2938
J. Phys. Chem. 1986, 90, 2938-2944
and the resonance frequency occurs at w , = wp(eO + If in the sample the neighboring particles are very close, their polarization fields will affect the surface plasma absorption of each nearby particle, through the position and width; therefore, single silver particle properties may be obtained only if the polarization effects are separated. For uniform spatial distributions of particles, effective medium theories of the Bruggeman type and its varia n t may ~ be ~ applied. ~ ~ ~ ~ It remains that the state of experimental confirmation of small particle properties lags behind their theoretical i n ~ e s t i g a t i o n ; ~ ~
but although these theories may differ quantitatively in the magnitudes of the effects on the surface plasma absorption band, they unanimously predict red shifting and band broadening with increasing f. With this background we are in a position to appreciate the results of depositing silver atoms into thin liquid films in a microsolution metal vapor experiment, although a detailed interpretation of the data is obviously not straightforward. Registry No. Ag, 7440-22-4;Pd, 7440-05-3;squalene, 11 1-02-4; poly(butadiene), 9003-17-2;1,10-diaza-18-crown-6, 23978-55-4;2methyltetrahydrofuran, 96-47-9;poly(isoprene), 9003-31-0;carbon, 7440-44-0.
(35)Kreibig, U.;Althoff, A; Pressmann, H. Surf.Sci. 1981, 106, 308. (36)Andrews, M. P.; Ozin, G. A. U S . Patent No.4569924,February 11, 1986. (37)Klabunde, K. J.; Groshens, T.; Brezinski, M.; Kennelly, W. J . Am. Chem. SOC.1978, JOO, 4437.
(38) Bohren, C.F.; Huffman, D. R.Absorption and Scattering of Lighl By Small Particles; Wiley: New York, 1983. (39)Granqvist, C.G. J . Phys. 1981, C1,42, 247.
Metal Cluster Growth In the Llquld Phase: 1 Mark P. Andrewst and Geoffrey A. Ozin* Lash Miller Chemical Laboratories, Chemistry Department, University of Toronto, Toronto, Ontario, Canada M5S I AI (Received: January 30, 1985; In Final Form: October 21, 1985)
In this paper (part I), a diffusion (pseudo-) first-order reaction equation is solved analytically subject to a constant (metal vapor) flux boundary condition. This analysis provides a qualitative insight into differences regarding the propensity for metal cluster growth in quiescent liquid vs. turbulently mixed polymer films, that is, the microscale metal vapor analogue of the macrosynthetic experiment.
Introduction The reaction of transition-metal atoms with arene functionalized liquid polymers had led to new classes of organometal polymers and polymer-supported metal clusters.' Quantitative studies of the metal atom reactions in these media were made possible by the development of a static, thin quiescent liquid film microscale analogue of the macrosynthetic experiments. The microscale technique exploits the characterization tools commonly used for matrix isolation experiments.' The near room temperature spectroscopy (UV-visible, EPR, IR, Raman, fluorescence) of these systems showed that initial depositions of group IVB, VB, and VIB (groups 14-16)23 transition-metal atoms produced oligomer and polymer bound bis(arene)M cross-links, which with increasing amounts of metal served as nucleating centers for the growth of arene-metal clusters. Among the clusters, much of the experimental and theoretical focus has been on (arene),M2 molecules because these are the most thermally robust species. Details of the growth and decay behavior of these and higher metal cluster species is of great interest from the point of view to better understand the associated kinetics, to probe the role of the oligomeric or polymeric medium in stabilizing the clusters, and to supplement inferences about the nuclearity of the clusters. In the macroscale metal vapor rotary reactor synthesis of poly(si1oxane) anchored bis(arene)chromium the maximum concentration of bis(arene)chromium that can be produced in the polymer corresponds to 45% conversion of the appended phenyl ligands to complex,la whereas in the metal vapor microscale fluid matrix synthesis the maximum complexation corresponds to 25-30% of the phenyl groups.lb The reduction in the maximum complexation in the latter instance is most likely a reflection of simple mixing dynamics. In the former case the polymer is continuously mixed in the spinning glass reactor, a fresh surface of polymer being exposed to the flux of metal vapor. Maximum coordination is known to be associated with a dramatic increase 'Current address: AT&T Bell Labs, Murray Hill, NJ.
0022-3654/86/2090-2938%01.50/0
in the measured macroscopic viscosity of the polymer.la Presumably at this point of maximum coordination, intra- and intermolecular crw-linking severely reduce the frequency of reactive encounters among phenyl substituents and metal atoms since the diffusion of any two arene ligands together is strongly correlated to the segmental motions of the polymer, and these will be dependent on the density and distribution of cross-links. In the early stages of metal deposition the effect of turbulent mixing is seen as exposing unreacted and partially reacted polymer to the incident metal atoms. In other words, mixing suffices to maintain a sufficiently high local concentration of unreacted ligand in the vicinity of a diffusing metal atom and short circuits the competitive route to metal atom polymerization. On the other hand, metal atoms deposited into a quiescent liquid polymer film are more likely to quickly exhaust the surface and near subsurface supply of arene. The path length for diffusion of a single metal atom to a site favorable for association of two arenes and a metal atom must rapidly increase during the deposition period. Surface renewal with unreacted polymer bound ligand is not likely to be an efficient process since this requires the collective motion of large groups of atoms (translation of polymer segments containing pendant arenes), a process which is likely to be disfavored both by low temperature (220-250 K) and by the presence of the ramifying, cross-linked polymer network through which the supply of ligand and metal atoms must pass. Then either colloid formation becomes the dominant or competing reactive fate of a diffusing metal atom or the newly formed bis(arene)-transitionmetal complexes themselves become targets for reaction. In this (1) Francis, C.G.;Timms, P. L. J . Chem. SOC.,Chem. Commun. 1977, 466. J . Chem. SOC.,Dalton Trans. 1980, 1401. Francis, C. G.;Huber, H. X.;Ozin, G. A. US.Patent 4292253,Sept 1981. Inorg. Chem. 1980, 19, 219. J . Am. Chem. SOC.1979,10, 1250. Angew. Chem., Int. Ed. Engl. 1980, 19, 402. Francis, C.G.; Ozin, G.A. J . Mol. Struct. 1980, 59, 55. J . Macromol. Sci. Chem., A(J) 1981, 16, 167. Ozin, G. A,; Andrews, M. P. Angew. Chem. 1982,94,219.Angew. Chem. Suppl. 1982, 1255. Inorg. Synth. 1983, 22, 116. Ozin, G. A. Chemtech 1985, 488.
0 1986 American Chemical Society
Metal Cluster Growth view more arene will remain unreacted in the static film than would remain if the polymer were continuously agitated. The problem of diffusion-plus-chemical reaction is an interesting one in relation to metal vapor chemistry. Consideration of the problem within a simplified quantitative theoretical model can give some qualitative insights into the chemical and physical processes accompanying a metal vapor thin film microsolution experiment. This issue is examined in the present study, part 1. In part 2 of this study, simple series parallel competitive and quenched reaction kinetic schemes are devised to account for the observed cluster growth behavior and the potential for assigning metal cluster nuclearities is tendered. Overall the kinetic analyses are internally consistent in coping with each cluster nuclearity n. Part 3 examines the thermal agglomeration kinetics of these liquid-polymer-supported metal clusters which leads to a qualitative view of the role of the polymer in promoting the growth and stabilization of the metal clusters. Part 4 concludes this series with an investigation of liquid and solid phase agglomeration of silver atoms in olefinic and ether media, culminating in an electrocatalytic application of the compositions generated by the technique.
Metal Atom Diffusion with and without Simultaneous Reaction The problem of diffusion with simultaneous chemical reaction has concerned a number of researchers."-f It is well-known that a closed form solution to the nonlinear equations describing diffusion with second-order irreversible reaction cannot be obtained. Our approach here is modest, motivated as it is by general insights to be gained by examining the analytical solution to the simpler issue of diffusion associated with a first-order or pseudo-first-order irreversible chemical reaction. Of relevance are the kinetics of iodine doping of poly(acety1ene) studied by Louboutin and Beniere.3 These authors employed the asymptotic forms of the solution to Fick's second law modified to account for first-order chemical reaction, first expressed by Danckwerts.2c His solution, however, is not directly applicable to our problem by virtue of the different boundary conditions: the metal vapor experiment requires a constant flux boundary condition at the surface, x = 0, whereas Danckwerts solution emerges from a constant concentration condition at x = 0. To our knowledge Danckwerts' Fick's law diffusion equation modified for chemical reaction has not been given for the constant flux boundary condition. Accordingly we present equations describing the transient bulk diffusion-kinetic behavior of metal atoms deposited at a constant rate at the surface x = 0 of a semiinfinite, quiescent liquid (polymer) film, in which the atom undergoes pseudo-first-order irreversible chemical reaction and is removed from diffusion. Expressions are derived for the instantaneous growth of metal species immobilized at a time-independent concentration of sites in the bulk of the liquid film. The asymptotic behavior of the equations describing the concentration distribution of both diffusing and immobilized atoms is discussed. The derived expressions are contrasted with those obtained for diffusion without chemical reaction. ( a ) Assumptions. Figure 1 depicts the system to be solved. ( i ) Semiinfinite Medium. The diffusing metal atom never reaches the face x = m of the liquid film. This is shown to be an adequate assumption even for extremely thin films (on the order of microns in thickness) when the (pseudo-) first-order rate constant is sufficiently large. If k is small but D is also small, the approximation remains valid. (ii)No Desorption Flux. Any atom impinging on the surface x = 0 is irreversibly absorbed. (iii) Irreversible (Pseudo-) First-Order Chemical Reaction. The reactions of interest are those leading to the formation of bis(2) (a) Crank, J. The Marhematics of Diffusion, Clarendon: Oxford, 1975; 2nd ed,Chapter 14. (b) Akins, D. L.; Snider, A. D. J. Cornput. Chem. 1981, 2, 368. (c) Sen,P. K.J . Indian Chem. SOC.1973, 51, 1040. (d) Miller, S . L. J. A m . Chem. SOC.1952, 74, 4130. (e) Danckwerts, P. V. Trans. Faraday SOC.1951, 47, 1014. ( f ) Roberts, G. Metal Sci. 1979, 13, 94. (3) Louboutain, J. P.; Beniere, F. J . Phys. Chem. Solids 1982, 45, 233.
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2939
8
X=cO
-? C =
at
Initial Condition
- kc
ax. CEO,
Boundary Conditions
O'C
,
x=o,
x=-
,
t=o t>o
Figure 1. Initial and boundary conditions for solution of eq 1
(arene)-transition-metal compounds, ML,, and higher nuclearity metal clusters, M,L2, strongly or weakly stabilized in the liquid film. If the clusters are weakly stabilized, this is only so at temperatures above those at which the clusters are formed; otherwise, they are indefinitely stable on the time scale of the experiment. A diffusing metal atom reacts at a site S which is an intra- or interchain bis(arene)-metal complex. In the initial stages of a thin-film metal vapor experiment the free atom diffusivity will depend on time through the dependence of the distribution of bis(arene) cross-links on the duration of the metal deposition experiment; however, once saturation loading with respect to formation of the bis(arene)-metal complex has been achieved, we can assume that the diffusivity again becomes constant, since a fixed, time-independent number of cross-links then exists in the film. It is at this stage that the model will be assumed to apply to the polymer. In this view the problem is one of a diffusioncontrolled chemical reaction in a medium with (randomly distributed) static traps. It is also assumed that D characterizes the diffusion of the metal atom alone. If the component with which the metal atom reacts can also diffuse then the equations developed below must be modified to include material diffusion. An approach to this problem has already been outlined by Danckwerts2e for the constant surface concentration boundary condition. With these assumptions, the equation to be solved is
subject to the initial condition c(x,O) = 0 , t = 0 and the far-field boundary condition lim c(x,t) = 0, t
X-0,
>0
(2) (3)
Here c(x,t) represents the concentration of free (unbound) metal atoms at depth x at time t in the polymer film. S(x,t) represents the concentration of bound metal atoms at depth x at time t . For a supposed first-order reaction as/at = kc Fick's law becomesZe
(4)
2940
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
& = D - -a2c kc (5) at ax2 where it is understood that c and s are bivariate. To deduce the condition at the boundary x = 0, we note that the impingement flux R is balanced by a diffusional flux into the bulk of the film; from Fick's first law this diffusional flux is equal to -D(dc/ax),,,. The number balance illustrated in Figure 1 yields the boundary condition d[c(x=O,t)]/dt = R D(dc/ax),,o = 0, t > 0 (6) where R represents the rate (for example, g cm-L s-l) at which metal atoms are deposited at the surface of the film. Equation 5 is solved subject to conditions 2, 3, and 6 by the method of Laplace transforms, the transform solution being
+
Inversion of eq 7 by means of the convolution theorem4 yields c(x,t) =
-
TI/'
0
(9)
For specified R, D, and k eq 8 expresses how the concentration of diffusing metal atoms supplied at a constant rate at the surface x = 0 varies with penetration into the film and with the time elapsed since the deposition was initiated. The gradient of c at x = 0 is given by
(kt)1/2)
-&[
R c(x=O,t) = -erf (kt)li2 (Dk) I l 2 Provided (kt)]J2> 3, erf (kt)l/2
exp(-x(k/D)'/2) erfc
+ exp(x(k/D)1/2) erfc
(
(
-
1 and
2(;)1/2
+ (kt)1/2)]
=
- R / D (10) which is independent of time; but this result is just the boundary condition 6 as required. (b) Distribution of Immobilized Metal Atoms. An equation which accounts for the concentration distribution of metal atoms immobilized in the film can be derived by integrating ds/dt = kc
[(
)
R 2kt - 1 erf (kt)'I2 s(x=O,t) = - (Dk)'I2
+ 2( L)1'2e-kf] irk
This expression approximates to s(x=O,t) = Rl/2(2k;I) (Dk)
--
2(Dt)1/2
(14)
Thus for (kt)'12 sufficiently large, the surface concentration of metal atoms is independent of time, affected only by the magnitude of D and k for a given flux of metal atoms. (ii) Bound Atoms. Equation 11 evaluated at the surface x = 0 gives
2( Dt)
-s
=
for diffusion without chemical reaction. (d) Variation of Surface Concentration of Free and Bound Atoms. The surface concentration of metal species is of interest for the cases involving diffusion with and without chemical reaction. (e) Diffusion with Chemical Reaction. (i) Free Atoms. Evaluating eq 8 at x = 0 yields
c(x=O,t) = R/(Dk)lI2
where the complementary error function is 2 2 erfc (2) = 1 - erf (2) = 1 e-Y2 dy
$)x=o
(c) Diffusion without Chemical Reaction. Solving the unmodified Fick's second law diffusion equation with the boundary conditions 2, 3, and 6 givesS
exp(-x(k/D)'/2) erfc
(kt)1/2) - exp(x(k/D)1/2) erfc
(
Andrews and Ozin
(4)
on substituting eq 8 for c in eq 4. The result is s = S,'kc dt =
for kt > 9. For sufficiently large (kt)Il2 the surface concentration of immobilized metal atoms is seen to increase linearly with time for given R and Dk. U, Diffusion without Chemical Reaction. From expression 12 we obtain
where M , (notation of CrankZB)is the total amount of metal atoms deposited in time t at the film surface. This equation indicates that the surface concentration of free atoms does not increase linearly with time but is reduced due to diffusion into the bulk of the liquid. In the above cases the total amount of metal MI deposited at x = 0 must be Rt over the deposition time; that is we require MI"=('= R t
(18)
This is so because the rate of absorption dMl/dt per unit area of surface is exp(-x(k/D)1/2) erfc
d[c(x=O,t)]
X(~/D)I+ / ~1
('+
dt
dt
= -D(
g)
x=o
(19)
meaning that eq 18 is satisfied (noting eq 10) for diffusion with or without chemical reaction. The total amount of metal atoms absorbed, as given by eq 18, comprises contributions from free and immobilized metal atoms
2k
exp(x(k/D)1/2) erfc 2( '?rk )I"
dMX=O
=-
L ) ] (11)
exp( -kt - 4Dt
MI = M,C
+ MIs
(20)
for diffusion plus chemical reaction. In any subsurface region, (4) Arfken, G. Mathematical Methods for Physicists; Academic: New York, 1970, 2nd ed, p 709.
( 5 ) Bockris, J.; Reddy, A. K. N . Modern Electrochemistry, New York, 1973; Vol. 1 , Chapter 4.
Metal Cluster Growth
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2941
0 I1 < a, the total amount of free atoms is I
M,C = (1,t) =
c dx =
-"[
2k exp(-l(k/D)'/2) erfc exp(/(k/D)'/2) erfc
(
2(Dt)' /2
+ (kt)l/2)
Integrating over the entire film gives
M,C" = -R/k Similarly the total amount of bound atoms is
M:" =
x"
s(l,t) dx = R t
R +k
over the entire thickness of the film. When the metal vapor deposition is interrupted to observe the product distribution in a thin film UV-visible absorption microscale experiment, there is no evidence of free metal atoms.Ib Thus M, = Rt, always, under such conditions. The distribution of metal atoms among products of various nuclearities can be derived from mass balance relationships (see below). (g) Asymptotes. In the absence of chemical reaction, eq 12 for the concentration profile of freely diffusing atoms has the following asymptotic form: c(x,t) = 2R( L)I'z TD exp(
-")
4Dt
6'
(24)
When the concentration profile of diffusing atoms is modified by chemical reaction the time scale for approaching the asymptote becomes of interest. In eq 8, if t 1 9/k (Le., (kt)'/z 1 3), the argument of erfc in the first term is (x/6(D - k)'/*) - 3. As x 6(D/k)'l2, erfc ( z ) 2 and exp(-x(k/d)'l2) = giving the value of x for which eq 8 approaches of its asymptotic value. If the ratio k/D is large then the penetration depth x depends only on the asymptotic form of eq 8 viz.
-
-
R c(x) = -exp(-x(k/ D) (Dk)'lZ the value of x being quite small in this case (see below). Note that the asymptotic expression 25 gives c independent of time. In other words, for appropriately large k and D a steady state is rapidly established for free atoms by the combination of diffusion and reaction, so &/at = 0. For those combinations of rate constants and diffusion coefficients to be considered, eq 8 always assumes the asymptotic form represented by eq 25. Thus the 'nonsteady-state" concentration of free atoms in the film is independent of time. This condition can be contrasted with that exhibited by the bound atom profile whose asymptote is s(x,t) = (Dk)
X(k/D)'/2 - 1 2k
exp(-x(k / D)'/2)
Discussion To date no rate constants have been determined for the reaction of metal atoms with organic or inorganic substrates, yet it is generally assumed that such reactions must have low activation energies to compete effectively wtih metal atom polymerization? Wilburn and Skel17have conducted a series of experiments concerned with assessing the competitive rates of reactions of molybdenum atoms with arenes. Motivated by the hypothesis that low discrimination between a pair of different substrates would (6) Timms, P.L. Ado. Inorg. Chem. Radiochem. 1972, 14, 121
10'
Distance
xmf
10'
l.0
Figure 2. Concentration profiles for free metal atoms diffusing in a medium in which the atoms can undergo an irreversible first-order chemical reaction. Chemical reaction results in immobilization of the
diffusant at specific sites. Curves have been normalized to the surface concentration,Co,and the distance axis plotted logarithmically. Curves show the effect of varying k and D on the penetration depth. support the low activation energy assumption, these researchers found that Mo atoms react with arene mixtures according to
R = toluene, tert-butylbenzene, o-xylene, a,a,a-trifluorotoluene, N,N-dimethylaniline, fluorobenzene, methyl benzoate, and anisole, with a small variation in the relative rates. The range of reactivities for this set of ligands is only 3.7. If differences in the rates were attributed entirely to differences in activation energies, this factor of 3.7 would correspond to a AE,,, of 200 cal/mol.' Assuming an activation entropy of -10 cal deg-' mo1-I (ref 6), this would correspond to a rate constant of roughly lo9 SKIat 77 K. Were AE,,, one order of magnitude larger, rate constants for reaction would still be found to be very large, being on the order of lo4 s-', As pointed out in ref 6 raising the temperature of the cold surface reduces the differences in reaction rates due to small differences in the activation enthalpy. Increasing the temperature to 250 K (a typical temperature for a metal atom, thin film liquid polymer experiment) lbleads to rate constants corresponding to roughly 1O'O and lo8 s-' for AE,,, = 200 and 2000 cal mol-', respectively. Given the above diffusion equations, let us restrict our attention to those reactions coupled with diffusion having rate constants in the range k Iloo s-I. For quantitative comparisons concentration profiles given by eq 8, 11, 12, and 24-26 were calculated for values of k = 1-1000 s-I. In Figure 2 the curves for the free atom concentration profile were evaluated according to the full solution, eq 8; yet for any of the given values of k the curves are equally well expressed by using the asymptotic solution, eq 25. Thus the free atom concentration distribution in the film is independent of time and dependent only on the choice of k and D. (7) Wilburn, B. E.; Skell, P. S . J . Am. Chem. SOC.1982, 104, 6989.
2942
Andrews and Ozin
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 h n d Atom Concentration Proflie
kz1000
S-'
t=3600sec
1.0
t=
-7200
_.._ sec 1800 _.
600
0.e
SiP or QO
0.E
0.4
0.i
-4
lo
Distance X
(cm)
16
1.0
Figure 3. Bound atom concentration profiles. Curves have been normalized to the surface concentration So,and the distance axis plotted logarithmically. Curves show the time dependence of the penetration depth for a given diffusivity at fixed k .
Some important features of these curves to note are as follows: (a) For all combinations of k and D the concentration of free metal atoms is restricted to regions of space very near the surface of the film, there being little penetration beyond 104-10-2 cm (10-z-102 pm) where the concentration of species declines rapidly to zero. Thus the assumption (i) that the thin (10-200 pm) films employed in these experiments can be used to approximate a semiinfinite medium is justified. (b) The larger the value of k, the less the metal atoms penetrate into the film for a given value of D. (c) Conversely, the larger the value D the greater the penetration depth for a given value of k . The asymptotic expression 26 also holds for bound species for the given k and D, however, the concentration distribution manifests a weak time dependence and this is exemplified in Figure 3 for k = lo3 s-I and variable D. The bound atom profile shows a dependence on k and D similar to that established for the unbound atoms. Actually the diffusion front of the bound atoms lags that of the unbound species, this difference being shown clearly in Figure 4 for a 1-h deposition period. Also depicted in the figure are curves computed from eq 12 for diffusion without chemical reaction. The latter curves demonstrate that in the absence of chemical reaction the diffusant penetrates the film substantially (compared with the actual film thickness). Clearly, the effect of chemical reaction on diffusion is to restrict the concentrations of free and bound species to a near subsurface of the film in a metal vapor thin static film experiment. Using Van Krevelin's empirical equation: we estimate a diffusion coefficient for a free C r atom of cm2 s-I in liquid, phenyl-free poly(dimethylsiloxane) at room temperature. This value of D establishes an approximate upper limit for the diffusivity of a free metal atom in the (noninteracting) liquid polymers. The lower limit of lo-* cmz s-l reflects likely reductions in the diffusivity of a metal atom as the temperature of the polymer film is reduced ~
(8) Van Krevelen, D. W. Properties of Polymers; Elsevier: New York, 1972. The empirical formula is - E / 2 . 3 R ( l / T - 1/435) - 4.0, where E is the activation energy for viscous flow (= 15 kJ mol-' for poly(dimethylsi1oxane)) and R is the gas constant.
108
1.0
Figure 4. Comparison of concentration profiles for free and bound atoms for diffusion with or without chemical reaction, for fixed time and k and variable D.
or as the cross-link density of the medium is increased (see part 2). On the basis of the foregoing analysis some remarks can be made regarding the fact that the pendant phenyl groups in the liquid DC5 10 copolymer cannot be quantitatively converted to bis(arene)-metal complexes in a static, thin-film metal vapor experiment.' According to the computed concentration profiles it would seem that the metal atoms simply do not penetrate the film sufficiently to consume the available ligand. In spite of the simplicity of the model, the restrictions that chemical reaction are expected to impose on the extent of penetration of a diffusant as reactive as a metal atom make sense. Evidently if high conversion of uncomplexed arene to mononuclear bis(arene)M complexes is desirable, this would best be accomplished by means of turbulent mixing. Formation of metal sites containing two or more metal atoms is therefore expected to be favored in quiescent films where conversion of bis(arene)-mononuclear transitionmetal complexes will occur competitively with their production. Reasonably, it would seem that the static thin film experiment is biased toward the generation of higher nuclearity metal species (including colloid) since free atoms are not converted efficiently into mononuclear complexes by mixing, but must convert solely on the basis of diffusion; consequently, additional reaction pathways (metal cluster formation) can become competitive with bis(arene) complex formation as the path length for diffusion to uncomplexed arene increases. Qualitatively, our analysis rationalizes why it is much more difficult in a macroscale experiment to prepare DC510-supported metal multimers of the type referred to in ref 1; that is, considerably higher quantities of deposited metal are required to achieve significant metal cluster growth in a rotary reactor experiment. Obviously bis(arene)M complex formation requires that the phenyl substituents of the siloxane copolymer communicate rather effectively if the product is to be favored over colloid formation in a thin-film microscale experiment. The encounters between phenyl pairs can be probed directly via fluorescence emission spectroscopy. For many vinylaromatic homopolymers it has been demonstratedg-16 in most cases that excimer formation in dilute
Metal Cluster Growth
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 2943 a t high overlap among polymer coils which becomes important in fluorescence quenching of anthracene can be determined as a deviation of the experimental data from the Stern-Volmer equation integrated over a Gaussian distribution for the density of segments about the polymer center of mass.17 In bulk liquid DC5 10 interpenetration and overlapping of coils will have a profound effect on the frequency of encounters between two phenyl substituents, other factors such as temperature and number of cross-links due to the formation of bis(arene) complexes being constant. Since only monomer fluorescence is detected from dilute solutions of the copolymer at room temperature, inter- and intramolecular encounters of the aromatic groups are slow compared with the lifetime of the excited singlet state phenyl groups. A rough estimate of the time available for excimer formation, once a monomer has been excited, can lead to an understanding as to why the polymer is so effective in convertingfree metal atoms into 2:l complexes with the arenes. We require the lifetime of the excited singlet state phenyl substituent. This can be estimated from the absorption spectrum of a small molecule analogue such as tris(trimethylsi1oxy)phenylsilane (emax = 3.57 X lo2, Amax = 264 nm, pentane). The lifetime is calculated from the equationI8
Figure 5.
Fluorescence from DC5 10, a poly(phenylmethy1-co-dimethy1)siloxane: (A) neat polymer; (B) dilute solution of DC510 in pentane; (C) excitation spectrum of DC5 10. Spectra uncorrected for response of photomultiplier or monochromators.
solution is mainly due to intramolecular interaction between adjacent chromophores (dyads) on the same polymer chain. Intramolecular excimer formation is controlled both by the configuration and the conformation of the macromolecule.15 In vinylaromatic copolymers the amount of intramolecular excimer formation (i.e., the ratio of monomer to excimer emission) is clearly dependent on the copolymer composition in dilute.solution." For excimer formation to be considered governed by intrachain interactions between pendant arenes on the chain, the ratio of monomer to excimer fluorescence intensity must be independent of polymer concentration in the limit of very dilute solutions. Neat or concentrated solutions of DC510 in pentane or DC200 show mainly excimer emission (Figure 5) at room temperature. The fluorescence spectrum of a neat thin film of DC510, such as that used in the metal vapor microsynthetic experiments, resembles that of poly(styrene) or 74/26 styrene/methacrylate films" a t room temperature. It is typical of phenyl-containing copolymers that the monomer/excimer emission intensity ratio alters as the polymer is made increasingly dilute. This is true of DC5 10, which, in the limit of high dilution in pentane or DC200, shows only monomer emission at 285 nm (ethylbenzene, 282 nm; tris(trimethylsiloxy)phenylsilane, 285 nm), although the possibility exists of some excimer emission lying under the broad tail of the DC5lO monomer band. The predominance of monomer emission here is also consistent with the low mole percent (9%) of methylphenylsiloxy units in the polymer. In more concentrated solutions the preponderance of excimer emission must be due to phenyl group overlap arising from the interpenetration of neighboring polymer coils. A similar concentration dependence is observed in solutions of copolymers of styrenemethyl methacrylate"J5 and styrene-methacrylate,Il in films and in solution. Interpenetration of macromolecules is evidenced for spin-labeled poly(4-vinylpyridine) at concentrations as low as 3% w/v. The concentration (9) Vala, Jr., M. T.; Haebig, J.; Rice, S . A. J. Chem. Phys. 1965, 43, 886. (10) Fox, R. B.; Price, T. R.; Cozzens, R. F.; McDonald, J. R. J . Chem. Phys. 1972, 57, 534. (11) David, C.; Lempereur, M.; Geuskens, G. Eur. Polym. J . 1973, 9. 1974, 10, 1181. (12) Fox, R. B.; Price, T. R.; Cozzens, R. F.; Echols, W. H. Macromolecules 1974, 7, 937. (13) Alexandru, L.; Somersall, A. C. J. Polym. Sci. Chem. 1977,15,2013. (14) Reid, R. F.; Soutar, L. J . Polym. Sei. Phys. 1978, 16, 231. (15) McCallum, J. R.; Rudkin, A. L. Eur. Polym. J . 1981, 17, 953. (16) McCallum, J. R. Eur. Polym. J . 1981, 17, 797.
where T,O is the intrinsic monomer fluorescence lifetime, vo is the maximum in the absorption band (cm-'), f is the oscillator strength, and A P , , ~is the width of the absorption band at halfmaximum. In general, T,O > T~ where T~ is the observed radiative lifetime, which compared to T~~ is reduced due to nonradiative processes. With this expression the intrinsic fluorescence lifetime is estimated to be 146 X s. This value gives an approximate upper limit to the time required for a ground-state and excitedstate aromatic group to diffuse together to quench the fluorescence of the latter species. T~ is probably a factor of 5 smaller, comparing T,O and T , known for aromatic molecules.'* Since mainly excimer emission is observed when neat DC510 is excited at 254 nm under photostationary state conditions, the effect of chain overlap is manifest. Excimer formation requires that the phenyl partners satisfy very specific geometric constraint~,'~ namely, a coplanar ring arrangement involving an optimum center of gravity ring-to-ring distance of 3.0 to 3.2 A. Interestingly this is the same geometry adopted by the transition-metal-bis(arene) sandwich complexes." The fact that excimer formation is a rather facile process for DC510 indicates that a basic criterion for 2:l complex formation is satisfied. The phenyl groups can make encounters favorable for excimer formation and presumably (Ar),M formation, on a nanosecond time scale. This result is in keeping with the essentially quantitative conversion of transition-metal atoms deposited into this polymer below the saturation loading limit in both the microscale and macroscale metal vapor reactions.' The addition of one of more intermolecular chemical cross-links via bis(arene) complex formation must drastically quench the diffusive reptating motions of the DC510 chain. The situation is analogous to that of poly(viny1benzocrown ethers)21a,bwhich can form 2:l sandwich complexes with cations whose diameter exceeds that of the crown cavity. In these polymers, competition exists between the formation of inter- and intramolecular 2:l crown-cation complexes. Their relative importance depends on the crown content of the polymer and the total polymer concentration. Intermolecular complexation, Le., cross-linking, was found to be favored at high polymer concentrations, although the percent (17) Duportail, G.; Froelich, D.; Weill, G. Eur. Polym. J . 1971, 7, 977. Maldovan, L.; Weill, G. Eur. Polym. J . 1971, 7, 1023. (18) Turro, N. J. Modern Molecular Photochemistry; Benjamin Cummings: Menlo Park, CA 1978, p 89. (19) Klopfer, W. In Organic Molecular Photophysics, Vol. 1 , Birks, J. B., Ed.; Wiley: New York, 1973, Chapter 7. (20) Muetterties, E. L.; Bleeke, J. R.; Wucherer, E. J.; Albright, T. A. Chem. Rev. 1982,82, 499. (21) (a) Shar, S . C.; Kopolow, S . L.; Smid, J. Polymer 1980, 21, 188. (b) Sinta, R.; Lamb, B.; Smid, J. Macromolecules 1983, 16, 1382.
2944
J . Phys. Chem. 1986, 90, 2944-2949
crown content was low, 2% in some In all cases where 2:l complexes could form, the reduced viscosity of the solution showed a steeply increasing dependence on polym-er concentration. Cross-linking in DC5lO must eventually inhibit those cooperative motions necessary for the production of phenyl pairs. At some point in a microscale thin-film metal vapor reaction some phenyl substituents must become unavailable for chemical reaction because they are unable to diffuse to other phenyl groups in time to undergo reaction with a metal atom. In this case when cross-linking reduces the number of motional degrees of freedom available to a polymer or polymer segment, or erects a barrier to diffusion of a metal atom, there must always be a residue of unreacted ligand. The consumption of arene should eventually cease with time without exhausting the supply of arene ligand. This is just what is observed in fhin-film metal ua~opDC51O experi&ents.~ This is not to say that'a free metal itom cannot react with an aromatic group; the product Of such a reaction, solvated by the polymer backbone or otherwise, must
be singularly unstable toward further reaction, as recently found for ( V ~ - C ~ H ~ ) V . ~ ~ Acknowledgment. The generous financial assistance of the Natural Sciences and Engineering Research Council of Canada's Operating and Strategic Grants Programmes and the Connaught Foundation of the University of Toronto is gratefully appreciated. The award of a 3M Corporation Grant to G.A.O. is also acknowledged with gratitude. (22) Ozin, G. A.; Andrews, M. P.; Mattar, S.; McIntosh, D. F.; Huber, H. x. J . Am. Chem. s o t . 1983,105,6170; Andrews, M. p.; Mattar, S. M.; Ozin, G. A. J. Phys. Chem. 1986, 90, 744. (23) In this paper the periodic group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
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Kinetic Modeling of Hydrocarbon and Oxygenate Formation Roger C. Baetzold* and John R. Monnier Research Laboratories, Eastman Kodak Company, Rochester, New York 14650 (Received: October 21, 1985)
Kinetic modeling is used to describe quantitatively the hydrocarbon- and oxygenate-forming reactions from CO/H, over a model catalyst. In particular, the effects on product yield of reaction variables such as ease of CO dissociation or heats of adsorption of CO or H2are shown. A mechanism involving olefin formation and subsequent reaction is used to describe the unexpected low amounts of two-carbon hydrocarbons and three-carbon oxygenates observed in experiments with a model Ru catalyst. Several catalysts are described quantitatively by this mechanism. Smaller olefins are reincorporated into the chain growth sequence and can react with CO after they become enlarged by one carbon atom.
Introduction Considerable progress has been made in understanding the mechanism of linear oxygenate formation from syngas. One may consider hydrogenation, CO dissociation, chain growth, and C O insertion functions to occur on the catalyst surface. Experiments with a variety of conventional catalyst preparations' have provided support for the CO-insertion step as introducing the oxygen function into the oxygenate chain as the final chain enlargement step in which C is added to the hydrocarbon fragment. One aspect we have pursued involves kinetic modeling2 that attempts to make quantitative some of the ideas developed for various mechanisms. We summarize here some recent applications of the technique to syngas chemistry. Kinetic modeling is the mathematical expression of the rate of prodwt formation, given the reactant conditions. Obviously, this is a demanding exercise in which current theoretical methods must be applied beyond normal conservative limits. We cannot expect to project fine details from such an approach; rather we must look for the broad picture. Fortunately, the more general aspects of this approach can be used profitably in understanding and analyzing experimental results. A mechanism is taken as a starting point of this kinetic modeling. This is the CO-insertion model of oxygenate formation.' Given this mechanism, the fundamental energetics of chemisorption3 can be used to estimate rate constants. Experimental (1) (a) Pichler, H. Adu. Catal. 1952, 4, 271. (b) Pichler, H.; Schulz, H. Chem.-Ing.-Tech. 1970, 42, 1162. (c) Henrici-Olive, G.; Olive, S . Angew. Chem. 1976.88, 144. (d) Muetterties, E.L.; Stein, J. Chem. Reu. 1979, 79, 479. (e) Sachtler, W. M. H. Proceedings of the 8th International Congress on Catalysis, Berlin; Dechema: Frankfurt, 1984; Vol. 1, p 159. (fj Ichikawa, M.; Fukushima, T.; Shikaura, K.Proceedings of the 8th International Congress on Catnlysis, Berlin; Dechema: Frankfurt, 1984; Vol. 2, p 69. ( 2 ) Baetzold, R. C. J . Phys. Chem. 1984, 88, 5583. (3) (a) Shustorovich, E. Solid State Commun. 1982, 44, 567. (b) Shustorovich, E. J. Phys. Chem. 1984.88, 1927. (c) Baetzold, R. C . Solid State Commun. 1982, 44, 781. (d) Kerr, J. A. Chem. Rev. 1966, 66, 465.
0022-3654/86/2090-2944%0 1.5010
SCHEME I: Sequence of Reaction Steps," Methanation Reaction
.&CO(a) H2(g) & 2H(a) C+0 CO(a) co(g)
k(l,l)
k(2.l)
C+H-CH CH
" g = gas phase;
+H
43.1) k(3,2)
CH,
a = adsorbed; kH = k(5,l).
SCHEME II: Methanation Plus Chain Growth
chain growth
and theoretical information such as heats of adsorption of stable surface s p e ~ i e and s ~ gas-phase ~~ bond energies3dare incorporated into the model. With this overall expression of product formation we can examine the total system behavior rather than looking at separate parts in a piecemeal fashion. 0 1986 American Chemical Society
