Continuous Molecular Weight Distribution

These moments are useful in describing the dependence of rheological properties on the MWD, because different properties vary a great deal in their sensitivity to various portions of the distribution. For example, the zero-shear viscosity depends primarily on and only very weakly on the higher moments of the distribution, whereas the steady-state compliance is a very strong function of the breadth of the distribution, as described by the higher moments. 

The upper limit is set equal to infinity, because while the largest molecule present is probably very large, we never know exactly what its molecular weight is. Also, it is practically impossible to detect molecules of every size in a sample. Thus, as in the case of the discrete distributions, if we scale experimental data in the form of w M) so that Eq. 2.46 is obeyed, we say that the distribution has been normalized. 

There is, of course, also a continuous number distribution function, n(A4). The value of M at the peak in the curve of w M) is always larger than that at the peak of the (M) curve, if there is a peak in the latter. 

The function w(M) is called the differential molecular weight distribution. We can also define a cumulative distribution, F M), which is the fraction of all the molecules in the sample that have molecular weights equal to or less than M. This can be represented in terms of w(M) as shown by Eq. 2.47. 

Likewise, the differential distribution can be expressed in terms of the cumulative distribution. df(JVf )  

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Whiteley, K.S., Garriga, A. Derivation of continuous molecular weight distributions from the generating function. Comput. Theor. Polym. Sci. 11(4), 319-324 (2001)... 

A very elegant version of this approach is the so-called continuous thermodynamics [56-59]. It can be considered as a reformulation of the classical thermodynamic relationships that allows for using continuous molecular weight distribution functions W M) rather than the mole fractions of discrete polymer components. Using this approach, e.g., (30) becomes ... 

The sum in Eq. 2.96 can be replaced by an integral for use with a continuous molecular weight distribution to give ... 

Detailed modifications in the polymerisation procedure have led to continuing developments in the materials available. For example in the 1990s greater understanding of the crystalline nature of isotactic polymers gave rise to developments of enhanced flexural modulus (up to 2300 MPa). Greater control of molecular weight distribution has led to broad MWD polymers produced by use of twin-reactors, and very narrow MWD polymers by use of metallocenes (see below). There is current interest in the production of polymers with a bimodal MWD (for explanations see the Appendix to Chapter 4). 

Since all of the chains are intiated at about the same time and because growth continues until all of the styrene has been consumed, the chains will have similar lengths, i.e. there will be a narrow molecular weight distribution. In addition the chains will still have reactive ends. If, subsequently, additional monomer is fed to the reactor the chain growth will be renewed. If the additional monomer is of a different species to the styrene, e.g. butadiene, a binary diblock copolymer will be formed. 

Molecular Weight Distribution Control in Continuous-Flow Reactors... 

Reactor Conditions for Experimental Runs. Operating conditions for the continuous, stirred tank reactor runs were chosen to study the effects of mixing speed on the monomer conversion and molecular weight distribution at different values for the number average degree of polymerization of the product polymer. 

Since in continuous degradation processes it is expected to reach a molecular weight distribution of the products, which is optimal for their further use, the investigation was devoted to test the effect of a key parameter such as the enzyme to substrate ratio (E/S). For a fixed mean retention time in the UF-membrane reactor, the following behaviour can be... 

Polycarbonates are manufactured via interfacial polymerization or through a melt esterification process. The properties of polycarbonate can differ greatly based on the method of polymerization. Specifically, the molecular weight distributions created by the two methods differ because of kinetic effects. Polycarbonates manufactured via interfacial polymerization tend to be less stable at high temperatures and less stiff than those produced via melt esterification, unless proper manufacturing precautions are taken. Therefore, when choosing a polycarbonate resin grade for a specific application, it is important to know the method by which it was produced. Either polymerization method can be performed as a continuous or batch process. 

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