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Selective hydrogen isotope binding

Our studies on the preferred tritiated water auto-dissociation confirm that T⁺ is the preferred target over TO^-.  With this in mind, we have started developing a model for hydrogen isotope conduction through a membrane channel.

I. The tritiated water auto-dissociation equilibria:  As a first step toward understanding the thermodynamics and kinetics of tritium exchange in a variety of materials, we considered the tritiated water auto-dissociation equilibria.  Identifying the preferred form of the tritium (T⁺ or TO^-) is key to choosing materials that can exchange it.  To find the change in free energy of each of these reactions, we found the solvation free energy of the individual species using a quasi-chemical theory of solvation.[1]  Lindiwe Ndebele '09 and Laura Fernandez Ô08 have found the most probable solvated structures for T⁺ and TO^- using a quasi-chemical theory of solvation with harmonic and anharmonic frequency estimates.  The most probable species using harmonic frequency estimates are the same as those found in previous quasi-chemical applications on H⁺ and HO^-.

Since differences between isotopes are crucial for the auto-dissociation of tritiated water, we have considered anharmonic frequencies.  A second order perturbation approach yielded highly suspect frequencies for the highly anharmonic hydrated hydroxide species so we turned our attention to simple scaling relations.  At room temperature, we find a pK_w of 14 for H₂O and both possible HTO dissociation harmonically.  Including scaling relations to anharmonic behavior changes the pK_w of HTO dissociation into HO^- and T⁺ to 11 while leaving the other dissociations at 14.  Since experimental studies suggest that raising the temperature from 20°C to 60°C increases the HTO dissociation preference towards HO^- and T⁺, we are considered the same equilibria at 60°C.  At this elevated temperature, we found that the preferred number of waters solvating hydroxide shifted to smaller numbers.  The pK_w for water dissociation also decreased to 12 and 9 using the harmonic and anharmonic approximations, respectively.  The direction of the shift agrees with water experiments but the magnitude of the shift is too high.  The CRC value for water pK_w is 13 at 60°C.   The shift is already wide in the harmonic case and too wide anharmonically suggesting that rescaling of frequencies is not sufficient to capture anharmonicities accurately.  Using the harmonic approximation the pK_w for HTO dissociation into either set of species is 12.  The anharmonic pK_w for tritiated water dissociation into HO^- and T⁺ shifts to 8 while the dissociation to TO^- and H⁺ shifts to 9.  While the preference for dissociation into HO^- and T⁺ agrees with experiment, the relative preference is not increasing with increasing temperature.  This highlights that using simple scaling relationships for anharmonicities is not enough.  Despite this, it is clear that the models suggest T⁺ rather than TO^- as the right target.

II. Model for hydrogen isotope conduction through a narrow channel

Figure 1.  Geometry of a Nafion channel based on average sulfonate side branch density and length.  Less regular arrays would also be considered.

To consider hydrogen and tritium ion conduction through a membrane we needed to find a well characterized membrane structure.  Due to its high interest in fuel cell applications, Nafion was been well characterized as water filled parallel cylinders with hydrophilic side branches.[2]  With the experimental parameters found, it is possible to make a 3D model of a nafion channel such as that shown in Figure 1.   Proton conduction in such a channel could make use of traditional water mechanisms in the interior with the extra option of temporarily binding at a sulfonic site (interior projections).  Modeling room-temperature proton conduction in this channel would help us understand how the mechanism for proton conduction in water is altered by a nafion and other polymer cavities.  We could also vary side chain interaction to gain more selectivity.  The dissociative water potential of Mahadevan and Garofalini is being coded by Lara Patel Ô10 for the water in the channel.[3]  Pure "hard cavity" interactions with some proton attraction to sulfonate sites are being considered.  Luong Nguyen '12 wrote a program to put randomly oriented waters in different shaped cavities.  This coming year we will stat studies of proton conduction through these water filled channels.            We have also started collaboration in writing an NSF proposal with the UMASS Fueling the Future for Chemical Innovation center.  The propoposal will contain a subcontract to Mount Holyoke through which I will continue studies on proton conduction in several membranes.  The quantum character of the proton will be included in these studies using our quantum/classical distribution.[4]  Through comparison of proton conduction in perovskite oxides (other project) and polymer membranes, we will begin to shed light on the effect of structure and proton quantum character on proton conduction and isotope selectivity.

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