J. Phys. Chem. 1994,98, 3924-3926
3924
Diffusion Model of Solid-state Catalytic Hydrogen Isotope Exchange-Isotopomer Formation Kinetics and Reaction Mechanism Anton V. Filikov'J and John R. Jones Chemistry Department, University of Surrey, Guildford GU2 5XH, Surrey, UK
Nikolai F. Myasoedov Institute of Molecular Genetics, Russian Academy of Sciences, Kurchatov Sq., 123182 Moscow, Russia Received: September 23, 1993; In Final Form: March 2, 1994"
Using the diffusion model previously proposed for solid-state catalytic hydrogenation, it has been possible to show that for a hydrogen isotope exchange reaction resulting in the formation of two or more isotopomers the presence of spillover deuterium (or tritium) gradient in the organic phase induces qualitative alterations in the shape of the kinetic curves which can be used as a criterion of reaction mechanism. For gradient-controlled kinetics the shape of the time dependence plot of the isotopomer ratio QRDDIQRHD must be convex, whereas for uniform concentration distribution this function must be concave. An experimental study of the kinetics of isotopomer formation in the solid-state metal-catalyzed deuteration of glycine has been undertaken, and the results are consistent with gradient-controlled kinetics.
Introduction
.
For the preparation of deuterium- and tritium-labeled compounds, the recent development of solid-state catalytic reactions, such as hydrogenation and hydrogen isotope exchange, by Myasoedov and colleagues' offers new opportunities. The reactions arise as a result of hydrogen spillover,Le., the penetration of activated hydrogen from the metal catalyst surface into the compound phase. In the diffusion model proposed,24itis assumed that there is a concentration gradient of spillover hydrogen resulting from diffusion and from reactions with the organic compound, and it is this gradient that determines the reaction kinetics. For reaction systems which exhibit parallel isotope exchange and hydrogenation reactions the followingfeature holds, namely, that the ratio of hydrogenation products to isotope exchange products increasesseveralfold as the reaction ratedecreases rapidly from its initial, maximum, value. This finding is in sharp contrast to the situation where the spillover hydrogen gradient has little or no effect on the reaction kinetics and can therefore be used as a criterion of reaction mechanism. In the present paper, we carry out a kinetic analysis of a hydrogen isotope exchange reaction resulting in the formation of two or more isotopomers and show how the data can, once again, be employed to distinguish between possible reaction mechanisms. In addition, an experimental study of the kinetics of isotopomer formation in the solid-statemetal-catalyzeddeuteration of glycine has been undertaken, and the results are shown to be consistent with gradient-controlled kinetics. Experimental Section
The vessel was inserted in a thermostat at 145 O C for a given time. After cooling and opening, 0.5 mL of water is added to the mixture and the suspension centrifuged. The clear solution is decanted off and rotary evaporated to remove labile deuterium. Each sample was analyzed by 1H NMR and then derivatized and analyzed by GC/MS. Each sample gave one set of points on the kinetic plot. NMR. Proton NMR spectra of the preparation showed practically pureglycine (singlet at ca. 3.473ppm) at the beginning of the reaction and ca. 17% of unidentified byproducts by the end of the reaction (123 min). In the 1H NMR spectrum, partially deuterated glycine gives the line with an isotopic upfield shift of 0.015 f 0.005 ppm overlapping with that of fully protonated glycine. The quantity of glycine after reaction was measured by lH and 2H NMR. The relative standard deviation of measurements was 20%. CC/MS Analysis. Derivatization of the amino acids (to tertbutyldimethylsilyl derivatives of glycine) was carried out using a standard proced~re.~ GC/MS analysis was performed using a commercial instrument (Fisons GC 8035 and MD 800). The glycine derivative gave, in particular, four prominent lines at m l z 246, 247, 248, and 249 (1:0.1772:0.09689:0.01753). We counted that the derivativesof [H,D]glycineand of [D,D]glycine gave lines at m / z 247, 248, 249, 250 and 248, 249, 250, 251, respectively, with the same intensity ratios. The ratios of [H,H]glycine:[H,D]glycine:[D,D]glycineafter reactions were calculated via multipleregression analysis. The standard errors of the sample regression coefficients for [H,D]- and [D,D]glycinewere within the range 0.9-8.7%. Results and Discussion
Materials. Glycine and the 5% Pd/CaC03 catalyst were purchased commercially (Aldrich). The D2 gas (99.7%) was available from SIP Analytical Ltd. Procedure. Glycine (50 mg) was dissolved in 2 mL of water to which 50 mg of catalyst was added. The water was then removed by lyophilization. Typically 2 mg of the mixture was placed in a reaction vessel (10 cm3) and the whole assembly evacuated before passing D2 gas up to a pressure of ca. 300 Torr. 7 Present address: CIC and Department of Microbiology, University of Texas, Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, TX 752354576. Abstract published in Advance ACS Abstracts, April 1, 1994.
0022-3654/94/2098-3924%04.50/0
There are different opinions concerning the nature of spillover hydrogen species.6 Several researchers count these as neutral atoms>-12 others as positive ions.13-21 The nature of the species ought to be discussed in connection with the given system. If the spillover deuterium particle is an atom, the hydrogen isotope exchange reaction resulting in formation of two or more isotopomers can be depicted as7 RHH
+ -
+ D,,
RH'
RH'
D,,
0 1994 American Chemical Society
+ HD
RHD
(1') (1")
Letters
-
RHD + D,, RD'
+ D,,
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994 3925
RD'
-
+ HD
RDD
t 2')
Concentration, l/[RHH]
t 2")
where Dsqis the spillover deuterium atom (which could equally well be tritium). We count both hydrogen atoms to be equally reactive. All consideration can be easily spread for unequally reactive hydrogens, but this gives no qualitative changes. The reaction may give any number of isotopomers;i.e., the compound may have any number of reactive hydrogen atoms comprised in R-. Here we only monitor isotope exchange of two. Each reaction, (1) or (2), consists of two steps: the release of a hydrogen atom from the organic compound, (1') or (2'), and recombination of the radical with a D, atom, (1") or (2"), with the first step being rate determining in each case.' Because of this, the kinetic equations can be written down as follows: d[RHH]/dt = -kl [RHH] [D,,]
(3)
d[RHDl/dt = k1 [RHHI P,,I - k1 [RHDI [DSpl
(4)
d[RDD]/dt = k,[RHD][D,,]
t5 )
0
+ [RDD] + [ R H H ]
(6)
where kl is therateconstant for reactions (1') and (2') and [RHH], is the initial organic compound concentration. We consider the reaction as proceeding under isothermal conditions, because no exothermal or endothermal effects have been reported and, anyway, the reaction usually is carried out with less than 1 mg of the compound placed in an ampule immersed in an oil or water bath. For ions the reaction of isotope exchange can be depicted as direct substitution;21
-
+ +Dsp R H D + +Dsp
RHH
+ +Hsp RDD + +Hsp
RHD
(7) (8)
This reaction system is described by the same kinetic equations, (3)-(6), but in this case [Dsp]and [H,,] denote the concentration of +Dspand +Hsp,respectively, and kl is the rate constant for reactions (7) and (8). The equations can be solved using the following initial conditions: at t = 0 [RDD] = 0 and d[RDD]/dt = 0 to give [RHHI = [RHHI, exP(-k,[D,,lt) [RHDI = [RHHIo kl[D,,lt ex~(-kI[D,,lt) [RDD] = [RHH], {l - exp(-k,[D,,]t)
1 5
2
25
3t1me,at 3 5
1
05
1
15
2
25
3time,at35
4
Figure 1. (a) Kinetics of formation of the isotopomers RHD and RDD without spillover-deuteriumgradient; (b) kinetics of the [RDD]/ [RHD] ratio without spillover-deuterium gradient.
constants of reactions destroying spillover hydrogen, D is the diffusion coefficient, [RHH]o is the initial organic compound concentration, and x is the distance from the catalyst surface. Since we are dealing with isotope exchange, i.e., no change in molecular and crystal structure, D is constant. We can only allow for a reaction proceeding in a stationary gradient if the characteristic time for the stationary distribution to be achieved tdisrr is much less than the characteristic time of. the reaction product concentration change rpd, i.e., if3 tprod/tdistr= Do~5(k[RHH]o)l~5(kll)-1 >> 1
(10)
(13)
Spillover hydrogen particles can disappear not only in reactions resulting in the product of interest (kl) but also in reactions resulting in byproducts and, probably, in reactions with labile, Le., easily exchangeable hydrogens3 (NH, NH2, COOH, SH). Hence, k can be much greater than kl. At present it is not known if this condition holds for real systems. However, attempts3v4to describe experimental data using equations inferred under the conditions of (13) have been successful. Overall quantities of [RHD] and [RDD] (per unit area of catalyst) are given by equations (14) and (15), respectively: QRHD(t) = b [ l - ex~(-at)l
(9)
(14)
Q R D D ~=~ )
bJol [ 1 - e~p(-aty)]y-~dy - b [1 - exp(-at)] (1 5)
-
k,[D,,l t exP(-k, [D,,l t)I t 11) No DwGradient. In the event of no D,, gradient, both [RHDIt and [RDD],areconstant throughout thecompound phase. Hence, they are proportional to the overall quantities of these compounds in the reaction mixture and vary as shown in Figure la, [RHD] passing through a maximum while [RDD] exhibitsa characteristic S-shaped curve. The ratio [RDD]:[RHD] exhibits a curve of gradually increasing slope (Figure 1b) . D,p Gradient. In the presence of a D,, gradient the situation is different. For a semiinfinite organic compound layer adjacent to a flat catalyst, the diffusion model earlier proposed24 gives the following expression for the stationary distribution: [D,,l = g exp(-fx)
1
[RDD]/[RHD]
0
[RHH], = [RHD]
05
(12)
where g = Z(k[RHH]oD)-0.5,f= (k[RHH]o/D)0.5, Z is the flux of spilloverhydrogen into the organic phase, k is the summed rate
where b = [RHH],/fand a = klg. The integration variable y is the result of substitution of variables and is related to the initial variable x through equation (16): y =~X~[-X(~[RHH]~/D)]~.'
(16)
Equation (15) can be rewritten in a more convenient form for computer calculations:
In real systems, the compound layer has a finite depth. Because of this the semiinfinite layer approximation is only valid for the early stages of the reaction. In other words, equations (14) and (15) are applicable to the early stages of the reaction when the initial compound conversion is
