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Highly decoupled ionic and protonic solid electrolyte systems, in relation to other relaxing systems and their energy landscapes. F. Mizuno*#, J.-P Belieres*, N. Kuwata@$, A. Pradel@, M. Ribes@, and C. A. Angell*

*Dept. of Chemistry and Biochemistry, Arizona State Univ., Tempe, AZ 85287-1604

#On leave from Dept. Applied Chemistry, Osaka Prefecture Univ., Osaka, Japan.

@ Dept. of Materials Chemistry, University of Montpelier, Montpelier, France

$ Now at Institute of Multidisciplinary Research for Advanced Materials, Tohoku University".

Abstract

With an interest in correlating the properties of ions in ionic glasses with other decoupled motion phenomena in glasses, we have analyzed several cases involving different modes of motion, and different mobile particles, for their similarities and distinctions, and then add new cases with protons as the mobile species. The deviations from Arrhenius relaxation kinetics, that are used to characterize liquids by their fragilities, are found also in the behavior of the non-liquid states. On appropriate temperature scaling, these deviations provide patterns with common features, but also distinctions due to the effective confinement stemming from the non-liquid states. The different degrees of fragility in the (ionic) subsystems of superionic glasses, seem to be related to the weak “mobile species glass transitions” that can be detected at lower temperatures. Such behavior suggests the existence of an “energy landscape” for the mobile sub-system, inviting the possibility of annealing effects within the subsystem.. Examples of de-coupled “dry” proton conductivity, up to 10-2 Scm-1 at 100ºC, are provided. We give a section to reporting these new liquid and plastic crystal systems which involve large cations and protonated anions, and represent improvements on the CsHSO4 type proton conductor.

Introduction

In the study of simple monatomic glassforming liquids, where there is only one type of atom to consider, e.g. the Dzugutov [1] and modified Stillinger-Weber (MSA) [2] cases , only translational motion need be considered, and all particles are equally mobile over the long period. With the normal laboratory glass-formers, however, various types of decoupling phenomena

may be encountered. These may involve different degrees of freedom of the same molecules (for instance, translational vs rotational) or different translational motions of distinguishable particles of different size (or charge). By way of extreme cases it is possible to observe rotational motion in the complete absence of translation by studying rotator phase crystals, and it is possible to study the translation of small particles in the complete absence of translations

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of large particles by examining dynamics in glasses containing both. In each of these cases it is found that there are patterns of behavior that are analogs of the strong/fragile pattern of viscous liquid behavior, though the really fragile cases are missing. The thrust of this article is to consider similarities and distinctions concerning the behavior of the different decoupled modes of motion. Ultimately, we are concerned with improving the description of the thermodynamic and dynamic behavior of mobile charged species in solid state conductors, which are a special cases of the second of the above extremes. In preparation for this effort, we consider the first extreme, decoupling of orientation from translation, and then examine the broad field of translation from translation decoupling.

Orientationally decoupled systems.

The first type of decoupling to consider is that between the orientational and translational motion in molecular systems with different asymmetries. When the asymmetry is large (rod-like molecules) a liquid-liquid first order transition to the “liquid crystal” state may occur on cooling. The fact that a change in symmetry accompanies the transition while the low temperature phase remains liquid results in a complexity that puts this case outside the range of phenomena that we wish to discuss. However, for molecules with small asymmetry, like the quasi-spherical carbon tetrachloride, or the disc-like pentachorotoluene, a first order transition to the “plastic crystal” state (or rotator phase) may occur. In this centre-of-mass-ordered state, no translation occurs at lower temperatures, but the individual molecules retain all their orientational degrees of freedom. While

most of these plastic crystalline phases undergo first order transitions to fully ordered crystals on cooling, a subset “slow down” continuously until an ergodicity-breaking phenomenon occurs which has most of the characteristics of the normal liquid-to-glass transition. Such materials were termed “glassy crystals” by Seki, Suga, and co-workers [3] who did pioneering work on this phenomenology.

Fig. 1, which is a “Tg-scaled Arrhenius plot”, is adapted from the work of Brand et al [4] by inclusion of additional cases of higher [5] and lower [6] fragility than the group of substances considered by those authors. Fig. 1 represents the entire known range of deviations from the Arrhenius law for this class of material.

Figure 1. Reorientation times for plastic crystals in which reorientation is highly decoupled from translational diffusion. Adapted from Brand et al [4], with additional data from refs. [4] and [5],. by permission.

Included for comparison is the behavior of the fragile liquid propylene carbonate [4, 7]. The most fragile molecular liquid known – the recently studied decahydro-isoquinoline [8, 9] (which is even more

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fragile than tri-phenylphosphite) - would lie close to the curve marked m = 200. The point to stress about Fig. 1 is that the range of deviation from the Arrhenius law seen with these rotator phases is much smaller than that encountered with viscous liquids. Some of the “glassy crystal”-forming rotator phases reported by Fujita and Oguni [4] are strictly Arrhenius in their relaxation time behavior and have pre-exponents of the physical (phonon cycle time) value.

To be correlated with the less fragile character of the orientational glasses is the smaller jump in heat capacity observed at Tg, after a scaling by the heat capacity of the “glassy crystal” phase is applied to take account of the different number of “rearrangeable units” possessed by different systems. The rearrangeable units correspond to the “beads” of Wunderlich [10] or the structural degrees of freedom defined by Takeda et al. [11]. (Strictly the scaling should be based on the excess entropy at Tg [9, 12, 13]). The reduced heat capacity jumps at Tg are shown in Figure 2. For the fragile liquid PC of Fig. 1, the jump would be to 1.8 on the vertical scale.

One should note also the shape of the Arrhenius law deviation, for comparison with the behavior of translationally decoupled systems which we consider next. The smaller range of “fragility” variations characterizing the plastic crystal phenomenology contrasts with the liquids case in which “strong” behavior is the exception, rather than the rule as in the plastic crystal case. The difference is presumably to be correlated, via an Adam-Gibbs equation [13] for the relaxation time,

τ = τ0 exp(-C/TSc), (1)

(where Sc is usually approximated by Sex - however, see [14]), with the smaller rate of change of the entropy above the Tg,. This, in turn, is to be related to the confining effect of the crystal lattice. When we turn to decoupling of translational motions, which produces mobile species locked into a glassy matrix, we may expect some similar effects, assignable to a “confinement” effect. The confinement effect referred to here is a “volume confinement” perhaps more closely to be identified with the difference between constant pressure and constant volume behavior in unconfined liquids [14].

Figure 2. Heat capacity jumps at Tg for selected plastic crystals contrasted with the corresponding case of a fragile liquid PC. (adapted from ref. 4, by permission).

Translationally decoupled systems.

In the discussion of ion conduction in glassy materials a scaled Arrhenius plot, with emphasis different from that of Fig. 1, is often used. The focus of attention is now on the behavior observed on the low temperature (glassy) side of the glass transition, cf. the high temperature (ergodic) side emphasized in Fig. 1.

An example is provided by Fig. 3. In Fig. 3, the full observable range of

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decouplings is shown for the case of ionic glasses. In ionic glasses, small and low-charged ionic species may retain a high degree of translational freedom. Fig. 3 uses the easily measured ionic conductivity as the property that manifests the decoupling. However we want to emphasize that this type of decoupling is a much broader phenomenon, extending all the way from the relatively free motion of large molecules (e.g. CO2 and acetone) in polymers, through water in biopolymers, all the way down to the motion of hydrogen atoms in metallic glasses and protons in protic salt systems. The latter case is of special interest and will be the subject of the latter part of this paper.

Figure 3. Tg-scaled Arrhenius plot for the conductivities of ionic glasses in which the mobile species ranges from Ag+ in an all-halide glass, through K+ in the strongly coupled case of CKN. The double arrow singles out the case of Na+ in sodium disilicate glass to show the 12 orders of magnitude difference between the conductivity at Tg and the conductivity expected for a fully coupled system. In the case of K+ in calcium-potassium nitrate “CKN” the decoupling is only four orders of

magnitude, OM. Comparable values have been seen in calcium rubidium nitrate CRN, and even smaller values (2 OM) are found in magnesium sodium nitrate[15].

To make comparisons of decoupling in this broader field, the conductivity cannot be used. The self-diffusivity of the mobile species is the property that should be observed. Fig. 4 presents a compendium of self-diffusivities culled from the literature[16-22] and presented in reduced Arrhenius plot form in order to demonstrate the idea. For details, refer to the cited articles on diffusivity of molecules in polymers [16, 17, 22] including water in polysaccharides [18] and inorganic glasses [21] sodium ions in geological glasses [19], atoms in metallic glass-formers [20], and dopant metal diffusion in amorphous silicon [23]. Recently great detail has been provided for the case of water diffusing in saccharides both monomeric and polymeric, by “coarse-grained” molecular dynamics simulations [24, 25].

In all cases in which the system remains uncrystallized above the glass transition, there is a well-defined break in the Arrhenius plot where the structure assumes liquid-like character i.e. begins to change structure with increasing temperature. This usually implies a higher expansion rate, though inverse cases exist in high silica glasses, and high water content systems, where entropy and volume become inversely correlated [26]. Data like those for the metals are also found for dyestuff molecules[27] and short chains in polymers[28].

Since the diffusivity in the glassy state (fixed structure) is usually a simple Arrhenius function of temperature

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(however see below for special features of highly decoupled systems), this break could easily be mistaken for a strong-to-fragile transition of the type being ascribed to certain systems, like water, within their liquid states [29]. Fortunately the two are easily distinguished by the presence of time-dependent effects in the former case, as the system seeks lower levels on the energy landscape. This is dealt with in more detail later in this paper.

Ionic systems.

Now we turn to details for the case of ionic systems in order to focus attention on the little understood (indeed little studied) phenomenon of super-Arrhenius behavior in superionic phases of both glassy and crystalline materials.

First noted in silver ion-conducting systems, both glassy [30] and crystalline [31], this deviation from Arrhenius behavior is now recognized as occurring in ionic systems of all types in which the ionic conductivity is very high, i.e. in which the extent of decoupling (and usually also the concentration of mobile ions) is particularly high [32].

A collection of data for a number of glassy systems is shown in Figure 5.

In order to bring the discussion of these data to the same basis as that of Figs. 1 and 2, we must ask the question [33] “Can a glass transition be observed when the mobile species relaxation time

Figure 4. Diffusivity Arrhenius plot for gas-in-polymer[16] water in polysaccharide [18], ions in silicate glass [19] metals in bulk metallic glasses [20]. Tg is assigned as the temperature where the break in D occurs, though this value will fall somewhat below that assigned by (faster) DSC scans.

crosses the experimental time scale of a heat capacity measurement?”. The answer obtained, when the common methods of determining glass temperatures, (differential thermal analysis DTA or differential scanning calorimetry DSC) are used, is “No”. But this is also the answer one obtains on scanning very dry silica, which everyone considers to be a glass. When sufficiently sensitive methods are used, namely adiabatic calorimetry, then a very weak glass transition can indeed be observed in the case of superionic glasses. We refer here to the calorimetric observations of Hanaya and Oguni [34] reproduced in Fig. 6. We conclude that ergodicity-breaking within the mobile ion sub-system does produce a detectable effect, but that the entropy fluctuations associated with the mobile

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ion population are very weak compared with those involved in the freezing-in of reorientational motions. This can probably be associated with the effects of volume confinement discussed in connection with the “stronger” behavior of “reorientational glassformers relative to liquid glassformers The low rate of entropy production above the “superionic glass transition” leads, via an Adam-Gibbs approach, to the expectation of very weak departures from Arrhenius behavior near the “Tg” – as is borne out by the observations.

Figure 5. Conductivity Arrhenius plots for a variety of systems, glassy and crystalline,

Figure 6. Heat capacity behavior in the superionic glass system AgI-Ag3PO4 at ~80K where the conductivity relaxation time reaches the time scale of the adiabatic heat capacity determination (from Hanaya et al, ref. [34]). The jump in heat capacity is only ~0.06 Jmol-1K-1, far smaller than any on record for even the weakest liquid-glass transition. (After Hanaya et al, ref. [34])

showing deviations from linearity for the better conductors.

To compare with Fig.1 we should plot the data of Fig. 6 on an Arrhenius plot in

which the temperatures are scaled by the “mobile ion Tg”. However this temperature is generally not known, and data extending to such low conductivities are sparse. Therefore it is more practical to choose an alternative. We choose the temperature at which the ionic conductivity is 10-9 S cm-1, which is included in many studies. When the data stop short of this value we obtain it by linear extrapolation (because all systems are Arrhenius-like in this temperature range).

Fig. 7 contains a compendium of data on systems of both glassy and crystalline character - in which the structure is

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constant throughout the measurement – plotted on the above basis. It includes the interesting case of fluorite crystal phases in which a progressive disordering of the anionic lattice occurs, without change of crystal symmetry.

Fig. 7 shows a pattern quite similar to that of the “strong” liquid variety, and akin to that of the likewise- constrained plastic crystals. However now the “lens” embracing the collection of data has the opposite shape from that of the plastic crystals - which deviated most strongly from the Arrhenius law nearest to the scaling temperature. This can be related via Eq. (1) to the difference in glass-transition thermodynamic behavior (viz the Cp jump) between the two classes of system. The ionic systems have almost no jump in hear capacity at the “mobile ion Tg”, while for the plastic crystals the jump is considerable (Fig. 2).

At temperatures well above Tg it seems that the thermodynamic strength of the glass transition, (which could be studied by specific heat spectroscopy) may increase, since large jumps in the tensile modulus are registered in mechanical relaxation measurements [22]. A gradual increase in heat capacity with increasing temperature would be consistent with the greater-than-simple Arrhenius slope seen in Fig. 7.

The general form observed for these systems would be consistent with a very weak, smeared-out, version of the lambda transition observed in certain crystals, usually of the fluorite type, e.g. SrCl2 [35]. This type of transition has a peak in the heat capacity at higher temperatures. Beyond the peak, it drops to the normal vibrational value and the conductivity should then return to Arrhenius behavior with pre-exponent of

Figure 7. Scaled Arrhenius plot for ionic conductivity. Scaling temperature chosen as T(σ =10-9Scm-1). Note that data mostly lie above the simple Arrhenius connection from the scaling point to the 10-1 pre-exponent. Most systems here are crystalline.

about 10 Scm-1 (corresponding to the conductivity of the ionic resonance in the far IR [33]).

A connection between entropy production and ionic conductivity was given some time ago by Voronin [36] and has recently been developed successfully, using the Adam-Gibbs approach, by Gray-Weale and Madden [37] in an account of the extraordinary conductivity behavior of the compound PbF2. PbF2 is the extreme case of behavior of the type shown in Fig. 4 by SnCl2. The conductivity jump [38] is considerably sharper than that of SnCl2 and is accompanied by a heat capacity spike that is so sharp that it resembles a kinetically spread-out first order transition [39]. Yet the crystal symmetry does not change.

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In the case of PbF2, the cause of the jump in conductivity is known from refs. [37, 40]. It is the sudden cooperative generation of interstitial defects which like to cluster around lattice vacancies rather then distribute themselves at random as in a Schottky anomaly. This stands as an excellent example of the relevance of the “cooperative excitations” model of ref. [41] which is a rewording, in defects language, of the original “non-ideal mixing, two species” model of Rappoport [42]. In the cooperative defects model the excitations are attracted to each other, and the mixing then follows the “regular solution” thermodynamics, a simple form. For sufficient deviations from ideality the model predicts a first order phase transition. which is indeed often seen in crystal chemistry. Rappoport’s model was invented to account for the existence of melting point maxima in certain one component systems, but has been found to have much wider applications.

In light of these observations, the less deviant crystals and the like-looking superionic glasses appear as weakened and smeared out versions of this same cooperative behavior.

The pattern of variable deviations from the Arrhenius law seen in plastic crystals, and now in superiionic glasses, has been given a lot of attention in the case of viscous liquids. There it has been found to have a thermodynamic equivalent – a pattern of different rates of generation of configurational entropy as the temperature rises above the glass transition temperature [12]. The thermodynamics, and to a lesser extent the associated dynamics, are now commonly described in terms of collective coordinates for the

configurational degrees of freedom of the system. The collectively defined microstates are the potential energy minima on the multidimensional potential energy surface first described by Goldstein. (One could describe the energy of a crystal in the same way. However, it is more fruitful in the case of ordered solids to use a real space, point defect, description since. for a crystal, the energy of one of the microstates in configuration space is simply the energy of a specified number of defects. Furthermore, except for cases like PbF2, the defect population never gets very large before the crystal melts).

The similarity of superionic crystal and superionic glass dynamics seen in Fig 7 suggests a common description for each, which could be either in configuration space, or in real space. In the latter, one would invoke a population of defect sites, specific to the mobile ions; in the former, an energy landscape with a population of energy minima equal to exp (∆S/R) per mole of mobile ions, where ∆S might be available in some cases from the entropy of transition between superionic and normal crystal states.

In the case of a potential energy landscape scenario for a superionic glass, it is interesting to reflect that the ionic subsystem under study is determined when the glass is formed by structural arrest within some potential energy minimum (or trap) on the energy landscape representing the configurational states of the liquid ionic system above the primary glass temperature. Thus the description of the mobile ion glass in energy landscape terms requires a “landscape within a landscape” scenario. (as represented in Fig. 8).

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The complexity of this situation is realized when it is remembered that the particles within the sub-landscape are in fact not trapped, in the sense that the system as a whole is trapped. Rather the ions in the subsystem can wander within the whole physical space of the system. In this respect the description in energy landscape terms is cumbersome and to an extent inelegant. By contrast, the concept of a quasilattice with excitable states analogous to crystal defects is simple and useful. Indeed a two-state model for the excess heat capacity of the superionic glass transition was already suggested by Hanaya et al [34] as a rationalization of the heat capacity jump observed.

The structure and energetics of this quasilattice are clearly some function of the energy landscape of the primary glass structure within which substructure under discussion occurs, as illustrated in Fig. 8. However, by study of quenching effects on glass conductivity, it is found that the dependence is a weak one when the subsystem is highly decoupled from the matrix, i.e., when the decoupling index is high. It is to be noted that, consistent with the existence of a distinct glass transition, and a distinct landscape, there is also a distinct Lindemann criterion for the onset of decoupled mobility. This has been noted in connection with temperature dependence of the mean square displacement in computer simulation studies of sodium silicate glasses [43, 44]. An analogy can be made with the behavior of the MSD in the case of coupled systems (e.g. CKN) near the normal (alpha relaxation)

glass temperature reported by Ngai [45].

Figure 8. Energy landscape rep- resentation of superionic glass, showing substructure of individual basins implied by observations in Figs. 6 and 7. It is predicted that there should be annealing effects observable in the temperature range of the mobile ion Tg. It is believed that the thermometer zero point problem is an example of this effect.

Protonic systems.

Finally, we address the currently “hot” issue of fast proton mobility in water-free condensed phases of both glassy, liquid, and crystalline character.

Much attention was given to the 2001 report by Haile and coworkers[46] that, before it melts (at 200-230 ºC [46]), the compound CsHSO4 undergoes a transition to a rotator phase in which the proton exhibits a long range mobility as indicated by the high conductivity in the absence of normal ion diffusion. Such “dry” proton mobility has been a much sought-after property of condensed phases for some time. Having observed ionic conductivities as high as 10-2 Scm-1 in mixed alkylammonium nitrates [47], and having also seen that, in ionic liquids, the conductivity is maximized when the anionic species is protonated [48], we decided to investigate the

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properties of the corresponding bisulfates and dihydrogen phosphates.

In the liquid state the nitrates have not shown any evidence of superionic transport indicative of “loose protons” [48] but the case with protonated anions had not previously been studied by us. If the large size of the cesium cation were in part responsible for the properties of CsHSO4, then there was reason to hope that the larger cations available to us might enhance the trend, or at least bring the transition to the conducting phase down to more favorable temperatures.

Salts of various alkylammonium cations were prepared by titrating the amines with the H2SO4 and H3PO4 until a single proton had been transferred, and the properties of the product then characterized over a range of temperatures up to and including the liquid phase. Indeed as seen in the following figures, in some cases the liquid phase is the only phase obtained - some of the products are excellent glassformers.

Only a few results are shown here. For a more detailed account the reader is referred to ref. [49]. Rather than showing a variety of individual salts we pass directly to the mixed system containing cesium bisulfate in order to compare the behavior of the new types of systems with that of the CsHSO4.

Fig. 9 shows conductivity data for the CsHSO4 crystal, in ordered and high temperature disordered forms (reproducing that of Haile et al [46]), in relation to that of liquid and crystal states of the mixed system CsHSO4 + dimethylammonium bisulfate. Fig. 10 (lower panel) shows the corresponding set of data obtained during heating from

the low temperature stable states, avoiding the supercooled states seen in the case of Fig. 9. We note immediately that addition of just 10% of the DMAHSO4 has stabilized the high

Figure 9. Ionic conductivities of CsHSO4 (filled squares) and its binary mixtures with dimethylammonium bisulphate. Note the extension of the stability range of the CsHSO4 rotator phase to lower temperatures produced by dissolution of the alkylated ammonium cation. These data were obtained during cooling, and contain information on supercooled states of liquid and rotator crystal.

Figure 10. Ionic conductivity data on the same systems as Fig. 9 but now representing stable states of the system. Data were obtained during heating from low temperature equilibrated states.

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temperature rotator phase of CsHSO4 almost to room temperature. Thermal analysis data relevant to this point is shown in ref. 46. With 25% of the alkylated cation a remarkable conductivity, greater than 10-2 Scm-1 can be obtained at 100ºC. The data of Fig. 9 do not establish that the conductivity obtained is purely protonic, though it is not easy to see what other charge-carrying species could be so mobile in the crystalline state.

Some idea of the extent of decoupling of mobile from immobile species can be obtained by examination of the conductivities of the liquid states of the system relative to their viscosities. This can be carried out in two different ways which give different representations of the same phenomena. The first, which has been used many times in the study of glassforming systems is to plot the conductivities in the Arrhenius form of Figs 9 and 10 but again to incorporate, as in Fig. 3, Tg scaling of the temperature. When Tg is determined at a standard rate of 20K/s it occurs when the structural relaxation time reaches a fixed value of about 100s. In the case in which the conducting species all move at the same rate as the species controlling the structural relaxation, the conductivity at the scaling temperature would be, by the Stokes-Einstein and Nernst-Einstein relations, about 10-15 Scm-1 - and would be immeasurable by normal methods. However if the conducting species are more mobile then the conductivity at Tg will be higher. This information has been used in the past to establish the “decoupling index” for the system which is the ratio of the structural relaxation time to the conductivity relaxation time [50, 51]. The decoupling index gives a very physical idea of the relation

between the conductivity and structural relaxation processes.

For superionic conductors this ratio can reach very large values which are best expressed by their logarithms. Empirically we have established an approximate relation between the log (decoupling index) and the conductivity measured at Tg [52]. The relation is:

decoupling index (log) = 1015log σTg

The conductivity Arrhenius plot using this reduced temperature scale is shown in Fig. 11, where the conductivity at Tg is seen, by short extrapolation, to reach the value 10-6.2 in the case of trimethylammonium dihydrogen phos-phate. (Note that we can only plot data for glassforming liquids according to this scheme. It does not assist us in understanding the behavior of the rotator phases of Figs. 9 and 10.) A conductivity

Figure 11. Tg-scaled Arrhenius plot for conductivity showing how the conductivity of the dihydrogen phosphate conductivity remains as high as 10-6.2 at the glass temperature. The dashed line indicates the expectation for the glassy state conductivity vs temperature relation extrapolated to Tg/T = 0 to give the pre-exponential constant (corresponding to the proton jump attempt frequency).

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of the above value corresponds to a log(decoupling index) of ~9, telling us that whatever is responsible for the conductivity, is nine orders of magnitude more mobile than the species becoming jammed at the glass transition. It seems unlikely that this excess mobility could be attributed to any ionic species, and it is therefore probably due to the motion of protons themselves.

Although this seems to be a major mobility gap, it is not large compared with others already seen in this paper. For instance, in Fig. 4, there are 11 orders of magnitude separating the diffusivity of Na+ ions from those associated with the glass transition, and the gap is even larger for molecules diffusing in polymers (and water diffusing in the polysaccharide polydextrose).

In technological applications of protic systems, for instance, fuel cells, interest lies more in the behavior at the upper limit of conductivity. For assessments in this range, a more satisfactory type of plot is that used in physical chemistry for more than a century, the Walden plot. In this case we plot the log of the equivalent conductivity (in Scm2/equiv) vs the log of the fluidity (in poise-1). For systems in which the mobility is controlled by the movement of the majority species, the relation will be linear. We calibrate using the data for unimolar aqueous KCl solution in which the ionic mobilities are almost equal.

Elsewhere [53] we have discussed the usefulness of this plot as a classification diagram for identifying subionic and superionic behavior in charge conducting systems. The plot shows again how the dihydrogen phosphate system is the most decoupled case, but

Figure 12. Walden plot for the substances of Fig. 11, (higher conductivities only, due to limited viscosity data) showing how marked superionic behavior at lower fluid-ities is lost at higher temp/higher fluidity.

also how the protonic motions become increasingly coupled to those of the matrix as the fluidity increases with increase of temperature.

Assessments of the mobile species identity case of the crystalline materials of Figs. 9 and 10 are of course of great interest. The methods used on the inorganic systems CsHSO4 and Cs2(HSO4-H2PO4) solid solutions by Mizuno and Hayashi [54-56] are diagnostic and will be applied to the present systems in future research. Likewise, we hope the techniques used to separate proton hopping from other degrees of freedom by Qi et al [57] might be applicable to our systems.

Concluding Remarks.

We will show separately that the highest decoupling of proton-from-matrix motion to be found in the liquid state is that in the celebrated case of dilute aqueous acid solutions, where the Grotthus mechanism operates. Unfortunately this mechanism becomes

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inoperative as solutions become more concentrated and the “water structure” is disrupted. It has so far not been demonstrated possible to reproduce cases with water-like efficiency in a solid material. One of the challenges for future work will be to identify “glassy crystal” behavior in the supercooling rotator phases of Fig. 9, and to investigate the relation between proton mobility and reorientation times in these systems. It is possible that proton decouplings exceeding those of the aqueous solutions will be identified.

Acknowledgements. The part of this work dealing with protic systems was supported by the Army Research Office under Contract No. W911NF-04-1-0060. We are indebted to the Japanese society for the Promotion of Science for a fellowship for FM, and to the University of Montpellier for Post-doctoral and Visiting professorship awards (NK and CAA).

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