Test article mass (g) - Please enter the total mass of the test article being evaluated expressed in grams.

Test article density (g/cm³) - Please enter the (approximate) density of the test article in grams per cubic centimeter.

Test article surface area (cm²) - Please enter the surface area of the test article in square centimeters.

Solvent volume (ml) - Please enter the volume of solvent used for each extraction iteration in milliliters.

# of iterations - Please enter the number of iterations used in the extraction study.

Time per iteration (h) - Please enter the extraction time for each iteration in hours.

Note: The extraction efficiency module makes the default assumption that all extraction iterations are equivalent in duration. However, if this is not the case, the module can still be used, although the input must be modified. Because of approximate scaling relationships, a single step extraction will be equivalent to an iterative extraction provided the the total solvent used and total time duration are also equivalent. For example, a three step iterative extraction using 10 ml for each iteration with time points of 24, 72, and 168 hours can be modeled using a single step extraction (# of iterations = 1) with 30 ml of solvent (3 x 10 ml) for 168 hours. This same approach can be used if the solvent volumes are different for each extraction iteration, however unlikely this scenario may be.

Diffusion coefficient (cm²/s) - Please enter a diffusion coefficient in square centimeters per second.

Note: The diffusion coefficient (D) is a material property that reflects the rate at which a compound can migrate through the matrix - formally it is a proportionality constant relating concentration gradient to flux. The value of D can vary dramatically depending on the polymer matrix and extractable compound, and even extraction solvent, for systems that exhibit significant swelling. If you are interested in comparing the extraction efficiency for a specific compound, we recommend estimating D for the system of interest based on available data. For comparing experimental conditions for extractable compounds in general, we recommend probing an appropriate range of D for the systems of interest. For example, compounds in the Mw range of 200 to 1200 g/mol extracted from HDPE have been found to lie in the range of 1e-9 to 1e-13 cm2/s for IPA and 1e-7 to 1e-9 cm2/s in hexane [1].

[1] P. Turner, et al., Toxicological Sciences 178 (1) (2020) 201–211.

Partition coefficient - Please enter a partition coefficient of interest for your system.

Note: The partition coefficient (K) is a material property that reflects the ratio of the concentrations of extractable compound in the polymer matrix and extraction solvent in equilibrium. As such, the value of K can vary dramatically depending on the extraction materials. If you are interested in comparing the extraction efficiency for a specific compound, we recommend estimating K for the system of interest based on available data. A number of empirical approaches have been developed for this purpose, e.g. [1,2]. However, these approaches do not necessarily capture the potential impact of temperature and matrix swelling, which can both dramatically impact this quantity [3-5]. For comparing experimental conditions for extractable compounds in general, we recommend probing an appropriate range of K for the systems of interest. We note that the range of interest will be restricted because large values of K will not permit substantive quantities of a compound to be extracted over relevant timeframes and for systems with small values of K extraction efficiency will be dictated solely by kinetic limitations.

[1] M. H. Abraham, et al., Journal of Chromatography A 1037 (1-2) (2004) 29–47.
[2] D. R. Jenke, B. E. Rabinow, PDA Journal of Pharmaceutical Science and Technology 71 (3) (2017) 225–233.
[3] T. P. Gandek, et al., Industrial & Engineering Chemistry Research 28 (7) (1989) 1036–1045.
[4] A. Hauk, et al., European Journal of Pharmaceutical Sciences 163 (2021) 105841.
[5] P. Turner, et al., Toxicological Sciences 178 (1) (2020) 201–211.

M / M₀ - Predicted extraction efficiency expressed as a ratio of total mass released over the initial mass (total pool) in the polymer matrix

C / C₀ - Predicted relative solvent concentration expressed as a ratio of extraction solvent concentration and the initial concentration of the extractable compound in the polymer matrix