pigmented colorants: dependence on media and time - Cornell ...

The rate of change of the concentration of a substance over time is proportional
to the concentration C raised to some power n:
dC
dt
= kCn
126
(4.11)
If the exponent is n =[0, 3] | n ∈ Z, the reaction is said to be zero, first,
or second order, respectively–these are the most commonly encountered modes of
chemical change.
The combination of optical properties and reaction kinetics allow for the pre-
diction of colorant loss in a fading glaze. Johnston-Feller et al. used Kubelka Munk
color matching techniques to determine the concentrations of pigments present at
any given stage in fading [JFFBC84]. The work demonstrated that the fading
process for many pigments can be described on the basis of first-order kinetics as
a function of time. From Equation 4.11, we have
− dC
dt = k1C (4.12)
ln C =lnC0− k1t (4.13)
where C0 is the initial concentration and C is the concentration remaining after
time t. Via Kubelka Munk theory, the percentage of colorant remaining after an
elapsed period of time can also be expressed as
where
(K/S)e
C = 100%
(K/S)o
(K/S)o are the coefficients derived from the original sample’s reflectance
(4.14)
(K/S)e are the coefficients derived from the aged, exposed sample’s reflectance