Tuning proton conductivity and energy barriers for proton transfer

Proton transport plays a critical role in many technologies and biochemical processes. Protic ionic liquids (PILs) have come under scrutiny as potential electrolytes in electrochemical devices^1–3 due to their high thermal stability, high open circuit voltage and efficiency, and low vapor pressure. Increasing proton conductivity, especially in a non-aqueous environment, presents a significant scientific challenge. Recent studies of lidocaine di-(di-hydrogen phosphate)^4,5 revealed strong decoupling of proton conductivity from structural relaxation. When compared at similar viscosities, the proton conductivity of this mixture exceeds that of phosphoric acid (PA), which has the highest intrinsic conductivity of all known substances. There is some evidence that this is due to the transport of protons occurring with a mechanism that is similar to the original idea of Grotthuss, where hydrogen was hypothesized to hop as a positively charged entity to one of the electrodes following the decomposition of water.^4,6–8 However, the molecular level information of the strong enhancement of proton conductivity at a given viscosity in lidocaine-PA mixtures remains elusive.

There are two main types of proton transport mechanisms: (1) vehicular, in which a proton is carried by a vehicular entity (e.g., a molecule), and (2) proton transfer events between molecules via the hydrogen bond network (often referred to as structural diffusion).^9–14 The second mechanism is usually more efficient because it does not require motion of the entire molecule. Proton transfer is known to dominate the conductivity in pure PA, especially at low temperatures.^15–18 In some PILs, the Brønsted–Lowry acid/base pairs create a network of hydrogen bonds, thereby facilitating proton transfer events. However, in many cases, the proton is transferred from an acid to a base, and the vehicular mechanism dominates. This is not the case for lidocaine-PA mixtures where the proton conductivity remains rather high even in a glassy state as molecular (vehicular) diffusion is frozen.⁴ This raises the question as to whether the right choice of an acid–base mixture may lead to a decrease in the energy barrier for proton transfer, resulting in exceptionally high proton conductivity. Recent electronic structure calculations of PA paired with different bases (including lidocaine) revealed little difference in the energy barrier for proton transfer from the acid to the base.¹⁹ However, these calculations did indicate that transfer barriers between distinct PA molecules in proximity to the base may become almost barrier-less.¹⁹ 

The goal of the current study is to experimentally verify the predictions from simulations. The proton conductivity of mixtures of PA with creatinine (CRT) and procaine was measured. We also reviewed the literature data for lidocaine-PA and trimethylamine (TMA)-PA mixtures (Fig. 1). Our results reveal an enhancement of the decoupling of proton transport from structural dynamics in all mixtures in comparison to pure PA. However, in agreement with the simulations, the energy barrier for the proton transfer increases with the addition of bases to PA. It appears that the addition of bases strongly increases the viscosity and glass transition temperature, T_g, of the mixtures relative to pure PA. As a result, the same viscosity is reached in mixtures at much higher temperatures. This, in turn, leads to higher proton conductivity at the same viscosity despite the higher energy barrier.

Mixtures of creatinine and phosphoric acid were prepared using creatinine (CRT, Sigma-Aldrich, 99%, used as purchased), 85% phosphoric acid (85 PA, Alfa Aesar, 85% solution), and crystalline phosphoric acid (100 PA, 99.99%, used as purchased). The mixtures were prepared in two different concentrations, 2:1 and 3:1 PA:CRT. Attempts to make samples with 1:1 ratio failed due to poor mixing and a high melting temperature of the mixture. The mixtures with 85% phosphoric acid were prepared in two different ways: (1) by dissolving the CRT in water and adding a slight excess of 85 PA and (2) by adding 85 PA directly to the CRT powder and stirring for 3 h–4 h. To remove water, each mixture was washed with acetone and held in a vacuum oven for no less than 24 h at 70 °C. The mixtures with 100 PA were prepared in a glove box by melting the crystalline PA (T_m = 42 °C) and adding it dropwise to the creatinine while stirring under heat (PA crystallizes quickly). The mixtures with pure PA were stirred for 24 h and held in a vacuum oven for 24 h at 70 °C before broadband dielectric spectroscopy (BDS) or differential scanning calorimetry (DSC) measurements were conducted. A mixture of 2:1 phosphoric acid and procaine (Pro, Sigma-Aldrich, used as purchased) was prepared similar to the CRT mixtures using 85 PA. Samples of pure phosphoric acid were prepared by melting crystalline PA, and the melt was directly transferred to the dielectric cell in a glove box to minimize exposure to moisture.

The glass transition temperatures of the mixtures were determined using a DSC spectrometer Q2500 (TA Instruments). Samples were put in hermetic pans in a glove box and measured with a scanning rate of 10 °C/min upon cooling. Tg was estimated as the middle point of the step in the heat flow.

BDS spectra were measured using a Novocontrol Alpha-A impedance analyzer and a Quatro Cryosystem temperature controller in the frequency range of 10⁻¹ Hz–10⁶ Hz with nine points per decade and an applied voltage of 0.1 V. The temperature was varied from 160 K to 360 K; prior to spectrum accumulation, samples were held at each temperature for 7 min, and the temperature was stabilized within 0.2 K. The samples were measured in an Invar steel/sapphire cell²⁰ with stainless steel electrodes with a diameter of 10.5 mm and a separation between the electrodes of 202 µm.

The dielectric loss modulus and conductivity spectra of the 3:1 PA:creatinine mixture are shown in Fig. 2. The dc (steady state) conductivity, σ₀, can be directly obtained from the plateau values of σ’(ν) [Fig. 2(a)]. In addition to conductivity, we also estimated the conductivity relaxation times, τ_σ, from the frequency of the dielectric modulus M” maximum [Fig. 2(b)]: τ_σ = 1/(2πf_max). The conductivity relaxation time provides estimates of characteristic ion re-arrangement rates and corresponds to the time at which AC conductivity crosses over to DC conductivity (Fig. 2).^21,22

The σ₀ and τ_σ results for the 3:1 and 2:1 PA:CRT mixtures did not show any significant dependence on preparation, suggesting that even if we have some traces of water in the samples, it does not affect strongly our results. Both conductivity [Fig. 3(a)] and conductivity relaxation time [Fig. 3(b)] show a Vogel–Fulcher–Tammann (VFT)-like temperature behavior above T_g, which crosses over to an Arrhenius dependence at T < T_g. This is the usual behavior for many ionic liquids,^23,24 and we used the crossover from the VFT behavior to Arrhenius behavior to estimate Tg for the mixtures.²⁵ The estimated T_g is very close to the T_g obtained from DSC (Table I). The slightly higher T_g obtained from DSC is caused by the significantly higher cooling rate used in calorimetric measurements in comparison to the BDS measurements. A similar difference between BDS and DSC measured T_g’s was reported by Colby and co-workers.²⁶ Using this Arrhenius dependence, we also estimated a characteristic energy barrier for conductivity at T < T_g (Fig. 3 and Table I).

The PA:CRT mixtures were found to have conductivities of σ(T_g) ∼ 3.5 × 10⁻⁹ S/cm and 1.7 × 10⁻⁸ S/cm at T_g for 2:1 and 3:1 mixtures, respectively, while the PA:Pro mixture has σ(T_g) ∼5.5 × 10⁻¹⁰ S/cm (Fig. 3). The latter is comparable to the previously measured lidocaine PA mixture.⁴ The PA mixtures with creatinine and with procaine clearly exhibit higher conductivity at T_g than 85% PA or pure PA (Fig. 3 and Table I).^4,17

In addition, we analyzed the dielectric constant of mixtures at frequencies below the conductivity relaxation process. For this analysis, we fit the real part of dielectric permittivity spectra by a Havriliak–Negami (HN) function, plus a power law for the electrode polarization contribution and high frequency dielectric constant ε_∞,

Here, A and a are the amplitude and the exponent for the electrode polarization contribution, respectively. The dielectric constant was calculated as ε_S = Δε + ε_∞. Our analysis revealed that the dielectric constant decreases upon cooling; this effect is known for many ionic conductors.^22,27 The values of ε_S at T ∼ T_g are presented in Table I.

The results from the present study clearly demonstrate that at any given temperature, the conductivity of PA mixtures with any of the various bases examined is always lower than the conductivity of pure PA [Fig. 3(a)]. To expand the number of analyzed mixtures, we also include prior results for the PA:lidocaine 2:1 mixture [lidocaine di-(dihydrogen phosphate), LDC]⁴ and PA:trimethylamine mixture (TMAH₂PO₄)²⁸ [Fig. 3(a) and Table I]. Only the conductivity of the 85wt. % aqueous solution of PA has a higher conductivity than pure PA. It is known that adding water enhances PA dynamics and reduces viscosity and T_g,^29,30 and this seems a plausible explanation for the higher proton conductivity in this case. Addition of any of the studied bases increases T_g and the viscosity of PA (Table I), and this leads to the observed reduction in conductivity [Fig. 3(a)]. According to recent quantum chemical calculations,¹⁹ adding any of these bases to PA results in proton transfer from PA to the base, creating a protic ionic liquid. Following the proton transfer, additional electrostatic interactions significantly slow down the liquid dynamics, and this results in the observed increase in viscosity and T_g.

It is known that in ionic systems with ionic conductivity that is coupled to structural relaxation (e.g., in the case of the vehicular mechanism of proton conductivity), the conductivity at T_g should be σ(T_g) ∼ 10⁻¹⁴ S/cm–10⁻¹⁵ S/cm.^28,31 The conductivity at T_g in all the studied mixtures is significantly higher, σ(T_g) ∼ 0.6–17^*10⁻⁹ S/cm [Fig. 3(a) and Table I]. This is clearly an indication that the proton conductivity in these mixtures, at least at temperatures close to and below T_g, is dominated by the proton transfer events. It results in conductivity that is ∼5–6 orders of magnitude higher than expected for a mechanism that is predominantly vehicular. The PA mixtures with creatinine and with procaine exhibit higher conductivity at T_g than 85% PA or pure PA [Fig. 3(a) and Table I].^4,17 Because the viscosity of all these materials at Tg should be comparable, the results [Fig. 3(a)] suggest that the mixtures provide higher proton conductivity at the same viscosity than pure PA or 85% aqueous PA solution.

Analysis of the conductivity below T_g [Fig. 3(a) and Table I] revealed that despite higher σ(T_g), the activation energy of the conductivity below T_g is higher in mixtures than in 85% PA or pure PA. It is ∼68 kJ/mol and 72 kJ/mol for 2:1 and 3:1 PA:CRT mixtures, respectively, and 83 kJ/mol for the PA:Pro mixture. The latter is comparable to the earlier data for a PA mixture with lidocaine (∼79 kJ/mol)⁴ and significantly higher than the activation energy for both 85% PA (∼58 kJ/mol) and pure PA (∼52 kJ/mol).^4,17,18 Review of literature data for TMAH₂PO₄ suggests that it might have an activation energy for proton transport of about 48 kJ/mol at temperatures close but above T_g (Fig. 3),²⁸ which is comparable or even lower than in pure PA. However, the estimates for TMAH₂PO₄ are done at T > T_g, and the expected VFT behavior for this material will probably result in higher activation energy at T < T_g. Thus, despite higher proton conductivity at the same viscosity, the activation energy for proton transfer is actually higher in mixtures of PA with the bases examined in this study.

The same conclusion can be achieved from the analysis of the conductivity relaxation time [Fig. 3(b)]. τ_σ reflects the charge re-arrangement time and might differ significantly from the structural relaxation time.²² This difference emphasizes decoupling of ionic conductivity from structural relaxation and is well known for polymer electrolytes^22,27 and for the case of the proton transfer mechanism of conductivity in protic systems.¹⁸ The observed values of τ_σ(T_g) (Table I) are significantly shorter than the 100 s expected for the structural relaxation time at T_g. This result is a clear indication of proton transfer dominating conductivity in all these mixtures. The shortest τ_σ(T_g) ∼5.8 × 10⁻⁵ s is in the PA:lidocaine mixture, and the relaxation times for the PA: creatinine mixtures are a bit longer, τ_σ(T_g) ∼ 2.3 × 10⁻⁴ s [Fig. 3(b) and Table I]. Similarly, the Pro:CRT mixture has τ_σ(T_g) ∼ 2 × 10⁻⁴ s. All these times are much shorter than those observed for pure PA (∼10⁻² s) or 85% PA (∼10⁻¹ s). These data demonstrate that proton transfer in mixtures at temperatures close to T_g happens much faster (∼5–6 orders) than molecular relaxation, and the decoupling of the proton mobility from structural relaxation is stronger in mixtures than in pure PA. Although τ_σ(T_g) is faster in these mixtures, their activation energies below T_g are higher than in 85% PA.^17,18 The activation energy for the conductivity relaxation time in pure PA is even lower (∼52 kJ/mol).¹⁷ 

The analysis presented here demonstrates that the proton transfer mechanism dominates conductivity in the studied mixtures. To estimate the energy barrier for the proton transfer E_a, we can assume that the characteristic conductivity relaxation time is defined by the proton transfer time and can be approximated with the equation τ_trans(T) ∼ τ_σ(T) = τ₀^*exp[E_τ(T)/RT]. Here, R is the gas constant and 1/τ₀ is the characteristic attempt frequency. We assume the characteristic attempt frequency to be comparable to the O–H vibrational frequency, i.e., τ₀ ∼ 10⁻¹⁵ s, and emphasize that choosing another value for τ₀ does not significantly affect the results. With this approximation, the activation energy for proton transfer can be estimated from the conductivity relaxation time E_τ(T) = RT^*ln[τ_σ(T)/τ₀]. Using this approach, the estimated activation energy (Fig. 4) confirms the results of a previous analysis—adding any of the studied bases to PA increases the activation energy for proton transfer. Moreover, the stronger the slowing down of the dynamics with the addition of a base (higher T_g), the higher the energy barrier. This result apparently indicates that an increase in inter-molecular interactions and/or slowing down of liquid dynamics of these mixtures also increases the energy barrier for the transfer of protons.

Another interesting observation is the correlation of the activation energy and T_g with the dielectric constant of the mixtures (Fig. 5). The strength of the electrostatic interactions varies inversely with the dielectric constant. The correlation between T_g and 1/ε_S is expected in ionic systems due to the contribution of the electrostatic interactions to the cohesive energy density.³² The energy barrier for proton transfer also shows a tendency to increase with increasing 1/ε_S (Fig. 5). However, this is merely a trend rather than a strong correlation because the dielectric constant of 85% PA is higher (due to water) than in pure PA, while the energy barrier is also higher (Table I). These correlations suggest that electrostatic interactions play a significant role in T_g and the activation energy for the proton transfer in the studied mixtures.

The results presented here agree with our recent computational study of these mixtures,¹⁹ which found that the bases retained a proton transferred from a PA molecule. In this case, they can only provide vehicular mechanism of proton conductivity. Moreover, these simulations predicted that the bases do not decrease the energy barrier for proton transfer between PA molecules, in good agreement with our experimental results. The same computational study also predicted that the 3:1 PA:CRT mixture might have a barrier-less proton transfer if PA molecules interact in a very specific way with the creatinine molecule. However, we did not find any reduction of the energy barrier in this mixture (Table I and Fig. 4). Apparently, this specific interaction between PA and CRT molecules was not observed in the experimental studies.

The performed studies of mixtures of PA with various bases revealed an increase in proton conductivity at the same viscosity when compared to the conductivity of pure PA. These results demonstrate stronger decoupling of the proton transfer mechanism from structural relaxation (viscosity) in these mixtures. However, the energy barrier for the proton transfer actually increases with the addition of any of the bases. The bases accept a proton from the phosphoric acid forming a protic ionic liquid. Strong electrostatic interactions between the resulting ions created by the proton transfer lead to a significant slowing down of the liquid dynamics and an increase in viscosity and the glass transition temperature. The increase in the energy barrier follows an increase in T_g for these mixtures, apparently emphasizing the role of molecular motions and interactions in the proton transfer mechanism. Correlations with the dielectric constant indeed emphasize the importance of the electrostatic interaction in these mixtures for their T_g and energy barrier for the proton transfer. However, the increase in activation energy is weaker than an increase in the T_g of these liquids. As a result, the ratio of E_a/T_g decreases and leads to a stronger decoupling of proton transport from structural relaxation at temperatures close to T_g. This study provides strong experimental confirmation to the earlier predictions from our electronic structure calculations.¹⁹ It would be interesting to find out whether there might be other mixtures exhibiting proton transfer energy barriers even lower than that observed in pure phosphoric acid.

This manuscript was written with contributions from all the authors. All authors have given approval to the final version of this manuscript.

This work was supported by the National Science Foundation under Grant No. CHE 1764409: “Mechanisms of Proton Transport in Ionic Liquids: Grotthuss vs Vehicular.”

The data that support the findings of this study are available from the corresponding author upon reasonable request.