Anomalies in the ion transport of phosphoric acid in water and heavy-water environments

Chakrabarti, Haimanti

doi:10.1088/0953-8984/8/38/006

Cited by 14 publications

(18 citation statements)

References 20 publications

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“…For example, concentrated phosphoric acid electrolytes have unusually high conductivity given their high viscosity. In addition, diffusion coefficient measurements for both protons and phosphorus-containing species exhibit unusual concentration and temperature dependence [16,17]. The relative invariance with electrolyte composition of the diffusion coefficients in Table 1 reinforces the conclusion that concentrated phosphoric acid is not a hydrodynamically simple fluid.…”

Section: Resultssupporting

confidence: 61%

“…However, previous authors have noted that the transport properties of concentrated phosphoric acid are anomalous, and they have suggested that transport cannot be described by the prototypical hydrodynamic model of slip-free particle motion through a liquid, or in other words, by the Stokes-Einstein equation [16,17]. For example, concentrated phosphoric acid electrolytes have unusually high conductivity given their high viscosity.…”

Section: Resultsmentioning

confidence: 99%

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Water diffusion coefficients during copper electropolishing

Suni

2004

Journal of Applied Electrochemistry

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Cu electropolishing was studied using a rotating disc electrode in a variety of phosphoric acid-based electrolytes, including several with ethanol and other species added as diluents. Diluents allow a wider range of water concentrations and electrolyte viscosities to be accessed and also reduce the removal rate during Cu electropolishing, simplifying possible application to damascene processing. Transient and steady state currents in the mass transfer limited regime are shown to depend on both the number of water acceptor molecules associated with each dissolving Cu ion and on the effective diffusion coefficient of water. Transient analysis samples the bulk transport properties, whereas steady state analysis integrates them through the diffusion layer. Assuming that the effective diffusion coefficients appropriate to transient and steady state behavior are the same, about one water molecule is associated with each dissolving Cu ion. This analysis yields effective diffusion coefficients for water on the order of 10 )9 cm 2 s )1 . However, the data is also consistent with an assumption that six water molecules are associated with each dissolving Cu ion, but the effective diffusion coefficient appropriate for a Levich analysis is somewhat lower than that in the bulk electrolyte. This analysis yields effective diffusion coefficients for water on the order of 10 )8 -10 )7 cm 2 s )1 . The latter interpretation, that six water molecules are associated with each dissolving Cu ion, appears more likely since it provides almost exact agreement with the effective diffusion coefficient reported previously by Vidal and West. In combination with previously published impedance results ruling out a salt film mechanism, the good agreement between the transient and steady state analyses confirm that water is the acceptor species that complexes dissolving Cu ions in phosphoric acid-based electropolishing baths.

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Section: Resultssupporting

confidence: 61%

Section: Resultsmentioning

confidence: 99%

Water diffusion coefficients during copper electropolishing

Suni

2004

Journal of Applied Electrochemistry

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“…The limitation of using this model is that the predicted effective radius of the solute is not the physical dimension. From the modified Levich analysis of the data an effective radius of 1.9-2.9 · 10 -9 m is obtained, which is an order of magnitude larger than expected for a water molecule with an O-H bond length of approximately 0.1 · 10 -9 m. This agrees with the complex behavior of the concentrated phosphoric acid system as suggested by Chakrabarti [10] and Chung [11]. In effect, due to the electrostatic interactions between water and the electrolyte bath, the effective diffusivity is an order of magnitude less than the StokesEinstein model predicts for a hard sphere model.…”

Section: Validity Of the Stokes-einstein Modelsupporting

confidence: 85%

“…Other authors [10,11] have proposed that the concentrated phosphoric acid/water system is not a hydrodynamically simple fluid. The hard sphere and simple fluid assumptions used in the Stokes-Einstein relationship suggest the equation does not physically model the diffusion of water in the phosphoric acid system.…”

Section: Modified Levich Analysismentioning

confidence: 99%

Effects of viscosity-dependent diffusion in the analysis of rotating disk electrode data

et al. 2007

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This paper demonstrates the application of a modified Levich equation for chemical systems with varying viscosity. A commonly used technique to analyze rotating disc electrode (RDE) experiments is to fit the data to the Levich equation assuming a constant effective diffusion coefficient which may be valid for conditions where the viscosity does not vary significantly (less than an order of magnitude). However, most diffusion coefficient models (e.g. Stokes-Einstein) show an inverse relationship with viscosity which consequently indicates that a constant effective diffusion coefficient may result in poorer model-to-data agreement. Here, data are presented for a series of RDE experiments for the electrodissolution of Cu in phosphoric acid, water and glycerin based baths. Viscosity changes of greater than one order of magnitude allow for testing the assumption of a constant effective diffusion coefficient. The collected data, as well as data published elsewhere, can be explained by a modified Levich equation which takes into account the viscosity dependence of the diffusion coefficient. List of SymbolsC A Concentration of A in solution (mol l -1 ) D Diffusion coefficient (m 2 s -1 ) D A Effective diffusion coefficient of A (m 2 s -1 ) D AB Mutual diffusivity at infinite dilution of A in B (m 2 s -1 ) D AB Mutual diffusivity (m 2 s -1 ) F Faraday's constant (C mol -1 ) I lim Limiting current per unit area (A m -2 ) k Boltzman's constant (J K -1 ) m Molality of solute (mol (kg of solvent) -1 ) n Ionic charge r Effective radius (m) s Solvent coordination number T Absolute temperature (K) V Molar volume (m 3 mol -1 ) c ± Mean ionic activity coefficient of solute l Absolute viscosity (cP) m Kinematic viscosity (m 2 s -1 ) u B Association factor for solvent B for Wilke-Chang equation w B Parachor parameter for component B for Tyn-Calus equation xRotational speed (rad s -1 )

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“…1,2) Moreover, in spite of its high viscosity, liquid phosphoric acid has high proton conductivity, which makes it useful as fuel cell electrolytes. Therefore, many experimental and theoretical studies have been carried out on the liquid phase [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] as well as on the monomer [21][22][23] ( Fig. 1), crystal, [24][25][26] and the polymeric gels [27][28][29][30] of phosphoric acid.…”

Section: Introductionmentioning

confidence: 99%

Ab InitioMolecular-Dynamics Simulation of Concentrated Phosphoric Acid

Tsuchida

2006

J. Phys. Soc. Jpn.

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We have investigated the properties of 100% phosphoric acid (H 3 PO 4 ) in the liquid state by the combination of gradient-corrected density-functional theory and norm-conserving pseudopotentials. Various structural properties as well as the vibrational density of states have been calculated through molecular-dynamics simulations under the Born-Oppenheimer approximation. Proton transfer is found to occur frequently between adjacent PO 4 groups along the OH···O hydrogen bonds, which makes the single and double bonds indistinguishable.

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Anomalies in the ion transport of phosphoric acid in water and heavy-water environments

Cited by 14 publications

References 20 publications

Water diffusion coefficients during copper electropolishing

Water diffusion coefficients during copper electropolishing

Effects of viscosity-dependent diffusion in the analysis of rotating disk electrode data

Ab InitioMolecular-Dynamics Simulation of Concentrated Phosphoric Acid

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