Page 122 - Read Online

Page 8 of 13 Ahmed et al. Energy Mater. 2025, 5, 500079 https://dx.doi.org/10.20517/energymater.2024.209

where q and are charge and velocity of i-th ions, respectively. Self-diffusion coefficients are used to
estimate the expected σ based on Eq. (1), corresponding to conductivity without ion-ion correlations. In
NE
contrast, σ is related to both self- and cross-correlations and is defined as follows [25-28]
DC

where V is volume. Separating self and distinct correlations in Eq.(5) we can write the σ as [21,22,39-41]
DC

where the first term is defined by Eq. (1) and the last three terms correspond to distinct cation-anion,
cation-cation and anion-anion correlations. Thus, the experimentally measured σ will coincide with the
DC
σ only in the absence of distinct ionic correlations. Using Eq. (6) and Eq. (1) can estimate the contribution
NE
of distinct ionic correlations, calculating the ionicity or inverse Haven ratio [23,24] .

Using the experimental values of σ , mobility fraction [Supplementary Figure 2B] and diffusion coefficient
DC
[Figure 2] can estimate the contribution of distinct ion-ion correlations. The ionicity of regular ionic liquids
is always less than one [23,42-47] , and as molecular dynamic simulations and experiments in molten salts [48-50]
[39]
showed, it is mostly caused by the negative distinct anion-anion and cation-cation correlations ( < 0,
< 0). Molecular dynamics is typically used to qualitatively estimate ionic correlations, but recently, an
alternative approach based on momentum conservation has been proposed to determine distinct ion
correlations from experimental data .
[41]

Figure 6 presents the temperature dependence of the inverse Haven ratio for [P ][TFSI] and [P ][PF ] in
1224
12
6
Phase I and melted states. We can see that in the melt state, H is in the range of 0.4-0.8 which is typical for
-1
-1
ionic liquids and molten salts [23,42-47] , where the values H < 1 are explained by the negative distinct anion-
anion ( < 0) and distinct cation-cation ( < 0) correlations [39,41,48-50] . However, in Phase I, H drops
-1
approximately ten times, indicating that the ion-ion correlations suppress conductivity ~10-50 times in
comparison with the expected σ based on high ionic diffusion in the solid phase.
NE
In our previous work , we suggested that there are two types of ion transport in plastic crystal [P ][PF ]
[21]
1224
6
in the solid phase: intra-cell and inter-cell motion. At the small intra-cell scale, ion transport is similar to
regular ionic liquid and appears as the highfrequency AC-DC crossover in the conductivity spectra and as
the relaxation process in the LS spectra. Larger scale inter-cell dynamic corresponds to the ion exchange
between the crystalline cells. We speculated that the inter-cell ion transport appears strongly correlated,
[21]
possibly due to ion momentum conservation or elementary cell charge neutrality . This correlation leads
to a kind of backflow - when one cation or anion leaves the elementary unit cell, another cation or anion