Kinetics and thermodynamics of β-cyclodextrin-NH₂/β-carotene complexation: how much energy is required to include a hydrophobic group in the macrocycle cavity?

To improve the efficiency of cyclodextrins as carotenoid carriers, the kinetics and thermodynamics of the inclusion complex formation between modified β-cyclodextrin (βCD-NH₂) and β-carotene (βCT) were studied using surface plasmon resonance (SPR) at pH 7.4 and theoretical calculations. The observed dissociation rate of the [βCD-NH₂/βCT]° inclusion complex is small \((2.59\times 1{0}^{-1} {\text{s}}^{-1}\) $(2.59\times 10^{-1}{\text{s}}^{-1}$ ), indicating that βCD-NH₂ only interacted with the βCT ionone group to form inclusion complex. The βCD-NH₂/βCT binding constant is \(2.80\times 1{0}^{4} \text{L} {\text{m}\text{o}\text{l}}^{-1}\) $2.80\times 10^4{\text{Lmol}}^{-1}$  (at 298.15 K), and its temperature dependence indicates that the [βCD-NH₂/βCT]° formation is driven by hydrophobic interactions ( \({\Delta }H^\circ = 28.83 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}\) $\mathrm{\Delta }{H}^{\circ }=28.83\text{kJ}{\text{l}}^{-1}$ and \(T{\Delta }S^\circ = 54.21 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}\) $T\mathrm{\Delta }{S}^{\circ }=54.21\text{kJ}{\text{l}}^{-1}$ ) caused mainly by the βCT end group desolvation. In contrast, the formation of the [βCD-NH₂/βCT]^‡ activated complex via association between free molecules and dissociation of [βCD-NH₂/βCT]° occurred with the overcoming of an energy barrier ( \(E_{a}^{\ddag } = 40.77~{\text{kJ mol}}^{{ - 1}} ~\) $E_a^{‡}=40.77{\text{kJ mol}}^{-1}$  and \({E}_{d}^{\ddag}=11.94 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}\) $E_d^{‡}=11.94\text{kJ}{\text{l}}^{-1}$ ) and decrease in entropy ( \(T{\varDelta S}_{a}^{\ddag}=-11.70 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}\) $T{\Delta S}_a^{‡}=-11.70\text{kJ}{\text{l}}^{-1}$ and \(T{\varDelta S}_{d}^{\ddag}=- 65.92 \text{k}\text{J} \text{m}\text{o}{\text{l}}^{-1}\) $T{\Delta S}_d^{‡}=-65.92\text{kJ}{\text{l}}^{-1}$ ).