Nanocomposite solid polymer electrolytes (NSPEs) with PEO as the matrix and (i) GO or (ii) GO-graft-PEG 6k or (iii) GO-graft-PEG 6k -block-P(MA-POSS) as nanofillers have been fabricated to elucidate the impact of the filler morphology on the lithium ion conductivity. GO-graft-PEG 6k was obtained by grafting PEG 6k onto GO via esterification. GO-graft-PEG 6k -block-P(MA-POSS) was prepared via surface-initiated atom transfer radical polymerization. Fourier-transform infrared spectroscopy revealed enhanced salt dissociation and complexation between the filler and PEO host that could be attributed to Lewis acid−base interactions. Electrochemical impedance spectroscopy revealed the improved ion conductivity of the fabricated NSPEs as compared with the pristine PEO-LiClO 4 . As an example, at 50 °C, the ion conductivity increased to 4.01 × 10 −5 and 6.31 × 10 −5 S cm −1 with 0.3% GO and 0.3% GO-graft-PEG 6k , respectively, from 2.36 × 10 −5 S cm −1 of PEO-LiClO 4 , suggesting that the filler with brush-like architecture (GO-graft-PEG 6k ) is more efficient in enhancing the ion conductivity. Further increase in filler content resulted in lowering of the ion conductivity that could be ascribed to aggregation of the filler. The most dramatic impact on conductivity was observed with the incorporation of brush-like GO-graft-PEG 6k -block-P(MA-POSS) as a nanofiller (3.0 × 10 −4 S cm −1 at 50 °C with 1.0 wt % filler content). The increase in ion conductivity in the current systems, as opposed to the conventional view, could not be correlated with the content of the amorphous phase of the matrix. The conduction mechanism is still unclear; nevertheless, it could be assumed that in addition to the ion conduction through the PEO matrix, the filler forms additional low-energy ion conducting channels at its interface with the matrix. The pendent POSS nanocages of GO-graft-PEG 6k -block-P(MAPOSS) might probably increase the free volume at the interface with the matrix that is associated with higher chain and ion mobility, thus further enhancing the ion conductivity as compared with GO and GO-graft-PEG 6k . The faster ion dynamics in 1.0 wt % GO-graft-PEG 6k -block-P(MAPOSS) NSPEs has also been verified by the dielectric relaxation studies. Thus, integration of both the PEG and POSS nanocages into GO-grafted brush-like architecture offers a new tool for tuning the lithium ion conductivity for potential Li ion battery applications.
Fluctuation theorems (FT) reveal crucial properties about the nature of non-equilibrium dynamics by constraining the statistical distribution of quantities such as heat, work and entropy production. Here, we report theoretical and experimental results regarding two FT for a new quantity, named coherent energy, which is an energy form directly associated with the coherences of a quantum state. The FT are verified using the two-point measurement protocol with an all-optical setup in which the system information is encoded in the polarization of one photon of a pair. From the outcomes of our experiment we directly assess the energy probability distributions. We also demonstrate an universal bound on the energy of thermal states under the action of unitary operations, which could be the first step to establish an arrow of time for reversible processes.
We find Survival rate estimates; parameter estimates for the inverse Gaussian distribution model using least-squares estimation method. We found these estimates for the case when partial derivatives were available and for the case when partial derivatives were not available. The simplex optimization (Nelder and Mead, and Hooke and Jeeves) methods were used for the case when first partial derivatives were not available and the Quasi -Newton optimization (Davidon-Fletcher-Powel (DFP) and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) methods were applied for the case when first partial derivatives were available. The medical data sets of 21 Leukemia cancer patients with time span of 35 weeks were used.
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