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Ultrafast two-dimensional infrared (2DIR) spectroscopy is a relatively new methodology, which has now been widely used to study the molecular structure and dynamics of molecular processes occurring in solution. Typically, in 2DIR spectroscopy the dynamics of a system is inferred from the evolution of 2DIR spectral features over waiting times. One of the most important metrics derived from the 2DIR is the frequency–frequency correlation function (FFCF), which can be extracted using different methods, including center and nodal line slope. However, these methods struggle to correctly describe the dynamics in 2DIR spectra with multiple and overlapping transitions. Here, a new approach, utilizing pseudo-Zernike moments, is introduced to retrieve the FFCF dynamics of each spectral component from complex 2DIR spectra. The results show that this new method not only produces equivalent results to more established methodologies in simple spectra but also successfully extracts the FFCF dynamics of individual component from very congested and unresolved 2DIR spectra. In addition, this new methodology can be used to locate the individual frequency components from those complex spectra. Overall, a new methodology for analyzing the 2D spectra is presented here, which allows us to retrieve previously unattainable spectral features from the 2DIR spectra. 

Polymer gel electrolytes (PGE) have seen a renewed interest in their development because they have high ionic conductivities but low electrochemical degradation and flammability. PGEs are formed by mixing a liquid lithium-ion electrolyte with a polymer at a sufficiently large concentration to form a gel. PGEs have been extensively studied, but the direct connection between their microscopic structure and macroscopic properties remains controversial. For example, it is still unknown whether the polymer in the PGE acts as an inert, stabilizing scaffold for the electrolyte or it interacts with the ionic components. Here, a PGE composed of a prototypical lithium-carbonate electrolyte and polyacrylonitrile (PAN) is pursued at both microscopic and macroscopic levels. Specifically, this study focused on describing the microscopic and macroscopic changes in the PGE at different polymer concentrations. The results indicated that the polymer-ion and polymer–polymer interactions are strongly dependent on the concentration of the polymer and the lithium salt. In particular, the polymer interacts with itself at very high PAN concentrations (10% weight) resulting in a viscous gel. However, the conductivity and dynamics of the electrolyte liquid components are significantly less affected by the addition of the polymer. The observations are explained in terms of the PGE structure, which transitions from a polymer solution to a gel, containing a polymer matrix and disperse electrolyte, at low and high PAN concentrations, respectively. The results highlight the critical role that the polymer concentration plays in determining both the macroscopic properties of the system and the molecular structure of the PGE.