DH
m ¼ ð2 aÞRT2ðdlnXCMC=dTÞ: ð2Þ
(d ln XCMC/dT) was calculated by fitting the ln XCMC versus temperature
data to a second order polynomial and differentiation.
Figure 7 represents the second polynomial fit of XCMC of etilefrine
HCl with no added NaCl vs. temperature.
DH
m values are negative at lower temperature i.e. at 298.15 K.
However, at higher temperature, DH
m values becomes positive in
the range of T = (303.15 to 313.15) K which means the micelle
formation process changes from exothermic to endothermic at
high temperatures. The negative DH
m values indicate that the
London–dispersion forces is predominant and play a significant
role in facilitating the micellization process [32]. The results were
represented in figure 8.
The (DS
m) can be calculated from the following equation:
DS
m ¼ ðDH
m DG
mÞ=T: ð3Þ
The DS
m values are small at low temperatures and increase by
increasing the temperature. The calculated DS
m values are always
large positive as shown in figure 9 for all the systems indicating
that the micellization is entropy driven process. Calculated
DG
m; DH
m and DS
m values are illustrated in table 3.
A Linear relation between DH
m and DS
m of micellization was
observed [33,34]. This phenomenon is called enthalpy–entropy
compensation. The enthalpy–entropy compensation plot is shown
in figure 10.