Pt-SPE의 제조에 관한 수학적 모델링

강 문식, 김 지윤, 한 학수, 설 용건, 조 영일

연세대학교 공과대학 화학공학과

Mathematical Modelling on Pt-SPE Preparation

Mun-Sik Kang,Ji-Yun Kim,Hak-Soo Han,Yong-Gun Shul,Yung-il Joe

Department of Chemical Engineering, Yonsei University

Introduction

Recently, the water electrolysis employing solid polymer electrolyte has been widly investigated for hydrogen production.  It has been well known that the process of electrocatalyst remarkably affect on the performance of water electrolysis.  The process, refered to as counter current diffusion, is accomplished by diffusing a metal ion into one surface of the film while simultaneously diffusing a reducing agent into the opposite surface of the film. There is no the abrasion of the electrocatalyst in water for this process.  In addition, the reaction of preparation of electrocatalyst could be controlled in this system.

In this study, we investigated the diffusion of PtCl62- and BH4- in the Nafion membrane film.  The mathematical model has been utilized to estimate the diffusivity of Pt ion and concentration within the membrane.

Experimental details

2-1. Materials

① Nafion 117 Perfluorosulfonic membranes(Dupont de Nemours)

② Deionized water (resistivity of 1 M□ at 25 ℃)

③ Hexachloroplatinic acid(H2PtCl6) and sodium borohydride(NaBH4)

2-2. Measurements of diffusion coefficients in the membrane

A schematic diagram to measurement the diffusion coefficient of H2PtCl6 and NaBH4 within the membrane by counter current diffusion was shown Fig. 1.  If the compartments are large volume, so that the concentration changes near the boundaries are negligible during the time of observation.  The area of the membrane exposed to the solution is 5.06 cm2.  The solution of each compartments for the experimental was stirred to remove concentration polarization.  The temperature of system was maintained at 25 ℃.

2-3. Sample characterization

The concentration of the PtCl62- transferred through the Nafion membrane was measured from the standard curve, that was obtained maximal absorbance at 260 nm by spectrophotometer(SHIMADJU 160).  Also, used instrument for the measurement of concentration of BH4- was  inductively coupled plasma-MS.

5

3

4                 1

2            2

1.membrane  2.impeller  3.sampling port  4.solution input  5.solution output

Fig. 1.  The cell used for membrane ionic flux measurement.

Diffusion-reaction model

The dynamics affecting the counter current diffusion process are illustrated schematically in Figure 2.  The parameters are defined as follows: In the counter current diffusion a free standing polymer in a membrane separating solution of a reducing agent, [eqn: { R}^{- }], at one surface (x = 0) and solution of metal ions, [eqn: { M}^{+ }], at the opposite surface(x = L).  The two components diffuse into the membrane and simultaneously react with each other to form reduced Pt in the membrane.

The parameters are defined as follows:[eqn: { D}_{m }] and [eqn: { D}_{r }] are diffusion coefficients for transport of metal ions, reducing agent in the solvent swollen polymer respectively.  [eqn: { K}_{m }] and[eqn: { K}_{r }] are equilibrium sorption coefficients which govern partitioning of the metal ions and reducing agent, respectively, between the solutions (concentrations[eqn: { [M^+ ]}_{S }] and[eqn: {[R^- ] }_{S }] ) and the film (concentrations [eqn: {[M^+ ] }_{L }] and[eqn: {[R^- ] }_{0 }]).  The reduction of metal is assumed to be governed by a second-order rate law with rate constant [eqn: { k}^{' }] for reduction by [eqn: { R}^{- }].   Assuming diffusion to be the sole transport mechanism, the time-dependent concentration profiles are governed by simultaneous equations for the reaction rate law and Fick's second law written here for the counter current diffusion[1,2].

[eqn: { PARTIAL [M^+ ]} over{ PARTIAL t} = {D }_{m } TRIANGLED^2 [M^+ ]-k＋[M^+ ][R^- ]]            (1)

[eqn: {partial[R^- ]} over {partialt} = {D }_{r } TRIANGLED^2 [R^- ]-k＋[M^+ ][R^- ]]	(2)

If we assume uniform concentration of reactants, eq(1) and (2) simplify to[eqn: { { d}^{2 } } / { { dx}^{2 } }].

Solution            Membrane                    Solution

[eqn: { K}_{r }]     [eqn: { D}_{r }]              [eqn: { D}_{m }]        [eqn: { K}_{m }]

[eqn: [R ]]      [eqn: { [R]}_{0 }]  [eqn: { [R ]}_{l }+ { [M^+ ]}_{l }]   [eqn: {[M^+ ] }_{L }]    [eqn: { [M^+ ]}_{S }]

[eqn: k＋]

[eqn: { M}^{0 }]

x = 0             x = l               x = L

Fig. 2.  Outline of the dynamics involved in the counter current

diffusion experiment.

[eqn: {partial[M^+ ]} over {partial t} = {D}_{m }d^2 over dx^2 [M^+ ]-k＋[M^ + ][R^ - ]]	(3)

[eqn: {partial[R^- ]} over {partial t} = {D }_{r } d^2 over dx^2 [R^- ]-k＋[M^ + ][R^ - ]]	(4)

[eqn: {[M^+ ] }_{L }] and [eqn: {[R^- ] }_{0 }]  are assumed to be in equilibrium with the solutions with concentrations [eqn: {[M^+ ] }_{S }] and[eqn: {[R^- ] }_{S }], respectively.  The relevant boundary conditions are summarized as follows:

for tＢ0

[eqn: {[M^+ ] }_{L } = { K}_{m } {[M^+ ] }_{S }]	(5)

[eqn: {[R^- ] }_{0 } = { K}_{r } {[R^- ] }_{S }]	(6)

for t=0

[eqn: {[M^+ ] }_{x } = 0 ~~~~~for~~ 0＠x＠L]	(7)

[eqn: {[R^ - ] }_{x } = 0 ~~~~~for~~ 0＠x＠L]	(8)

Results and Discussion

1. Diffusion coefficients of PtCl62-

The diffusion coefficients of PtCl62- for the modelling of Pt-SPE composites by counter current diffusion were measured as followed.

The partition coefficients of diffused PtCl62- was estimated from the standard curve by measuring the absorptivity using the spectrophotometer at 260 nm.

The moles of transferred PtCl62- as a function of time with Pt aqueous solution concentration are shown in Fig. 3.  The solution for steady state flux under linear diffusion becomes [eqn: J~=~ { DK { C}_{0 } } / {d }].  The linear portion represents steady-state conditions, and the slope of line is the steady-state flux, J.  Figure 4 is shown the flux change of  PtCl62- in the membrane as a function of Pt concentration.  We found that transferred flux of Pt was proportioned to initial concentration of Pt aqueous solution.

2. Diffusion coefficients of BH4-

It had been reported by Aramata et al that BH4- is governing factor of reaction when Pt-SPE composite was prepared irreversible chemical reaction of NaBH4 and H2PtCl6.

Fig. 5 is shown a plot of concentration of BH4- transported per unit area of membrane vs. time.  As the reducing agent concentration is increased, concentration of BH4- transported per unit area of membrane is increased.  lt is indicated that the higher reducing agent concentration, flux of transported BH4- increased.

Fig. 6 is shown the value of transferred flux divided by time, refered to as a slope of the graph.  The flux of BH4- increases linearly increasing the concentration of reducing agent.  Those are approximately of the order of 10-7 mol/cm2·s.  It should be noteworthy that the flux of BH4- is greatly larger than that of PtCl62-.

Fig. 3.  The moles of transferred PtCl62-   Fig. 4.  The fluxes of transferred PtCl62-

as a function of time.                      to H2PtCl6 concentration.

Fig. 5.  The moles of transferred BH4-    Fig. 6.  The fluxes of transferred BH4-

as a function of time.                      to reducing agent concentration.

References

1. Dee, Gregory T., Manring, Lewis E., and Mazur, Stephen:J.Physical

Chemistry, 91, 27 (1987)

2. Kang, M.S., Ph.D. Thesis, Yonsei University, Seoul, Korea(1997)