Temperatures and Molar Mass

TABLE 8.3 Temperature and molar mass dependences of the surface tension of some polymers... 

I describe the Maxwell-Boltzmann distribution of speeds and the effects of temperature and molar mass on molecular speed. 

An interesting phase behavior was observed experimentally [38] for the system poly(ethylene-co-methyl acrylate) in the solvent ethylene (Figure 10.13). Starting from low-density polyethylene, an increasing content of methyl acrylate in the copolymer shifts the demixing curve to lower pressures up to 13 mol% of methyl acrylate in the copolymer, whereas with further addition of methyl acrylate the solubility again decreases. In this case, the binary parameter is a linear function of the copolymer composition [38]. Figure 10.13 demonstrates the performance of the PC-SAFT EOS. The model is able to describe the observed dependence on temperature and molar mass as well as the nonmonotonic dependence on copolymer composition. 

For real polymer-solvent systems the experimental x values and their dependences on composition, temperature, and molar mass provide useful indications of the nature and extent of the polymer-solvent interaction. For a polymer to be soluble in a solvent at a particular temperamre, x must be below 0.5 at high levels of j. If the x value is only slightly larger than 0.5, the polymer is expected to be swollen by the solvent. 

For the description and prediction of thermodynamic data, e.g. volumetric and compositional derivatives of thermodynamic functions of state, many theoretical models are available. The Simha-Somcynsky theory can be considered to be very succesful if one is interested in the quantitative description of thermodynamic properties. Especially, for the equation of state properties this has been shown on many occasions. For the phase behavior of polymer systems, the theory hasn t been evaluated yet in great detail. In this contribution the influence of composition, temperature and molar mass distribution of the polymer is studied for the system polystyrene/cyclohexane. 

After integration, the pressure in the gas column is expressed as a direct function of the elevation, absolute temperature, and molar mass ... 

Obviously the leakage rate Qpv depends on the temperature and molar mass of the leaking gas. Therefore in a statement of a leakage rate in volume throughput units the gas species, for example air or nitrogen and a reference temperature, for example 23 C must be stated additionally. 

In Figure 6-16, we show how the distribution of molecular speeds depends on temperature and molar mass. When we compare the distributions for 02(g) at 273 K and 1000 K, we see that the range of speeds broadens as the temperature increases and that the distribution shifts toward higher speeds. 

Gel permeation chromatograms actually give information about molecular size. For any polymer, size is determined hy a number of factors. These include not only molar mass but also temperature and thermodynamic quality of the solvent. Hence the relationship between size and molar mass is unique for each particular polymer-solvent combination, and we caimot assume that because two peaks of different polymers, even in the same solvent at the same temperature, have the same elution volume their molecules have the same molar mass. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

Separation of heat-sensitive materials. High molar mass material is often heat sensitive and will decompose if distilled at high temperature. Low molar mass material can also be heat sensitive, particularly when its nature is highly reactive. Such material will normally be distilled under vacuum to reduce the boiling temperature. Crystallization and liquid-liquid extraction can be used as alternatives to the separation of high molar mass heat-sensitive materials. 

Example 15.4 A reboiler is required to supply 0.1 krnol-s 1 of vapor to a distillation column. The column bottom product is almost pure butane. The column operates with a pressure at the bottom of the column of 19.25 bar. At this pressure, the butane vaporizes at a temperature of 112°C. The vaporization can be assumed to be essentially isothermal and is to be carried out using steam with a condensing temperature of 140°C. The heat of vaporization for butane is 233,000 Jkg, its critical pressure 38 bar, critical temperature 425.2 K and molar mass 58 kg krnol Steel tubes with 30 mm outside diameter, 2 mm wall thickness and length 3.95 m are to be used. The thermal conductivity of the tube wall can be taken to be 45 W-m 1-K 1. The film coefficient (including fouling) for the condensing steam can be assumed to be 5700 W m 2-K 1. Estimate the heat transfer area for... 

Viscosity and molar mass measurements for 70 and 71 supplemented with broad H-NMR signals which depended on concentration, temperature, and solvent but independent of NMR frequency, strongly suggested self-association of these macromolecules (in a CHC13 solution). 

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 experimental inaccessibility of the configurational entropy poses no problem for the LCT, apart from a consideration of whether to normalize the configurational entropy per lattice site or per monomer in order to provide a better representation of experiment within the AG model. Once the appropriate normalization of Sc has been identified, t can be calculated from Eq. (33) as a function of temperature T, molar mass Mmoi, pressure P, monomer structure, backbone and side group rigidities, and so on, provided that Ap is specified [54]. The direct determination of Ap from data for T > Ta is not possible for polymer systems because Ta generally exceeds the decomposition temperature for these systems. Section V reviews available information that enables specifying Ap for polymer melts. 

Still other applications of the ideal gas law make it possible to calculate such properties as density and molar mass. Densities are calculated by weighing a known volume of a gas at a known temperature and pressure, as shown in Figure 9.10. Using the ideal gas law to find the volume at STP and then dividing the measured mass by the volume gives the density at STP. Worked Example 9.7 gives a sample calculation. 

Oehme et al. investigated the influence of addition orders for the catalyst system Nd(OCOR)3/TIBA/EASC [163]. The catalyst components were mixed at 25 °C and aged for 30 min at the same temperature. Catalyst activities and molar masses decreased in the order (1) > (2) > (3) ... 

Influence of Polymerization Temperature on Molar Mass and Molar Mass Distribution... 

As the influence of polymerization temperature on molar mass and MMD is addressed in Sect. 2.2.7 this issue is not discussed in this context. The residual aspects are reviewed in the following subsections. 

The viscosity of a dilute polymer solution depends on the nature of polymer and solvent, the concentration of the polymer, its average molar mass and molar mass distribution, the temperature and the rate of deformation. In the following exposition it is assumed that the rate of deformation is so low, that its influence can be neglected. 

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