Impact of Mass Transfer Limitation of Polyurethane Reactions
February 2017 www.coatingsworld.com Coatings World | 45
Results and Discussion
Approach 1a: Inter-Molecular Diffusion Rate
The experimental and simulation results of reaction temperature and viscosity profile for the formulas in Table 2 are shown
in Figure 1. For the diffusion of the reacting moieties considered
as only inter-molecular diffusion, the simulation shows that the
reactions stop at the gel point. Resin viscosity increases to infinity at the gel point and the rate of diffusion of the reacting
moieties decreases to zero according to Equation 6. After the
gel point, the temperature and height cease to increase and un-reacted moieties cease to further react. The good fit of the simulation results of reaction temperature and viscosity profiles in
the region before the gel point supports using the second order
reaction kinetic parameter and fraction alcohol moieties that
were reported in previous studies [ 5].
Figure 2 shows the ratio of the diffusion rate to the reac-
tion rate. The results show that the ratio is decreasing rapidly
when the viscosity of the resin increases rapidly at the gel point.
In comparison, the rate of reaction increases according to the
An example of a concentration of one encounter complex
(AB)* is shown in Figure 3. The higher rate of diffusion at the
beginning of the reaction leads to instant increase in complex
concentration, and then the concentration decreases as the driv-
ing force for formation of the encounter complex decreases.
Approach 1b: Inter- and Intra-Molecular Mass Transfer
The simulation results of Figure 4 show that the reactions continue after the gel point. The movement of sections of a polymer
allow the reaction without a net movement of polymer molecules relative to each other. This result supports the addition of
the intra-molecular movement.
The A1 and A2 parameters in the rate of diffusion were optimized to provide a fit to the data.
Figure 1. Experimental data and simulation results of reaction temperature,
viscosity profile, isocyanate moieties and alcohol moieties considering the
inter-molecular movement approach. 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.
Figure 2. Ratio of the rate of diffusion to the rate of reaction for inter-molecular diffusion. Blue and green lines represent the ratio and viscosity profile
respectively.
Figure 3. Concentration profile of the encounter complex during the reaction
using inter-molecular movement. Blue and green lines represent the complex
concentration and viscosity profile respectively.
