Nearly all natural polymers are monodisperse. A polymer material is denoted by the term disperse, or non-uniform, if its chain lengths vary over a wide chemical reaction engineering levenspiel solution pdf of molecular masses. This is characteristic of man-made polymers. In this sense, the dispersity values are in the range from 0 to 1.
For some natural polymers Đ is almost taken as unity. Typical dispersities vary based on the mechanism of polymerization and can be affected by a variety of reaction conditions. Such is the case also in biological polymers, where the dispersity can be very close or equal to 1, indicating only one length of polymer is present. The reactor polymerization reactions take place in can also affect the dispersity of the resulting polymer.
This is largely because while batch reactors depend entirely on time of reaction, plug flow reactors depend on distance traveled in the reactor and its length. Since time and distance are related by velocity, plug flow reactors can be designed to mirror batch reactors by controlling the velocity and length of the reactor. The effects of reactor type on dispersity depend largely on the relative timescales associated with the reactor, and with the polymerization type. In conventional bulk free radical polymerization, the dispersity is often controlled by the proportion of chains that terminate via combination or disproportionation.
The rate of reaction for free radical polymerization is exceedingly quick, due to the reactivity of the radical intermediates. When these radicals react in any reactor, their lifetimes, and as a result, the time needed for reaction are much shorter than any reactor residence time. As a result, reactor type does not affect dispersity for free radical polymerization reactions in any noticeable amount as long as conversion is low. In batch reactors or PFRs, well-controlled anionic polymerization can result in almost uniform polymer. When introduced into a CSTR however, the residence time distribution for reactants in the CSTR affects the dispersity of the anionic polymer due to the anion lifetime.
Since the anionic polymerization dispersity for a batch reactor or PFR is basically uniform, the molecular weight distribution takes on the distribution of the CSTR residence times, resulting in a dispersity of 2. Heterogeneous CSTRs are similar to homogeneous CSTRs, but the mixing within the reactor is not as good as in a homogeneous CSTR. As a result, there are small sections within the reactor that act as smaller batch reactors within the CSTR and end up with different concentrations of reactants. As a result, the dispersity of the reactor lies between that of a batch and that of a homogeneous CSTR. Step growth polymerization is most affected by reactor type. To achieve any high molecular weight polymer, the fractional conversion must exceed 0. 99, and the dispersity of this reaction mechanism in a batch or PFR is 2.