Distribution of relative molecular mass

The phrase typical length of chain was used above because, unlike those of other chemical compounds, the molecules of polymers are not all identical. There is a distribution of relative molecular masses Mf) often called molecular weights) and the corresponding molar masses, M. This topic is considered further in section 3.2. The value of Mr for the chain considered in the previous paragraph would be 280 000, corresponding to M = 280 000 g mol. Commercial polymers often have average values of M between about 100000 and 1000000 g moP, although lower values are not infrequent. 

Distribution of relative molecular mass for two low density polyethylenes determined by gel permeation chromatography one with a narrow distribution, the other broad (after R. B. Staub and R. J. Turbett, Modem Plastics Encyclopedia. 1973-4). 

The two cases considered above are rather idealized and in practice the situation may be very much more complicated. For instance, the mechanism of termination may be a mixture of combination and disproportionation, branching reactions may occur and chain transfer can take place. All of these may affect the distribution of relative molecular mass. 

The observation of molecular size or polydispersity and the subsequent determination of relative molecular mass, (MJ or molecular mass (weight) distribution (MWD), is the most common analytical application of SEC. The goal of these types of experiments is to either observe the solvated size of one or more molecular species or to observe the distribution of sizes present in a mixture... 

Using regression analysis on a data set of about 50 different molecules, it was found that a. = —4.4,8 = —0.5, Df = 12 cm2/s, and =2.5x 10 5 cm2/s [192], A graphic representation of the effect of relative molecular mass (Mr) and distribution coefficient on corneal permeability is shown in Fig. 13. One observes a rapid reduction in permeability coefficient with decreasing P and increasing Mr. The addition of pores to the model, a mathematical construct, is necessary to account for permeability of polar molecules, such as mannitol and cromolyn. These would also be required for correlating effects of compounds, such as benzalkonium chloride, which may compromise the... 

Colloidal systems are generally of a polydispersed nature - i.e. the molecules or particles in a particular sample vary in size. By virtue of their stepwise build-up, colloidal particle and polymer molecular sizes tend to have skew distributions, as illustrated in Figure 1.2, for which the Poisson distribution often offers a good approximation. Very often, detailed determination of relative molecular mass or particle size distribution is impracticable and less perfect experimental methods, which yield average values, must be accepted. The significance of the word average depends on the relative contributions of the various molecules or particles to the property of the system which is being measured. 

The distribution is thought of as a series of closeiy spaced fractions. The /th fraction, of which the specimen contains a mass W , is of relative molecular mass M/. 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

Relative molecular mass distributions for components of biochemical and polymer systems can be determined with a 10% accuracy using standards. With biochemical materials, where both simple and macro-molecules may be present in an electrolyte solution, desalting is commonly employed to isolate the macromolecules. Inorganic salts and small molecules are eluted well after such materials as peptides, proteins, enzymes and viruses. Desalting is most efficient if gels with relatively small pores are used, the process being more rapid than dialysis. Dilute solutions of macro-molecules can be concentrated and isolated by adding dry gel beads to absorb the solvent and low RMM solutes. 

A partially purified HIV viral lysate is laid onto a sodium dodecyl sulfate (SDS)-polyacrylamide gel slab and then electrophoresed, which distributes the HIV peptides through the gel by their relative molecular mass. The higher-molecular-mass proteins form bands near the top of the gel. The proteins on the gel are then transferred electrophoretically onto nitrocellulose paper. The paper is sliced into thin strips, each having the full distribution of HIV antigen bands. The strip is used as a solid support of an indirect immunoassay, and antigen-antibody reactions form insoluble colored bands on the strip. 

Also known as relative molecular mass. mo lek-ya-lar w3t) molecular-weight distribution org chem Frequency of occurrence of the different... 

Eq. 2 pKt, inhibition constant Mr, relative molecular mass, log D1A, logarithm of the distribution coefficient at pH 7.4 HBA, number of hydrogen bond acceptors. 

The use of MALDI-MS for the measurement of low molecular mass compounds is widely accepted now [61], but quantification remains problematic. The main problem is the inhomogeneous distribution of the analytes within the matrix [62]. This leads to different amounts of ions and therefore to different signal intensities at various locations of a sample spot. The simplest and most effective way to overcome this problem is the use of an appropriate internal standard [63]. The use of deuterated compounds with a high molecular similarity to the analyte as internal standards leads to a linear correlation between relative signal intensities and relative amount of the compound to be quantified (Fig. 4b) [64]. Using this approach it is possible to quantitate substrates and products of enzyme catalyzed reactions. Two examples were shown recently by Kang and coworkers [64, 65]. The first was a lipase catalyzed reaction which produces 2-methoxy-N-[(lR)-l-phenylethyl]-acetamide (MET) using rac-a-... 

MALDI-TOF mass spectrometry analysis of poly(methyl acrylate) prepared by the free-radical polymerization of methyl acrylate (MA) in the presence of a cyclic dixanthate under y-ray irradiation revealed that there are at least three distributions, i.e., molecular mass for [ 1-(MA) -H]+ of cyclic polymers, [1-(MA) -THF-H]+, and [1-(MA) -(THF)2-H]+ of linear polymers were observed. The relative content of the cyclic polymers markedly increases at a lower temperature, which may be related to the reduced diffusion rate and the suppressed chain-transfer reaction at the low reaction temperature [39]. 

The constant Kd is known as the partition, or distribution, coefficient. Some experimental results are collected in Table 1.19. It is important to note that the ratio c2/Cj is constant only when the dissolved substance has the same relative molecular mass in both solvents. The distribution or partition law may be formulated thus when a solute distributes itself between two immiscible solvents there exists for each molecular species, at a given temperature, a constant ratio of distribution between the two solvents, and this distribution ratio is independent of any other molecular species which may be present. The value of the ratio varies with the nature of the two solvents, the nature of the solute, and the temperature. 

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