscosity measurement are shown in Fig. 4,45. The flow times through the capillaries are measured and converted to viscosity measurements using the concepts of Newtonian flow. It should be remarked, however, that polymer solutions are normally non-Newtonian but the error is small with properly designed equipment. For a more complete discussion of this technique, see Rosen, (1993). 

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Development of the Mooney viscometer gave compounders an indication of the processibiUty of different lots of the uncompounded polymer. This machine measures the torque resistance encountered by a rotor revolving in a chamber surrounded by polymer at a constant temperature. The resulting Mooney number describes the toughness of the polymer and is an indirect measure of molecular weight. 

Polymers ranging in melt flow index (an inverse measure of molecular weight) from less than 0.1 to greater than 600 can be obtained by this process but commercial products have a melt flow index of only 0.2-5 and have the highest density of any commercial polyethylenes ( 0.96 g/cm ). 

With the availability of the higher density polymers the value of the melt flow index as a measure of molecular weight diminishes. For example, it has been found that with two polymers of the same weight average molecular weight (4.2 X 10 ), the branched polymer (density = 0.92 g/cm ) had only 1/50 the viscosity of the more or less unbranched polymer (density = 0.96 g/cm ). This is due to long chain branches as explained above. 

The standard melt flow index machine is often used for characterising the flow properties of polypropylene and to provide a rough measure of molecular weight. Under the conditions normally employed for polyethylene (2.16 kg load at 190°C) the flow rate is too low for accurate measurement and in practice higher loads, e.g. 10 kg, and/or higher temperatures are used. It has been found that a considerable pressure drop exists in the barrel so that the flow towards the end of a test run is higher than at the beginning. 

Unlike other water-soluble resins the poly(ethylene oxide)s may be injection moulded, extruded and calendered without difficulty. The viscosity is highly dependent on shear rate and to a lesser extent on temperature. Processing temperatures in the range 90-130°C may be used for polymers with an intrinsic viscosity of about 2.5. (The intrinsic viscosity is used as a measure of molecular weight.)... 

The measurement of molecular weight and RMS radius provides the means to examine the conformational characteristics of a polymer using the relationship... 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

Making careful use of an ebulliometer we can make an accurate measurement of Molecular weights of... 

Staudinger was probably the first to recognize this, for in 1928 he proposed that synthetic macromolecules were poly-disperse and their molecular weights would have to be expressed as average values (93). He also recognized the dependence of physical properties on molecular weight, and pursued this dependence as a measure of molecular weight determination. The result was his application of solution viscosity. 

In Vienna, Mark published a number of fundamental papers. Their topics include polymerization mechanism (46, 47, 48), thermal polymerization (49, 50), polymerization kinetics (51), the effect of oxygen on polymerization (52), and measurement of molecular weight distribution (53). Guth and Mark expanded their modeling of extended and balled thread molecules to include rubber. The result of their studies was a series of very important papers in which the thermal effect on expansion and relaxation of rubber is explained (54, 55, 56). 

To the accuracy of the measurement of molecular weights for the giant planets, only hydrogen and helium have significant abundances. The relative proportions of these elements, expressed as the molar fraction He/H, are 0.068+0.002 for Jupiter, 0.068+0.013 for Saturn, 0.076+0.016 for Uranus, and 0.100+0.016 for Neptune (Lunine, 2004). None of these ratios are like those of the nebula (0.085, Table 4.1). 

A number of problems arise in connection with the measurement of molecular weights of galactomannans. Firstly, it is very difficult to obtain true solutions of many of the gums, especially of locust-bean gum and guar gum consequently, the solutions must be filtered or centrifuged to remove undissolved or partially hydrated gum. This immediately raises the problem of fractionation of the sample, as the... 

Because sample homogeneity is particularly important for a Standard Reference Material, it was carefully assessed for both polystyrenes using solution viscosity, a measure of molecular weight, as an index. There is essentially no variation with location within the lot, or from pellet to pellet, within the limits of error of the viscosity measurements. Viscosity measurements may be made with a standard deviation of a single determination of about 0.3%. 

Because of Ihis striking dependence on molecular size, the measurement of molecular weight and dimensions is very important. Some of the... 

In contrast to these thermodynamic methods, the viscosity molecular weight determination depends on the interference in the flow of the solvent caused by the dissolved molecules. In contrast to osmometry and light scattering, it has not been possible to develop the viscosity effect into an absolute measure of molecular weight. Rather, it must be calibrated, preferably by light scattering measurements. 

The availability of soluble polymers has permitted measurements of molecular weight, as discussed below. The glass transition temperatures are quite low, from 145 °C for polymethylthiophene to 41 °C for polybutylthiophene. X-ray diffraction shows a broad peak which has been interpreted by different groups as showing a structure which is either partly crystalline or is amorphous. The temperature of fusion decreases from 280 °C to 80 °C as the length of the alkyl chain increases from 4 to 22 carbons 263). 

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