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Ionic Conductivity and Glass Transition of Phosphoric Acids Yangyang Wang,*,† Nathan A. Lane,§ Che-Nan Sun,‡ Fei Fan,∥ Thomas A. Zawodzinski,§,‡ and Alexei P. Sokolov†,∥ †

Chemical Sciences Division and ‡Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Department of Chemical and Biomolecular Engineering and ∥Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States ABSTRACT: Here we report the low-temperature dielectric and viscoelastic properties of phosphoric acids in the range of H2O:P2O5 1.5−5. Both dielectric and viscosity measurements allow us to determine the glass-transition temperatures of phosphoric acids. The obtained glass-transition temperatures are in good agreement with previous differential scanning calorimetric measurements. Moreover, our analysis reveals moderate decoupling of ionic conductivity from structural relaxation in the vicinity of the glass transition.

1. INTRODUCTION Phosphoric acids (H3PO4·xH2O) are one of the most important acids in modern industry.1 A tremendous amount of phosphoric acid is produced globally each year, with the majority being used for agricultural fertilizers and the rest for detergents, feed supplements, metal treatment, and insecticide production.2 In recent years, phosphoric-acid-doped polymers are widely studied for their promising applications in fuel cells.3−5 Moreover, phosphorus-based molecules play an important role in biological systems.5−7 Phosphates are essential constituents of adenosine diphosphate (ADP), adenosine triphosphate (ATP), phospholipid membranes, and nucleotides. A clear understanding of the dynamics of phosphoric acids is therefore of great scientific as well as practical importance. Surprisingly, some basic physicochemical properties of phosphoric acids have not been characterized, despite a long history of scientific research on phosphate-based materials. For example, almost all of the experimental studies of electrical conductivity of phosphoric acids known to date are limited to the high-temperature regime.8−12 Similarly, to the best of our knowledge, low-temperature viscosity data of phosphoric acids do not exist, either. Although phosphoric acids can be easily supercooled, their structural dynamics in the vicinity of glasstransition has not been systematically studied. Moreover, the glass-transition temperature (Tg) of phosphoric acids is still a subject of controversy. Kobeko et al. first reported Tg = 152 K for neat phosphoric acid (H3PO4), using electrical conductivity measurement. The later nuclear magnetic resonance (NMR) study by Ellis revealed much higher Tg.13 Ellis’ result of concentrated phosphoric acids seemed to be in agreement with © 2013 American Chemical Society

the dilatometric measurement of HPO3 (R = 1.0) by Eisenberg et al.14 The Tg from more recent differential scanning calorimetric (DSC) measurements8,15 lied in between the conductivity and NMR Tg values. The present work is partially motivated by the need to characterize the basic dielectric and viscoelastic properties of phosphoric acids in the low-temperature regime and to resolve the uncertainties concerning their glass transition. From a fundamental point of view, phosphoric acids are model systems for understanding the molecular mechanism of proton transport. The studies of other common acids such as hydrochloric acid and sulfuric acid are typically limited to high temperature because of the practical difficulty of supercooling these liquids. In comparison, phosphoric acids can be easily vitrified and studied over a wide temperature range.15 Furthermore, the molecular insights from the investigation of phosphoric acids can shed light on our understanding of many other proton conductors, including superprotonic crystals, aciddoped polymers, and protic ionic liquids. Two principal mechanisms have been recognized for proton transport in liquids.3,4,16,17 One is the so-called vehicle mechanism, where proton transport is assisted by the translational diffusion of bigger carrier species. The other is frequently referred to as the Grotthuss mechanism.16 In this case, proton migration is achieved through local proton hopping within hydrogen bonds connecting one “vehicle” to another. It is generally conceived that the Grotthuss mechanism Received: April 18, 2013 Revised: June 13, 2013 Published: June 13, 2013 8003

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water vapor in a closed chamber. The degree of hydration was controlled by varying the hydration time. When the absorbed water was close to the theoretical value, the sample was taken out of the hydration chamber, and the remaining water was added with an adjustable micropipet. To facilitate the mixing of H2O and P2O5, we heated the mixture to 140 °C and vigorously stirred it with a Teflon-coated magnetic bar. The second method was based on mixing of phosphoric acid solution (85%) and polyphosphoric acid (116%). Once the mixtures were made, they were treated with the same heating and stirring procedures. We carried out dielectric measurement on samples obtained from both methods and confirmed that the two methods yielded identical samples. 2.2. Methods. Dielectric measurements of phosphoric acids were performed on a Novocontrol alpha analyzer (0.01 Hz to 10 MHz) with a gold-plated cell. To reduce the effect of electrode polarization, we used a relatively thick spacer of 0.9 mm. Viscosity measurements of the same samples were carried out on a TA Instruments AR2000ex rheometer with glasscovered parallel plates. The temperature was controlled by an environmental test chamber with liquid-nitrogen option. Both the dielectric spectra and viscosities were taken at every 5K interval, starting from the lowest temperature. In the dielectric measurements, the samples were equilibrated for 20 min after each temperature change. The equilibration time was 5 min in the case of rheological measurements. The effective rates of temperature change in both measurements were much lower than those of the previous DSC experiments (10 K/min).15 The 1H line-width measurements were performed on a Bruker Avance 400 MHz spectrometer with a Broad Band Inverse probe at temperature ranging from −80 to 40 °C. The sample was equilibrated at each temperature for 20 min prior to the steady-state pulse sequence. The width at half-maximum (fwhm) of the central line was chosen to represent the line width in this work.

is responsible for the abnormally high proton mobility in water. A recent study by ab initio molecular dynamics simulation suggests that the high proton conductivity of orthophosphoric acid (H3PO4) also comes from a Grotthuss-type transport mechanism.5 Despite the development of this theoretical framework, the connection between proton migration and structural relaxation has not been well understood. In the vehicle mechanism, the proton transport should be strongly coupled to the structural dynamics of the carrier species by definition. The understanding in the case of Grotthuss mechanism is still limited. To examine the degree of coupling and decoupling of different molecular motions, it is always desirable to perform experiments over a wide temperature window. In this regard, phosphoric acids offer a unique opportunity to closely examine the relation between proton transport and structural dynamics in a prototype system where the Grotthuss mechanism plays an important role. In the present work, the ionic conductivity and glass transition of phosphoric acids are systematically studied using dielectric spectroscopy and rheology. We clarify some uncertainties concerning the glass-transition temperature of phosphoric acids and confirm the results of previous DSC measurements. The relation of electrical conductivity of phosphoric acids to their structural relaxation has been analyzed using the Walden plot. It is shown that the ionic conductivity and viscoelastic relaxation are decoupled in the vicinity of the glass transition. However, the degree of decoupling is only moderate compared with the decoupling phenomena observed in other ionic conductors.

2. MATERIALS AND METHODS 2.1. Materials. Before describing the details of sample preparation, we would like to indicate that different notations have been used in literature to label the concentration of phosphoric acids. One way is to present the chemical composition in terms of H2O and phosphorus pentoxide (P2O5). Another way is to use H2O and H3PO4. For example, orthophosphoric acid can be regarded as binary mixture of H2O and P2O5 at molar ratio 3:1. It is also considered as a 100% H3PO4 aqueous “solution”. In this work, we follow the notation of ref 13 and label our phosphoric acids in terms of the molar ratio (R) of H2O to P2O5. The interconversion between different notations is provided in Table 1.

3. RESULTS 3.1. Dielectric Spectra. Representative dielectric spectra of phosphoric acids are shown in Figure 1, where the real part of complex conductivity (σ′), the imaginary part of complex electrical conductivity (M″), and the real part of complex permittivity (ε′) are shown as a function of frequency ( f). Generally speaking, the dielectric behavior of phosphoric acids is similar to molten inorganic salts and ionic liquids. The conductivity relaxation (Figure 1a) is accompanied by a visible change of the real part of dielectric permittivity (Figure 1c). This behavior is in qualitative agreement with the prediction of Dyre’s model: σ*(ω) = σ0[iωτe/ln(1 + iωτe)], where σ0 is the conductivity in the dc limit and τe is the characteristic attempt time associated with ion hopping.18,19 The increase in ε′ at low frequencies is due to the electrode polarization phenomenon,20 which arises from the accumulation of charges on the surfaces of electrodes. It has been shown that Dyre’s model works reasonably well for ionic liquids.21 Because phosphoric acids can be regarded as an extreme case of protic ionic liquids, where the carriers for positive charges are protons themselves, such a qualitative agreement is not surprising. However, a closer examination reveals that Dyre’s model alone cannot fully describe the dielectric spectra. At least one more relaxation process has to be added to obtain a quantitative fitting.22 In addition, analysis of the derivative spectra reveals that there appears to be a “hidden” Debye-like relaxation at low frequency. This process

Table 1. Interconversion of Different Notations of Phosphoric Acids H2O:P2O5

H3PO4·xH2O

wt % of P2O5

wt % of H3PO4

1.5 2 2.5 3 4 5

H3PO4·(−0.75)H2O H3PO4·(−0.5)H2O H3PO4·(−0.25)H2O H3PO4 H3PO4·0.5H2O H3PO4·H2O

84.0 79.8 75.9 72.4 66.3 61.2

116 110 105 100 91.6 84.5

Phosphorus pentoxide, phosphoric acid solution (85%), phosphoric acid (crystal), and polyphosphoric acid (116%) were obtained from Sigma-Aldrich and used as received. Phosphoric acids of various concentrations were prepared using two different procedures. The first method was based on hydration of phosphorus pentoxide. To avoid uncontrollable heat release, the phosphorus pentoxide was slowly hydrated by 8004

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Figure 2. Temperature dependence of dc conductivity. Here R is the molar ratio of H2O to P2O5 in each sample. The data above the glasstransition temperature are fitted by the Vogel−Fulcher−Tammann (VFT) equation (solid lines): σ = σ0 exp[−B/(T − T0)], with σ0, B, and T0 being free-fitting parameters.

Figure 1. Dielectric spectra of the R = 1.5 sample (116% H3PO4): (a) real part of complex conductivity σ*, (b) imaginary part of complex electrical modulus M*, and (c) real part of complex permittivity ε*. Here the lowest temperature is −85 °C (red circles), and the highest temperature is −15 °C (violet hexagons). The temperature difference between two neighboring curves is 10 °C. The main relaxation process in ε′ is related to conductivity relaxation.

gives us an extra frequency window to track the conduction behavior near or below Tg. The super-Arrhenius-to-Arrhenius transition is more clearly depicted in Figure 3a. 3.3. Rheological Behavior. The results of viscosity measurement are shown in Figure 4. Unfortunately, we were unable to determine the viscosity of neat phosphoric acid (R = 3) at low temperature because of crystallization. The viscosity of phosphoric acids exhibits VFT-like temperature dependence (Figure 4a). At a given temperature, the viscosity increases dramatically with decrease in the ratio of H2O to P2O5. The viscosity of small-molecule glass formers at Tg is usually on the order of 1012 Pa·s.27 The glass-transition temperature therefore can be estimated by extrapolating viscosity to 1012 Pa·s using the VFT fitting function. Because the viscosity near Tg is very sensitive to the change of temperature, the choice of viscosity at Tg will not strongly influence the result. For example, the Tg values of these phosphoric acids would be roughly 2K higher if the viscosity at Tg was taken as 1011 Pa·s. Nevertheless, one should keep the uncertainties of this method in mind, when comparing the Tg from viscosity with the Tg values from other experimental techniques. The normalized Arrhenius plot for phosphoric acids (Figure 4b) has been constructed using the obtained Tg values. From the slope of the viscosity curve at Tg, we can extract the fragility index (m) of these phosphoric acids:

interferes with the electrode polarization and therefore it is not trivial to resolve this slow relaxation unambiguously. This part is out of the scope of the current report and will not be further discussed. Here the most relevant quantities are dc conductivity (σ) and conductivity relaxation time (τσ), which can be extracted directly from the dielectric spectra without fitting. The dc conductivity is taken from the value of σ′ in the plateau region, where σ′ is independent of frequency (Figure 1a). Conductivity relaxation time is evaluated from the frequency at M″ maximum as τσ = 1/(2πf max). 3.2. Conductivity Behavior. The temperature dependence of dc conductivity in phosphoric acids exhibits distinctive behavior above and below the glass-transition temperature, Tg (Figure 2). The temperature dependence of conductivity is super-Arrhenius above Tg, and σ can be described by the Vogel−Fulcher−Tammann (VFT) equation: σ = σ0 exp[−B/ (T − T0)].23−25 Below Tg, the dc conduction appears to be an activated process and follows the Arrhenius equation: σ = σ0 exp(−Ea/kT). Similar super-Arrhenius-to-Arrhenius transition has been observed in many other ionic conductors, including protic ionic liquids.26 The underpinning physics is straightforward: the ionic transport above Tg is assisted by the structural relaxation, which typically has VFT-like temperature dependence; when the structural dynamics is arrested below Tg, the ion migration can only proceed through activated local hopping. In the studied temperature and composition range, the dc conductivity at a given temperature increases with increasing water content. This effect comes mostly from the decrease in Tg (see later). The temperature dependence of conductivity relaxation time (τσ) is presented in Figure 3a. Figures 2 and 3a, in principle, should provide similar information about ionic transport. However, the conductivity relaxation frequency (1/τσ) is typically higher than the frequency, where dc conductivity is fully developed. As a result, using conductivity relaxation time

m=

d log η d(Tg /T )

T = Tg

(1)

The fragility of phosphoric acids increases with decrease of water content but shows a slight drop at R = 1.5 (Figure 4c). Compared with other small-molecule glass-formers,28 these phosphoric acids have relatively high fragility indices (95−150). In particular, the m of the R = 2.0 is as high as 150. Such a high fragility has rarely been observed in small molecules. This is especially surprising for a hydrogen-bonding system. It is worth noting that the viscoelastic relaxation of neat P2O5 was recently studied by photon correlation spectroscopy.29 It was found that P2O5 has an extremely low fragility of 20, similar to strong glass former SiO2. This implies that the fragility of phosphoric acids should eventually decrease with decrease in water content. 8005

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Figure 3. (a) Temperature dependence of conductivity relaxation time τσ. The data above the glass-transition temperature (Tg) are fitted by the VFT equation: τσ = τσ0 exp[B/(T − T0)], and the data below the Tg are fitted by the Arrhenius equation: τσ = τ0 exp(Ea/kT). The composition dependencies of τ0 (limiting conductivity relaxation time) and Ea (activation energy) in the Arrhenius fit are shown in panels b and c, respectively.

Figure 4. (a) Arrhenius plot of viscosity. (b) Tg-scaled Arrhenius plot of viscosity. (c) Composition dependence of fragility (m).

4.2. Limiting Viscosities of Phosphoric Acids. The viscosity data have been fitted with both VFT and Mauro (η = η0 exp[(K/T) exp(C/T)]) equations.31 The limiting viscosity at infinitely high temperature, η0, from the Mauro equation is higher than the VFT equation. This is a fact that has been wellrecognized in literature.31 Here, rather than discussing which equation gives more reasonable η0, we simply point out an interesting fact: within each fitting method, the limiting viscosities of phosphoric acids are significantly higher than those of other typical glass-forming liquids of comparable molecular weight. For example, Mauro equation gives the η0 of 0.26 Pa·s for the R = 1.5 phosphoric acid. In comparison, the η0 of typical glass-former propylene carbonate and m-toluidine is only 8.7 × 10−4 and 9.6 × 10−4 Pa·s, respectively. Several factors presumably contribute to the observed high viscosity. Phosphoric acids dehydrate and form polyacids at high concentrations. For example, the average degree of “polymerization” is 4 in the R = 1.5 sample. Moreover, their strong intermolecular hydrogen bonds and high ionicity must also play an important role. 4.3. Glass-Transition Temperature. The glass-transition temperature of phosphoric acids can be determined from both rheological and dielectric measurements. As previously indicated, the dc conductivity changes its temperature dependence around Tg. Therefore, we can estimate the glass-transition

4. DISCUSSION 4.1. Activation Energy of Conductivity Relaxation Below Tg. To further analyze the ionic transport behavior below Tg, the τσ data are fitted by the Arrhenius equation. The activation energy Ea and the prefactor τ0 (limiting conductivity relaxation time) of the Arrhenius fits are presented in Figure 3b,c as a function of composition. At high H2O to P2O5 ratio, R = 4 and 5, and τ0 is on the order of 10−18 s. This time is rather short, suggesting that there might be a considerable entropic contribution to the activation free energy. This is because τ0 and Ea are interrelated. The Arrhenius fit assumes that Ea is independent of temperature, but when the entropic contribution is properly considered, the true activation energy Ea at high temperatures should become significantly lower and thus the true τ0 should be higher. However, the limited data range for the two samples does not allow us to draw a definitive conclusion at this moment. The Ea of these phosphoric acids is in the range of 50−60 kJ/mol, which is relatively low compared with the Ea observed in other common proton conductors. For example, the activation energy for proton migration in perovskite metal oxides typically ranges from 52 to 100 kJ/ mol.30 The Ea of recently reported protic ionic liquid procainamide hydrochloride is 96 kJ/mol.26 Therefore, these phosphoric acids seem to have chemical structures that are favorable for proton transport. 8006

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solid state. In many applications, it is indeed desirable to decouple the proton conductivity from the structural dynamics of the material. Typical superprotonic solid acids are based on sulfuric and phosphoric acids.35 In addition, phosphoric acids are widely used in proton-conducting polymer electrolytes and protic ionic liquids. Therefore, an analysis of the relation of ionic transport and structural relaxation in phosphoric acids would be very helpful for rational design of superprotonic conductors. Whereas the discussion of the vehicle and Grotthuss mechanisms has been a dominating theme in the study of proton conductors, decoupling analysis has been given much less attention. Walden plot analysis, which is inspired by the classical Walden’s rule, is a useful method to examine the relation of ionic transport to structural dynamics.36 In this analysis, the molecular ionic conductivity of a material is plotted as a function of its fluidity (reciprocal viscosity, 1/η). The Walden’s rule states that the molar conductivity of a given ion is proportional the fluidity of the viscous medium, that is, Λη = Constant. The underlying assumption is that the ionic transport is completely coupled to the structural dynamics. The black line with slope of 1.0 in Figure 6 represents the ideal Walden’s rule.

temperature of phosphoric acids from the conductivity measurement. Tg can be calculated from the viscosity measurement by extrapolating the viscosity to 1012 Pa·s using the VFT equation. The obtained glass-transition temperatures are presented in Figure 5, together with previously reported Tg values from DSC

Figure 5. Glass-transition temperatures determined from conductivity (red circles) and viscosity (black stars) measurements as a function of the composition of the phosphoric acids. R is the molar ratio of H2O to P2O5. The blue diamonds are the glass-transition temperatures from differential scanning calorimetry (ref 15), and the orange squares are from NMR measurements (ref 13). Inset: temperature dependence of the line width at half-maximum (lwhm) of the spin−spin relaxation (T2) in the R = 1.5 sample, measured in this study.

and NMR measurements.8,13,15 The conductivity and viscosity glass-transition temperatures not only are consistent with each other but also agree with the DSC measurements. The glasstransition temperatures from NMR are significantly higher than all of these three measurements. To further confirm such a difference, we performed proton NMR measurement on the R = 1.5 sample using the method suggested by Ellis.13 The temperature dependence of the line width at half-maximum (lwhm) of the proton spin−spin (T2) relaxation is shown in the inset of Figure 5. Ellis proposed that the inflection point of the lwhm versus T curve could be used to estimate the Tg.13 However, the inset of Figure 5 indicates that there is a real difference between the Tg values from line-width analysis and other methods (viscosity, conductivity, DSC), which is clearly beyond experimental error. Because our NMR, dielectric, and rheological measurements were performed on the same sample, this discrepancy of Tg cannot be due to the difference in sample preparation but reflects a real intrinsic difference between different methods. Different physical processes, such as intramolecular vibrations and phonons, may contribute or even dominate the NMR relaxation in viscous and glassy regimes.32 It is difficult, if not impossible, to identify the dominating relaxation mechanism that gives rise to the change of line width in the NMR measurement. However, it is clear that in the case of phosphoric acids the NMR line-width analysis does not seem to be a suitable method for Tg determination. 4.4. Decoupling. According to the classical theory, the diffusivity of ions should be dictated by the fluidity of their surrounding medium.33 However, violations of this rule have been in the so-called superionic conductors, where the ionic transport is strongly decoupled from structural relaxation.34 As a result, these materials exhibit high ionic conductivity even in

Figure 6. Walden plot: molar conductivity (Λ) as a function of fluidity (1/η). The (black open) star denotes the molar conductivity of hydrochloric acid in dilute aqueous solutions.33 The black line with slope of 1.0 represents the “ideal” Walden line, where ionic conductivity is completely coupled to the structural relaxation. The regions above and below the ideal line are traditionally defined as superionic and subionic regimes, respectively.

In reality, decoupling causes deviation from the linear relation, and the Walden’s rule typically can be replaced by a fractional rule: Ληα = Constant. The exponent α characterizes the degree of decoupling. The ionic conductivity is completely decoupled from viscosity in the case of α = 0. The classical Walden’s rule is recovered when α = 1. Furthermore, the Walden plot analysis has been used to classify ionic conductors. Materials located above the ideal Walden line are considered as “superionic conductors”, whereas those that fall below the line are referred to as “subionic conductors”.36,37 In the high-temperature (low-viscosity) region, the data of phosphoric acids (R = 1.5, 2.5) fall onto the “ideal” line of dilute hydrochloric acid solution. It has been suggested that the neat phosphoric acid has the highest intrinsic conductivity among any known substance.5 However, the Walden plot analysis indicates that phosphoric acids are similar to normal acidic aqueous solutions at high temperatures. No “anom8007

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low temperatures. The ionic conductivity undergoes a superArrhenius-to-Arrhenius transition at the glass-transition temperature. The viscosity measurement reveals that these phosphoric acids are fragile glass-formers with fragility in the range of 95−150. The Tg values determined from both conductivity and viscosity measurements are consistent with the result of previous DSC measurements. We have also confirmed that NMR line width analysis indeed overestimates the glass-transition temperature and therefore is not a suitable method for Tg determination. Finally, our Walden plot analysis indicates that phosphoric acids behave like other aqueous acidic solutions at high temperatures but exhibit moderate decoupling between ionic conductivity and structural dynamics in the vicinity of the glass transition.

alously fast” proton transport is observed. In addition, all of the phosphoric acids data (R = 1.5−5) merge onto the same curve in this region. The coincidence of the high-temperature molar conductivity in the Walden plot for phosphoric acids with different R and for hydrochloric acid implies that the protonconduction mechanism is not very sensitive to the specific chemical structure of these liquids. In other words, it seems unlikely that the neat liquid phosphoric acid has a special mechanism for proton transport.5 In the low-temperature (high-viscosity) region, phosphoric acids deviate from the ideal Walden line into the superionic region, exhibiting moderate decoupling between conductivity and fluidity. The degree of decoupling can be quantified by fitting the data in this region with the fractional Walden’s rule: Ληα = Constant. The slope, α, is in the range of 0.69 to 0.87. It has been shown that the degree of decoupling in many glass-forming liquids correlates with their fragility.38−40 To explore this idea, we examine the relation of fragility and decoupling index (β), defined as β = 1 − α, in Figure 7. The

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. F.F. thanks the NSF Polymer Program (DMR-1104824) for funding. A.P.S. acknowledges the financial support from the DOE BES Materials Science and Engineering Division.

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REFERENCES

(1) Goldwhite, H. Introduction to Phosphorus Chemistry; Cambridge University Press: Cambridge, U.K., 1981. (2) Gard, D. R. Phosphoric Acids and Phosphates. In Kirk-Othmer Encyclopedia of Chemical Technology; John Wiley & Sons, Inc.: Hoboken, NJ, 2000. (3) Kreuer, K.-D. Proton Conductivity: Materials and Applications. Chem. Mater. 1996, 8, 610−641. (4) Kreuer, K.-D.; Paddison, S. J.; Spohr, E.; Schuster, M. Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology. Chem. Rev. 2004, 104, 4637−4678. (5) Vilčiauskas, L.; Tuckerman, M. E.; Bester, G.; Paddison, S. J.; Kreuer, K.-D. The Mechanism of Proton Conduction in Phosphoric Acid. Nat. Chem. 2012, 4, 461−466. (6) Heberle, J.; Riesle, J.; Thiedemann, G.; Oesterhelt, D.; Dencher, N. A. Proton Migration along the Membrane Surface and Retarded Surface to Bulk Transfer. Nature 1994, 370, 379−382. (7) Westheimer, F. Why Nature Chose Phosphates. Science 1987, 235, 1173−1178. (8) Aihara, Y.; Sonai, A.; Hattori, M.; Hayamizu, K. Ion Conduction Mechanism and Thermal Properties of Hydrated and Anhydrous Phophoric Acids Studied with 1H, 2H, and 31P NMR. J. Phys. Chem. B 2006, 110, 24999−25006. (9) Chin, D.-T.; Chang, H. H. On the Conductivity of Phosphoric Acid Electrolyte. J. Appl. Electrochem. 1989, 19, 95−99. (10) Greenwood, N. N.; Thompson, A. The Mechanism of Electrical Conduction in Fused Phosphoric and Trideuterophosphoric Acids. J. Chem. Soc. 1959, 0, 3485−3492. (11) MacDonald, D. I.; Boyack, J. R. Density, Electrical Conductivity, and Vapor Pressure of Concentrated Phosphoric Acid. J. Chem. Eng. Data 1969, 14, 380−384. (12) Wydeven, T. Electrical Conductivity of Concentrated Phosphoric Acid from 25° to 60° C. J. Chem. Eng. Data 1966, 11, 174−176.

Figure 7. Correlation between decoupling exponent and fragility (m). The numbers on the plots indicate the R of each corresponding sample. Inset: Comparison of the decoupling in polymer electrolytes and phosphoric acids. Solid lines are the guide for the eyes.

decoupling index of these phosphoric acids correlates reasonably well with their fragility: similar to other glassforming liquids, the degree of decoupling increases with increase in fragility. But contrary to the expectation that the Grotthuss-type hopping mechanism would strongly decouple proton conductivity from structural relaxation, the degree of decoupling in phosphoric acids is only moderate. Much more pronounced decoupling has been observed in our recent investigation of polymer electrolytes (Figure 7 inset).40 However, it is important to bear in mind that the protons in phosphoric acids are the participants of structural relaxation, whereas the ions in polymer electrolytes can be considered as guest species. The correlation of decoupling of proton conductivity with fragility can be rationalized using current understanding of fragility:38−42 It has been suggested that the stronger the frustration in packing the higher the fragility will be. In that case proton motion should exhibit stronger decoupling from structural relaxation in structure with higher frustration in packing, that is, in more fragile liquids.

5. CONCLUSIONS In the present work, we report for the first time detailed viscosity and dielectric measurements of phosphoric acids at 8008

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The Journal of Physical Chemistry B

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dx.doi.org/10.1021/jp403867a | J. Phys. Chem. B 2013, 117, 8003−8009