Editing Dispersity (section)

==Effect of reactor type==
The reactor polymerization reactions take place in can also affect the dispersity of the resulting polymer. For bulk radical polymerization with low (<10%) conversion, anionic polymerization, and step growth polymerization to high conversion (>99%), typical dispersities are in the table below.<ref name=":0">{{Cite book|title= Polymerization Process Modeling|last1= Dotson|first1= Neil A.|last2= Galván|first2= Rafael|last3= Laurence|first3= Robert L.|last4= Tirrell|first4= Matthew|publisher= VCH Publishers, Inc.|year= 1996|isbn= 1-56081-693-7|pages= 260–279}}</ref>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Polymerization Method !! Batch Reactor !! Plug Flow Reactor (PFR) !! Homogeneous CSTR !! Segregated CSTR
|-style="text-align: center;"
| Radical Polymerization (RP) || 1.5-2.0 || 1.5-2.0 || 1.5-2.0 || 1.5-2.0
|-style="text-align: center;"
| Anionic Polymerization || 1.0 + ε || 1.0 + ε || 2.0 || 1.0-2.0
|- style="text-align: center;"
| Step-Growth || 2.0 || 2.0 || Unbounded (~50) || Unbounded (~20-25)
|}

With respect to batch and [[plug flow reactor model|plug flow reactors]] (PFRs), the dispersities for the different polymerization methods are the same. 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. [[Continuous stirred-tank reactor|Continuously stirred-tank reactors]] (CSTRs) however have a residence time distribution and cannot mirror batch or plug flow reactors, which can cause a difference in the dispersity of final polymer.

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.<ref>{{Cite book|title= Introduction to Polymer Science and Chemistry: A Problem-Solving Approach, Second Edition|last= Chanda|first= Manas|publisher= CRC Press|year= 2013|isbn= 978-1-4665-5384-2}}</ref> 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. For FRPs that have a constant monomer and initiator concentration, such that the [[degree of polymerization|DP<sub>n</sub>]] is constant, the dispersity of the resulting monomer is between 1.5 and 2.0. As a result, reactor type does not affect dispersity for free radical polymerization reactions in any noticeable amount as long as conversion is low.

For anionic polymerization, a form of [[living polymerization]], the reactive anion intermediates have the ability to remain reactive for a very long time. 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. For a homogeneous CSTR, the residence time distribution is the [[geometric distribution|most probable distribution]].<ref>{{Cite book|title= Chemical Reaction Engineering, Third Edition|last= Levenspiel|first= Octave|publisher= John Wiley & Sons|year= 1999|isbn= 0-471-25424-X}}</ref> 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.<ref name=":0"/>

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 2.0. Running a step-growth polymerization in a CSTR will allow some polymer chains out of the reactor before achieving high molecular weight, while others stay in the reactor for a long time and continue to react. The result is a much more broad molecular weight distribution, which leads to much larger dispersities. For a homogeneous CSTR, the dispersity is proportional to the square root of the [[Damköhler numbers|Damköhler number]], but for a heterogeneous CSTR, dispersity is proportional to the natural log of the [[Damköhler numbers|Damköhler number]].<ref name=":0"/> Thus, for the similar reasons as anionic polymerization, the dispersity for heterogeneous CSTRs lies between that of a batch and a homogeneous CSTR.