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Using the Beer-Lambert Law and Kubelka-Munk Theory to Model Percent Transmittance of Multilayer Composite Coatings

Transmission of light through automotive topcoat and primer layers can lead to degradation of the underlying electrocoat layer and to topcoat delamination. In order to protect against this, it is critical that transmission of both ultraviolet wavelengths and certain visible wavelengths be effectively blocked by the topcoat and primer layers. The clearcoat, basecoat and primer each have their own role and combine to protect against light transmission. The transmittance of these combined layers is typically measured by the Integrating Sphere UV-Visible Spectrophotometer. It would both simplify measurement of the topcoat systems and allow better system modeling if these layers could be measured separately and combined mathematically. We demonstrate here that absorbing and reflecting pigments can be effectively modeled using the Beer-Lambert law while results for scattering pigments are consistent with the Kubelka-Munk theory. By using these models, with the proper consideration for boundary conditions between layers, one can combine several individual layers and correctly predict the total topcoat transmittance. This is demonstrated for even complicated multilayer colorcoats such as white pearls. These models further allow interpolation within and extrapolation beyond the dataset used for generating the models.

Donald H. Campbell, BASF Corp.

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