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A mathematical approach for the analysis of data obtained from the monitoring of biocides leached from treated materials exposed to outdoor conditions

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Leaching processes are responsible for the release of biocides from treated materials into the environment.
Adequate modeling of emission processes is required in order to predict emission values in the
framework of the risk assessment of biocidal products intended for long-term service life. Regression
approaches have been applied to data obtained from the long-term monitoring of biocide emissions in
experiments involving semi-field conditions. Due to the complex interaction of different underlying
mechanisms such as water and biocide diffusion and desorption, however, these attempts have proven to
be of limited usefulness e at least, for the available biocide emission data. It seems that the behavior of
the biocide emission curve depends to a considerable extent on whichever underlying mechanism is
slowest at a given point in time, thus limiting the amount of biocide available for release. Building on
results obtained in the past few years, the authors propose a criterion for determining which mechanism
controls the leaching process at a given point in time based on the slope of the log-log emission curve. In
addition, a first-order approximation of this slope value is presented which displays advantages both in
terms of computability and interpretability. Finally, an algorithm for the determination of breakpoints in
the slope of the log-log emission curve is presented for the demarcation of phases within which one
mechanism acts as a limiting factor.

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