Harith H. Al-Moameri and Galen J. Suppes,
Chemical Engineering, University of Missouri, Columbia, MO
Abstract
During urethane reactions, large changes in viscosity lead to
large changes in mass transfer rates. After the gel point, the
mass transfer of blowing agents from the gel to cells essentially
ceases; however, mass transfer for reactions continues, albeit at
a slower rate. This paper discusses fundamental approaches to
account for the impact of these changes in mass transfer on reaction rates.
Three different approaches were studied to describe the rate
of molecular movement of the reactive moieties during polyurethane reactions. Inter- and intra-molecular moiety movements
were studied as separate diffusion steps. Inter-molecular movement stops at the gel point and intra-molecular movement has
been added to describe moiety movement after the gel point. The
collision frequency factor in the Arrhenius equation was modified based on inter- and intra-molecular approaches. Simulation
results for reaction temperature and viscosity profiles show
good agreement with the experimental data.
Introduction
Diffusion-limited reactions are reactions that occur quickly and
the rate of diffusion of the reacting components in the reaction medium is the limiting step. Smoluchowski [1], Collins and
Kimball [2], and Noyes [ 3] were the first to discuss and develop
this phenomena. When the reacting components are mixed in a
reacting media, diffusion rate is proportional to the time it takes
to bring these components (or the reactive part in these components) into a reacting distance to allow a reaction to occur.
For a liquid phase reaction, the viscosity of the reaction mixture is the key physical property to which rates of diffusion correlate. In a thermoset polymerization reaction, the viscosity of
the resin increases due to the formation of long chain polymers
and polymer crosslinking. This leads to increasing viscosity and
decreasing the rate of diffusion of the reacting components. For
thermoset reactions, viscosity ultimately approaches infinity
and, so, diffusion becomes the controlling step at some point
during polymerization.
For a simple irreversible reaction of two reacting compo-
nents, A and B, the diffusion and the reaction steps can be rep-
resented by the following steps:
• The diffusion of the two components from a large separate
distance in the reaction medium to a proximity at which
the chemical forces become dominant and the pseudo spe-
cies (AB)* is forming.
• The dissociation of the pseudo species as the reacting components diffuse apart.
• The reaction of the pseudo species to form a product.
The pseudo species (AB)* is considered as an active complex
if it is at the saddle point of the potential energy surface of A and
B, or as a collision complex if there is no interaction between A
and B. The term “encounter complex” has been used to cover
cases of either the active or collision complex [ 4].
Polyurethane (PU) forming reactions were considered for
studying and discussing the impact of diffusion of the reacting
components on the reaction rates during the reaction. A polyurethane is defined as a long chain of organic units joined by
urethane links. Alcohol moieties in the polyol and isocyanate
moieties react to produce urethanes according to Equation 2.
The properties of the polyol and the isocyanate (molecular
structure and molecular weight) impact the properties of the
polyurethane produced [ 5]. Catalysts, crosslinkers, and light
stabilizers also impact the polymerization reaction [ 6-8].
Modeling Approaches
This paper discuss two approaches to provide an insight and effective method to more accurate simulation of urethane forming
reactions. These approaches are as follows.
• Approach 1a assumes that the reactive moieties diffuse together in the mixture to form an encounter complex which
may disassociate or react to form a product. This type of
diffusion is considered as the inter-molecular movement of
the reactive alcohol and isocyanate moieties.
• Approach 1b is intra-molecular movement of the reactive
moieties which is considered in parallel to the inter-molecular movement. Intra-molecular movement is the movement of segments of the molecule (no breaking of chemical
Impact of Mass Transfer Limitation
of Polyurethane Reactions
