Molar mass effects

The molar mass of the polymer is an important factor in consideration of Tg. Since free volume is a rate-controlling factor, it may be anticipated that the ends of the chain will be less restricted than the central portion in terms of their ability to move. It is found empirically that the molar mass dependence for a large number of polymers can be described by the following simple relationship  

For a technical polymer, the molar mass distribution (MMD) is a direct result of the statistics of the polymerisation process. In the process itself, it results from  

For both PE and PP degradation processes are possible. The reaction to free radicals, in the case of PE, is strongly dependent on the catalyst type. For chromium-based catalysts branching is normally predominant, while for titanium-based catalysts degradation is more important. 

As a result of all these possibilities, the shape and moments of the MWD can be varied over a wide range. In principle, correlations with all rheological properties are possible from the MWD if all chains are fully linear. 

Another possible way to determine MWD-related parameters is the application of generalised Newtonian flow models for the viscosity curve r (y ). 

Reproduced with permission from M. Gahleitner, Progress in Polymer Science, 2001, 26, 895. 

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To do so, however, a tandem of several columns would be needed. In the case of a two-component polymer system, the molar mass effect can be suppressed selectively for one component and the molar mass of the second component can be assessed by means of one single SEC measurement. A more general approach is represented by the two- and multidimensional procedures in polymer HPLC (Section 16.7), in which the coupled methods of polymer HPLC are included as an important (usually the first) separation steps. 

In any 2D HPLC, it is important to attain certain degree of both the complementarity and the orthogonality between the two separation dimensions [255-257]. The so far most universal approach to 2D polymer HPLC assumes the partial or possibly full suppression of the molar mass effect in the first dimension of the separation so that the complex polymer is separated mainly or even exclusively according to its chemical structure. Selected coupled methods of polymer HPLC are to be applied to this purpose. In the second dimension of separation—it is usually SEC—the fractions from the first dimension are further discriminated according to their molecular size. Exceptionally, SEC can be used as the first dimension to separate complex polymer system according to the molecular size. This approach is applicable when the size of polymer species does not depend or only little depends on their second molecular characteristic, as it is the case of the stereoregular polymers... 

Ion Scattering Spectroscopy mass, molar mass effective mass of electron concentration of ions or charge carriers concentration of acceptors concentration of donors coordination number of shell j complex refraction index photo ionization cross-section electric charge gas constant... 

From the theoretical point of view, a more feasible way of analyzing copolymers is the prefractionation through HPLC in the first dimension and subsequent analysis of the fractions by SEC [89,90]. HPLC was found to be rather insensitive towards molar mass effects and yielded very uniform fractions with respect to chemical composition. 

Low molar mass LC polymers would be expected to be biphasic over a wide temperature range, as both the chemical heterogeneity and the molar mass effects on the clearing temperature are large for short chains. A further complication in understanding this behavior arises in cases where the components form mesophases of different types as discussed in a chapter by Ober et al. 

Due to the attractive interaction of monomer with the column packing, also its retention volume exceeds V. An important case of the coupled exclusion - interaction processes is in Figure 3 represented by curve d. It mirrors the full mutual compensation of exclusion and interaction, which leads to the independence of retention volume of polymer molar mass. This situation is important for characterization of complex polymers. It allows elimination or at least suppression of the molar mass effect of macromolecules so that their unbiased separation according to another molecular characteristic can be performed. The experimental conditions leading to this specific elution behavior are called critical conditions of enthalpic interactions. They will be more in detail discussed in section 11.8.3. 

To suppress the effect of certain molecular characteristic on sample retention volume so that the resulting chromatogram reflects mainly or even exclnsively other molecular characteristic(s) of sample. In practice, it is usually attempted to partially or fully suppress the influence of polymer molar mass. In this instance, the coupling of LC retention mechanisms may allow assessment of chemical structure or physical architecture of a complex polymer irrespective of its molar mass average and dispersity. Under favorable conditions, also the constituents of a complex polymer system with similar molar masses can be discriminated and molar mass of one constituent determined. For example, in the case of a two-component polymer system, the molar mass effect can be suppressed selectively for one constituent so that it elutes in a completely different retention volume compared with the retention volume pertaining to SEC. In some cases, the... 

For a typical condensation polymerisation, the molar mass distribution function is generally in the range 3—20, but is sometimes even greater. On the other hand, in vinyl polymerisation the values typically wiU be in the range 1.05—3.0. The narrowest molar mass distributions are observed with anionic and certain cationic initiated polymerisations. Molar mass effects are observed with aU polymer systems but they are more important in the physical properties of amorphous polymers than in their crystalline analogues. 

At high ionic strength the electrostatic contributions are screened. Therefore, the chemical interactions become important. Very high adsorption may be observed if the solvent is very poor for the polyelectrolyte under these conditions. At high ionic strength molar mass effects are important. 

The semi-dilute regime constitutes a sizeable concentration range vl V2 1, where u is the volume fraction corresponding to the concentration c. The semi-dilute solution case is in fact the simplest to describe. Molar mass effects are highly suppressed but still the solution is diluted. The solution activity and the osmotic pressure are independent of molar mass but dependent on the distance between the entanglement points in the loose network. The latter is controlled simply by the volume fraction of polymer V2), and the osmotic pressure is given by des Cloiseaux law ... 

The fact that the molar mass effect on elution of a given homopolymer disappears has been named chromatographic invisibilit/ to explain the LCCC behavior of polymer blends and segmented copolymers. For example, in diblock copolymers, chromatographic conditions can be found where one block elutes irrespective of molar mass at LCCC (the invisible block), while the other block elutes at SEC conditions (the visible block). Provided suitable detection and calibration procedures are used, the molar mass of the visible block can be quantified in the diblock copolymer. " Other applications of LCCC include the separation of homo- and copolymers according to funaional end-groups (see Sections 2.03.5 and 2.03.6 for more details). 

In order to achieve the best efficiency the SEC column should be operated at optimized operating parameters. The most important ones are flow rate [cf. van Deemter equation for band-broadening effects (21)], sample viscosity (depends on molar mass and concentration of the sample), and injection volume (7). 

Effect of Molar Mass on Boiling Points of Molecular Substances... 

When iodine chloride is heated to 27°C, the weak intermolecular forces are unable to keep the molecules rigidly aligned, and the solid melts. Dipole forces are still important in the liquid state, because the polar molecules remain close to one another. Only in the gas, where the molecules are far apart, do the effects of dipole forces become negligible. Hence boiling points as well as melting points of polar compounds such as Id are somewhat higher than those of nonpolar substances of comparable molar mass. This effect is shown in Table 9.3. 

Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

There have been very few examples of PTV derivatives substituted at the vinylene position. One example poly(2,5-thienylene-1,2-dimethoxy-ethenylene) 102 has been documented by Geise and co-workers and its synthesis is outlined in Scheme 1-32 [133]. Thiophene-2,5-dicarboxaldehyde 99 is polymerized using a benzoin condensation the polyacyloin precursor 100 was treated with base to obtain polydianion 101. Subsequent treatment with dimethyl sulfate affords 102, which is soluble in solvents such as chloroform, methanol, and DMF. The molar mass of the polymer obtained is rather low (M = 1010) and its band gap ( ,.=2.13 eV) is substantially blue-shifted relative to PTV itself. Despite the low effective conjugation, the material is reasonably conductive when doped with l2 (cr=0.4 S cm 1). 

Within the wide range of phosphorus compounds described as activating agents for polyesterification reactions,2,310 triphenylphosphine dichloride and diphenylchlorophosphate (DPCP) were found to be the most effective and convenient ones. In pyridine solution, DPCP forms a A-phosphonium salt which reacts with the carboxylic acid giving the activated acyloxy A -phosphonium salt. A favorable effect of LiBr on reaction rate and molar masses has been reported and assumed to originate from the formation of a complex with the A-phosphonium salt. This decreases the electron density of the phosphorus atom... 

M.10 Nicotine, the stimulant in tobacco, causes a very complex set of physiological effects in the body. It is known to have a molar mass of 162 g-mol. When a sample of mass 0.385 g was burned, 1.072 g of carbon dioxide, 0.307 g of water, and 0.068 g of nitrogen were produced. What are the empirical and molecular formulas of nicotine Write the equation for its combustion. 

We see that, for a given pressure and temperature, the greater the molar mass of the gas, the greater its density. Equation 10 also shows that, at constant temperature, the density of a gas increases with pressure. When a gas is compressed, its density increases because the same number of molecules are confined in a smaller volume. Similarly, heating a gas that is free to expand at constant pressure increases the volume occupied by the gas and therefore reduces its density. The effect of temperature on density is the principle behind hot-air balloons the hot air inside the envelope of the balloon has a lower density than that of the surrounding cool air. Equation 10 is also the basis for using density measurements to determine the molar mass of a gas or vapor. 

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