The ability of a drug to be liberated from the vehicle can be characterized by the ratio of the solubility of the active compound in the stratum corneum (C _SC) to the solubility of the active compound in the vehicle (C _V). This dependency can be described by the partition coefficient K _SC/V according to Eq. 15.1 (Wiechers et al. 2004).
Thus, the drug amount which is liberated from the formulation into the stratum corneum can be enhanced either by increasing the solubility of the compound in the stratum corneum or by decreasing the solubility of the compound in the formulation (Wiechers et al. 2004).

Topically applied compounds have to overcome the main skin barrier, the stratum corneum, which represents a complex mixture of various lipid and protein domains (Cross et al. 2001) in order to reach the underlying regions (Hadgraft and Pugh 1998). Thus, two processes, partition and diffusion, are important determinants for drug delivery into and through the skin (Wiechers et al. 2004), which in turn can be found in the flux of a compound according to Fick’s law of diffusion (Eq. 15.2) (Scheuplein 1976; Potts and Guy 1992):
where J is solute flux, D is diffusion coefficient, K _ow is octanol/water partition coefficient, Δc is drug concentration difference between the formulation and the deepest skin layer, and x is the length of the diffusion pathway of the active compound.

Furthermore, the permeability coefficient K _p is often used in order to simplify the permeation rate of an active compound through the skin (Eq. 15.3) (Hadgraft and Pugh 1998), since the actual diffusion pathway through the skin (x) is unknown. K _p is furthermore the parameter used for statistical analysis of results of skin diffusion studies.
The number of transdermal applied compounds is still limited due to the lack of achieving therapeutic concentrations in the target tissue within the skin or in other body tissues after systemic circulation via blood or the lymphatic system (Bach and Lippold 1998), usually due to limitations in transdermal permeation caused by physicochemical drug characteristics (Magnusson et al. 2004). Especially the lipophilicity, the molecular weight (MW), and the melting point have to be taken into account in order to deliver a compound through the skin (Hadgraft and Pugh 1998; Magnusson et al. 2004; Nielsen et al. 2004). Potts and Guy (1992) demonstrated that the permeation of a topically applied drug in an aqueous solution can be estimated by two physicochemical characteristics, which are combined in Eq. 15.4 with MW as molecular weight of the active compound:
From Eq. 15.4 it can be concluded that small molecules (low MW) with adequate affinity to the horny layer (log K _ow from −3 to +6) can be expected to exhibit a sufficient drug penetration (Bach and Lippold 1998; Potts and Guy 1992; Wiechers et al. 2004). Compounds with good affinity to both water and oil will show a good penetration behavior. Such compounds tend to exhibit a low melting point (Hadgraft 2004). According to Potts and Guy (1992), Eq. 15.4 can be used for substances with MW from 18 to >750 and log K _ow from −3 to +6.

Furthermore, the rate of diffusion depends on the thermodynamic activity of the drug in the absence of penetration enhancing substances (Bach and Lippold 1998). It is characterized by the ratio of the drug concentration in the vehicle (C _V) to the maximum solubility in the vehicle (C _S) according to Eq. 15.5, with α as thermodynamic activity, C _V as concentration of the active compound in the vehicle, and C _S as saturation concentration of the active compound in the vehicle (Bach and Lippold 1998):
In this process the thermodynamic activity rises with the concentration of the compound up to the maximum concentration (saturation) in the vehicle (Hadgraft 2004). Thus, solutions show a decline of activity with the duration of incubation, while suspensions (having drug concentrations above their solubility) exhibit a constant activity (Bach and Lippold 1998).

Commercially available topical formulations present a complex mixture of several classes of substances (Wiechers et al. 2004). The effect of all added substances in the formulation and the thermodynamic activity of the active compound have to be considered when transdermal and dermal drug delivery is predicted (Bach and Lippold 1998).

According to that, not only the properties of the active compound but also the vehicle influence the diffusion of the active compound through the skin. Vehicle ingredients can interact with the skin or with the active compound, so that its diffusion is enhanced or decreased.