Impact of Mass Transfer Limitation of Polyurethane Reactions
February 2017 www.coatingsworld.com Coatings World | 47
Approach 2: Incorporating Rate of Diffusion into
Frequency Factor
Equation 13 is considered as a reaction rate expression for both
catalytic and homogeneous reactions. Good agreements were
obtained with the experimental result profiles. One value of A1
and A2 (shown in Table 4) was used for the rate of all reactions including homogeneous and catalytic reactions. A good fit
to the data demonstrates that these frequency factor values are
independent of the actual encounter complex where the impact
of catalysis is reflected in lower activation energies and catalyst
count complexes.
Table 4 lists the kinetic parameters used in the simulation
approaches for inter-and intra-molecular movements and the
frequency factor.
Conclusion
For a chemical reaction to occur, the reacting molecules need to
diffuse to proximity and a sufficient energy state to overcome
the activation energy. The impact of the rate of mass transfer on
reaction rate was simulated for rigid urethane polymerization
reactions using two approaches.
The first approach simulates the mechanism of the rate of
diffusion. This approach shows that the reaction is reaction
limited in the region before the gel point, and diffusion limited
after the gel point. When only the inter-molecular movement is
considered, the simulation results of the temperate profile stops
increasing at the gel point as the rate of diffusion of the moieties
decreases to zero due to the increase in viscosity.
Temperatures continue to increase after the gel point (infinite
viscosity) in urethane polymerization systems and, so, it is clear
that reaction mechanisms exist that do not rely on movement of
entire molecules relative to the polymer matrix. Reactions based
on moiety collisions from intra-molecular movement must be
responsible for reactions after the gel point and this mechanism
is in parallel with inter-molecular.
The second approach incorporates the sum of the inter- and
intra-molecular movements as a pre-exponential factor in the
Arrhenius equation. This approach uses fewer parameters and
solving fewer differential equations.
The two approaches provide a good fit to the experimental
data of reaction temperature and resin viscosity; however, the
use of diffusion mechanisms is critical to simulate polymerization and incorporating the diffusion mechanisms in the reaction
rate expression is more efficient. CW
Figure 6. Concentration profile of the encounter complex during the reaction
using inter-and intra-molecular movement. Blue and green lines represent the
complex concentration and viscosity profile respectively.
Figure 7 (left). Experimental data and simulation results of reaction temperature, viscosity profile, isocyanate moieties and polyol moieties considering
intra- and inter-molecular movement as a collision frequency factorion. Circles
and squares refer to experimental data of temperature and viscosity respectively. Black, green, blue, and orange lines refer to the simulation results of
temperature, viscosity, isocyanate moieties, and alcohol moieties respectively.
