Ind. Eng. Chem. Res. 1996, 35, 3907-3914
3907
Effects of Magnetic Field on Nickel-Catalyzed Oxidation of Hypophosphite Ion by Water/Deuterium Oxide Chia-Chien Lee and Tse-Chuan Chou* Department of Chemical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China 701
The effect of a magnetic field on the oxidation of hypophosphite ion catalyzed by electrolessly deposited nickel in aqueous deuterium oxide solution was studied. The steady rate of gas evolution was affected by both the magnetic field and the concentration of deuterium oxide. Such an effect was due to the magnetic spin rephasing of a radical pair of atomic hydrogen and atomic deuterium. The ratio of fractions of active sites occupied by atomic hydrogen and deuterium increased with magnetic flux density, but decreased with the mole percentage of deuterium oxide. The results indicated that the recombination rate of the radical pair of atomic hydrogen and atomic deuterium was affected by the magnetic field. A reaction mechanism of the oxidation of hypophosphite ion based on adsorption was proposed, and a steady rate equation was obtained experimentally. Based on the results of the steady rate, an empirical rate equation was obtained for the magnetic flux density B in the range 0.15-0.30 T, rs ) 6.20(0.965 × exp(5.62B)[H2O]/[D2O])/(1 + 0.965 exp(5.62B)[H2O]/[D2O]) + (2.92 exp(1.46B))/(1 + 0.965 × exp(5.62B)[H2O]/[D2O]). 1. Introduction In our previous studies (Lee and Chou, 1994, 1995), magnetic field effects on the reaction kinetics of electroless nickel deposition were reported. The results indicated that the reaction order with respect to hypophosphite ion was affected by the magnetic field significantly. Hypophosphite ion plays an important role in electroless nickel deposition; however, the catalytic oxidation of hypophosphite ion within a magnetic field is unclear. Nickel-catalyzed oxidation of hypophosphite ion within a magnetic field was studied in this work. Oxidation of hypophosphite ion catalyzed by metals has been studied widely (Sutyagina et al., 1963a,b; Holbrook and Twist, 1972; Marshall, 1983; Jusys et al., 1991a) because of its importance on the electroless deposition of metals (Jusys et al., 1991b). In spite of a metallic catalyst (Marshall, 1983), hypophosphite ion is also electrochemically oxidized by anodes (Trasatti and Alberti, 1966; Hickling and Johnson, 1967; Burke and Lee, 1992). Several reaction mechanisms, with an an emphasis on electrochemistry, have been reported (Lukes, 1964; Holbrook and Twist, 1972; Marshall, 1983; Jusys et al., 1991a,b). Heterogeneous hydrogenations of unsaturated hydrocarbons catalyzed by electroless nickel were studied by Ko and Chou (1993, 1994) and Ko et al. (1995). The results indicated that electroless nickel is a good heterogeneous catalyst. Accordingly, the oxidation of hypophosphite ion catalyzed by electroless nickel is interesting. Two forms of hypophosphite ions were proposed by some reports (Trasatti and Alberti, 1966; Larson, 1990). The active three-centered hypophosphite ion will adsorb on the surface of the catalyst and react with water to release atomic hydrogen and an electron. There are two main intermediates, atomic hydrogen and electron, involved in electroless nickel deposition (Jusys et al., 1991a,b). Atomic hydrogen is derived from either catalytic oxidation of hypophosphite ion (Jusys et al., 1991a,b) or electrochemical reduction of a proton by an electron (Lee and Chou, 1994, 1995). Accordingly, the * Author to whom correspondence should be addressed.
S0888-5885(96)00106-6 CCC: $12.00
mechanism of oxidation of hypophosphite ion includes both catalytic oxidation and anodic oxidation: in catalytic reactions, hypophosphite ions are oxidized catalytically, and in electrochemical reactions, electrons are released during the oxidation of hypophosphite ion. Adsorption plays an important role in both the catalytic and electrochemical reactions because oxidation of hypophosphite ion and evolution of hydrogen gas depend strongly on adsorption. The effects of magnetic field on free radical reactions have been well developed in organic reactions (Sagdeev et al., 1973, 1977a,b; Hayashi and Nagakura, 1978; Lersch and Michel-Beyerle, 1983; Khudyakov et al., 1993). Theoretical analyses and experimental results of magnetic field effects have been reported (Buchachenko and Zhidomirov, 1971; Atkins and Lambert, 1975; Atkins, 1976; McLauchlan, 1981, 1989; Carlin, 1987). Chemically induced nuclear dynamic polarization (Lawler, 1972; Ward, 1972; Steiner and Ulrich, 1989) and spin-orbit coupling (Turro, 1983; Dougherty, 1991; Khudyakov et al., 1993) were the theoretical bases of the magnetic field effect. The magnetic field affects the recombination of a radical pair of two odd-electron atoms or molecules. The geminate recombination of two free radicals (Werner et al., 1978; Levin et al., 1989; Lee and Chou, 1994, 1995) occurs only when spins of the two free radicals are opposite. The radical pair is singlet-phased or triplet-phased when the spins of two free radicals are opposite or parallel. The two free radicals in a triplet-phased radical pair will not recombine, but may diffuse out or be separated by solvent molecules. Spins of two free radicals can rephase from singlet-phased to triplet-phased or vice versa by a magnetic field (Atkins and Lambert, 1975; Atkins, 1976). Accordingly, reaction kinetics and related phenomena (Steiner and Ulrich, 1989) are affected by the magnetic field. Studies of magnetic field effects on electroless metal deposition have been developed recently. Chiba et al. (1989) and Osaka et al. (1992) reported the effects of a magnetic field on the material properties of electroless nickel and cobalt deposits. Takebayashi et al. (1993) reported that the structure and crystalline character© 1996 American Chemical Society
3908 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
istics of electroless nickel deposits were affected by the magnetic field. In spite of the properties of the electroless deposit, the reaction rate of electroless deposition was suppressed by the magnetic field (Tabulina, 1993). The effects of a magnetic field on the reaction kinetics of electroless nickel deposition were preliminarily reported in our previous studies (Lee and Chou, 1994, 1995). The catalytic oxidation of hypophosphite ion is one of the key factors of electroless nickel deposition. The catalytic oxidation of hypophosphite ion by water/ deuterium oxide in the presence of a magnetic field was studied in this work.
of D2 causes depletion of 2 mol of HD and production of 1 mol of H2 theoretically, as shown in eq 9.
2. Theoretical Analysis
where θP is the fraction of active sites of the first type occupied by atomic hydrogen derived from hypophosphite ion. θH and θD are the fractions of active sites of the second type occupied by atomic hydrogen and atomic deuterium derived from water and deuterium oxide, respectively. K1 and K2 are rate constants for the catalytic oxidations of hypophosphite ion by water and deuterium oxide, respectively. The adsorption rates of hypophosphite ion, water, and deuterium oxide are
2.1. Adsorption. Electroless nickel was a good heterogeneous catalyst for the hydrogenation reaction (Ko and Chou, 1993, 1994; Ko et al., 1995). Accordingly, oxidation of hypophosphite ion by water catalyzed by electroless nickel is considered to be a heterogeneous catalytic reaction of the Langmuir-Hinshelwood adsorption model. Both hypophosphite ion and water adsorb on the active sites of the catalyst and react to form phosphite ion and hydrogen gas, respectively. The atomic hydrogens are generated from the reduction of adsorbed protons by electrons. Hydrogen gas is generated by the combination of atomic hydrogens (Jusys et al., 1991a,b; Lee and Chou, 1994, 1995):
H2PO2
Ni
a
+ H2Oa 98 H a + H2PO3 + H + e -
•
+
-
2HD T H2 + D2
(9)
Accordingly, formation of D2 is considered to be involved in the formations of H2 and HD. The evolutions of H2 and HD are parallel reactions with respect to the catalytic oxidation of hypophosphite ion as shown in eqs 1-8. According to eqs 1 and 5, the gas evolution rate is
r ) K1θPθH + K2θPθD
(10)
rap ) kap[H2PO2-](1 - θP)
(11)
rah ) kah[H2O](1 - θH - θD)
(12)
rad ) kad[D2O](1 - θH - θD)
(13)
(1)
H +e fHa
(2)
where the superscripts “p”, “h”, and “d” indicate hypophosphite ion, water, and deuterium oxide, respectively. The desorption rates are
H•a + H•a f H2
(3)
rdp ) kdpθP
(14)
where subscript “a” indicates adsorbed species. The overall reaction for the oxidation of hypophosphite ion is
rdh ) kdhθH
(15)
rdd ) kddθD
(16)
+
H2PO2
-
•
Ni
a
+ H2Oa 98 H2PO3 + H2 -
(4)
If deuterium oxide is used instead of water, the hydrogens in eqs 1-4 are all or partially replaced with deuterium. The evolution gas is a mixture of H2, HD, and D2 (Holbrook and Twist, 1972). The oxidation of hypophosphite ion by deuterium oxide is Ni
H2PO2-a + D2Oa 98 H•a + HDPO3- + D+ + e-
At steady state, the rates of adsorption and desorption are equal and the fractions of active sites occupied by hypophosphite ions, water, and deuterium oxide are
θP )
(5)
θH )
H2, HD, and D2 are generated from reactions of two atomic hydrogens, one atomic hydrogen and one atomic deuterium, and two atomic deuteriums, respectively.
D +e fDa
(6)
H•a + D•a f HD
(7)
D•a + D•a f D2
(8)
+
-
•
As shown in eq 1, the two hydrogen atoms of H2 are derived from hypophosphite ion and water, respectively. The hydrogen atom and deuterium atom of HD are derived from hypophosphite ion and deuterium oxide, as shown in eq 7, respectively. The two deuterium atoms of D2 are derived from deuterium oxide, as shown in eq 8. Combining eqs 3, 7, and 8, formation of 1 mol
θD )
kap[H2PO2-]/kdp
(17)
1 + kap[H2PO2-]/kdp kah[H2O]/kdh
(18)
1 + kah[H2O]/kdH + kad[D2O]/kdd kad[D2O]/kdd
(19)
1 + kah[H2O]/kdh + kad[D2O]/kdd
Inserting eqs 17-19 into 10, the steady rate of gas evolution rs is
rs )
(
)
K1kah[H2O]/kdh + K2kad[D2O]/kdd 1 + kah[H2O]/kdh + kad[D2O]/kdd
(
×
kap[H2PO2-]/kdp
)
1 + kap[H2PO2-]/kdp
(20)
In the absence of deuterium oxide, the concentration of deuterium oxide is zero and the concentration change of water is negligible in aqueous solution. Accordingly,
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3909
the steady rate of gas evolution in the absence of deuterium oxide is simplified:
kap[H2PO2-]/kdp rs ) K1 1 + kap[H2PO2-]/kdp
(21)
The values of K1 and kap/kdp are obtained experimentally. 2.2. Magnetic Field Effect. A free radical which possesses an odd number of electrons is an active species, and the chemical bond is constructed by the combination of two radicals. The radical pair is a transition state between the free radicals and the chemical bond (Lawler, 1972; Levin et al., 1989). The chemical bond is constructed only when the electronic spins of two radicals are opposite. Two radicals with the same spin direction will not combine, but may diffuse out or be separated by solvent molecules (Atkins and Lambert, 1975; Atkins, 1976). The singlet-phased radical pair can form the product, and the triplet-phased radical pair will not do so until it rephases from tripletphased to singlet-phased. Spin rephasing is controlled by temperature in general chemical reactions, but the magnetic field provides another way to rephase the spin (Turro, 1983; Carlin, 1987; Levin et al., 1987). The effect of a magnetic field on the difference of rephasing frequency, ∆ω, of the two radicals in a radical pair (Steiner and Ulrich, 1989) is illustrated as eq 22,
∆ω ) (g1 - g2)µbB/h
(22)
where g1 and g2 are g values with respect to two free radicals in a radical pair, µb is Bohr magneton, h is Planck’s constant, and B is the magnetic flux density, respectively. On the basis of eq 22, a magnetic field will affect the difference of rephasing frequency only when the g values are different. For example, the magnetic field can affect the rephasing frequency of a radical pair of atomic hydrogen and atomic deuterium according to eq 22 because the g values of atomic hydrogen and atomic deuterium are different. However, only a singlet-phased radical pair can combine to form the product. Consequently, surface concentrations of singletphased and triplet-phased radical pairs are functions of the magnetic field. The reaction rate is related to the surface concentration of radical pairs based on the adsorption model. In brief, the magnetic field affects the recombination of atomic hydrogen and atomic deuterium in the oxidation of hypophosphite ion in aqueous deuterium oxide solution. 3. Experimental Section 3.1. Preparation of Catalyst. The nickel catalyst was prepared by electroless nickel deposition on γ-alumina powder. Sensitization and activation of raw γ-alumina powder were described in our previous work (Lee and Chou, 1994, 1995). The electroless nickel deposition solution was made of 0.1 M nickel sulfate, 0.1 M sodium hypophosphite, and 0.1 M sodium succinate. The deposition ratio of activated γ-alumina powder to solution was 50 g/L. The deposition temperature and period were 70 °C and 20 min, respectively. The prepared catalyst was stored in acetone at room temperature. The weight percentage of nickel, which was determined by the UV absorption method, was 7.4% with respect to the whole catalyst. The weight percent-
Figure 1. Typical plot of gas evolution versus time for the oxidation of hypophosphite ion in aqueous solution: [H2PO2-] ) 0.20 M, [Ni2+] ) 0.02 M, [C4H4O42-] ) 0.02 M, temperature ) 31 °C.
age of phosphorus, which was determined by the molybdenum gravimetric method, was 4.2% with respect to the electrolessly deposited nickel. 3.2. Apparatus and Preparation of Solution. The glassy reactor was water-jacketed to keep the desired temperature by a water thermostat. Agitation was provided by a Teflon-coated rod with six Teflon propellers which was driven by an electric motor. A solution for oxidation of the hypophosphite ion was made of 0.20 M sodium hypophosphite, 0.02 M nickel sulfate, and 0.02 M sodium succinate of extra pure grade and deionized water. The deuterium oxide solution was prepared from deuterium oxide (99.8 atom %) and deionized water. 3.3. Experimental Runs. A 50 mL volume of freshly prepared solution was placed in the reactor. One gram of electrolessly deposited nickel catalyst was added into the solution when the desired temperature was reached. The volume of evolved gas was measured by a gas burette, and the magnetic field was generated from an electric magnetic field. The magnetic flux density was controlled by the input current from a power supply. 4. Results and Discussion 4.1. Preliminary Work for Kinetic Control. The volume of evolved gas was calibrated to be the volume at STP according to the atmospheric pressure and room temperature. The stability of the catalyst was an important factor to the experimental reproducibility, which was poor if the solution contained only hypophosphite ion. The poor reproducibility was due to the instability of the catalytic surface. The acid etching method (Marshall, 1983) for the treatment of nickel wire was not suitable to the powder catalyst used in this work. An alternative method was used to provide reproducibility of the activity of the nickel catalyst. In spite of the hypophosphite ion, 0.02 M nickel ion and 0.02 M succinate ion were also introduced into the solution. A dynamic surface renewed nickel catalyst was produced when the nickel ion was electrolessly deposited on the surface of the catalyst. The gas evolution during the first 3 min of a run was somewhat unstable, as shown in Figure 1; however, a straight line was observed in the period from 4 to 8 min from the beginning of a run with good reproducibility.
3910 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 1. Rates of Reduction of Nickel Ion and Gas Evolutiona
[H2PO2-], M
RNi × 106, mol/min
RH2 × 106, mol/min
RNi RNi + RH2
0.10 0.15 0.20 0.25
61.3 65.2 62.7 61.2
276.8 276.8 276.8 276.8
0.181 0.191 0.185 0.181
a
[Ni2+] ) 0.02 M. [C4H4O42-] ) 0.02 M. Temperature ) 31
°C.
Figure 3. Effect of magnetic flux density on the steady rate of gas evolution: [H2PO2-] ) 0.20 M, [Ni2+] ) 0.02 M, [C4H4O42-] ) 0.02 M, temperature ) 31 °C, agitation ) 300 rpm.
Figure 2. Effect of agitation rate on the steady rate of gas evolution: [H2PO2-] ) 0.20 M, [Ni2+] ) 0.02 M, [C4H4O42-] ) 0.02 M, temperature ) 31 °C.
The results revealed that a steady gas evolution rate was obtained. The evolution of gas was reduced by the introduction of the nickel ion, but the effect of the concentration of hypophosphite ion was negligible, as shown in Table 1. The results indicated that the reduction of nickel ion would not affect the gas evolution significantly. The results were also confirmed by our previous reports (Lee and Chou, 1994) that the magnetic field effect on the reaction order with respect to the nickel ion was insignificant. In addition, the concentration of nickel ion was one-tenth that of hypophosphite ion. Consequently, the gas evolution rate was unaffected by the introduction of a low concentration of nickel ion, and the oxidation of hypophosphite ion was catalyzed by a dynamic surface renewed nickel catalyst. A steady rate of gas evolution was obtained according to the result of Figure 1, and such a steady rate was chosen for the evaluation of parameters. A mechanical agitation was applied to mix the solution and powder catalyst and to sweep away the accumulated gas bubbles on the surface of the nickel catalyst. Mechanical agitation was also used for increasing the mass transfer rate of the hypophosphite ion from the bulk solution to the surface of the catalyst. Figure 2 shows that the steady rate of gas evolution is affected insignificantly by the agitation rate in the range 200-350 rpm. The steady rate of gas evolution without agitation was slightly lower than that with agitation because a natural agitation was generated by the gas bubbles when they buoyed through the solution. The results of Figure 2 show that mass transfer resistances were ignored and the oxidation of hypophosphite ion was kinetically controlled by applying a suitable mechanical agitation. 4.2. Change of Rate and Spin Rephasing. The effects of magnetic flux density and mole percentage of deuterium oxide on the steady rate of gas evolution are
Figure 4. Effect of mole percentage of deuterium oxide on the steady rate of gas evolution: [H2PO2-] ) 0.20 M, [Ni2+] ) 0.02 M, [C4H4O42-] ) 0.02 M, temperature ) 31 °C, agitation ) 300 rpm.
shown in Figures 3 and 4, respectively. As shown in Figure 3, the steady rate of gas evolution increases from 4.80 to 5.63 mL at STP/min with the magnetic flux density increasing from 0.00 to 0.30 T at 59.8 mol % deuterium oxide. As shown in Figure 4, the steady rate of gas evolution decreases from 6.20 to 4.80 mL at STP/ min with deuterium oxide increasing from 0.0 to 59.8 mol % at a magnetic flux density of 0.00 T. The results of Figure 3 indicate that the surface concentration of the singlet-phased radical pair increases with the magnetic flux density. The steady rate of gas evolution or the surface concentration of the singlet phased radical pair depends not only on the magnetic flux density but also on the concentration of deuterium oxide. The steady rate of gas evolution is affected by the magnetic field more significantly at higher concentrations of deuterium oxide, as shown in Figure 3. The magnetic field will affect the steady rate of gas evolution because the surface concentration of the singlet-phased radical pair is changed by the magnetic field. Accordingly, the steady rate of gas evolution rs is a function of the difference of the rephasing frequency,
rs ) f(∆ω)
(23)
The difference of the rephasing frequency is proportional to the magnetic flux density based on eq 22. Thus, rs is
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3911
Figure 5. Plot of kf versus mole percentage of deuterium oxide.
Figure 6. Plot of rs - r0.15 versus B - 0.15.
a function of the magnetic flux density,
rs ) f(B)
(24)
If function f(B) is a linear function with respect to the magnetic flux density, the difference of the steady rate of gas evolution is proportional to the difference of the magnetic flux density as shown in eq 25. The steady
∆rs ∝ ∆B
(25)
rate of gas evolution at a magnetic flux density of 0.15 T is chosen as the base because the spin rephasing caused by spin-orbit coupling is effective when the magnetic flux density is low. Three straight lines are observed in Figure 5 for different concentrations of deuterium oxide by plotting the difference of the steady rate of gas evolution versus the difference of the magnetic flux density. The results indicate that the difference of the steady rate of gas evolution is proportional to the difference of the magnetic flux density as predicted in eq 25. Consequently, the steady rate of gas evolution is proportional to the difference of the rephasing frequency as shown in eq 26. The values of the
rs ∝ ∆ω
(26)
slopes of the straight lines in Figure 5 increase with the mole percentage of deuterium oxide. The results indicate that the magnetic spin rephasing is more significant when the mole percentage of deuterium oxide is higher. Equation 25 is rewritten to a linear function as shown in eq 27 according to the results of Figure 5,
∆rs ) kf∆B
(27)
where constants kf are the slopes of the straight lines in Figure 5. ∆rs is assumed to be proportional to the mole percentage of deuterium oxide,
kf ) kf0[D2O]
(28)
A plot of kf versus the mole percentage of deuterium oxide is shown in Figure 6, resulting in a straight line, which indicates that the steady rate depends both on the magnetic flux density and on the mole percentage
Figure 7. Effect of initial concentration of hypohosphite ion on the steady rate of gas evolution: [Ni2+] ) 0.02 M, [C4H4O42-] ) 0.02 M, temperature ) 31 °C, agitation ) 300 rpm.
of deuterium oxide, as shown in eq 29,
∆rs ) 0.0632[D2O]∆B
(29)
where [D2O] is the mole percentage of deuterium oxide. 4.3. Rate Constant. The effects of the magnetic flux density on the steady rate of gas evolution in pure aqueous solution under different initial concentrations of hypophosphite ion are shown in Figure 7. The steady rate of gas evolution in pure aqueous solution is not affected by either the magnetic field or the initial concentration of hypophosphite ion within the experimental error of (1%. The magnetic field effect is null because the radical pair consists of two identical atomic hydrogen radicals. Comparing the results of Figure 7 and eq 21, K1 is 6.20 mL at STP/min and kap[H2PO2-]/ kdp is much larger than unity. That is to say, kdp is much smaller than kap, and desorption reactions are the rate-determining steps. (kah[H2O]/kdh + kad[D2O]/kdd) in eq 20 is assumed to be much larger than unity because desorption reactions are rate-determining steps. Accordingly, the second term at the right-hand side of eq 20 vanishes, and the steady rate of gas evolution rs is simplified to
rs )
K1kah[H2O]/kdh + K2kad[D2O]/kdd kah[H2O]/kdh + kad[D2O]/kdd
(30)
3912 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 2. Coefficients of Polynomial Regression of Eq 32 B, T
a
b
c
R2
0.00 0.15 0.20 0.25 0.30
-0.000 206 -0.000 162 -0.000 169 -0.000 194 -0.000 169
-0.011 058 -0.009 403 -0.005 638 -0.001 306 0.000 827
6.197 5 6.200 1 6.194 5 6.195 6 6.192 5
1.000 1.000 0.999 0.999 0.994
Table 3. Effects of Magnetic Flux Density on Values of K2, kahkdd/kadkdh, and θH/θDa kahkdd
θH/θD
B, T
K2
kadkdh
19.8b
39.8b
59.8b
0.00 0.15 0.20 0.25 0.30
3.04 3.64 3.94 4.12 4.58
2.345 2.366 2.609 4.340 5.096
9.569 9.655 10.647 17.711 20.796
3.589 3.621 3.993 6.642 7.798
1.595 1.609 1.744 2.952 3.466
a [H PO -] ) 0.20 M. [Ni2+] ) 0.02 M. [C H O 2-] ) 0.02 M. 2 2 4 4 4 Temperature ) 31 °C. b [D2O], mol %.
Equation 30 can be rearranged as
(
)
kahkdd[H2O] 1 1 1 ) + rs - K1 K2 - K1 K2 - K1 k dk h[D O] a d 2
(31)
where K1 is 6.20 mL at STP/min according to the results of Figure 7. K2 is the steady rate constant of gas evolution when water is fully replaced with deuterium oxide. Unfortunately, K2 cannot be obtained experimentally because deuterium oxide is highly hygroscopic. However, K2 can be estimated from the results of Figure 4 by the second-order polynomial regression as shown in eq 32
rs ) a[D2O]2 + b[D2O] + c
(32)
where [D2O] is the mole percentage of deuterium oxide. The results of the coefficients of the polynomial regression of eq 32 are listed in Table 2. The values of K2 at different magnetic flux densities are obtained by extending the solid lines of Figure 4 to the intercept at 100 mol % deuterium oxide, according to the results of Table 2. For example, K2 in the absence of a magnetic field is 3.04 mL at STP/min based on the above method, which is shown as the dashed line in Figure 4. Similarly, the K2 values at other magnetic flux densities are obtained according to the results of Figure 4. The results of K2 are listed in Table 3. Based on eq 31, the plot of 1/(rs - K1) versus [H2O]/[D2O] is a straight line with an intercept of 1/(K2 - K1) and a slope of (1/(K2 K1))(kahkdd/kadkdh). The analytical results and effects of the magnetic field are shown in Figure 8. Constants kahkdd/kadkdh at different magnetic flux densities are obtained according to the slopes of straight lines in Figure 8 and K2 in Table 3. In another aspect, the ratio of the fractions of active sites occupied by atomic hydrogen and deuterium is obtained according to eqs 18 and 19,
( )
θH kahkdd [H2O] ) θD k dk h [D2O] a d
(33)
The results of θH/θD at different magnetic flux densities and mole percentages of deuterium oxide are listed in Table 3. As shown in Table 3, θH/θD increases from 9.569 to 20.796 with the magnetic flux density increasing from 0.00 to 0.30 T at 19.8 mol % deuterium oxide.
Figure 8. Plot of 1/(rs - K1) versus [H2O]/[D2O].
On the other hand, θH/θD decreases from 20.796 to 3.466 with deuterium oxide increasing from 19.8 to 59.8 mol % at a magnetic flux density of 0.30 T. θH/θD decreases with mole percentage of deuterium oxide because of a higher concentration of deuterium oxide. The results of the magnetic field effect on θH/θD indicate that the adsorption of deuterium oxide is suppressed by the magnetic field. Such suppression is more significant at a lower mole percentage of deuterium oxide. Both the θH and θD depend on the recombination rate of the radical pair, and such a recombination rate depends strongly on the spin rephasing of radical pairs. The change of θD or θH indicates that the recombination rate of the radical pair of atomic hydrogen and atomic deuterium was affected by the magnetic field. The rate constants K2 and kahkdd/kadkdh in Table 3 are assumed to be exponential functions of the magnetic flux density. Rate constants K2 and kahkdd/kadkdh at 0.00 T are neglected because of the effect of spin-orbit coupling as mentioned in the previous section. Accordingly, an empirical rate equation based on the theoretical prediction of eq 30 is obtained, as shown in eq 34, by combining the experimental results of Figure 7 and Table 3:
[H2O]
0.965 exp(5.62B) rs ) 6.20
[D2O] [H2O]
1 + 0.965 exp(5.62B) 2.92 exp(1.46B)
+
[D2O] 1
1 + 0.965 exp(5.62B)
[H2O]
(34)
[D2O]
where B is the magnetic flux density in units of tesla. The available magnetic flux density for the empirical rate equation is 0.15-0.30 T. 5. Conclusions The reproducibility of the activity of the catalyst was successfully improved by introducing nickel ions into the solution to create a dynamic surface renewed catalytic surface. A mechanical agitation was used for the complete mixing of the powder catalyst and the solution and placed the reaction under kinetic control. A reaction mechanism based on adsorption was proposed, and a steady rate equation for oxidation of hypophosphite ion was obtained theoretically. In the presence of
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 3913
deuterium oxide, the steady rate of gase evolution was affected both by the magnetic field and by the concentration of deuterium oxide in aqueous solution. The steady rate of gas evolution increased with magnetic flux density but decreased with concentration of deuterium oxide. The experimental results of the steady rate of gas evolution correlated well with the theoretical analyses. The ratio of fractions of active sites occupied by atomic hydrogen and deuterium is affected both by the magnetic field and by the mole percentage of deuterium oxide. The results indicate that the competition of adsorption of water and deuterium oxide is affected by the magnetic spin rephasing. Based on the theoretical and experimental results, an empirical rate equation is obtained to interpret the magnetic field effect on the oxidation of hypophosphite ion by water/ deuterium oxide in the range 0.15-0.30 T. Acknowledgment The authors gratefully acknowledge the financial support provided by the National Science Council through Grant NSC 83-0416-E-006-016 and National Cheng Kung University. Nomenclature B ) magnetic flux density, T g ) g values of free radicals h ) Planck constant, J s K, k ) rate constants r ) gas evolution rate, mL at STP min-1 Superscripts d ) deuterium oxide h ) water p ) hypophosphite ion Subscripts a ) adsorption state D ) deuterium oxide d ) desorption state H ) water P ) hypophosphite ion s ) steady state Greek Letters ω ) rephasing frequency, rad s-1 θ ) fraction of active site µb ) Bohr magneton, A m2
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Received for review February 15, 1996 Revised manuscript received June 12, 1996 Accepted July 17, 1996X IE960106W
X Abstract published in Advance ACS Abstracts, September 15, 1996.
