Hydrophobic solvation increases thermal conductivity of water

Carlos López-Bueno a, Manuel Suárez-Rodríguez a, Alfredo Amigo b and Francisco Rivadulla *ac
aCIQUS, Centro de Investigación en Química Biolóxica e Materiais Moleculares, Universidade de Santiago de Compostela, 15782-Santiago de Compostela, Spain. E-mail: f.rivadulla@usc.es
bDepartamento de Física Aplicada, Facultad de Física, Universidade de Santiago de Compostela, 15782-Santiago de Compostela, Spain
cDepartamento de Química-Física, Universidade de Santiago de Compostela, 15782-Santiago de Compostela, Spain

Received 15th July 2020 , Accepted 11th September 2020

First published on 11th September 2020

The interaction of water with small alcohols can be used as a model for understanding hydrophobic solvation of larger and more complex amphiphilic molecules. Despite its apparent simplicity, water/ethanol mixtures show important anomalies in several of their properties, like specific heat or partial molar volume, whose precise origin are still a matter of debate. Here we report high-resolution thermal conductivity, compressibility, and IR-spectroscopy data for water/ethanol solutions showing three distinct regions of solvation, related to changes in the H-bond network. Notably, the thermal conductivity shows a surprising increase of ≈3.1% with respect to pure water at dilute concentrations of ethanol (x = 0.025), which suggests a strengthening of H-bond network of water. Our results prove that the rate of energy transfer in water can be increased by hydrophobic solvation, due to the cooperative nature of the H-bond network.


The cooperative nature of H-bonds in liquid water allows an unusually fast intermolecular transmission of O–H stretch excitations, which extends over a large number of water molecules.1,2 This constitutes an effective mechanism of information transfer, particularly in biological media, where the concentration of solutes is high.3,4

Dissolving hydrophobic molecules in water modifies the H-bond network of water around the solute.5 For small alcohols, the observed negative excess entropy of mixing led to the proposal of a local ordering of water in clathrate-like hydrates around the hydrophobic groups of the solute (the iceberg model).6 Other studies suggested however that incomplete mixing of water and alcohol at the molecular level is the main cause of the thermodynamic anomalies observed in these mixtures, at least at large concentrations of alcohol.7 Local ordering in the form of micro-segregated pockets of alcohol and water within a globally disordered fluid is the most accepted picture at x(EtOH) ≈ 0.2–0.7.8

But the situation is even more complex at very low concentrations, x(EtOH) < 0.1. Molecular dynamic (MD) simulations by Ghosh et al.9 also pointed towards incomplete mixing at x ≈ 0.05–0.10. However, spectroscopy10–13 and MD-simulations14 did not provide conclusive support to this picture, and suggested instead a surprising strengthening of H-bonds around the small alcohols, with the structural arrangement of water molecules not differing much from the bulk.15,16

In the vast majority of cases, the changes reported in the H-bond structure were studied by local spectroscopic techniques.17–21 Therefore, the effect on bulk properties of the liquid, beyond the first hydration shells of the solute, is still not clarified. Particularly interesting is to elucidate how hydrophobic solvation could influence the transport of energy through the bulk system, given its relevance for processes of biomolecular communication and recognition.

The cooperativity of H-bonding makes thermal diffusivity in water (α ≈ 1.4 × 10−7 m2 s−1) nearly two orders of magnitude faster than molecular self-diffusion (D = 2.3 × 10−9 m2 s−1). Therefore, the structural rearrangements of H-bonds induced by hydrophobic solvation could, in principle, be observable in thermal conductivity experiments if they extend beyond the first hydration shell of the solute and affect to a large portion of molecules.

Here we report precise thermal conductivity (and thermal diffusivity) measurements, complemented with spectroscopic and mechanical properties of water/R–OH mixtures at small concentrations of alcohol (R refers to alkyl chains of ethanol, propanol and isopropanol). Our observations confirm the presence of three different regions of solvation, in excellent agreement with MD-simulations calculations,14 with a dependence on the length and shape of the alkyl chain.


Water solutions of alcohols were prepared by dissolving ethanol (≥99.8%), 2-propanol (99.5%) and 1-propanol (99.7%) in Milli-Q grade water. DSC measurements were performed in a TA Instruments Q200 system. Adiabatic compressibility data was obtained from density and ultrasound velocity (∼3 MHz) measurements recorded with an Anton Paar DSA 5000 calibrated with water and dry air. Specific heat was measured in a Setaram Micro DSC-III, also calibrated with Milli-Q water. Thermal conductivity measurements were performed at room temperature and ambient pressure in a homemade setup based on the 3ω method.22 Our setup uses a very small amount of liquid (<1 μL) and a variable range of frequencies and dissipated powers, which minimizes convective effects and improves the accuracy of the method. All measurements were repeated at least three times, for reproducibility. IR measurements were performed using a Nicolet 5700 ATR-FTIR spectrometer. The liquid was placed between two CaF2 windows with a 100 μm spacer.

Results and discussion

Fig. 1 summarizes the most important findings of this work. The absorption IR band centered at ≈2130 cm−1 is the combination of the intramolecular H–O–H bending and the intermolecular librational motion of H-bonded water molecules. Due to the much smaller sensitivity of the intramolecular mode to temperature and/or water–solute interactions, this band is an very sensitive probe to the strength of the H-bond network in bulk water.18,23
image file: d0cp03778h-f1.tif
Fig. 1 (a) The IR combination band of water and (b) its frequency dependence with the concentration of EtOH. The scheme in (b) represents the librational motion associated to this vibrational band. In (a) only the bands for x = 0 (pure water) to x = 0.2, Δx = 0.025, are shown for clarity. (c) Thermal conductivity of the solutions. The red dotted line is the fit to a binary mixture model, as explained in the ESI. The three different regimes of hydration discussed in the text are highlighted.

Adding a small amount of EtOH to water results in an overall blue-shift of the combination band, which indicates an increasing rigidity of the H-bond network (Fig. 1b). Three different regimes can be distinguished from the frequency dependence of x: firstly, a fast increase of the band frequency is observed up to x ≈ 0.025 (region I); this increase is slowed down from x ≈ 0.025 to x ≈ 0.10 (region II), and remains approximately constant above x ≈ 0.10 (region III).

We have then measured the thermal conductivity, κ, for the same series of samples.22 Our experimental setup uses very small amounts of liquid (<1 μL) and a variable range of frequencies and dissipated powers, which minimizes convective effects and improves the accuracy of the method. The value measured for pure water at 293–295 K (0.596 ± 0.009 W m−1 K−1) is within the range of the most accurate measurements in literature.24 A detailed explanation of the method was reported elsewhere.22

The thermal conductivity (and thermal diffusivity α = κCp−1ρ−1; see Fig. S1 in the ESI) measurements confirm the existence of the three different regions of solvation deduced from the IR spectra. Importantly, there is a progressive enhancement of κ in region I, with a maximum increase of ≈3.1% at x = 0.025. Water has the highest κ among liquids (except liquid metals) due to the extensive H-bond interaction; an increase of its κ would require a strengthening of the H-bond network. Note however, that dissolving kosmotropic or chaotropic ions result in a decrease of κ with respect to pure water.25 Therefore, the increase of κ in region I, although quantitatively it may seem a small effect, qualitatively it is very important since it indicates an arrangement of water molecules and strengthening of the H-bond network around the alcohol on a time scale similar to that of thermal diffusivity.

Increasing further the concentration of EtOH reduces κ until x = 0.1 (region II); beyond this concentration, the experimental values of κ follow nicely the calculation for a binary mixture, considering the different possible interactions (region III) (red dashed line; see ESI for a detailed discussion of this calculation). The comparison of the experimental κ of x = 0.025 with the value calculated for the binary mixture shows an increment of ≈10%.

The boundaries between the three regions discussed above match almost perfectly mass spectroscopy experiments13,26 and the predictions of MD-simulations.9,14 In the very diluted region (regime I), they show the formation of densely packed hydration shells, with greater tetrahedral order and stiffer H-bonds in average. Raman spectroscopy and molecular dynamics simulations estimated that the number of H2O molecules in the first hydration shell of EtOH is ≈36.12 Taking this number, the hydration shells will come into contact above x ≈ 0.028, i.e. at the upper boundary of region I. Thus, our observation of an increase of κ in region I reported in Fig. 1, may be related to an increasing strengthening (in average) of the tetrahedral network around the alcohol. Remarkably, the cooperative nature of the H-bond makes this local effect to determine the transport of energy in the bulk fluid, despite the very low concentration of solute.

In region II, the hydration shells coalesce, and the alkyl chains begin to associate, promoting an increasing H-bond between water and the –OH group of the alcohol. Above this limit, H-bonding among ethanol molecules replace part of the waters bonded to the hydroxyl group, recovering the binary solution limit in region III.

The temperature dependence of the thermal conductivity also shows different behavior across this composition range: region I shows the dκ/dT > 0 characteristic of water, while negative values are recovered in region III (see Fig. S2 and its discussion in the ESI).

The excellent agreement between boundary regions defined by κ and those predicted by MD-simulations,14 supports an scenario with homogeneous distribution of alcohol molecules, with a complex water–solute structure as concentration changes, determined by the extension of the hydration shells.

Similar results were obtained for the thermal conductivity of isopropanol, although the extent of region I is smaller than for EtOH (Fig. 2; see also Fig. S1 in the ESI); regarding 1-propanol, no increase of κ was observed in the very diluted region.

image file: d0cp03778h-f2.tif
Fig. 2 Thermal conductivity for water solutions of iso-propanol (a), and 1-propanol (b), at different concentrations of alcohol.

The changes in κ were correlated with the frequency dependence of the IR combination band for the three alcohols (see Fig. S4 in the ESI). The distinction between region I and II becomes less clear as the length of the alkyl chain increases, and the extension of region III also grows with the alkyl chain.

These results demonstrate the main role played by the alkyl chain length and shape on κ (over the effect of –OH group), reproducing the chain-length dependence of the mechanism of hydrophobic solvation suggested from previous studies. For instance, Li et al.21 reported THz spectroscopy and pulsed NMR data consistent with a molar fraction of alcohol beyond which the hydration shells around the alcohol molecules coalesce, so isolated alcohol molecules no longer exist. This fraction decreases from 10, to 7, and to 2 mol% as n increases from n = 0, 1, and 2 in CH3(CH2)nOH, respectively.

On the other hand, Davis et al.12 reported a strong effect of temperature on the tetrahedral order of the hydration shell characteristic of region I, particularly for long-chain alcohols. They reported a transition above ≈60 °C towards a less ordered (higher entropy) water structure, with weaker H-bonds for alkyl chains larger than ≈1 nm.

The reduced mobility of water coordinating the alcohol10 also affects the enthalpy of fusion, ΔHf, of ice in regions I & II. This magnitude is the change of enthalpy between solid and liquid water at constant pressure (ΔHf = ΔUfPΔVf), so that it contains the change in the free energy of water in the solid/liquid state, plus the work needed to make room for the change in volume upon the transition. In Fig. 3 we plot ΔHf for different solutions, corrected by the actual amount of water in the mixture. In regime I there is a lower than expected ΔHf, which is compatible with two scenarios: (i) a reduction of the internal energy of liquid water, or (ii) a smaller volume expansion of ice upon crystallization.

image file: d0cp03778h-f3.tif
Fig. 3 Dependence of the enthalpy of fusion of ice with the concentration of ethanol. The dashed line is a guide to the eye.

The strengthening of the H-bonds observed in IR measurements reduces the number of degrees of freedom activated at room temperature and, consequently, reduces ΔUf, supporting the scenario (i). However, it is also known that hydrophobic solvation leads to a local expansion of the tetrahedral network of liquid water, which is the responsible to the increase of its partial molar volume.14,27,28 Thus, hydrophobic solvation makes both scenarios (i) and (ii) to contribute to the observed reduction of ΔHf in regimes I and II.

From the difference between the actual and expected (dotted line) values of ΔHf, and effective number of water molecules which do not contribute the enthalpy of fusion can be estimated. This number is ≈22 for x < 0.01, i.e. around 11 water molecules per methyl group, similar to the value predicted in MD-simulations.14

On the other hand, the progressive formation of an extended and cooperative H-bond network in water leads to a characteristic minimum in its isentropic compressibility, K, at a temperature T* ≈ 60 °C.29,30 Below this temperature structural fluctuations that minimize H-bond energy dominate, while random thermal fluctuations control K above T*, as in any other liquid.31 Thus, an extensive (cooperative) modification of the H-bond network of bulk water should be also reflected in the magnitude and temperature dependence of K.

Fig. 4 shows the temperature dependence of K for several water/EtOH solutions. In highly diluted solutions (region I), T* decreases slightly and the curvature of K around the minimum remains practically constant, confirming that the H-bond network of bulk is not dramatically affected. In region II, T* decreases faster, the minimum becomes shallower, and the curvature smoother below this temperature. Increasing further the concentration of EtOH suppresses the increase of K at low temperature, resulting in a “common liquid behavior”.

image file: d0cp03778h-f4.tif
Fig. 4 Temperature dependence of the isentropic compressibility of water/EtOH solutions.

The transition reported Davis et al.12 discussed before, occurs precisely at the temperature of the minimum K in pure water, above which thermal fluctuations dominate over structural ones. Also, according to our data in Fig. 4, this effect is reinforced by the presence of alcohols, particularly at moderate-large concentrations (an effect of the alkyl chain length and shape was also observed over K; see Fig. S5 and S6 in the ESI). Thus, the data suggest that the effect of temperature over hydrophobic solvation is linked to the internal energy scale of H-bond in neat water.


In summary, we have shown the excellent sensitivity of thermal conductivity to minor changes in the conformation of the solute–solvent molecules. Our data demonstrate that small concentrations of short-chain alcohols in water increase the thermal conductivity of the solution. The rate of energy transfer confirms the three different regions in the hydration of EtOH suggested by MD-simulations. Our results also show the strong effect of hydrophobic solvation on the mechanical properties of the H-bond network of water. Hydrophobic solvation determines, to a large extent, several biological processes including protein folding and biomolecular recognition. The increase of the rate of energy transfer reported in this work demonstrate that water may be particularly suitable for communication of structural rearrangements among biomolecules, even at moderate-long distances.32

Conflicts of interest

There are no conflicts to declare.


Authors would like to acknowledge the help of Prof. Massimo Lazzari from USC for his help with IR measurements and Dr María Gimenez from USC for helpful discussions. This work was supported by the Ministry of Science of Spain (Projects No. MAT2016-80762-R), the Consellería de Cultura, Educación e Ordenación Universitaria (ED431F 2016/008, and Centro singular de investigación de Galicia accreditation 2016–2019, ED431G/09), the Xunta de Galicia and the European Regional Development Fund (ERDF). C. L.-B. Acknowledges Xunta de Galicia and ESF for a PhD Grant (ED481A-2018/013). M. S.-R. acknowledges Ministry of Education and Vocational of Spain for a Collaboration Grant.

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Electronic supplementary information (ESI) available: Additional information about materials and methods, as well as additional thermal conductivity, compressibility and IR data and analysis. See DOI: 10.1039/d0cp03778h

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