polymer systems, the frequency factor should include a driving
force for collision according to Equation 11.
To quantify this driving force, these rates were multiplied
by the probability of successful reaction as a result of collision which is referred to as the steric hindrance factor “ρ”. This
mechanism results in Equation 12.
Substituting this result into Equation 8 and Equation 9 yields
Equation 13.
This approach requires two fitted kinetic parameters as compared to modeling diffusion separately which requires a total of
four parameters.
Several researchers proposed different mechanisms, ap-
proaches, and equations to identify the impact of resin viscosity
and mass transfer limitation during the reaction [ 12-15]. These
works included assumptions such as:
• Constant rate of reaction.
• Neglecting the impact of temperature changes.
• Using empirical or semi-empirical equations for rates of
diffusion and reaction.
The results of these studies are highly specific to the sys-
tem studied. The research presented here differs from previous
works as follows:
• The impact of mass transfer on polymer reactions was suc-
cessfully evaluated using two fundamental approaches.
• Modeling is performed through the gel point where there is
a transition from the mass transfer from the inter- to intra-molecular movement.
• Modeling is performed with over 50 ordinary differential equations to account for the elementary reactions
and processes.
The fundamental nature of the research presented in this
paper, including approaches to account for mass transfer
in the frequency factor of reaction rates, has the prospect
of being widely applicable to a number of polymerization
reactions.
Simulation has been built on the simulation code of Zhao,
Ghoreishi, and Al-Moameri [ 5, 6, 16-19] for the reaction kinetics and blowing agents. Group contribution simulation
presented by Fu [ 20] has been used for viscosity calculations.
Experimental
Table 2 shows the gel formulation of the urethane forming reaction. The experiments were performed by the following steps.
1. The B-side components in Table 2 were mixed together in
a closed beaker.
2. The A- and B-side materials were poured in a plastic cup
and mixed using a 2000 rpm mixer blade attached to a
floor-model drill press for 10 seconds.
3. LabView software with type-K thermocouple was used to
measure reaction temperature.
4. The viscosity profiles of the polyurethane gel were measured using a Cole-Parmer basic viscometer.
All experiments were carried out at ambient temperature to
avoid deviations in reaction kinetics [ 21].
Mixing rate was kept the same for all gel experiments as it
may affect the viscosity profiles [ 22]. All experiments were carried out at ambient temperature in order to avoid deviations
in reaction kinetics and molecular weights of the polymer [ 21].
Foam forming data from a previous publication [ 17] was used
to evaluate the simulation approaches of this paper in foam-forming reactions. Table 3 shows the specification of the polyol
and isocyanate.
Table 2. Formula for polyurethane gel reaction.
Table 3. Specifications of P360 and PMDI.
