Polymer molecular weight, true value

To enable a comparison of polymerization of different monomers and of catalysts based on different metals, activities are usually given as turnovers per hour, TO h (TO = mol substrate converted per mol of metal). When comparing activities determined by different authors under strongly varying conditions the values should be taken as an indication of the order of magrtitude. The same holds true for polymer molecular weights. 

The dependence of the second virial coefficient on basic quantities such as the solution ionic strength or the polymer molecular weight is usually of greater scientific interest than the knowledge of true vs. apparent values. Therefore the time-consuming dialysis step leading to true rather than apparent values is usually omitted. Hence measured second virial coefficients are usually only apparent values. 

Equation (2.57) provides a means of determining the relative contribution of the termination and transfer steps. Thus, if kp is largely relative to kt, the molecular weight will be virtually independent of monomer concentration, but if the reverse is true, X will be directly proportional to [A/]. Hence this relation lends itself to a simple experimental test, i.e., a plot of 1/X" (the reciprocal of the initial X value) against 1 /[MY (the reciprocal of the initial monomer concentration). It has actually been found that the polymerization of styrene by SnCU in ethylene dichloride (Pepper, 1949), and of vinyl alkyl ethers by SnCU in m-cresol (Eley and Richards, 1949), showed a dominance of termination over transfer, i.e., X a [M] however, for isobutylene polymerization catalyzed by TiCU in -hexane (Plesch, 1950), the observed polymer molecular weights were independent of monomer concentration, i.e., transfer appeared to predominate. 

The reptation idea could account for the effect of polymer molecular weight and solvent concentration on the dissolution rate. However the key concentration identified in this approach [57,59] is one at the surface. This implies independence of the solvent concentration history. This may not be true as the disentanglement of polymer chains does not commence till the local solvent concentration is greater than a critical value at which the local glass transition temperature is lowered below the experimental temperature so that the glassy polymer changes into a gel. Also, all of the efforts discussed so far failed to take into account the effect of the viscoelastic properties of the polymer on the dissolution mechanism. 

Equation (52) o (55) describes the experimental data quite well except at low molecular weights (large values of M % and has been used extensively to describe the T -M relationship for polymers. We note, however, that Gibbs and DiMarzio have pointed out that the glass is not a true iso-free-volume state, and the free-volume description of Simha and Somcynsky also precludes such a description of the glass transition. 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

From these definitions one may corroborate the intention of HTS in chemistry and materials science. The total speed-up factor of this part of the R D (Research and Development) process, as stated earlier, is between 5 and 50, but contrary to most of the pharma applications true (semi-) quantitative answers will result. As a result, this approach is essentially applicable in any segment of R D. On the other hand, this approach requires methods of experimentation that have almost the same if not the same accuracy as in the traditional one-experiment-at-the time approach. This is key as (i) in process optimisation accuracy is key and (ii) in research, also in academic research, accuracy is important as some polymer properties do not span a wide range of values (e.g., the elastic modulus of amorphous polymers) or may depend critically on molecular weight distribution or molecular order. 

In Eq. (88), dn0/dl expresses how the refractive index % of the binary solvent alone varies with its composition expressed as volume fraction 4>y of liquid-1. Clearly, if liquids 1 and 3 are iso-refractive or nearly so, then M = M2, that is, a LS experiment will yield the true molecular weight irrespective of the composition of the mixed solvent. This situation is exemplified133) by the system polystyrene -ethyl-acetate (l)-ethanol (3) for which the molecular weight in mixed solvents of different 0i is the same as that obtained in pure ethylacetate (Fig. 40). The values of dn /d0j for the mixed solvents are only of the very small order of ca. 0.01, whilst the values of dn/dc for the polymer solutions are large (ca. 0.22 ml/g). 

Table 10. Typical values of the selective adsorption coefficient y, as expressed as the ratio of the apparent (M ) to true (M) molecular weight for polymer - mixed solvent systems131 ...

If c and dc/dx are known as a function of x and the measurement is carried out in a theta solvent, the molecular weight M of monodisperse polymers can now be calculated precisely. If the solvent is not a theta solvent, the obtained value of M is an apparent molecular weight from which the true value can be calculated upon plotting 1/M vs. c and extrapolation to c —> 0. For polydisperse samples, one has to insert the average of dc/dx in the above equation, and the thus calculated molecular weight represents a weight-average,... 

Like dissolves like, and this is true with both polymers and smaller molecules. Thus linear amorphous polymers with nonpolar groups are typically soluble in nonpolar solvents with solubility parameter values within 1.8 H of that of the polymer. Thus polyisobutylene (PIB) is soluble in hot lubricating oils, and small amounts of high-molecular-weight PIB are used as viscosity improvers. 

In Table IV, the values of Mn, Mw, [77], and Mw/Mn for the PMMA fractions D and H and whole polymers 122-7 and 122-9 calculated from the direct Mv vs. PRV calibration curve are compared with the available corresponding true values. In general, the calculated values of [ ] from the direct calibration curve are larger than the true values at low molecular weights as indicated in the values for fraction D and tend to converge to the true values as the molecular weight increases as indicated... 

It was once thought that the Tc of THF was very low, in fact near room temperature (23). However, in recent years, as catalyst systems have been improved and more intensive studies have been carried out, the presumed Tc has risen first to 60—70° (18,24) and finally to 85 2° C (25, 26, 27). The lower values were probably the result of working with systems where a true monomer-polymer equilibrium was not obtained. Possibly also, careful enough techniques were not used in the isolation of the lower molecular weight polymers obtained near the ceiling temperature. Precipitation in water cannot always be used because low molecular weight PTHF s are partially soluble in water. 

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