Are Nanoscale Ion Aggregates Present in Aqueous Solutions of

Oct 11, 2010 - Orion Shih , Alice H. England , Gregory C. Dallinger , Jacob W. Smith , Kaitlin C. Duffey , Ronald C. Cohen , David Prendergast , Richa...
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J. Phys. Chem. B 2010, 114, 13617–13627

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Are Nanoscale Ion Aggregates Present in Aqueous Solutions of Guanidinium Salts? Johannes Hunger, Stefan Niedermayer, and Richard Buchner* Institut fu¨r Physikalische und Theoretische Chemie, UniVersita¨t Regensburg, D-93040 Regensburg, Germany

Glenn Hefter* Chemistry Department, Murdoch UniVersity, Murdoch, W.A. 6150, Australia ReceiVed: February 19, 2010; ReVised Manuscript ReceiVed: September 21, 2010

A detailed investigation using broadband dielectric relaxation spectroscopy (DRS) has been made of the aqueous solutions of guanidinium chloride and carbonate, GdmCl(aq) and Gdm2CO3(aq), at 25 °C. The spectra indicate that Gdm+ ions, C(NH2)3+, do not bind strongly to water nor are they hydrophobically hydrated; rather they appear to have a most unusual ability to dissolve in water without altering its dynamics. Although DRS is particularly sensitive to the presence of ion pairs, only weak ion pairing was detected in Gdm2CO3(aq) solutions and none at all in GdmCl(aq). Surprisingly, no evidence was found for the existence of the higher order homo- and heteroionic nanoscale aggregates that have been identified in recent years by Mason and co-workers using molecular dynamics simulations and neutron diffraction. Possible reasons for this discrepancy are discussed. The present DR spectra and other solution properties of GdmCl(aq) and Gdm2CO3(aq), such as apparent molar volumes and electrical conductivities, are shown to have strong similarities to those of the corresponding Na+ salts. However, such solutions also differ remarkably from their Na+ analogues (and all other simple electrolytes in aqueous solution) in that their average water relaxation times correlate strongly with their bulk viscosities. The biological implications of the present results are briefly discussed. 1. Introduction Guanidinium (C(NH2)3+, Gdm+) salts have been widely employed for almost three-quarters of a century for the denaturing or unfolding of protein molecules in aqueous solution,1 a process that can be made reversible in some cases by careful control of conditions.2 As the folding and unfolding of proteins is thought to be a key to understanding many of their biological functions,3 it is not surprising that the nature of guanidinium salt solutions has received considerable attention. Indeed, a panoply of techniques including NMR4 and IR5,6 spectroscopies, calorimetry,7 and other thermodynamic measurements8 have been used to try to elucidate the special characteristics of these intriguing solutions. Most investigators have favored the idea that the denaturing process involves direct interaction between the Gdm+ ions and the protein molecules, or at least parts of them. Nevertheless, Scott et al.5 have emphasized that Gdm+ ions might instead (or also) destabilize folded proteins by altering the latter’s hydration network. In recent years, Mason et al. have published9-12 a series of studies of various guanidinium salt solutions using NDIS (neutron diffraction with isotope substitution) in conjunction with MD (molecular dynamics) simulations. These studies have indicated significant formation of previously unsuspected large aggregates in all the Gdm+-containing solutions studied, extending up to nanometer scale. The original identification of these species, which include both homoionic (involving only Gdm+ ions) and heteroionic (conventional Gdm+/Xn- ion pairs and larger groupings) aggregates, was via the MD simulations. However, Mason et al. have shown that the presence of such aggregates is consistent with their NDIS data and, at least for Gdm2CO3(aq),12 also with small-angle neutron scattering (SANS) * Towhomcorrespondenceshouldbeaddressed.E-mail:Richard.Buchner@ chemie.uni-regensburg.de (R.B.); [email protected] (G.H.).

experiments, which are believed to be sensitive to the presence of nanoscale particles in solution. They have further suggested that such particles may be widespread, even in conventional aqueous electrolyte solutions.12 While the chemical and especially the biological implications of these aggregates are not yet clear (there are indications that Gdm+ preferentially interacts with the aromatic side chains of proteins13-15), their possible ramifications are great: not just for Gdm+-containing solutions but for electrolyte solutions in general.12 It would therefore be desirable to confirm the findings of Mason et al. by a completely independent technique. Dielectric relaxation spectroscopy (DRS) studies the interaction of a sample with electromagnetic radiation in the microwave (GHz) region.16,17 It is a relatively little-used but powerful technique for the investigation of electrolyte solutions.18 For example, DRS has provided probably the most direct experimental evidence yet19,20 for the re-enforcing of the water structure around hydrophobic solutes: so-called hydrophobic hydration, which is thought to be critical for explaining the behavior of many biological solutes in aqueous solutions.21,22 In addition, DRS can provide significant, and often quantitative, insights into ionic hydration, water dynamics and the formation of ion pairs and higher aggregates in electrolyte solutions.18 Haggis et al.23 and Lileev et al.24 have reported dielectric data for GdmCl(aq), while Lileev et al.25 have also studied Gdm2CO3(aq) and some related salts. However, while these pioneering studies deserve recognition, the information that could be gained from them was limited because the spectra were recorded (mostly due to the technological limitations of the time) at only three frequencies between ca. 3 and 25 GHz. Accordingly, the present paper reports a broad bandwidth (0.2 j ν/GHz e 89) dielectric relaxation investigation of the aqueous solutions

10.1021/jp101520h  2010 American Chemical Society Published on Web 10/11/2010

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Figure 1. (a) Relative permittivity, ε′(ν), and (b) dielectric loss, ε′′(ν), spectra of aqueous solutions of GdmCl at 25 °C. Symbols show typical experimental data (others are omitted for visual clarity); lines represent the CC fit (see text); arrows indicate increasing cGdmCl.

of two of the guanidinium salts studied by Mason et al., GdmCl(aq) and Gdm2CO3(aq), over a wide concentration range at 25 °C. 2. Experimental Section Materials. Guanidinium carbonate (Gdm2CO3, >99%) was obtained from Merck, Germany, while guanidinium chloride (GdmCl) was synthesized by adding ∼20% molar excess of concentrated HCl (analytical grade, 36%, Fisher Scientific, UK) to an aqueous solution of Gdm2CO3. The raw product was dried and recrystallized thrice from ethanol (analytical grade, >99.9%, J. T. Baker, The Netherlands). Both salts were dried under vacuum (p < 10-8 bar) at ∼ 80 °C for 3 days. Aqueous solutions were prepared by weight without buoyancy corrections from degassed Millipore Milli-Q water, using an analytical balance, thereby yielding concentrations that were accurate to about (0.2% relative. Measurements. All measurements were performed at 25.00 ( 0.05 °C. Total complex permittivity spectra, ηˆ (ν) ) η′(ν) iη′′(ν), were measured in the frequency range 0.2 j ν/GHz e 20 with a frequency-domain reflectometer based on a HewlettPackard (HP) model 85070 M dielectric probe connected to a HP 8720D vector network analyzer (VNA).26 For selected samples, the frequency range was extended up to 89 GHz with two waveguide interferometers (IFMs) operating at 27 e ν/GHz e 89.27 Raw VNA data were obtained using air, mercury, and water as primary calibration standards. Calibration errors were corrected with a Pade´ approximation using N,N-dimethylacetamide and propylene carbonate as secondary standards.28 Typical experimental spectra for the GdmCl and Gdm2CO3 solutions are displayed in Figures 1 and 2, respectively. Solution densities, F, required for the calculation of molar concentrations, c/mol L-1, were measured with an accuracy of (0.05 kg m-3 using a vibrating-tube densimeter (Paar DMA60/ 601HT) calibrated with N2(g) and water, assuming densities from standard sources.29 Electrical conductivities of the mixtures, κ, were determined with an accuracy of (0.5% using an ac bridge and capillary cells as described in detail elsewhere.30 All of these data are collected in Table 1. For the calculation of the polarizability of the Gdm+ ion, the refractive indices at 25 °C, nD25, of some aqueous GdmCl solutions were measured using the sodium D line with an Abbe´-type refractometer (Carl Zeiss Jena, Germany) with an accuracy of (0.05% (Table 2).

Hunger et al.

Figure 2. (a) Relative permittivity, ε′(ν), and (b) dielectric loss, ε′′(ν), spectra of aqueous solutions of Gdm2CO3 at 25 °C. Symbols show typical experimental data (others are omitted for visual clarity); lines represent the fits for spectra with the DDD model (ν e 20 GHz) or the DDDD (ν e 89 GHz)ssee text and Table 4; arrows indicate increasing cGdm2CO3.

3. Data Analysis Dielectric spectroscopy records the total polarization, b P(t), of a sample in a time-dependent field, b E(t), as a function of the field frequency, ν. The measured quantity is the overall complex permittivity ηˆ (ν) ) η′(ν) - iη′′(ν) (Figure 3a) but for discussion the sample response is usually expressed in terms of the complex permittivity:17,31

εˆ (ν) ) ε′(ν) - iε′′(ν)

(1)

where

ε′(ν) ) η′(ν),

ε′′(ν) ) η′′(ν) -

κ 2πνε0

(2)

In eq 2, κ is the dc conductivity and ε0 the permittivity of free space. The relative permittivity, ε′(ν), shows a dispersion from its static value at low frequency, ε, to the high-frequency limit, ε∞. The dielectric loss, ε′′(ν), expresses the energy dissipation within the sample, arising from the coupling of b E(t) to dipole fluctuations, whereas κ characterizes the stationary (diffusive) charge transport. Note that εˆ (ν) contains all contributions to b P(t) that depend on frequency, irrespective of their rotational, vibrational, or translational character. The value of κ for the solutions can be determined, in principle, either as an additional parameter in the fitting of the DRS data or from conventional low-frequency conductance measurements.26 In practice, fitted κ values deviate slightly from directly measured values due to field imperfections, which arise from the geometry of the VNA probe.32 Accordingly, experimental κ values were chosen as a starting approximation in the fitting procedure. Dielectric spectra were rejected if the experimental and fitted κ values differed by more than 5%. From eq 2 and Figure 3 it is apparent that at low frequencies the contribution of the dc conductivity dominates the experimentally determined total loss, η′′(ν), because ε′′(ν) f 0 as ν f 0 (as a consequence of the causality principle) whereas κ/(4πνε0) f ∞.31 Thus, there is a threshold, νmin, below which the uncertainty in η′′(ν) will be larger than the quantity of interest, ε′′(ν). Additionally, ε′(ν < νmin) often becomes too noisy to extract reliable information. For κ j 2 S m-1, the cutoff frequency for meaningful measurements is slightly lower than

DRS of GdmCl(aq) and Gdm2CO3(aq)

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TABLE 1: Weight Fractions, w, Densities, G, Concentrations of Gdm+, cGdm+, and of Water, cH2O, and Electrical Conductivities, K, of Aqueous Solutions of GdmCl and Gdm2CO3 at 25 °Ca wGdmCl

F

0.01483 0.02879 0.04316 0.05733 0.07240 0.08538 0.1004 0.1150 0.1286 0.1428 0.1663 0.1913 0.2855 0.3800 0.4789 0.5713

1001.42 1005.34b 1009.31b 1013.41 1017.41b 1021.01b 1025.46 1029.27b 1033.26 1037.04b 1043.81 1050.68b 1077.09 1104.58b 1133.10 1160.85

cH2O

κ

wGdm2CO3

F

54.748 54.184 53.593 53.014 52.372 51.823 51.191 50.549 49.968 49.333 48.291 47.153 42.708 38.004 32.767 27.614

1.599 2.983c 4.259c 5.409 6.690c 7.716c 8.815 9.959c 10.86 11.95c 13.48 15.17c 20.39 24.43c 26.59 26.40

0.01480 0.02763 0.04009 0.05176 0.06644 0.08072 0.09154 0.1036 0.1179 0.1314 0.1665 0.2007 0.2304 0.2590 0.2884 0.3089

1003.87 1009.45 1014.83 1019.94 1026.03 1032.05 1036.61 1041.75 1047.61 1053.26 1068.53b 1082.18 1096.37b 1110.11 1122.04b 1130.93

cGdm+ GdmCl 0.1555 0.3030 0.4560 0.6082 0.7711 0.9125 1.078 1.239 1.390 1.550 1.817 2.104 3.219 4.394 5.680 6.943

cGdm+ Gdm2CO3 0.1650 0.3096 0.4516 0.5860 0.7568 0.9247 1.053 1.198 1.371 1.536 1.975 2.411 2.804 3.192 3.592 3.879

cH2O

κ

54.884 54.471 54.059 53.671 53.155 52.650 52.259 51.823 51.282 50.771 49.424 48.004 46.825 45.646 44.310 43.370

1.187 1.916 2.530 3.040 3.628 4.144 4.509 4.854 5.308 5.679 6.519c 7.182 7.637c 7.983 8.224c 8.335

a Units: w in g solute/g solution; F in kg m-3; cGdm+, cH2O in mol L-1; κ in S m-1. b Interpolated with a quadratic equation. c Interpolated with the Casteel-Amis equation.82

TABLE 2: Weight and Mole Fractions, wGdmCl and xGdmCl, Densities, G, and Refractive Indices, nD25, of Dilute Aqueous Solutions of GdmCl at 25 °Ca wGdmCl

xGdmCl/10-4

F

nD25

0.004956 0.009565 0.01384 0.01937

9.386 18.18 26.40 37.12

998.56 999.93 1001.20 1002.79

1.33336 1.33419 1.33494 1.33609

a

Units: F in kg m-3.

the minimum frequency of 0.2 GHz of the present instrumentation. However, νmin continuously increases with increasing c, reaching 0.47 GHz for 3.2 M GdmCl and finally 0.75 GHz for the most concentrated (6.9 M) GdmCl solution. For the significantly less-conducting Gdm2CO3 solutions, Table 1, νmin ) 0.35 GHz at the highest concentration. In the investigated frequency range, resonant modes (such as intermolecular vibrations) can be neglected and only relaxation processes arising from the delayed response of b P(t) to the driving field b E(t) have to be considered.31 For the formal description of the spectra, various models based on the sum of n individual relaxation processes n

εˆ (ν) )

S

j ∑ [1 + (i2πντ )1-R ]β j

j)1

j

+ ε∞

(3)

j

were tested using a nonlinear least-squares routine that simultaneously fitted ε′(ν) and ε′′(ν). Each dispersion step j, of amplitude Sj ) εj - εj+1 and relaxation time τj, was modeled by a Havriliak-Negami equation (HN, eq 3) with relaxationtime distribution parameters 0 e Rj < 1 and 0 < βj e 1. The simplified variants of this equation are the Cole-Davidson (CD, Rj ) 0), Cole-Cole (CC, βj ) 1) or Debye (D, Rj ) 0, βj ) 1) models.31,33 To evaluate the quality of the fit, the reduced error function34 N

χr2 )

∑

1 δε′(νk)2 + [ 2N - m - 1 k)1

N

∑ δε′′(νk)2]

k)1

(4)

Figure 3. (a) Relative permittivity, ε′(ν), total loss, η′′(ν), and dielectric loss, ε′′(ν), spectra of 1.198 mol L-1 Gdm2CO3 at 25 °C. Symbols represent experimental data, and lines show the DDDD fit. (b) Enlarged view of ε′′(ν) for this solution with shaded areas indicating the contributions of solvent-separated ion pairs (SIP), contact ion pairs (CIP), the cooperative relaxation of water H-bond network (H2O), and the fast water relaxation (fast H2O).

was calculated, where δε′(νk) and δε′′(νk) are the residuals, N is the number of the data triples (νk, ε′k, ε′′k), and m is the number of adjustable parameters. No weighting was used. Note that because of the nonlinear nature of the fitting procedure, it is not possible to assign statistically meaningful standard uncertainties to the individual fit parameters.34 The detection of slow modes with relaxation frequencies νj ) (2πτj)-1 < νmin will only be possible if their contribution to

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TABLE 3: Fit Parameters of Eq 3 for the Observed DR Spectra of Aqueous Solutions of GdmCl at 25 °C, Assuming a CC Model: Static Permittivitiy, ε, Relaxation Time, τ1, CC Broadness Parameter, r1, Infinite Frequency Permittivity, ε∞, and Reduced Error Function of the Overall Fit, χr2 a cGdm+

ε

τ1

R1

ε∞

χr2/10-4

0.1555 0.3030 0.4560 0.6082 0.7711 0.9125 1.078 1.239 1.390 1.550 1.817 2.104 3.219 4.394 5.680 6.943

76.44 74.96 73.43 71.87 70.10 68.75 67.11 65.71 64.19 62.90 60.08 57.77 49.25 41.39 34.61 27.81

8.19 8.15 8.15 8.20 8.13 8.13 8.16 8.11 8.16 8.07 8.15 8.06 8.02 8.51 8.57 8.78

0.0213 0.0324 0.0405 0.0415 0.0467 0.0506 0.0494 0.0588 0.0529 0.0631 0.0528 0.0653 0.0874 0.112 0.172 0.157

4.98 4.86b 4.9b 4.76 4.99b 5.03b 4.91 5.13b 5.14 5.22b 5.56 5.41b 5.57 6.41b 5.74 6.90

115 124 138 258 64 60 130 69 218 90 195 147 383 476 581 965

a

-1

b

Units: cGdm+ in mol L , τ1 in ps. Value fixed by linear interpolation of ε∞ values obtained from spectra recorded at ν e 89 GHz (see text).

εˆ (νJνmin) is significant. For the noise level of the present spectra this means that systematic positive deviations of ∆ε′(νmin) ) 2∆ε′′(νmin) ≈ 2 from the present fits would be required for a clear hint of the presence of low-frequency relaxations with νj < νmin. However, as discussed below, our data do not indicate any such contributions. Similar considerations apply to fast modes with νj > 89 GHz. As discussed below, such a (high frequency) contribution could only be detected for Gdm2CO3(aq). 4. Results and Discussion 4.1. Guanidinium Chloride. The experimental spectra for aqueous solutions of GdmCl (Figure 1) were best described by a single Cole-Cole equation (n ) 1, β1 ) 1 in eq 3, the CC model) as has been observed previously for the aqueous solutions of a number of electrolytes.26,35,36 To avoid systematic deviations in the fit parameters of the spectra for which only VNA data (at ν e 20 GHz) were available, ε∞ values were fixed by linear interpolation of the ε∞ results obtained from spectra recorded at ν e 89 GHz. The parameters derived in this manner for GdmCl(aq) are summarized in Table 3. The observation of a single, symmetrically broadened (CC) relaxation process for GdmCl(aq) is analogous to the DRS results reported in the earlier study of Lileev et al.24 and also for aqueous solutions of NaCl,26 MgCl2,36 KCl,35 and CsCl.35 This process can be assigned to the cooperative reorientation of the water molecules in their three-dimensional H-bond network.37 The very fast water mode centered at 600 GHz in neat water37 that is often,33,38 but not always,36,39 observed in the high-frequency DR spectra of aqueous solutions of electrolytes could not be resolved in the present GdmCl(aq) spectra. Any small contribution from this mode will be subsumed in the symmetrically broadened CC model. Perhaps the most remarkable feature of the DR spectra of GdmCl(aq) solutions (Figure 1) is that they show almost no variation, even up to a solute concentration of ∼7 mol L-1, in the position of the peak maximum, νj, which defines τj, the average relaxation time for the process. To relate the observed values of τj, which are a collective property, to specific

molecular processes they must be converted to microscopic relaxation times τ′j. This can be done using the Powles-Glarum40,41 equation

τ′j ) τj

(

2ε + ε∞ 3ε

)

1/(1-Rj)

(5)

n Sj ) limνf0ε′(ν)). where ε is the static permittivity ()ε∞ + ∑j)1 Providing that the observed processes are due to diffusive rotation, the τ′j values for the reorienting dipolar species can be predicted from their geometry via the Stokes-Einstein-Debye (SED) equation42

τj′ )

3Veff,jη kBT

(6)

where Veff,j is the effective volume of rotation of the species j, η is the bulk viscosity, kB is Boltzmann’s constant, and T is the thermodynamic temperature in kelvin. The value of Veff,j ()fCVm,j) is determined by the molecular volume, Vm,j, the shape factor f of the rotating particle,43 and a hydrodynamic friction coefficient, C. The last is generally treated as an empirical parameter but its limiting values for stick (Cstick ) 1) and slip (Cslip ) 1 - f-2/3) boundary conditions can be obtained from theory.42 The data in Table 3 reveal a slight decrease in τ1 from ∼8.2 to ∼8.0 ps, as the analytical solute concentration, cGdmCl, increases to ∼3 mol L-1. This is consistent with an attenuation of the local field of the relaxing species (i.e., the electrical field experienced by the rotating water molecules) due to the decrease in ε (eq 5). This means that, as shown in Figure 4a, the corresponding τ1′ values are remarkably constant at cGdmCl j 3 mol L-1. At higher concentrations, the small but steady increase in the experimental τ1 values (Table 3) tracks reasonably well with the bulk solution viscosity. This is most unusual in aqueous electrolyte solutions where the main relaxation process is due, as already noted, to the cooperative motions of the H-bond network rather than (as is assumed in the derivation of eq 6) the rotational diffusion of single-molecule dipoles. These findings indicate that the water relaxation mechanism remains unchanged up to high cGdmCl and that the dynamics of water molecules around the solute particles are very similar to those in the bulk solvent. Further discussion of these effects is deferred until presentation of the Gdm2CO3(aq) spectra (section 4.2). Although τ1 shows only small changes with cGdmCl, there is a steady increase in the CC broadness parameter R1 (Table 3). This signifies36 an increasing heterogeneity of the environments in the water network due to the presence of the Gdm+ and Clions (and their aggregates, if present). Similar increases in R1 have also been observed for other chloride salts such as NaCl(aq),26 MgCl2(aq),36 KCl(aq), and CsCl(aq),35 which suggests that the H-bonds of water molecules to Cl- differ slightly in strength from those formed with other water molecules. The relaxation of GdmCl(aq) can be further analyzed with the Cavell equation,44 which relates the observed amplitude Sj to the effective dipole moment µeff, j of the molecular-level species responsible for that process

NAcj 2 ε + (1 - ε)A µ Sj ) ε 3kBTε0 eff,j

(7)

DRS of GdmCl(aq) and Gdm2CO3(aq)

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Figure 5. Effective solvation numbers, Zib, of aqueous solutions of (a) GdmCl and (b) Gdm2CO3 at 25 °C. Error bars were estimated assuming ∆S1 ) 0.01ε. Lines represent (a) Zib(GdmCl) ) 0 and (b) Zib(CO32-) obtained from Na2CO3(aq).55

Figure 4. (a) Relative microscopic relaxation times, τ′/τ′, 0 of bulk water relaxation of aqueous solutions of GdmCl (9) and Gdm2CO3 (b). Lines represent relative viscosities, η/η0, for GdmCl (dotted line)77 and Gdm2 SO4 (solid line).52 (b) τ′/τ0′ values for NaCl (9)26 and Na2CO3 (b)38 at 25 °C (left-hand axis) with the corresponding relative viscosites (righthand axis) of NaCl(aq) (solid line)78 and Na2CO3(aq) (dotted line).79 Dashed lines are included as a visual aid; the subscript “0” refers to the pure solvent.

where NA is Avogadro’s constant, cj is the molar (mol L-1) concentration of the species j, and A accounts for the shape of the reaction field.45 The Cavell equation can be used to calculate an apparent (i.e., DRS-detected) concentration of H2O, capp H2O, by assuming a spherical reaction field (A ) 1/3) and that µeff, H2O is the same as in neat water.46,47 Kinetic depolarization effects,26,48,49 due to the coupling of solvent-dipole reorientation and ion translation in the oscillating electromagnetic field, were accounted for by assuming slip boundary conditions.26 Effective hydration numbers, Zib, corresponding to the number of water molecules “irrotationally bound” (ib) or “frozen” on the DRS time scale per unit of solute concentration, can then be obtained from the difference between capp H2O and the analytical (total) water concentration, cH2O:

Zib )

cH2O - cHapp2O c

(8)

Note that the value of Zib mainly reflects the strength of solute-solvent interactions; i.e., it is a dynamical hydration number that reflects the number of water dipoles effectively locked by the solute. It is therefore generally different from the coordination (structural hydration) number of water molecules in the primary hydration shell as determined by scattering experiments or computer simulation.18,50

Evaluation of the data for GdmCl(aq) yields, within the probable error limits, Zib(GdmCl) ≈ 0 over the whole concentration range investigated (Figure 5a). The absence of either irrotationally bound or slow19 water molecules around Cl- at 25 °C has been noted for numerous chloride salts,26,35,36 and has even been used as a basis for obtaining Zib(ion) from the observable whole salt quantities.19,26 Since Zib(GdmCl) ) Zib(Gdm+) + Zib(Cl-), a safe conclusion from the DR spectra for GdmCl(aq) (Figure 1) is that Zib(Gdm+) ≈ 0 at all concentrations. The slightly negative values of Zib(Gdm+) at high c seen in Figure 5a are not physically meaningful. It can also be noted that the DR spectra of GdmCl(aq) show no indication of hydrophobic hydration of Gdm+ or (as is well-known19,26,35,36) Cl-. This type of hydration evidence itself by a detectable slowing down of the water dynamics, corresponding either to a marked decrease in νj or a resolvable spectral feature at ν < νj.18 The absence of either irrotationally bound or slow water molecules around the Gdm+ ion is consistent with its very low charge density (produced by the delocalization of the cationic charge) and the absence of any hydrophobic groups of atoms on Gdm+.19,20 These findings indicate that Gdm+/H2O interactions are remarkably similar to H2O/H2O interactions and that Gdm+ ions fit into the 3-D water structure without disrupting it significantly. The present DR spectra therefore support the statement of Mason et al., made on the basis of their neutron diffraction measurements, that Gdm+ “has no recognizable hydration shell”.9 However, in contrast with their later study, based mainly on MD simulations, no features were observed in the spectra to indicate the formation of either ion pairs or higher aggregates in these solutions (but see section 4.4 below). 4.2. Guanidinium Carbonate. In contrast to GdmCl(aq), the DR spectra of Gdm2CO3(aq) (Figure 2) required up to four relaxation processes to model them satisfactorily. The lowest χr2 values for spectra measured at ν e 89 GHz were obtained with a superposition of four Debye equations (Rj ) 0, βj ) 1 in eq 3, 1 e j e 4, the “DDDD” model). For spectra where only VNA data were available (ν e 20 GHz) the highest frequency process was outside the spectral range and therefore just three Debye modes were sufficient (i.e., 1 e j e 3, the “DDD” model). The parameters so obtained are summarized in Table 4. A representative spectrum showing the individual contributions of the four processes, which are identified below, is displayed in Figure 3.

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TABLE 4: Fit Parameters of Eq 3 for the Observed DR Spectra of Aqueous Solutions of Gd2CO3 at 25 °C Assuming a DDDD or DDD Model for Spectra with νmax ) 89 and 20 GHz, Respectively: Static Permittivities, ε; Relaxation Times, τj, and Limiting Permittivities, εj and εj+1, of Process j (ε1 ) ε, ε5 ) ε∞) and Reduced Error Function of the Overall Fit, χr2 a cGdm+ 0.1650 0.3096 0.4516c 0.5860 0.7568c 0.9247 1.053c 1.198 1.371c 1.536 1.975c 2.411 2.804c 3.192 3.592c 3.879 a

ε 79.39 79.91 79.19 79.49 78.92 77.91 78.25 76.91 76.05 75.71 73.16 70.29 68.01 64.89 62.78 61.05

τ1 219 176 129 156 143 107 191 116 116 180 155 155 209 167 258 309

ε2 76.45 75.15 73.81 74.29 73.72 70.72 73.99 69.95 69.36 71.66 67.82 64.63 63.42 59.46 58.28 56.57

τ2

ε2 b

40.0 40.0b 40.0b 49.7 51.0 35.6 55.8 35.6 38.2 55.3 43.3 37.2 44.8 46.3 44.3 48.1

75.27 73.73 72.18 70.38 69.35 66.77 66.23 63.52 62.46 62.32 57.65 52.77 51.74 46.29 46.57 45.80

τ3 8.23 8.33 8.19 8.34 8.58 8.38 8.60 8.34 8.49 8.81 8.75 8.56 9.28 8.79 9.87 11.1

ε4 5.76 5.87 6.68 7.10 7.32 6.58 7.43 6.82 7.13 7.58 7.53 7.21 8.32 8.06 8.72 11.80

τ4 b

0.5 0.5b 0.80 1.1 0.59 0.84 0.5b 0.5b 1.9

ε∞

χr2/10-4

3.86 4.62 1.78 5.55 3.87 4.52 5.85 2.94 4.23

88 113 21 71 38 115 44 74 40 130 26 75 25 55 27 45

Units: cGdm+ in mol L-1, τj in ps. b Parameter fixed during fitting procedure. c νmax ) 20 GHz.

SolWent Relaxations. The two higher-frequency modes (Figure 3b), processes 3 and 4, are water relaxations. The dominant cooperative relaxation of the H-bonded water network is centered at ∼18 GHz while the much smaller amplitude fast water process is at ∼600 GHz.37 The latter is almost outside the range of the present measurements and was detectable only in the spectra recorded up to 89 GHz by a small but systematic increase in amplitude at higher frequencies (see section 3). For Gdm2CO3(aq) solutions, the main relaxation time τ3′, obtained via eq 5 from the corresponding macroscopic τ3 values in Table 4, increases monotonically with increasing solute concentration (Figure 4a, Table 4) but the change is markedly larger than for the corresponding (τ1′) values in GdmCl(aq). No viscosities for Gdm2CO3(aq) at high c could be located in the literature51 but data for Gdm2SO4(aq),52 which would be expected to be very similar,53 are available and are also plotted in Figure 4a. Even more than for GdmCl(aq), there is a remarkable and unexpected tracking of the water relaxation time (τ′) 3 and the solution viscosity. To emphasize the unusual nature of the apparent nexus between τ and η for guanidinium salt solutions, the corresponding data for NaCl(aq) and Na2CO3(aq) are plotted in Figure 4b. The viscosities of these solutions, values of which are quite typical for simple salts in water,18,54 show a complete decoupling of τ and η, as would be expected from the cooperative nature of the main water relaxation process. It will be argued below that there are significant similarities between the DR spectra of GdmCl(aq)/Gdm2CO3(aq) and their sodium analogues but, as can be seen from Figure 4, the effect of solute concentration on their water relaxation dynamics is dramatically different. The effective solvation numbers, Zib, for Gdm2CO3(aq) can be obtained as described above. Assuming ionic additivity and the value of Zib(Gdm+) ≈ 0 derived from the GdmCl(aq) spectra, it follows that Zib(Gdm2CO3) ) 2Zib(Gdm+) + Zib(CO32-) ≈ Zib(CO32-). The values of Zib(CO32-) obtained in this way are plotted (points) in Figure 5b along with the results previously derived from the DR spectra of Na2CO3(aq) (full line).38,55 Ionic additivity is strictly expected only at infinite dilution so it is pleasing that the Zib(CO32-) obtained at low concentrations of Gdm2CO3(aq) and Na2CO3(aq) trend toward the same values, within the rather large error limits. At higher salt concentrations, the present values are somewhat lower than those obtained from Na2CO3(aq). These differences might be related to the presence

of nanoscale aggregates in Gdm2CO3(aq);12 however, the formation of such aggregates would require an increasing difference with increasing salt concentration, which is hardly borne out by the data (Figure 5b). It is therefore more likely that the observed difference between Zib(CO32-) in the two salt solutions is due to a difference in the nature of the ion-pair species present. In Na2CO3(aq) both solvent-shared (SIPs) and double-solvent-separated (2SIPs) ion pairs were detected38 whereas (see below) in Gdm2CO3(aq) a mixture of contact ion pairs (CIPs) and SIPs appears probable. A combination of CIPs + SIPs would be expected to release more water molecules (i.e., would lower the value of Zib) than an SIP + 2SIP combination, consistent with the data in Figure 5b. Solute Relaxations. The two lower frequency modes in Gdm2CO3(aq), processes 1 and 2 (Figure 3), can be assigned to two different ion-pair species, analogous (but as just noted not identical) to those observed for Na2CO3(aq).38 Within the experimental accuracy, the rather constant values of their relaxation times (τ1 and τ2) over the entire investigated composition range indicates that the chemical nature of the ionpair species related to these two modes is the same at all concentrations. The possible structures of ion pairs involving Gdm+ are more complex than those containing the monatomic closed-shell spherical Na+. Thus, in addition to the usual doubly solvent-separated (2SIP), solvent-shared (SIP), and contact (CIP) ion-pair types,39 the trigonal planar unsaturated Gdm+ ion can, at least in principle, coordinate to the similarly shaped and delocalized CO32- ion either “face-on” or “end-on” (Figure 6). The possibility of triple ions (TIs) or the even larger aggregates reported by Mason et al.10,12 must also be considered. Apart from 2SIPs, which would be very unlikely to form given the relatively weak hydration of Gdm+, none of these species can be excluded a priori.56 For the remaining possibilities comparison of observed and calculated values of τ′j provides a means of identifying the nature of the relaxing species.39,45,57,58 To this end the geometry of Gdm+ was approximated as an oblate ellipsoid, whose dimensions were estimated, using crystallographic data59 and the van der Waals radii of Bondi,60 to be ra ) rb ) 311 pm and rc ) 170 pm for the major and minor radii respectively. For convenience and following previous practice,38 both carbonate and water were assumed to be spherical,61 with rCO32- ) 178 pm62 and rH2O ) 142.5 pm.57 The experimentally determined

DRS of GdmCl(aq) and Gdm2CO3(aq)

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Figure 6. Geometries of the “end-on” and the “face-on” coordination for CIPs of Gdm2CO3.

TABLE 5: Microscopic Relaxation Times, τ′, of Different Ion Pair Species Estimated via Eq 6 Assuming Stick and Slip Boundary Conditions and Prolate Ellipsoidal Geometry with Semiprincipal Axis, ra and rb ) rca IP species

a

ra

rb

τ′stick

CIP SIP 2SIP

Face-on Coordination 348 311 94 491 311 160 633 311 250

CIP SIP 2SIP

End-on Coordination 489 178 89 632 178 160 774 178 250

τ′slip 1.9 21 63 35 80 150

Units: r in pm; τ′ in ps.

mean microscopic relaxation times for the dilute solutions, τ1′ ) 104 ( 26 ps and τ′2 ) 30 ( 5 ps, agree very well with the relaxation times estimated for the “end-on”-coordinated SIP and CIP species, respectively, assuming slip boundary conditions (Table 5). Triple ions can be ruled out as the species responsible for the observed low-frequency processes in Gdm2CO3(aq), since their larger molecular volume would result in much longer relaxation times, for which there is no evidence of in the DR spectra (Figures 2 and 3). The same applies to larger aggregates (but see further discussion below). Similarly, the relaxation times predicted for the “face-on” CIP or SIP ion pairs are significantly lower than the observed values (Table 5). The absence of “faceon” species is consistent with the MD simulations of Mason et al.12 and also with the stereochemical rigidity of Gdm+, which prevents optimal alignment for favorable N · · · H · · · O interactions (Figure 6b). To analyze the two ion-pair relaxations quantitatively via eq 7, the effective dipole moments and polarizabilities of the ion pairs have to be estimated,63 as described in detail elsewhere.57 Assuming end-on coordination with rGdm+ ) 311 pm,59,60 rCO32) 178 pm,62 and rH2O ) 142.5 pm57 and with the center of hydrodynamic stress as the pivot,57 the gas-phase ion-pair dipole moments were found to be µCIP ) 37.1 D and µSIP ) 58.8 D (1 D ) 3.335 64 × 10-30 C m).64 Medium effects on the gasphase dipole moments are accounted for by estimation of the effective dipole moment

µeff,IP )

µIP 1 - fIPRIP

(9)

where RIP is the polarizability and fIP is the reaction field factor45 of the relevant ion pair. Polarizabilities of the anion and water were taken from the literature (RH2O ) 1.44 Å3, RCO32- ) 4.56

Figure 7. (a) Relative concentrations of CIPs and SIPs in aqueous solutions of Gdm2CO3 at 25 °C. Dotted lines are included as a visual aid. Note that (cj/cGdm2CO3) f 0 as cGdm2CO3 f 0. (b) Extrapolation of the overall association constant, KA, vs stoichiometric ionic strength, I, according to eq 10.

Å3),57,62 while the polarizability of Gdm+ was obtained from refractive index (nD) measurements of GdmCl(aq) as a function of concentration (Table 2). Linear regression of the measured molar refractivity R [)(4π/3)NAR ) (n2D - 1)/(n2D + 2)c] against the mole fraction of GdmCl yielded RGdmCl. Subtraction of RCl-62 then gave RGdm+ ) 5.97 Å3. Insertion of the ion-pair parameters into eq 7 yielded the ionpair concentrations cCIP and cSIP (Figure 7a). Although the data scatter considerably, a physically coherent picture is found that is broadly consistent with that observed for many other weakly associating electrolytes in aqueous solution and with the wellestablished Eigen-Tamm mechanism of ion association.18 That is, at low salt concentrations the associated species are mostly SIPs, which are progressively displaced by CIPs as c increases. From the ion-pair concentrations obtained via eqs 7 and 9, the overall association constant KA ) cIP/(cGdm+ × cCO32-) can be calculated, where cIP ) cCIP + cSIP. To obtain the standard association constant at infinite dilution, KA0, the values of KA measured at finite concentrations were fitted for convenience to a semiempirical Guggenheim-type equation

log KA ) log KA0 -

2|z+z- |ADH√I 1 + √I

+ BI

(10)

In eq 10, I ) 3cGdm2CO3 is the stoichiometric ionic strength, ADH ) 0.511 L1/2 mol-1/2 is the Debye-Hu¨ckel constant for activity coefficients in water at 25 °C, B is an adjustable parameter, and z+ and z- are the formal charges of the ions. The extrapolation (Figure 7b) of KA via eq 10 yielded the rather small value of log(KA0/L mol-1) ) 0.59 ( 0.05 with B ) -0.20 ( 0.02 L mol-1. This association constant is broadly consistent with the value of log KA0 ) 0.31 for GdmSO4- obtained from conductance measurements.52 This rather weak association, corresponding to very small ion pair amplitudes, is of course the major reason for the considerable scattering of the data. 4.3. Features of Aqueous Solutions of Guanidinium Salts. Dielectric Data. The present DRS results have revealed a number of remarkable features of the aqueous solutions of guanidinium chloride and carbonate. Perhaps the most important is that Gdm+ ions, even up to high concentrations, appear to dissolve without significantly altering the water dynamics or structure (see particularly Figure 1). Consistent with its electronic structure, Gdm+ has a very low charge density and thus

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Hunger et al.

Figure 8. Apparent molar volumes, Vφ, at 25 °C calculated from eq 11 for aqueous solutions of (a) GdmCl (9) and NaCl26 (0) and (b) Gdm2CO3 (b) and Na2CO380,81 (O). Dotted lines are included as a visual aid.

does not bind water molecules sufficiently strongly so as to immobilize them on the DR time scale (i.e., Zib(Gdm+) ≈ 0). Nor do the DR spectra (Figures 1-3) provide any evidence for hydrophobic hydration of Gdm+(aq) by the appearance of “slow” water.19,20 The second remarkable aspect of the solutions of the two guanidinium salts studied is that, in contrast to all other salts in aqueous solution,65 there is a close correlation between water relaxation times and solution viscosities (Figure 4a). While this implies (but does not prove) a common cause, there is no indication from the spectra as to its origin. It might possibly arise from the presence of nanoscale aggregates but, as will be argued below, this appears unlikely. The third surprising feature of the DR spectra of GdmCl(aq) and Gdm2CO3(aq) is their similarity to those of the corresponding sodium salts. For example, as for NaCl(aq),26 the DR spectra of GdmCl(aq) were well fitted by a single CC model and no ion pairing could be detected. On the other hand, Gdm+ is more weakly hydrated than Na+ since no irrotational bonding could be detected (Zib(Gdm+) ≈ 0, cf. Zib(Na+) ≈ 4.526). Likewise, for Gdm2CO3(aq) two ion pair processes were detected but, consistent with the weaker hydration of Gdm+ cf. Na+, they appear be due to SIPs and CIPs rather than the 2SIPs and SIPs observed for Na2CO3(aq).38 Consistent with the lower charge density of Gdm+, the overall association constant, log KA0(GdmCO3-(aq)) ) 0.59 ( 0.05, is smaller than the value of log KA0(NaCO3-(aq)) ) 0.98 ( 0.02.38 Further similarities in the behavior of Gdm+ and Na+ chloride and carbonate solutions are discussed in the following paragraphs. Apparent Molar Volumes. Apparent molar volumes Vφ can be obtained from the experimental densities, F, via the usual expression

Vφ )

F - F0 M F mFF0

(11)

where M is the molar mass of the solute, F0 the density of the neat solvent, and m the molality (moles solute/kg solvent). The Vφ values so obtained are shown in Figure 8. While Vφ(GdmCl(aq)) changes little with concentration, again suggesting that GdmCl fits comfortably into the water structure, Vφ(Gdm2CO3(aq)) values show a pronounced but reasonably smooth increase with increasing concentration, which probably reflects the strong hydration of CO32-.

Figure 9. Equivalent molar conductivity, Λe ()κ/cGdm+), of GdmCl(aq) (9), Gdm2CO3(aq) (b) together with the corresponding values for NaCl(aq) (0)26 and Na2CO3(aq) (O)38 at 25 °C.

Interestingly, the apparent molar volumes of both guanidinium salt solutions closely parallel their sodium analogues over the entire concentration range, that is ∆Vφ(GdmCl) ) Vφ(GdmCl) - Vφ(NaCl) ≈ 50 cm3 mol-1 and ∆Vφ(Gdm2CO3) ≈ 105 cm3 mol-1 (Figure 8). Thus, in both cases the difference between the apparent molar volumes of Gdm+ and Na+ remains constant at ∼50 cm3 mol-1 for all c. This finding excludes major structural changes specific to the guanidinium salt solutions when their concentration is increased. Electrical ConductiWities. Electrical conductivity data (Tables 1) were measured for correction of the DR spectra (eq 2). Although not of an accuracy nor at sufficiently low concentrations for quantitative analysis,66 it is instructive to compare the equivalent molar conductivities, Λe ) κ/cGdm+, with those of the corresponding Na+ salts. While there are some differences (Figure 9), particularly at intermediate concentrations, the chief feature of these data is the broad similarity in the behavior of the Gdm+ and Na+ chloride and carbonate solutions. Since the molar conductivity, Λ, probes the diffusive motions of the ions, i.e., their long-timescale dynamics, this similarity is a strong argument against the formation of large long-lived aggregates in the Gdm+-containing solutions. This is because ions participating in such clusters would be considerably less mobile than the essentially freely moving anions and cations in NaCl(aq) and Na2CO3(aq). Neither experiments67 nor simulations68 show any features that are indicative of formation of larger aggregates in these sodium-salt solutions. 4.4. Chemical Speciation in Guanidinium Solutions. It is well established that DRS is unusually sensitive to the formation of ion pairs.18,54,69 Thus, it is particularly significant that the present DR spectra (Figure 1) for GdmCl(aq) provide no evidence for the presence of either the hetero (Gdm+ Cl-) or the homo (Gdm+ Gdm+) ion pairs reported by Mason et al.10 on the basis of MD simulations and neutron diffraction data. The level of such species found by Mason et al. from their MD simulations10 should be readily detected by DRS because the ion pairs would have large dipole moments (bearing in mind that DR-process amplitudes are proportional to µ2)54 and their size would tend to give them relaxation rates (peak positions) that are well away from the dominant bulk water process. In contrast to GdmCl(aq), two low-amplitude solute-related processes, centered at ∼0.9 and ∼4.0 GHz, were detected for Gdm2CO3(aq) (Figures 2 and 3). The characteristics of these two processes were consistent with them arising from the presence of “end-on” coordinated solvent-shared (SIPs) and

DRS of GdmCl(aq) and Gdm2CO3(aq) contact (CIPs) ion pairs, which is consistent with the hydration levels of Gdm+ and CO32- and qualitatively with the findings of Mason et al.12 However, again no evidence was found for any of the other species reported by Mason et al. With regard to the higher order aggregates detected by Mason et al., it is possible that they may have zero or near-zero dipole moments and therefore would not be detectable by DRS. However, such large species would be expected to have permittivities and/or conductivities that differ significantly from the ε and κ values of the surrounding bulk solution. On this basis, they would be expected to produce a distinct feature in the DR spectra due to interfacial polarization or related effects.70 Simultaneously, and by analogy with micelle-forming ionic surfactant solutions, a significant decrease in the equivalent molar conductivity would be expected and its concentration dependence should differ markedly from Λe(c) of the corresponding Na+ salt due to the considerably reduced number of freely moving ions. Furthermore, formation of the aggregates claimed by Mason et al. should be manifested in the apparent molar volumes. The observation (Figure 5) of a similar concentration dependence of Zib(CO32-) in Gdm2CO3(aq) and Na2CO3(aq) also argues against the presence of nanoscale aggregates. According to the MD simulations,12 such species have at least some water molecules incorporated in them; it would be extraordinary if these did not show up in the DR spectra either as irrotationally bound or, at the very least, slow water. Furthermore, if the aggregates are present in Gdm2CO3(aq), Le Chatelier’s principle demands that their formation increases with increasing solute concentration and thus a much steeper decrease of Zib(CO32-) at high c would be expected. It might also be argued that the persistence of discrete ion pairs in Gdm2CO3(aq) up to high salt concentrations (Figure 7) makes the presence of larger aggregates unlikely. Three plausible explanations spring to mind as to why the nanoscale aggregates reported by Mason et al. for guanidinium salt solutions are not detected by the present DR measurements. First, as noted above, such large aggregates may have no (or near-zero) dipole moment, remembering that DRS detects only species possessing a permanent dipole moment.18 It is not a trivial exercise to calculate the dipole moments of the Mason et al. aggregates because of their size but certainly it is possible that they could be close to zero. In addition to the argument made above regarding interfacial polarization, it can also be noted that, while the nanoscale aggregates may have a net dipole moment of zero, asymmetric internal fluctuations would be expected to produce nonzero instantaneous dipoles of sufficient fluctuation rate and/or lifetime to be readily detected by broadband DRS. Symmetric internal fluctuations would not change the dipole moments of such particles significantly. In this context, optical Kerr-effect spectroscopy (OKES) would be of interest because it has recently been shown71 to be sensitive to aggregates similar to those proposed by Mason et al. Second, the lifetimes of such species might be too short to be detected by DRS. Given that the upper frequency of the present spectra covers lifetimes as short as 2 ps, this seems unlikely for such large species. Furthermore, conventional kinetic theory indicates that collisions involving more than two particles occur too infrequently to be a significant pathway for the formation of multiparticle species.72 Such species are instead thought to be created by successive bimolecular collisions. The aggregates proposed by Mason et al. can therefore be thought of as being built up from ion pairs. According to Mason et al., the homo ion pairs in Gdm2CO3(aq) have a lifetime of 29 ps

J. Phys. Chem. B, Vol. 114, No. 43, 2010 13625 (they do not provide estimates of the hetero ion pair lifetimes). This would not seem to be long enough for them to combine to form significant quantities of larger aggregates. To put it another way, because of their size, the corresponding rate of formation of the Mason et al. aggregates must be fairly slow, i.e., the formation rate constant kf must be relatively small. If the lifetimes of the aggregates are very short (as required if they are undetectable by DRS), then the rate constant of decomposition kd must be very large. Assuming pseudo-first-order conditions, the formation constant for the aggregates, Kagg ) kf/kd, would have to be close to zero. That is, the aggregates would not form to any significant extent. Third, because of their large size, the relaxation time of the aggregates might be too long to be detected over the present frequency range. This explanation also seems unlikely. DR modes are typically very broad, e.g., the presence of the fast water process centered at 600 GHz is still (just) discernible in the present spectra recorded at ν e 89 GHz (Figure 3). In the present case (see section 3, Data Analysis) a slow mode of relaxation frequency νj ) 10 MHz would be detectible if its amplitude were ∼20; for νj ) 1 MHz an amplitude of ∼200 would be required. For polyelectrolyte systemssand the aggregates postulated by Mason et al. can be seen as suchsrelaxation amplitudes of that magnitude in the appropriate frequency region, arising from the fluctuations of bound counterions, are fairly common.73 Thus, some evidence for even a very slow relaxation would be expected at low frequencies in the present spectra. If, however, the ions are so strongly bound in the aggregates that their mobility becomes negligible and thus the corresponding relaxation amplitude vanishes, then the equivalent molar conductivity should be significantly affected. According to Figure 9 this is not the case. To summarize: if there were large aggregates of the kind claimed by Mason et al. some signature should be seen in the dielectric spectra or in the equivalent molar conductivities or the apparent molar volumes. No such effects were observed. It is not our intention here to criticize the work of Mason et al. which has provided many important insights into the nature of guanidinium salt solutions. However, the following three points are noteworthy. First, the neutron diffraction data of Gdm+ solutions are dominated by intramolecular features (see, for example, Figure 1a of ref 9). As noted by Mason et al., the intermolecular information, which is vital for the identification of hydration, ion pairs, and higher aggregates, is largely hidden under these fairly intense intramolecular features. Second, MD simulations are well-known to have difficulties in accurately modeling many-body interactions in that the results obtained are sensitive to the accuracy of the force fields adopted. Mason et al. have noted that their force field for Gdm+ had some unsatisfactory characteristics and furthermore that reasonable improvements to it resulted in worse fits to the experimental scattering data (ref 10, pp 11464 and 11465). Finally, Mason et al. have noted and commented upon significant differences between their MD simulations and their experimental results. By way of example, they have stated (ref 12, p 13482) that for Gdm2CO3(aq) solutions their NDIS data “produced no direct experimental evidence [of] nanoscale ion clusters... seen in the MD simulations” 4.5. Biological Implications. As reviewed recently by Scott et al.,5 there are two major schools of thought about the mechanism of protein unfolding brought about by guanidinium salts: direct interaction of Gdm+ ions on the protein structure (or at least parts of it) or modification of the water structure around the protein molecules. The present findings suggest that

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even quite high concentrations of Gdm+ ions have a most unusual ability to fit into the structure of water without in essence altering it. This would seem to argue in favor of the “direct interaction model”, facilitated by the absence of a discrete solvation shell around the Gdm+ ions, and is in keeping with the conclusions of Mason et al.9 The weaker protein denaturing activity of Gdm2CO3 compared to GdmCl might be based on the higher degree of association of the carbonate salt, lowering the concentration of Gdm+ ions available. Recent simulations of Mason et al.15 point into this direction. On the other hand, most proteins (or at least parts of them) can be expected to show hydrophobic hydration, where the water structure and dynamics are considerably altered from those of bulk water. The present results provide no information about the effects of Gdm+ ions on such structure-enhanced (“slow”) water molecules. Clearly, there is a lot more that is yet to be learned about guanidinium salt solutions. 5. Conclusion The present DR spectra of GdmCl(aq) and Gdm2CO3(aq) solutions indicate that Gdm+ ions, consistent with their low charge density, do not exhibit the irrotational binding of water observed for many simple cations such as Na+. Neither do the spectra show any evidence of hydrophobic hydration of Gdm+. Rather, consistent with the findings of Mason et al.,9 Gdm+ ions appear to have a remarkable ability to fit into water without altering its structure or dynamics. This suggests that Gdm+-H2O interactions are similar in strength to H2O-H2O interactions. No ion pairing could be detected by DRS in GdmCl(aq) solutions and only rather weak “end-on” coordinated solventshared and contact IPs were found in Gdm2CO3(aq). The results for the latter were broadly consistent with the results of Mason et al.12 However, no evidence was obtained from the DR spectra for either GdmCl(aq) or Gdm2CO3(aq) regarding the formation of the large ion aggregates reported by Mason et al. for these solutions.9,10,12 Possible reasons for this discrepancy have been discussed. The present guanidinium salt solutions show surprisingly strong similarities to the corresponding sodium salt solutions, not only with respect to their DR spectra but also their apparent molar volumes and electrical conductivities. This is a further strong argument against formation of the nanoscale ion aggregates. On the other hand, the dielectric relaxation times for water in Gdm+ solutions correlate well with solution viscosity, which is unexpected in aqueous solutions of electrolytes and does not occur in NaCl(aq) or Na2CO3(aq) or indeed for most simple salts. Acknowledgment. The authors thank Prof. P. Mason for providing the MD simulation snapshots. Prof. W. Kunz is acknowledged for provision of laboratory facilities at Regensburg and Dr. A. Stoppa for performing the refractometer measurements. G.H. thanks the Deutsche Forschungsgemeinschaft (DFG) for the award of a Mercator Visiting Professorship at Universita¨t Regensburg. J.H.’s time in Perth was funded by Murdoch University. References and Notes (1) Svedberg, T. Nature 1937, 139, 1051. (2) Neurath, H.; Cooper, G. R.; Erickson, J. O. J. Biol. Chem. 1942, 142, 249. (3) Pace, C. N.; Grimsley, G. R.; Scholtz, J. M. In Denaturation of Proteins by Urea and Guanidine Hydrochloride.; Buchner, J., Kiefhaber, T., Eds.; Wiley-VCH: Weinheim, Germany, 2005.

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DRS of GdmCl(aq) and Gdm2CO3(aq) (48) Hubbard, J. B.; Onsager, L. J. Chem. Phys. 1977, 67, 4850. (49) Hubbard, J. B. J. Chem. Phys. 1978, 68, 1649. (50) Tielrooij, K. J.; Garcia-Araez, N.; Bonn, M.; Bakker, H. J. Science 2010, 328, 1006. (51) One report74 was located for (Gdm2CO3(aq)) but the values were restricted to c < 0.1 mol L-1. (52) Kumar, A. Fluid Phase Equilib. 2001, 180, 195. (53) The viscosities of Gdm2CO3(aq) solutions would be expected to be similar to but somewhat higher than those of Gdm2SO4(aq), on the basis of the Jones-Dole viscosity B coefficients of CO32-(aq) and SO42-(aq).75 (54) Buchner, R. Pure Appl. Chem. 2008, 80, 1239. (55) The DR data of refs 38 and 26 were reanalyzed, assuming eq 7 and ε∞ ) 3.4863 throughout, yielding the effective solvation numbers Zib(NaCl(aq), c) and Zib(Na2CO3(aq), c) at 25 °C. Since Zib(Cl-) ) 0,19,26 Zib(NaCl) ) Zib(Na+). The solvation numbers for the carbonate anion were obained assuming the total number density of ions as the main criterion for the concentration dependence: Zib(CO32-, c) ) Zib(Na2CO3, c)-2Zib(NaCl, c ) (3/2)cNa2CO3). (56) Bicarbonate (HCO3-) can be precluded as the relaxing species for mode 1 or 2 on basis of the HCO3- formation constant76 and the observed amplitudes S1 or S2 which would require that µ(HCO3-) > 50 D. (57) Barthel, J.; Hetzenauer, H.; Buchner, R. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 1424. (58) Wachter, W.; Fernandez, S.; Buchner, R.; Hefter, G. J. Phys. Chem. B 2007, 111, 9010. (59) Runde, W.; Neu, M. P.; Van Pelt, C.; Scott, B. L. Inorg. Chem. 2000, 39, 1050. (60) Bondi, A. J. Phys. Chem. 1964, 68, 441. (61) Calculations using a more realistic oblate ellipsoid for CO32- had only a small effect on the τ′ values. (62) Marcus, Y. Ion Properties; Marcel Dekker: New York, 1997. (63) Schro¨dle, S.; Wachter, W.; Buchner, R.; Hefter, G. Inorg. Chem. 2008, 47, 8619.

J. Phys. Chem. B, Vol. 114, No. 43, 2010 13627 (64) Using different pivots (e.g., the geometric center or the center of mass of the ion pairs) changes these values by about 5%, which is less than the scatter of the data. (65) Barthel, J.; Hetzenauer, H.; Buchner, R. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 988. (66) Barthel, J. M. G.; Krienke, H.; Kunz, W. Physical Chemistry of Electrolyte Solutions-Modern Aspects; Steinkopff, Springer: Darmstadt, Germany, 1998. (67) Besˇter-Rogacˇ, M.; Neueder, R.; Barthel, J. J. Solution Chem. 2000, 29, 51. (68) Sherman, D. M.; Collings, M. D. Geochem. Trans. 2002, 3, 102. (69) Hefter, G. Pure Appl. Chem. 2006, 78, 1571. (70) Asami, K. Prog. Polym. Sci. 2002, 27, 1617. (71) Turton, D. A.; Hunger, J.; Stoppa, A.; Hefter, G.; Thoman, A.; Walther, M.; Buchner, R.; Wynne, K. J. Am. Chem. Soc. 2009, 131, 11140. (72) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw Hill: New York, 1977. (73) Bordi, F.; Cametti, C.; Colby, R. H. J. Phys.: Condens. Matter 2004, 16, R1423. (74) Miyajima, K.; Inari, K.; Nakagaki, M. Bull. Chem. Soc. Jpn. 1974, 11, 2031. (75) Marcus, Y. Ion SolVation; Wiley: Chichester, UK, 1985. (76) Capewell, S. G.; Hefter, G.; May, P. M. J. Solution Chem. 1998, 27, 865. (77) Kawahara, K.; Tanford, C. J. Biol. Chem. 1966, 241, 3228. (78) Zhang, H. L.; Han, S. J. J. Chem. Eng. Data 1996, 41, 516. (79) Gonc¸alves, F. A.; Kestin, J. Int. J. Thermophys. 1982, 2, 315. (80) Hershey, J. P.; Sotolongo, S.; Millero, F. J. J. Solution Chem. 1983, 12, 233. (81) Pesce, G. Z. Phys. Chem. Abt. A 1932, 160, 295. (82) Casteel, J. F.; Amis, E. S. J. Chem. Eng. Data 1972, 17, 55.

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