Salt containing liquid electrolytes are classic room temperature electrolytes extensively used in modern Li-based batteries. It is a matter of fact that such highly reactive electroactive masses used as electrodes typically exclude aqueous electrolytes. The commonly used organic solvents, however, possess comparably low dielectric constants and do not efficiently split the salt molecules into free solvated ions leading to presence of large fraction of ion pairs or even high order aggregates. The ion pairs are unfavorable as they are neutral and do not contribute to the Li-ion conductivity. Liquid electrolytes have – unlike ceramic electrolytes – the advantage of facile contact formation to electroactive matter typically consisting of micro- or nanoparticles, coupled with high ionic conductivity.

**Fig. 1:** Different consistencies of 1M lithium perchlorate / polyethylene glycol-150 based soggy-sand electrolytes depending on the SiO_{2 }(fumed, 7nm) volume fraction.

On the other hand, their chemical and physical stability can cause severe operation problems, such that intense research is focused on identifying appropriate solid electrolytes. In this context the soggy-sand electrolytes (dispersions of surface active insulating oxides in salt-containing liquid solvents) offer tremendous potential by not only combining the advantages of liquid and solid state but even going beyond. Mechanically, the consistency that can be varied from rather liquid to the extreme case of infiltrated solids (**Fig. 1**) via very advantageous semi-solid behavior. Electrically, synergistic properties are achieved as a consequence of the ability of oxide fillers such as silica to adsorb anions hence breaking up ion pairs in the space charge zones and increasing the free Li^{+}-concentration and decreasing the free X^{-}concentration. The locally increased conductivity results in an increase of the overall Li^{+}-conductivity if the particles form coherent networks – observed even for very small volume fractions, provided the particle grain size is small. The decreased anion conductivity is an asset in its own as a high anion transference number leads to a detrimental concentration polarization during battery performance.

For the stationarity of the soggy-sand electrolytes the particle network kinetics is crucial and has been previously studied by confocal microscopy, impedance spectroscopy and Monte-Carlo modeling [1]. A further step ahead is the use of mesoporous silica particles as they offer additional internal ionic pathways. For soggy-sand electrolytes the Li-ion conductivity enhancement and the effective transference number *t*_{m+} can be connected by applying the heterogeneous doping concept:

**Fig. 2:**AC conductivity effects in soggy-sand electrolytes (1M lithium triflate / polyethyleneglycol-150) with MSU-H mesoporous silica fillers as a function of temperature for various volume fractions. Inset: TEM micrograph of a typical worm-like MSU-H particle.

where *t*_{+} is the transference number of liquid electrolyte, Δσ_{m} is the increase of overall conductivity between composite and liquid electrolyte and σ_{m} is liquid electrolyte conductivity [1]. Taking as a typical example 1M lithium triflate / polyethylene glycol-150 electrolyte containing 2 vol% of mesoporous MSU-H particles at room temperature with a relative conductivity according to **Fig. 2**, Eq. (1) predicts *t*_{m+} to be 37%, while the experimental result is 49%. One reason for the deviation lies in the fact that in the presence of mobile ion pairs and mobile anions Eq. (1) is no longer correct. While the conductivity is available from impedance spectroscopy, the transference number is measured by a steady state DC experiment [2]. Typically, two electrodes are applied that are reversible for Li-exchange (Li^{+}⁄e) but blocking for anion exchange. Consequently, salt concentration gradients establish eventually, nullifying the initially possible anion transport until only Li^{+} is transported.

**Fig. 3:**The complex diffusion reaction behavior in an electrolyte can be handled by considering the two conservative ensembles (represented by circles, left). In the polarization experiment the neutral ion pair is solely driven by concentration gradients, the other species (as indicated by arrows) also by electric fields (right).

The situation is gravely different if mobile ion pairs are present where in the steady state Li-ions can be additionally transported in an indirect way. In that case, the ion pair moves and the Li^{+} from the ion pair is discharged at the minus pole while the remaining anion is back-transported in the gradient of its electrochemical potential; on the other electrode side it can take up a Li^{+} formed by oxidation of Li (**Fig. 3**). Thus, contributions from the aggregates are contained both in the battery steady state current as well as in the steady state of a polarization. Notably the effects considered so far have already been treated by Bruce and Vincent [2]. Here we apply the concept of Conservative Ensembles which is well-suited to handle such reaction-diffusion situations whereby internal reactions (association/dissociation of aggregates) are fast [3]. It considers the motion of ensembles the overall source/sink terms of which disappear (Fig. 3). Hence boundary conditions as well as internal flux-force reactions become formally simple. The concept allows for a straightforward generalization and hence also inclusion of higher order aggregates (e.g. ion triples). The result for the conductivity in the steady state is given by:

where the quantities are determined by contributions from all the individual species shown in Fig. 3 (σ^{+}_{Li }effective conductivity of the Li ensemble, σ^{*}_{X }the analogous quantity for the anionic ensemble, ζ^{*} is completely determined by contributions from aggregates; see Ref. [3] for details). It can be shown that a combination of AC, DC and tracer techniques allows for the determination of the individual contributions. Such a study is underway for polyethylene glycol based electrolytes. Here we restrict to ion pairs only (in addition to Li^{+ }and X^{-}) where then σ^{*}_{Li} reduces to σ_{+} and the second addend determines the indirect contributions σ^{ind}_{∞}. The correction to the transference number of a pure solvent is then:

with σ_{∞} denoting the bulk conductivity and, where σ_{-} is the conductivity of the anion and *s* is the contribution of the ion pairs to the overall transport. Incorporation of aggregate effects in the space charge picture of soggy-sand electrolytes is particularly tricky, as polarization in space charge zones and bulk is different. The situation can be greatly simplified by taking account of the fact that the cation is accumulated in the space charge zones while the anions are depleted. Hence, in a first approximation the indirect Li-transport can be neglected in the space charge zones whilst the bulk contribution is strongly affected by it. This results in an effective, measured transference number in the composite given by:

where σ_{m} is the overall conductivity of the composite, σ_{m∞} the cationic conductivity in the bulk, <σ^{ex}_{+}> the mean cationic conductivity in the space charge zone, σ^{ind}_{∞+} indirect cationic contribution in the bulk, β_{L} measures the proportion of the space charge pathways contributing to σ_{m} and φ_{L}the volume fraction of the space charge zones. If we take up our material example mentioned above (for 1M lithium triflate / polyethylene glycol-150 containing 2 vol% of MSU-H) the observed discrepancy between *t*^{pol}_{m+} and *t*_{m+}allows us to estimate σ^{ind}_{∞+} from Eq. (4). According to Eq. (3) this results in the finding that only 7% (*t*_{+}) of the current is carried by direct transport of Li^{+} while 15% is carried by anion and ion pair. The rest is due to direct transport of the anion. This is in satisfactory agreement with recent pulsed field gradient nuclear magnetic resonance (PFG-NMR) results.

In short, synergetic solid-liquid composite electrolytes ("soggy-sand electrolytes") are not only exciting in terms of potential application, they refer to a very rich materials science topic offering a large window of tunable parameters and realizable properties as well as addressing a variety of fundamental electrochemical problems.