Polyurethane formulation simulation could save time, money

A team at the University of Missouri is working on a new approach to polyurethane systems formulation that leans heavily on experience gained in the chemical engineering sector.

The goal is to be able to simulate virtual formulations to make the process of designing real formulations faster, cheaper and more efficient.

Putting computer simulation at the heart of formulations design has the potential to transform the polyurethane industry in the same way that process simulators have transformed engineering design.

If the process is as successful in polyurethane formulation design as it has been in engineering design, it will enable faster and better development of new formulations as well as the use of bio-based raw materials. It will also improve our understanding of fundamental processes, and as a bonus, the application of artificial intelligence will help to efficiently address aspects of safety, environment, and patentability.

The university group is several years into developing a formulation simulation system that would achieve these goals. They are beginning to realise both expected and unexpected benefits.

Why use simulation?

Simulators are used to model a large number of systems and processes which can be understood in physical chemistry terms through multiple differential equations. Improving computing power gives simulators access to dozens of reaction and thermodynamic parameters, and several degrees of freedom. These complexities are as relevant to building a complex petrochemical plant as to the smaller but equally complicated job of designing and modelling the chemical and physical processes in polyurethane foam-forming processes.

In chemical engineering, for example, once thermodynamic and kinetic parameters are obtained for pure components, the formulation simulation is able to predict the behavior of the many combinations of these pure components. The same is increasingly true of polyurethane formulations.

The Missouri team has examined the processes used in making a viable polyurethane formulation and looked at the levels of complexity in each stage. It grouped these into four sets ranging from the comparatively simple in Level 1 to complex in Level 4. This gave the team a direction of work and it has substantially completed all of the Level 2 problems.

The details of all the methods and applications use, and yet to use, exceed the space available, so the team will concentrate on three current predicted temperature profiles, tack-free times, and successful foam formation with a short look at possible applications of vapour phase emissions of foams.

Figure 1 shows representative concentration, temperature, degree of polymerisation, and height (density) profiles generated by the simulation.

Figure 1.  Typical profiles generated by simulation of box foam.  Unreacted monomer concentration is not included in the degree of polymerisation calculation.

Temperature profiles provide an indirect measure of reactivity.  If the temperature profile of a good-performing foam is measured or known, that profile can be used to benchmark the performance of the formulation simulation against reality and it can be used to tune the simulation to more closely match reality.

For example, preheating reactants give faster reaction rates; simulation can help identify how much catalyst loadings can be lowered to give the same reaction profile as the control recipe without preheating.

In another example, some foams must only achieve a very minimal peak exotherm to enable the final foam to cure properly and meet specification. Here simulation can be used to predict how alternative monomers, preheating and co-reagents would affect temperature profiles.

Tack-free times are a standard property used to tell if a formulation will cure within a time frame to enable further processing.  The tack-free time correlates closely with the gel time of the polyurethane.   The rate of polymer formation, inter-polymer reaction, and intra-polymer reaction is simulated in Figure 1.  The polymer concentration profile includes an initial increase in polymer concentration (mol/l) followed by a decrease in concentration due to polymer-polymer reactions. Polymer concentration will typically rapidly decrease and approach zero at the point where crosslinking is so substantial that the entire solution is essentially one molecule.  This is the gel point.  The tack-free point closely follows the gel point in time.

Figure 2.  Illustration of viscosity window where successful foams can be formed by the evaporation of blowing agents or reaction of water to form carbon dioxide.

Predicting a successful foam formation, versus a failure, is show in Figure 2.  This is a more complex algorithm.

Just as the degree of polymerisation profile shown above in the tack-free time calculations, the viscosity profile of the reaction mixture can be estimated by a group-contribution approach.  Group contribution approaches can be used to estimate physical properties of large molecules where the molecular property is estimated as the sum of contributions to that property by the parts of that large molecule.  For a reaction mixture undergoing polymerisation, the mixture may have hundreds of different molecules which can be represented by about a dozen different groups—basing properties on the groups is a much more manageable task.

Parallel calculations can be used to estimate the extent to which the blowing agent evaporates in the reacting mixture.  A comparison of the viscosity to evaporation shown in Figure 2 gives an estimate of the efficacy of foam formation.  If large increases in viscosity happen before enough blowing agent has evaporated then, large amounts of blowing agent can become entrapped in the resin not the foam cell. This leads to inadequate rise and gives higher densities than desired.  If the blowing agent evaporates before the viscosity is high enough, gases can escape from the mixture and a spongy or solid polyurethane is formed rather than a foam.  Only within a window of properly matched evaporation and viscosity increase does the blowing agent effectively form a foam of the right density.

Making Progress

In the team's formulation simulation, Level 1 and Level 2 calculations were based on estimates of bulk resin and bulk gas properties. the team also applied empirical physical property models such as those used for group contribution estimates of viscosity and for estimating the impact of degree of polymerisation on mass transfer of blowing agent in the resin phase.  Many of the Level 3 and Level 4 advances require more information on the morphology of the resin phase such as hard segment versus soft segment properties and formation. They also call for an understanding of the displacement of empirical physical property models from fundamentally based models.  Work on the Level 3 calculations is just starting.

Fortunately, even at the Level 2, there are many useful applications in addition to the three described above. These include characterisation of polyol properties, hydroxyl number, fraction of each type of alcohol group, functionality, and equivalent molecular weight.  Figure 3 shows the reaction profile details which are useful in characterising a polyol.

Figure 3.  Illustration of key profile details useful for obtaining parameters to characterise polyols.

The characterisation method is based on the rheology of a gel and we simultaneously measure the temperature and rheology profiles. The rate of rise of the temperature profile curve is gives us the fraction of primary, secondary, and hindered secondary hydroxyl groups. In turn, this indirectly specifies the reactivity in terms of Arrhenius reaction parameters for each of these reactive species.  The maximum temperature difference is useful for finding the hydroxyl number based on heats of reaction.  Finally, the gel point gives us functionality.

While locations of the profile can be directly related to physical properties of the polyol, the simulation package considers the entirety of both profiles in the calculations to maximise accuracy.   For example, the rapid increase in viscosity as the gel point approaches is highly dependent upon the functionality of the monomers, and so, that part of the rheology would be used to estimate the functionality of a sample of unknown functionality.

Simulation is often used in environmental impact analyses.  The polyurethane industry typically takes air samples close to the foam after the initial foaming process is complete to determine emissions.  This approach has a number of shortfalls: the measurements tend to be over a few points in time and are not continuous; they give no indication of how to reduce some types of the emissions; and, fundamentally they are not usually able to identify the causes of the emissions.

Simulation can provide continuous profiles which can be compared to experimental measurements. The different components of the simulation – like index, peak temperatures, blowing agent mix -- can then be varied to identify how critical emissions can be reduced by adjusting the formulation.

To the future

Because the simulation package, is based on fundamental properties and parameters of the components that make up the formulation it allows performance to be directly related to those fundamental properties and to provide insight on how to further reduce emissions.  This could be useful for immediate solutions or for setting the path for research into more efficient longer-term solutions.

Formulation simulation bridges the gap between fundamental kinetic and thermodynamic parameters and application in thermoset polymerisation.  As a result, computational chemistry approaches that are able to predict trends in reactivity can find increased application for commercial products.

An exciting aspect of simulation of thermoset polymerisation is the ability to enable fundamental sciences to more directly impact commercial product development.  Niche successes in this application can expand and transform how new materials are created.  The databases and standards of performances established by simulators can form a foundation for advancing science and engineering that exceed alternatives like archival refereed publications.  Simulators represent a key step in evolution of science and technology when fields reach a certain point of sophistication.

This paper was written by

Galen J. Suppes, Professor [email protected]

Al-Moameri, Harith H. (MU-Student)

Ghoreishi, Rima . (MU-Student)

Zhao, Yusheng (MU-Student)