Molar mass elevation

Although low-molar-mass aliphatic polyesters and unsaturated polyesters can be synthesized without added catalyst (see Sections 2.4.1.1.1 and 2.4.2.1), the presence of a catalyst is generally required for the preparation of high-molar-mass polyesters. Strong acids are very efficient polyesterification catalysts but also catalyze a number of side reactions at elevated temperature (>160°C), leading to polymers of inferior quality. Acid catalysts are, therefore, not much used. An exception is the bulk synthesis of hyperbranched polyesters reported in Section 2.4.5.1, which is carried out at moderate temperature (140°C) under vacuum in the presence of p-toluene sulfonic acid catalyst. The use of strongly acidic oil-soluble catalysts has also been reported for the low-temperature synthesis of polyester oligomers in water-in-oil emulsions.216... 

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

The freezing point depression and boiling point elevation techniques are useful in calculating the molar mass of a solute or its van t Hoff factor. In these cases, you will begin with the answer (the freezing point depression or the boiling point elevation), and follow the same steps as above in reverse order. 

SEC became the most widely used method for molar mass and molar mass distribution determination due to its broad applicability, easy sample preparation, and the large amount of information resulting from the full distribution curve. The commercially available SEC systems work automatically with small sample amounts and even at elevated temperatures. In addition, chromatographic systems coupled with spectroscopic methods giving chemical information on the separated fractions gain more and more importance for analysis of complex polymer systems and mixtures. 

The HBA/HNA system provides a more suitable system for study, since it is prepared by melt polymerization of the two monomers and is far more stable at elevated temperatures compared to the PHBA/PET. The HBA/HNA copolymers are soluble in pentafluorophenol permitting use of NMR techniques to characterize diad sequences. In Fig. 13b,c the 13CNMR spectrum of the carboxyl carbon region of the HBA/HNA copolyesters of the 73/27 and 48/52 systems is shown [34]. Also shown in Fig. 13a,d are the spectra of 13C enriched HBA and HNA containing copolymers permitting unique identification of the diad sequences. As a result of this technique it was possible to determine the reactivity ratios of the two monomers by analyzing the 50/50 copolymer after polymerization to a molar mass value of 2000 [35]. Examination of the copolymer by 13C NMR showed the same ratio of monomers as in the starting... 

X V iution), the determination of the molar mass of a solute requires a measurement of mass, volume, temperature, and osmotic pressure. Osmotic pressures are generally large and can be determined quite accurately, thus yielding accurate molar masses. Boiling-point elevations and freezing-point depressions are usually small and not very accurate, so molar mass determinations based on those measures often are not accurate. 

A boiling point elevation measurement can be used to estimate the molar mass of a solute. 

Thus the elevation of the boiling point, AZb, of a liquid (molar mass, Mm, boiling point, Tb and enthalpy of vaporisation, AvapH° at 1 bar pressure) caused by addition of zwSoiute can be calculated using equation (52.12). 

Table 3.6 lists Kf and Kb for several solvents. In general, the higher the molar mass of the solvent, the larger the values of Kf and Kb. If the freezing point depression and boiling point elevation constants are known, the molecular weight of the dissolved solute, M2, can be determined ... 

For the determination of very high molar masses, freezing-point depressions, boiling-point elevations, and vapor-pressure lowerings are too small for accurate measurement. Osmotic pressures are of a convenient order of magnitude, but measurements are time-consuming. The technique to be used in this experiment depends on the determination of the intrinsic viscosity of the polymer. However, molar-mass determinations from osmotic pressures are valuable in calibrating the viscosity method. 

In the 1920s, it was not feasible to accurately measure the molecu-f lar weight of natural or synthetic polymers. Classical methods 1 of molecular weight determina-V tion, those based upon colligative x properties, elevation of boiling point, depression of freezing point and lowering of vapor pressure, worked very well for low-molar-mass compounds, but were essentially useless for macromolecules. Modern instrumental methods that... 

The molar mass of a solute can be determined from the observed boiling-point elevation, as shown in Example 17.2. 

Like the boiling-point elevation, the observed freezing-point depression can be used to determine molar masses and to characterize solutions. 

The normal boiling point of a pure liquid T, or a solution is the temperature at which the vapor pressure reaches 1 atm. Because a dissolved solute reduces the vapor pressure, the temperature of the solution must be increased to make it boil. That is, the boiling point of a solution is higher than that of the pure solvent. This phenomenon, referred to as boiling-point elevation, provides a method for determining molar masses. 

Measurements of the drop in the freezing point, like those of elevation of the boiling point, can be used to determine molar masses of unknown substances. If a substance dissociates in solution, the total molality of all species present (ionic or neutral) must be used in the calculation. 

Both freezing-point depression and boiling-point elevation can be used to determine whether a species of known molar mass dissociates in solution (Fig. 11.13), as the following example shows. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

While novolac links may form at elevated temperature during resole synthesis (Scheme 1.12), the preferred synthesis of novolac resins takes place under acid conditions (pH from 1 to 4) and with an excess of phenol. In this case the methylol intermediates cannot be isolated since they react rapidly to give methyene-bridged structures with relative molar mass <2000, as shown in Scheme 1.15. 

Polycarbonates are processed at very elevated temperatures (>300 °C) so that hydrolysis of the carbonate linkage to yield carbon dioxide and a phenol end group can occur if the polymer is not rigorously dried (residual water <0.02 wt.%). Complex chemistry can follow (Scheirs, 2000), resulting in the formation of low-molar-mass species and darkening of the polymer in addition to chain scission. The degradation is very sensitive to trace acidic or basic impurities, and it has been noted that in blends (e.g. PC/ABS) there may be initiation of the degradation by impurities in the ABS (Cook et al, 1996). 

In condensation polymerization, the use of NIR to follow the reactant concentrations at elevated temperatures (200-300 °C) has been applied to the synthesis of aromatic and aliphatic polyesters (Dallin, 1997). This provides an accurate alternative to the routine measurement of acid values, hydroxyl number and viscosity, with the added advantage of providing continuous data throughout the polyesterification, which allows optimum conversion. Related examples of the use of NIR include studies of esterification of low-molar-mass analogues (Blanco and Serrano, 2000) or transesterification of an existing polymer or copolymer (Sasic et al, 2000). The NIR method allowed quantitative determination of rate constants, end points and yield and equilibrium constants as well as mechanistic information, which allowed the esterification to be optimized through the use of higher temperatures and an excess of acetic acid (Blanco and Serrano, 2000). 

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