Relative molar mass

If the sample consists of atoms of one element, the mass spectrum gives the isotopic distribution of the sample. The relative molar masses of the isotopes can be determined by comparison with atoms of carbon-12. If the sample is a compound, the formula and structure of the compound can be determined by studying the fragments. For example, the + 1 ions that CH4 could produce are CH4, CH3+, CH, CFI4, C+, and H4. Some of the particles that strike the detector are those that result when the molecule simply loses an electron (for example, to produce Cl I4+ from methane) ... 

The size of a polymer molecule may be defined either by its mass (see Chapter 6) or by the number of repeat units in the molecule. This latter indicator of size is called the degree of polymerisation, DP. The relative molar mass of the polymer is thus the product of the relative molar mass of the repeat unit and the DP. 

There is no clear cut boundary between polymer chemistry and the rest of chemistry. As a very rough guide, molecules of relative molar mass of at least 1000 or a DP of at least 100 are considered to fall into the domain of polymer chemistry. 

A typical Ziegler-Natta catalyst is the complex prepared from titanium tetrachloride and triethylaluminium. It is fed into the reaction vessel first, after which ethylene is added. Reaction is carried out at low pressures and low temperatures, typically no more than 70 °C, with rigorous exclusion of air and moisture, which would destroy the catalyst. The poly(ethylenes) produced by such processes are of intermediate density, giving values of about 0.945 g cm. A range of relative molar masses may be obtained for such... 

This polymer, which has the structure [—CH2CH(CH3)—] arose as a commercial material following the work of Natta on catalysts for the preparation of high relative molar mass polymers from alkenes. Following his work on the polymerisation of ethylene, Natta showed in 1954 that it was possible to prepare analogous polymers of propylene. Commercial exploitation followed rapidly, and poly (propylene) was first marketed in 1957. 

Polyurethanes are thermoset polymers formed from di-isocyanates and poly functional compounds containing numerous hydroxy-groups. Typically the starting materials are themselves polymeric, but comprise relatively few monomer units in the molecule. Low relative molar mass species of this kind are known generally as oligomers. Typical oligomers for the preparation of polyurethanes are polyesters and poly ethers. These are usually prepared to include a small proportion of monomeric trifunctional hydroxy compounds, such as trimethylolpropane, in the backbone, so that they contain pendant hydroxyls which act as the sites of crosslinking. A number of different diisocyanates are used commercially typical examples are shown in Table 1.2. 

The possibility of all kinds of morphology from linear, low relative molar mass molecules to three-dimensional networks means that silicones are found in a range of physical forms, from fluids through to insoluble solids. 

Amylopectin is the polymeric component of starch and consists mainly of glucose units joined at the 1,4-positions. Relative molar mass tends to be very high, e.g. between 7 and 70 million. A variety of modified starches are used commercially which are produced by derivatisation to give materials such as ethanoates (acetates), phosphates, and hydroxyalkyl ethers. Modified and unmodified starches are used in approximately equal tonnages, mainly in papermaking, paper coatings, paper adhesives, textile sizes, and food thickeners. 

The polymer in natural rubber consists almost entirely of ci -poly(isoprene) (1.6). The molecules are linear, with relative molar mass typically lying between 300 000 and 500 000. The macromolecular nature of rubber was established mainly by Staudinger in 1922, when he hydrogenated the material and obtained a product that retained its colloidal character, rather than yielding fragments of low relative molar mass. 

In nature, there are 20 amino acids available for incorporation into the protein chain. They are arranged in a specific and characteristic sequence along the molecule. This sequence is generally referred to as the primary structure of the protein. Also part of the primary structure is the relative molar mass of the macromolecule. 

Plasticisers are substances with relative molar masses well below those of polymers, usually liquids that, when added to polymers, give apparently... 

Another commercially important crosslinking process that involves unsaturated polymer precursors is the so-called drying of alkyd resins in paints. This process is not drying at all, at least not in the sense of mere loss of solvent to leave behind a solid residue. Instead, the main process is the conversion of high relative molar mass molecules to a crosslinked structure via... 

This structure has a relative molar mass of 340 typical commerical liquid glycidyl ethers have relative molar masses in the range 340-400 and so are obviously composed largely of this substance. 

Dissolution of polymers is a very slow process it can take days or even weeks for particularly high relative molar mass substances. Two stages are discernible during the process of dissolution. Firstly, a swollen gel is produced by solvent molecules gradually diffusing into the polymer. Secondly, this gel gradually disintegrates as yet more solvent enters the... 

Polymers undergoing dissolution show much smaller entropies of mixing than do conventional solutes of low relative molar mass. This is a consequence of... 

One factor which affects the extent of polymer-solvent interactions is relative molar mass of the solute. Therefore the point at which a molecule just ceases to be soluble varies with relative molar mass, which means that careful variation of the quality of the solvent can be used to fractionate a polymer into... 

The main polymers used as thickeners are modified celluloses and poly(acrylic acid). Several different modified celluloses are available, including methyl-, hydroxypropyl methyl-, and sodium carboxymethyl-cellulose and their properties vary according to the number and distribution of the substituents and according to relative molar mass of the parent cellulose. Hence a range of materials is available, some of which dissolve more readily than others, and which provide a wide spread of possible solution viscosities. Poly(acrylic acid) is also used as a thickener, and is also available in a range of relative molar masses which give rise to give solutions of different viscosities. 

The preferred term throughout this book is relative molar mass, but we should note that the use of this term is not common in polymer chenfistry. More often the older term molecular weight is used, both throughout the polymer industry and among acadenfic polymer scientists. This usage extends even to the current research literature. 

Table 6.1 Experimental methods for determining different types of average relative molar mass of polymers...

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is ... 

The temperature differences found experimentally are less than expected theoretically because of heat losses within the apparatus. As indicated in the earlier part of this chapter, the experimental approach is to measure these temperature differences at a number of different concentrations and extrapolate to c = 0. The apparatus is calibrated using standard solutes of low relative molar mass, but despite this, the technique can be used on polymers up to of about 40 000. 

The polarisability, a, of the molecule is proportional to the refractive index increment dn/dc, and to the relative molar mass of the molecule in question. The full relationship is ... 

Hence, the value of I/Iq is dependent on relative molar mass of the molecules involved in the light scattering. The Rayleigh ratio, Rg, may be defined as ... 

Equation (6.12) is important it shows that we can determine the relative molar mass of the molecule from the experimental measurement of the Rayleigh ratio in fight scattering. 

Overall, as is apparent from this description, light scattering is a difficult, time-consuming technique, despite its great importance. Despite this, the technique has been used to measure relative molar masses as low as that of sucrose and as high as those of proteins, and has been found to have a useful range for polymers of relative molar masses between ten thousand and ten million. 

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