# Effect of temperature in the free radical polymerization of acrylic acid

I am working with the model of a free radical polymerization process in a tubular reactor. In the simulations, I observe that by keeping the feed flow of the initiator (sodium persulfate) and the monomer (acrylic acid) constant and just by increasing the jacket temperature, the concentration of the monomer (for example of the product) increases, even though the reaction is exothermic. I have used the method of moments to model the chain length distribution of polymers. Change of viscosity has not been modeled.

My question is: Is the increase in the monmoer concentration by the increase of temperature, an expected behavior in polymerization? If so, do you know some literature that I can learn more about this?

• Can you please make clear what kind of simulation this is?
– Karl
Aug 26, 2016 at 9:26
• Actually, I am working on the design of a model-based controller for this. The controller works properly and there is no problem in that part. But in the simulation of the process, I observe the above mentioned phenomena which seems a bit wierd for me.
– Reza
Aug 26, 2016 at 9:34
• You are not explaining what your simulation takes into account and how it works. The way it is, this question should get closed. There is no way to answer it.
– Karl
Aug 26, 2016 at 10:54
• So you need those kind of details... The model consists of 8 pdes, which describe the evolution of following states: Initiator and Monomer concentrations, zeroth, first and second moment of active polymers, first and second moment of inactive polymers and temperature. The reation rate coefficients are modeled by Arhenius approach. Viscosity is not taken into account. No fouling is considered. If you need to know some other details, I can provide.
– Reza
Aug 26, 2016 at 11:06
• So it is a simple chemical reaction kinetics model. Please put that in the question. And what do you mean by "conversion reduces"? The rate? The final absolute conversion after some end condition you impose is reached? By making a secret out of essential parts of your problem, you waste everybodys time!
– Karl
Aug 26, 2016 at 11:41

Yes, this is expected.

With higher temperature, there is a larger concentration of radicals in the polymerization mixture, and initially the polymerization goes faster than at lower temperatures. This leads to a faster increase in viscosity, which slows the ability of molecules to diffuse in solution. This means it is more difficult for unreacted monomer to find growing radicals, and for unreacted initiator to find monomer. Radicals are highly reactive so when they can't react the have a habit of engaging in termination reactions which are nonproductive regarding conversion.

This is normally called autoacceleration, and is fairly well described in Odian's 'Principles of Polymerization'. Generally, you do not need to heat radical polymerizations beyond the bare minimum to decompose your thermal initiator.

• Thanks a lot for the response and clear explanations. The thing which I still do not understand is that, in the simulations, the concentration of the monomer, under the conditions which I have pointed in the question, increases. If by increasing the temperature, the concentration of the monomer would remain constant, it would be more understandable for me. Can you imagine that this behavior is correct? Thanks in advance,
– Reza
Aug 25, 2016 at 15:19
• You are going much too fast. At higher temperature, the initiator decays much more rapidly, increasing the radical concentration and thereby also the rate of recombination. The radical chain reaction itself is not so very much influenced by the temperature (being exothermic, it actually slows down at some point). The result is leftover, unreacted monomer, and very few radicals left to work on them. What you describe is the "Trommsdorff-Norrish effect", btw. I'll doubt that this "simulation" takes viscosity into account. Does it?
– Karl
Aug 25, 2016 at 21:29
• Thanks @Karl for the response. Actually, we do not consider viscosity into account in the simulations. But as a fact, we know that viscosity increases as the polymerization progresses.
– Reza
Aug 26, 2016 at 8:32