Spectroscopic Fingerprints of Cavity Formation and Solute Insertion as a Measure of Hydration Entropic Loss and Enthalpic Gain

Abstract

Hydration free energies are dictated by a subtle balance of hydrophobic and hydrophilic interactions. We present here a spectroscopic approach, which gives direct access to the two main contributions: Using THz-spectroscopy to probe the frequency range of the intermolecular stretch (150-200 cm^-1 ) and the hindered rotations (450-600 cm^-1 ), the local contributions due to cavity formation and hydrophilic interactions can be traced back. We show that via THz calorimetry these fingerprints can be correlated 1 : 1 with the group specific solvation entropy and enthalpy. This allows to deduce separately the hydrophobic (i.e. cavity formation) and hydrophilic contributions to thermodynamics, as shown for hydrated alcohols as a case study. Accompanying molecular dynamics simulations quantitatively support our experimental results. In the future our approach will allow to dissect hydration contributions in inhomogeneous mixtures and under non-equilibrium conditions.

Keywords: Alcohol Hydration; Enthalpy; Entropy; Hydrophobic Hydration; THz Spectroscopy; THz-Calorimetry.

Figure 1

The hydration free energy of a generic solute can be modelled as a two‐step process: 1) create a cavity in water where the solute can be accommodated, with associated free energy cost $\Delta {\mu }_{\mathrm{cavity}}$ ; 2) insert a solute (tBuOH in the example) at the center of the cavity, with associated free energy gain $\Delta {\mu }_{\mathrm{bound}}$ . Hydration water molecules are illustrated with red oxygen and white hydrogen, H‐Bonds are in blue. The alcohol (tBuOH) solute in step 2 is depicted with red oxygen, white hydrogen and cyan carbon atoms.

Figure 2

Group specific entropy contributions (at room temperature) to alcohol hydration from THz‐calorimetry. A) Individual contributions of CH₃, CH₂ and OH groups to hydration entropy, $\Delta S_{\mathrm{hyd}}$ . The green curve shows $\Delta S_{\mathrm{hyd}}$ values predicted from classical MD simulations by means of a 3D‐2PT approach. B) Effective hydration numbers (n _hyd) derived from THz experiments, compared to n _hyd values from MD simulations (green). The theoretical n _hyd values are arbitrarily scaled by 0.3 to compare with experiments, as they are obtained from direct counting of hydration water molecules while experimental values depend on spectroscopic activity. C) Illustration of the building blocks composing alcohols, i.e. CH₃ (black), OH (red), CH₂ (cyan). D) Experimental $\Delta S_{\mathrm{hyd}}$ values divided by n _hyd and averaged separately over apolar (CH₂ and CH₃) and polar (only OH) groups.

Figure 3

THz signature of the bound water population. A) Experimental hydration‐shell resolved THz spectra of hydrated tBuOH at various temperatures, showing a characteristic intensity increase in the 400–600 cm⁻¹ region. The black solid lines are linear fits of the THz intensity in the 450–600 cm⁻¹ region, from which the slope plotted in panel C is obtained. B) Theoretical THz spectrum calculated from DFT‐MD (same as in ref. [27]) considering only the contribution (both self and cross correlation terms) of bound water molecules hydrating the polar OH group of tBuOH. C) Slope of the THz‐intensity in the 450–600 cm⁻¹ region for various experimentally investigated alcohols as a function of temperature.

Figure 4

Small alcohol hydration free energy is the sum of A) an entropic cost of cavity formation, involving formation of a HB‐wrap over the whole hydration layer, and B) an enthalpic gain due to the attractive interactions formed by the alcohol OH group with bound water molecules. C) THz‐calorimetry quantifies both terms from THz translational (due to HB‐stretching, red) and librational (blue) fingerprints of the hydration layer. In the example, the THz spectrum at room T is decomposed into the two terms for tBuOH. D) The 164 cm⁻¹ THz fingerprint in the HB‐stretching region probes the HB‐wrap, while E) the librational band probes bound water molecules.