Equilibrium molecular weight distribution

Solution viscosity measurements for Mn are calibrated from the flow characteristics of linear molecules of the equilibrium molecular weight distribution. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. One, therefore, expects different flow properties as branching increases, hence causing the viscosity numbers to become less and less accurate and so should only be used for trends - not exact calculations. 

The molecular weight increases with increasing conversion. Regulation of the molecular weight can be achieved by adding small amounts of substances (e.g., benzoic acid) that can react with the polyamide chains by transamidation. Because of the transamidation reaction and hydrolysis of amide bonds, an equilibrium molecular-weight distribution is finally attained (see Sect. 4.1). 

Transamidation is an important process in the melt phase for polyamides because it is usually the process by which an equilibrium molecular weight distribution is reestablished and, in the case of the melt blending of two or more polyamides to form a copolymer, it is the process by which randomization of the individual monomers along the chain is effected. In the solid phase, chain mobility is restricted and equilibrium in either case often is not achieved. 

MQ is usually made by a condensation polymerisation, which gives a theoretically dictated equilibrium molecular-weight-distribution. This means there is significant amount of the low MW fraction. The extremely low MW fraction is removed prior to finish manufacturing. However, the intermediate low MW fraction weakens the crosslinked product, because the free-ends do not contribute to the strength. The condensation mechanism does not create a very high MW tail, which is often found with other rubbers. The polymer may also be made with an anionic system. In this case the MW distribution is very narrow and it does not contain a low MW fraction. 

The theoretical equilibrium molecular weight distribution for the system... 

Howardt describes a model system used to test the molecular weight distribution of a condensation polymer The polymer sample was an acetic acid-stabilized equilibrium nylon-6,6. Analysis showed it to have the following end group composition (in equivalents per 10 g) acetyl = 28.9,... 

Generally, the models used for simulation of living polymers can be divided roughly into two classes, focused on static or dynamic properties of the LP or GM. The static models are mainly designed to study equilibrium conformational properties of the polymer chains, critical behavior at the polymerization transition, and molecular weight distribution... 

The equilibrium between monomer and living polymer is dynamic and therefore the molecular weight distribution of the polymer will change with time until the equilibrium distribution is reached. This is a peculiar process in which the amount of polymer present in the system, as well as its number average molecular weight is constant. This means also that, the number of polymeric... 

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

Failure to remove the alcohols generated in either of the equilibrium condensation steps will reduce the efficiency of the polymerization process. This effect can be explained by Le Chatelier s principle, which was discussed in Chapter 3. The volatile alcohols produced during polymerization act as a chemical stress on the product side of the reaction, which inhibits polymerization. Another implication of the equilibrium nature of this polymerization process is seen in the molecular weight distribution of the final polymer. All polyesters contain a few percent of low molecular weight oligomers, regardless of the polymerization process. 

Additionally, deactivation rate constants (kd) for the more active catalysts such as Cu X/Me4CYCLAM have been estimated from the initial degree of polymerization without reactivation, end functionality, and molecular weight distributions [138,141,142], With recent advances in determination of the equilibrium constant for atom transfer (KATRP=kJkd), deactivation rate constants (k =k KX[M,) can now be easily obtained from readily accessible activation rate constants (k) [115],... 

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