## 1 Introduction  
Supercritical solvents and, in particular, supercritical carbon dioxide (sc-CO\({}_{2}\)) has gained world-wide attention in recent decades as a green processing media for the impregnation of porous matrices like wood, textile, monolithic and porous polymers with various solutes such as pharmaceutically active compounds, pesticides, or organometallic compounds, among others [1, 2, 3]. Sc-CO\({}_{2}\) is an environmentally friendly alternative to conventional organic solvents. The reasons for which sc-CO\({}_{2}\) has attracted attention are as follows: (1) its high diffusivity and low viscosity diminish mass transfer limitations; (2) mild conditions (above 31 \({}^{\circ}\)C, 73 bar), that are easily achievable with standard lab and industrial compressors and fittings, allow the processing of sensitive and thermoplastic materials; (3) non-flammability, low price, and GRAS status (generally recognized as safe) by the European Food Safety Authority and Food and Drug Administration(USA). Furthermore, impregnated materials can be recovered free of solvent residues by simple depressurization. As a result of all these advantages, sc-CO\({}_{2}\)-based processes have a great potential, particularly, for impregnation in the biomedical field [4; 5; 6; 7; 8]. Two mechanisms play the major roles in the impregnation processes: adsorption of the solutes on the matrix surface and precipitation upon solvent evaporation [1]. In this work, we mainly focus on the first mechanism and aim to quantify adsorption interactions between a given solute on a given matrix, which contributes to the rational development of such impregnation processes. Broadly, methods for studying adsorption equilibria in supercritical solvents can be classified into static and dynamic ones [9]. Although static methods offer superior precision, they are often too time consuming for screening of the affinity of numerous solutes towards a selected matrix. To ensure a high throughput, dynamic methods are employed instead [10; 11; 12; 13]. Dynamic methods rely on the fundamental link between thermodynamic and kinetic properties. One common example is the partitioning of the solute between an adsorbent and flowing fluid in chromatographic experiments, where retention factor \(k_{0}\) can be used to obtain distribution coefficients and adsorption isotherms [14]. Thus, supercritical fluid chromatography (SFC) using a porous matrix of interest as stationary phase and solutes injected into pure sc-CO\({}_{2}\) (mobile phase) can provide direct access to adsorption equilibria. Such an implementation of SFC is referred to as inverse SFC (iSFC), stressing the fact that retention characteristics of a single solute are studied. Using fundamental thermodynamic relations for the retention factor \(k_{0}\) (Subscript \"0\" refers to the condition of using pure sc-CO\({}_{2}\) as mobile phase) [14; 15], iSFC with pure sc-CO\({}_{2}\) as a mobile phase has been used to determine distribution coefficients, adsorption enthalpies, and partial molar volumes at infinite dilution on activated carbons, resins, and plain and modified silicas (see [14]). Typically, even moderately polar solutes demonstrate a high affinity to porous matrices [10], so their retention time is extremely large and the peak broadening is severe with pure sc-CO\({}_{2}\), given its comparably low solvation power. Thus, it is not possible to determine the precise retention factor. Addition of a few percent of organic solvents, so-called modifiers, are commonly employed to remedy this issue. This--at first sight, just a practical difficulty--has serious negative consequences for the interpretation of the retention factor in terms of thermodynamic quantities: the retention factor \(k\) measured in systems with modifier cannot be directly related to the retention factor \(k_{0}\) in modifier-free conditions.