Appendix A: Derivation of k’ for Neutral Compounds

$k' = \dfrac{moles_{micelle}}{moles_{aqueous}} \tag{equation 3.1}$

$υ_{apparent} = υ_{eof} \dfrac{η_{aqueous}}{η_{micelle} + η_{aqueous}} + υ_{micelle} \dfrac{η_{micelle}}{η_{micelle} + η_{aqueous}} \tag{equation 3.2}$

substitute equation 3.1

$υ_{apparent} = υ_{eof}\dfrac{1}{1 + k'} + υ_{micelle}\dfrac{k'}{1 + k'}\tag{equation 3.3}$

Given that velocity is the arrival time at the capillary window

$υ_{apparent} = \dfrac{l}{t_R} \tag{equation 3.4a}$

$υ_{eof} = \dfrac{l}{t_{eof}} \tag{equation 3.4b}$

$υ_{micelle} = \dfrac{l}{t_{micelle}} \tag{equation 3.4c}$

substitute equations 3.4a-c

$\dfrac{l}{t_R} = \dfrac{l}{t_{eof}} ( \dfrac{1}{1 + k'} ) + \dfrac{l}{t_{micelle}} ( \dfrac{k'}{1 + k'} ) \tag{equation 3.5}$

$\dfrac{1}{t_R} = \dfrac{1}{t_{eof}} ( \dfrac{1}{1 + k'} ) + \dfrac{1}{t_{micelle}} ( \dfrac{k'}{1 + k'} ) \tag{equation 3.5a}$

$\dfrac{1 + k'}{k' t_R} = (\dfrac{1 + k'}{k'} )[\dfrac{1}{t_{eof}} ( \dfrac{1}{1 + k'} ) + \dfrac{1}{t_{micelle}}( \dfrac{k'}{1 + k'} )] \tag{equation 3.6}$

$\dfrac{1 + k'}{k' t_R} = \dfrac{1}{k' t_{eof}} + \dfrac{1}{t_{micelle}} \tag{equation 3.7}$

$\dfrac{1 + k'}{k' t_R} − \dfrac{1}{k' t_{eof}} = \dfrac{1}{t_{micelle}} \tag{equation 3.8}$

$\dfrac{1 + k'}{k' t_R} − \dfrac{(\dfrac{t_R}{t_{eof}})}{k' t_R} = \dfrac{1}{t_{micelle}} \tag{equation 3.9}$

$\dfrac{1}{k' t_R} (1 + k − \dfrac{t_R}{t_{eof}}) = \dfrac{1}{t_{micelle}}\tag{equation 3.10}$

$(1 + k' − \dfrac{t_R}{t_{eof}}) = \dfrac{k' t_R}{t_{micelle}} \tag{equation 3.11}$

$k' − \dfrac{k' t_R}{t_{micelle}} = \dfrac{t_R}{t_{eof}} − 1 \tag{equation 3.12}$

$k' (1 − \dfrac{t_R}{t_{micelle}}) = \dfrac{1}{t_{eof}} (t_R − t_{eof}) \tag{equation 3.13}$

$k' = \dfrac{(t_R − t_{eof})}{t_{eof} (1 − \dfrac{t_R}{t_{micelle}})} \tag{equation 3.14}$