TY - JOUR
T1 - Stochastic model of lithium ion conduction in poly(ethylene oxide)
AU - Gitelman, L.
AU - Averbuch, A.
AU - Nathan, M.
AU - Schuss, Z.
AU - Golodnitsky, D.
N1 - Funding Information:
The first three authors were supported by a Grant No. 2004403 from the U.S.-Israel Binational Science Foundation. The research of Z. Schuss was partially supported by a research grant from TAU. Thanks for Dr. Ela Lifshits for providing the experimental data from her Ph.D. studies under the supervision of Professor E. Peled and Professor D. Golodnitsky, School of Chemistry, Tel Aviv University. FIG. 1. Left panel: the helical loop and right panel: closeup of the loop. FIG. 2. The polymer folded into a helix containing a circular loop. FIG. 3. Schematic model of poly(ethylene oxide). The same two turns of the helix appear at the bottom of the figure. FIG. 4. The potential Φ ( s ) + Ψ E ( s ) [Eqs. (2) and (3) ] for N = 13 , α = 0 , and η = π / 5 (consisting of N = 11 for the loop and N = 2 for two line segments) in an unstretched (top) and for stretched (bottom) N = 13 , α = 0 , and η = 0 (consisting of N = 4 for the loop and N = 9 for two line segments). The local extrema of the potential correspond to the leftmost and rightmost points on the loop in Fig. 2 . FIG. 5. Energy landscape of the configurations of one lithium ion at central angle x and one iodide ion at central angle y in a loop of type Fig. 2 with nondimensional radius ρ = 0.03 . The energy barrier height is about 8 k B T . FIG. 6. Energy contours of the landscape Fig. 5 . FIG. 7. Energy landscape of one lithium and one iodide ion in the helical loop of Fig. 2 with nondimensional radius ρ = 0.02 . The energy barrier height is about 5 k B T . FIG. 8. Contours of the landscape Fig. 7 . Once over the barrier near the diagonal, the lithium-iodide dipole leaves the loop by free Brownian motion along the diagonal. FIG. 9. Energy landscape of a pair of lithium and iodide ions in a loop of nondimensional radius ρ = 0.0009 . There is no trap and the ions form a dipole near the diagonal. FIG. 10. Contours of the landscape Fig. 9 . The saddle point disappears when the nondimensional radius is ρ = 0.0009 . FIG. 11. Sections of the energy surfaces of a single disjoint pair of Li + and I − along the line x + y = 2 π . The barrier disappears at ρ = 0.0009 . FIG. 12. Sections of the energy surfaces of two disjoint pairs of Li + and I − along the line x + y = 2 π . The barrier disappears at about ρ = 0.002 . FIG. 13. Energy barrier height in units of k B T vs ρ . FIG. 14. Normalized current vs ρ . The normalized current with two disjoint pairs in the loop is magnified by 10 3 . FIG. 15. Simulation conductivity ( S / cm 2 ) vs stretching at concentration ratios LiI : P ( EO ) 20 at room temperature. FIG. 16. Simulation conductivity ( S / cm 2 ) vs stretching at concentration ratios LiI : P ( EO ) 7 at room temperature. FIG. 17. Experimental and Simulation conductivity ( S / cm 2 ) vs stretching at concentration ratios LiI : P ( EO ) 7 at room temperature. FIG. 18. Experimental and Simulation conductivity ( S / cm 2 ) vs stretching at concentration ratios LiI : P ( EO ) 20 , LiI : P ( EO ) 40 , and LiI : P ( EO ) 100 at room temperature.
PY - 2010
Y1 - 2010
N2 - We develop, analyze, and simulate a physical model of Li+ -ion conduction inside polyethylene oxide (PEO) helical tubes, which are the solvent of LiI salt. The current is due to diffusion and electric interactions with a permanent external field, the PEO charges, and ion-ion interactions. Potential barriers are created in the PEO by loops in structure. We calculate the energy of configurations of one or two lithium ions in the loop and derive an explicit expression for the activation energy. We use Kramers' formula to calculate the conductivity as function of mechanical stretching, which lowers the barrier and causes an exponential rise in the output conductivity.
AB - We develop, analyze, and simulate a physical model of Li+ -ion conduction inside polyethylene oxide (PEO) helical tubes, which are the solvent of LiI salt. The current is due to diffusion and electric interactions with a permanent external field, the PEO charges, and ion-ion interactions. Potential barriers are created in the PEO by loops in structure. We calculate the energy of configurations of one or two lithium ions in the loop and derive an explicit expression for the activation energy. We use Kramers' formula to calculate the conductivity as function of mechanical stretching, which lowers the barrier and causes an exponential rise in the output conductivity.
UR - http://www.scopus.com/inward/record.url?scp=77950584145&partnerID=8YFLogxK
U2 - 10.1063/1.3357272
DO - 10.1063/1.3357272
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AN - SCOPUS:77950584145
VL - 107
JO - Journal of Applied Physics
JF - Journal of Applied Physics
SN - 0021-8979
IS - 6
M1 - 064318
ER -