5946
J. Phys. Chem. B 2007, 111, 5946-5955
Dielectric Spectroscopy of Hydrogen Bond Dynamics and Microheterogenity of Water + Dioxane Mixtures Simon Schro1 dle,† Glenn Hefter,‡ and Richard Buchner*,† Institute of Physical and Theoretical Chemistry, UniVersita¨t Regensburg, D-93040 Regensburg, Germany, and Chemistry Department, Murdoch UniVersity, Murdoch, Western Australia 6150, Australia ReceiVed: February 16, 2007; In Final Form: March 30, 2007
Mixtures of water or D2O + 1,4-dioxane (DX) have been studied at 25 °C by dielectric relaxation spectroscopy over a wide range of frequencies (0.2 e ν/GHz e 89) for DX mole fractions 0 e x2 e 0.67. The spectra were best fitted by the sum of two Debye terms. The slower process was assigned to the cooperative relaxation of the hydrogen-bond network of water, whereas the faster mode reflects the dynamics of H2O molecules in a DX-rich environment. Analysis of the relaxation parameters revealed a largely microheterogeneous structure of the mixtures. The marked slowing-down of the cooperative mode on addition of DX is ascribed to the reduction of available H-bond acceptor sites and geometrical constraints on the H2O molecules in the waterrich regions.
1. Introduction The outstanding importance of hydrogen bonding as a force governing the structure and dynamics of chemical and biological systems has been pointed out in a plethora of papers and monographs.1 Of all H-bonded liquids, water as a basic component of all living matter is certainly the most well-studied. The limited strength of H-bonds, as compared to covalent interactions, and their strongly directional, anisotropic character create multimolecular clusters. Such clusters reorganize themselves in a cooperative way on ultrafast time scales, typically on the order of picoseconds. These fast dynamics make the investigation of liquids much more challenging, compared with the H-bond structures of solids, for which a variety of tools have been established in the last decades. Even more challenging are liquid mixtures due to the generally large number of possible site-site interactions. Mixtures of water (W) + 1,4-dioxane (DX) have played an important role in the history of physical chemistry2 and have been widely studied ever since.3 They are also of considerable industrial importance and are used in many chemical reactions and other applications. Dioxane is often considered to be an exemplar of a typical nonionic, nonpolar solute in water. However, its complete miscibility with water hints at a more complex picture. On one hand, DX exposes a substantial number of noninteracting sites (the hydrophobic -C2H4- segments) to water molecules. On the other, its ether oxygens offer H-bond acceptor sites, even though DX cannot self-associate due to the lack of H-bond donor positions. It is therefore not surprising that thermodynamic and transport properties of water + DX exhibit pronounced deviations from ideality (Figure 1). Figure 1a shows the molar heat of mixing, ∆mixHE, obtained from a fit of selected literature data,4-7 as a function of the mole fraction of H-bond acceptor sites (oxygen atoms) in the mixture provided by DX, defined as8 * To whom correspondence should be addressed. E-mail: richard.
[email protected]. † Universita ¨ t Regensburg. ‡ Murdoch University.
xO,2 )
nO,2xDX nO,2xDX ) ; nO,2 ) 2 nO,2xDX + xW 1 + xDX(nO,2 - 1)
(1)
In the water-rich region, ∆mixHE is exothermic but at higher DX concentrations, xO,2 J 0.6, it becomes endothermic. The corresponding molar excess entropies are strongly negative over almost the whole composition range4,9,10 with the minimum at xO,2 ≈ 0.45 indicating the region of maximum order.10 Around this concentration, the excess molar volume shows a pronounced minimum (Figure 1a), and the excess viscosity, ηE(x2) ) η(x2) - ηW(1 - x2) - ηDXx2, a maximum (Figure 1b). The thermodynamic and transport properties summarized in Figure 1 thus indicate that the mixtures represent a denser state than the pure liquids and that the various degrees of freedom, such as rotational and translational motions, are restricted. This observation could be interpreted as a structure enhancement within the mixture, but it should be kept in mind that thermodynamics cannot discriminate between the contributions from water-ether or water-water interactions; neither is there a clear relationship between thermodynamic properties and the dynamics of the H-bond network. Structuring may occur at various levels and does not necessarily have to be limited to pairwise molecule-molecule interactions, especially in liquids showing strong cooperative effects, such as water. Infrared, Raman, and NMR spectroscopy, as well as scattering techniques, have long been used to gain molecular level information on mixtures. However, these techniques can only probe vibrational states or local dynamics and structure, whereas the central feature of H-bonds is their nonadditive behavior in the build-up of mesoscopic fluctuating structures. Recent advancements of laser technology open up new possibilities for pump-probe experiments. In addition, nonlinear effects can now be exploited.16-18 However, so far, none of these methods is yet able to generate suitable ultrashort pulses in the frequency range of H-bond interactions (wavenumbers < 500 cm-1, wavelength > 20 µm)1 and until now, dielectric relaxation spectroscopy (DRS) is one of the few ways to access this region. DRS determines the response of a sample to an applied
10.1021/jp0713413 CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007
Microheterogenity of H2O + DX
J. Phys. Chem. B, Vol. 111, No. 21, 2007 5947
Figure 1. Thermodynamic and transport properties of water + 1,4-dioxane mixtures at 298.15 K. (a) Heat of mixing (red), ∆HEmix,4-7 and excess molar volume (blue), VE;11,12 (b) viscosity (blue), η, and excess molar viscosity (red), ηE.13-15
electric field of frequency ν in terms of the complex permittivity, ˆ (ν) ) ′(ν) - i′′(ν), where ′(ν) is the permittivity and ′′(ν) is the dielectric loss associated with energy absorption by the sample. This technique has proven to be a powerful tool in the investigation of cooperative and molecular dynamics of Hbonded systems.19-22 Water + DX mixtures are particularly suited to DRS studies because DX has almost zero dipole moment, so that its contribution to ˆ (ν) is negligible, and all observed effects can be associated with water. Not surprisingly, water + DX mixtures have been studied previously with DRS, but due to a lack of commercial instrumentation and technical difficulties associated with the study of the dielectric response of liquids at higher frequencies, these investigations23-28 suffered from insufficient frequency coverage, limited accuracy, or both. In this contribution, we report broad-band spectra, covering the frequency range 0.2 e ν/GHz e 89 for DX mole fractions 0 e xDX e 0.67, corresponding to 0 e xO,2 e 0.80. Here and throughout this paper, water (or D2O) is taken as component 1 and DX as component 2 of the studied mixtures. This work complements a previous study on dilute solutions of water in DX where the small ′′(ν) values permitted us to reach frequencies up to 3 THz.29 2. Experimental Details and Data Processing 1,4-Dioxane (Merck, Germany; analytical grade) was refluxed over solid calcium hydride and then distilled under a dry nitrogen atmosphere.30 The purified material (xDX g 0.9997 by GC) had a water content of 10 GHz because of the clearly asymmetric band shape of ˆ (ν) (Figures 2, 3). As a consequence, some of the conclusions of Mashimo et al.,26 in particular, the claimed water cluster percolation deduced from the nonlinear decrease of the normalized relaxation strength (see Figure 5), are flawed by systematic errors in and ∞. The asymmetric broadening of a dielectric spectrum on the high-frequency side can be taken into account either by using a single Davidson-Cole (DC) equation51 or by increasing the number of relaxation processes in the fit. For spectra of W + DX mixtures recorded between 0.2 and 20 GHz, HernandezPerni et al. observed, in terms of the quality of the fit, a crossover from the DC model, being superior in mixtures with high water content, to the 2D model, giving better fits at xO,2 J 0.3, where the broadening of the spectra is more pronounced.27 As indicated in the previous section, for the present ˆ (ν) data covering 0.2 e ν/GHz e 89 (i.e., spanning > 95 % of the total dispersion of ′(ν)), both the 2D and the Davidson-Cole model can be used for a satisfactory description of the data, although for the latter with increasing DX content, systematic deviations become more and more pronounced at high frequencies. In fact, within a limited frequency range, any superposition of two
Schro¨dle et al. closely spaced Debye terms can be represented by the empirical DC model to some level of accuracy. There are, however, three important observations that are in favor of the use of a 2D fit: First, the 2D model yields smoothly varying relaxation parameters i and τi (Table 1, Figures 5 and 6) over the entire concentration range of this study. Second, it was found that the relaxation-time distribution parameter β of the DC equation, a measure of the asymmetry of the band shape, approaches ∼0.5 at high DX concentrations. This implies widely differing timescales with distinct relaxation times for the processes governing the dynamics of water + DX. Third, a recent combined microwave DRS + THz study29 of dilute solutions of H2O and D2O in DX (xDX g 0.8, xO,2 g 0.889) revealed the presence of two Debye relaxation modes associated with water dynamics. Additionally, there is an intermolecular vibration in the THz region that is mainly associated with the dioxane molecules and can be modeled by a damped harmonic oscillator term. Both water relaxations, assigned to the relaxation of water clusters (slow) and to H2O molecules in a DX-rich environment (fast) persist down to the lowest water concentration studied, xO,2 ) 0.988.29 Similarly, the investigation of neat water at microwave + THz frequencies clearly revealed that the relaxation contribution to ˆ (ν) is a superposition of two Debye processes.52 Here, the interpretation of the dominating low-frequency relaxation (τ1 ) 8.32 ps) as the cooperative relaxation of the H-bond network is well-established.19,52-54 The assignment of the small-amplitude, high-frequency mode (in the range of τ2 ) 0.42 ps52 to 0.264 ps33) is less clear. Possibly, this relaxation reflects nonseparable contributions from the fast reorientation of the few “free” water molecules, an explanation put forward by Buchner et al.,54 and of memory effects of dielectric friction plus density fluctuations, as suggested on theoretical grounds by Yamaguchi et al.55 Obviously, the interpretations of the τ1-mode for pure water and for DX-rich solutions are equivalent, whereas those for the τ2-relaxations differ because almost certainly, different mechanisms are probed.29 Although THz data could not be determined for the present samples due to their excessive absorption at ν > 100 GHz, the limiting permittivities, i, and relaxation times, τi, of Table 1 smoothly match the corresponding fit parameters for the Debye modes at high DX concentration29 (Figures 5 and 6). Thus, there is substantial evidence that the dynamics of water + DX mixtures are governed by two relaxation modes (plus very much faster intermolecular vibrations beyond the range of this study) over the entire composition range. 3.2. Interpretation of the Relaxation Parameters The bulk properties of W + DX mixtures have often been interpreted in terms of a structural enhancement, attributed to the strengthening of the hydrogen bond network near noninteracting surfaces, the so-called hydrophobic effect.56 This hypothesis about the nature of the interactions in aqueous-organic mixtures has been interwoven with various other ideas. These include the formation of a stable dioxane-water (donor-acceptor) complex,10,57 higher aggregates formed by water molecules bridging between two ether molecules5,10 or even the formation of micelle-like clusters.26 Water cluster percolation at xO,2 ≈ 0.3-0.4 was invoked from DRS studies,26,27 whereas low-frequency Raman spectra were interpreted in terms of a breakdown of the tetrahedral water structure at xO,2 J 0.35 (xW j 0.8).58 Plotted as a function of the mole fraction of H-bond acceptor sites offered by DX, xO,2, the present results show a linear decrease in the concentration-normalized relaxation strength, S1/cW (cW is the molar concentration of water in the mixture),
Microheterogenity of H2O + DX
J. Phys. Chem. B, Vol. 111, No. 21, 2007 5951
Figure 6. Relaxation times, τ1 (a, 9; red line) and τ2 (b, b; blue line), of the two Debye processes found in water + 1,4-dioxane mixtures at 298.15 K. τ2R (b, O) is the NMR rotational correlation time of D2O in 1,4-dioxane-D8.72 Data at high DX concentrations (]) are from Schro¨dle et al.29
of the dominating lower-frequency relaxation process (S1, τ1) over the entire mixture range of DX + water (Figure 5). Simultaneously, the normalized amplitude of the faster process, S2/cW, increases linearly. On the other hand, the relaxation times of both processes, τ1 and τ2, show a pronounced maximum at xO,2 ≈ 0.55 (Figure 6). According to our data in Figures 5 and 6, there is no evidence for a breakdown of the water structure in general or of a percolation threshold at xW j 0.83 (xO,2 J 0.29), inferred by Mashimo et al.26 from their Cole-Cole relaxation amplitudes (Figure 5, green symbols). The present work, providing far more accurate data and wider frequency coverage than previous studies, quantitatively show that the break in the relaxation parameters of Mashimo et al.26 is almost certainly an artifact arising from the use of the unsuitable Cole-Cole fit model in combination with the insufficient bandwidth of their spectra and possible experimental problems at low water concentration (see Figure 2). The present results also explain the crossover in the quality of the fitting models reported by Hernandez-Perni et al.:27 Since the fast relaxation increases significantly in amplitude with increasing DX concentrations (Figure 5), the asymmetric broadening of the spectra becomes more and more pronounced. However, the asymmetry increases in a way that cannot be accommodated by the rather specific shape of the DavidsonCole function. Systematic deviations appear between the experimental ˆ (ν) data and the spectrum calculated from the DC model, which for a given concentration become more pronounced the higher the frequency. Accidentally, at xO,2 ≈ 0.3-0.4, a situation is reached in which these systematic deviations are large enough to be detected at frequencies
