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Determination of standard affinity at varying temperatures allows subsequent determination of standard heat of dyeing by calculation as the thermodynamic temperature, T, the standard affinity, Δμ^o and the standard heat of dyeing, ΔH^o are all related by equation.

Entropy can be considered to be a measure of disorder within a system. Entropy can therefore be considered to represent the degree of orientation of dye molecules within a dyed substrate.

Electrical effects, the assumption of a Donnan distribution of ions and the concept of fibre internal volume are concepts used in the study of the distrubution of an anionic dye between the dyebath and cellulosic fibre phase in the presence of an added inorganic electrolyte.

When studying titration data for the adsorption of anionic dyes interacting with wool or polyamide, the following mathematical treatments are usually employed;

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When considering the equilibrium adsorption of basic dyes onto PAN fibres the following equation can be considered;
[D⁺]_f/[D⁺]_s = K^D_H/[H⁺]_s ([S]_f – [D⁺]_f

Regarding the above equation we can say the following;