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Reply to Comment on “Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids and Hydrogel Polyelectrolytes” Leoncio Garrido, Inmaculada Aranaz, Alberto Gallardo, Carolina García, Nuria García, Esperanza Benito, and Julio Guzman J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b10603 • Publication Date (Web): 12 Nov 2018 Downloaded from http://pubs.acs.org on November 13, 2018
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The Journal of Physical Chemistry
Reply to Comment on “Ionic Conductivity, Diffusion Coefficients and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids and Hydrogel Polyelectrolytes”
Leoncio Garrido*, Inmaculada Aranaz,† Alberto Gallardo, Carolina García, Nuria García, Esperanza Benito, Julio Guzmán*
Instituto de Ciencia y Tecnología de Polímeros, Consejo Superior de Investigaciones Científicas (ICTP-CSIC), Juan de la Cierva 3, 28006 Madrid, Spain.
*Corresponding
authors: Leoncio Garrido and Julio Guzmán Departamento de Química-Física Instituto de Ciencia y Tecnología de Polímeros, CSIC Juan de la Cierva 3 E-28006 Madrid, Spain E-mail:
[email protected];
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Concerning Prof. Harris’ comment on our recently published work,1 we would like to start by pointing out that the Nernst-Einstein equation has not been formulated recently; its meaning and the limiting conditions of its validity are well known within the scientific community. In our work, the Nernst-Einstein equation is used to assess the extent to which the conductivity measured with impedance spectroscopy and the conductivity calculated using the values of the diffusion coefficients determined with PGSE NMR (eq 15 in ref. 1) are correlated, in electrolyte solutions from 0.01 up to 5 M. Taking into consideration Prof. Harris’ observation, we should have added the word “modified” next to Nernst-Einstein equation to be specific in describing eq 1 in our work. Alternatively, we should have indicated explicitly that eq 1 is equal to Nernst-Einstein equation when = 1. The commentary continues stating that the proposed model relating the diffusion coefficients determined with PGSE NMR to the electrical conductivity based on that equation and the theory of partial dissociation is incorrect. It is argued that the approach lacks theoretical justification and a distinction between electrical and ionic mobilities is not made. In contrast with those arguments, it could be said that there is an increasing body of experimental evidence showing the presence of ionic association in different types of electrolytes.2-5 Advances in hardware, electronics, computation and methodologies are enabling spectroscopic techniques to detect the presence of ion-pairs and larger aggregates in different types of electrolytes. The results suggest that those associations are more frequent than previously assumed, providing support to the partial dissociation theory. Furthermore, it has been shown that the electrical mobility of ions in solution measured with electrophoretic NMR is directly correlated with the diffusion coefficients determined with PGSE NMR.6 In this regard, it should be noted that this correlation is found, despite
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The Journal of Physical Chemistry
the fact that the electric field applied in the electrophoretic NMR measurements perturbs and drives away the system from equilibrium, state at which the PGSE NMR diffusion measurements are performed. In our case, the electric field applied to measure conductivities, 7.5 10-2 V/cm, is over three orders of magnitude smaller than the field used in the electrophoretic measurements (120 V/cm) and, consequently, it is expected to cause just about negligible perturbation to the systems under study. Thus, it could be anticipated that the interactions between the various species present in the electrolyte solutions would exert the same influence on the conductivity and diffusivity processes and the correlation between the electrical mobilities and ionic diffusivities would be maintain throughout the range of concentrations studied. We reiterate that the aim of our work was to provide a model able to separate the contribution of dissociated and non-dissociated species to the diffusion coefficients determined with NMR and, thus, facilitate a direct estimation of the electrical conductivity. In fact, it is only required to take into consideration the ratio between the electrolyte diffusion coefficients at infinite dilution () and the diffusion coefficients determined with PGSE NMR at a given concentration to calculate the conductivity of the solution. From eq 15, ref. 1 Λ𝑐𝑎𝑙 =
𝛾 + 1 𝐹2 (𝐷 ― 𝐷𝐿𝑖) 𝛾 ― 1 𝑅𝑇 𝐴
(1)
We would add that, in the systems studied, the experimental results show a good agreement between the measured (impedance spectroscopy) and the calculated (PGSE NMR) conductivities in a wide range of concentrations. The application to a larger number of systems would determine its validity or the need to be corrected. 3 ACS Paragon Plus Environment
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REFERENCES 1. Garrido, L.; Aranaz, I.; Gallardo, A.; García, C.; García, N.; Benito, E.; Guzmán, J. Ionic conductivity, diffusion coefficients and degree of dissociation in lithium electrolytes, ionic liquids and hydrogel polyelectrolytes. J. Phys. Chem. B 2018, 122, 8301−8308. 2. Marcus, Y.; Hefter, G. Ion pairing. Chem. Rev. 2006, 106, 4585-4621. 3. Pregosin, P. S. NMR understanding and ion pairing: measuring and understanding how ions interact. Pure Appl. Chem. 2009, 81, 615-633. 4. Stassen, H. K.; Ludwing, R.; Wulf, A.; Dupont, J. Imidazolium salt ion pairs in solution. Chem. Eur. J. 2015, 21, 8324-8335. 5. van der Vegt, N. F. A.; Haldrup, K.; Roke, S.; Zheng, J.; Lund, M.; Bakker, H. J. Watermediated ion pairing: occurrence and relevance. Chem. Rev. 2016, 116, 7626-7641. 6. Bielejewski, M.; Giesecke, M.; Furó, I. On electrophoretic NMR. Exploring high conductivity samples. J. Magn. Reson. 2014, 243, 17-24.
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