116
J. Phys. Chem. 1981, 85,116-119
Evaporative Hopping as a Mechanism for Surface Mobility in the Autoxidation of Adsorbed Fatty Acids Arthur W. Adamson* and Vlda Slawson Department of Chemistry. University of Southern California, Los Angeles, California 90007 (Recelved: September 3, 1980)
A study is reported on the rate of transport of ‘‘C-labeled palmitic acid between silica gel coated chromatographic plates. The labeled acid was deposited on one plate, in an amount typically correspondingto half-monolayer coverage, and the rate of transfer to an adjacent plate determined. The rate obeys a square root of time law, corresponding to bulk diffusion out of individual silica gel particles as the rate-limiting step. The temperature dependence corresponds to that for vaporization of palmitic acid. It is concluded that vapor-phase hopping between particles and within particle pores is fast enough to permit significantmolecular mobility. In particular, this mechanism appears to be able to account for the bimolecular reactions that have been invoked in explanation of the chemiluminescent autoxidations of unsaturated fatty acids adsorbed on silica gel. Introduction A difficult and often discussed question is whether a substance adsorbed on a solid surface is mobile and, if so, by what mechanism. A complication is that the term “mobility” has been used in more than one sense. One criterion has been a thermodynamic one, applied in the form of asking whether the adsorption isotherm fits a model which assumes two-dimensional translation. Alternatively, the experimental adsorption entropy may be separated into internal and translational components, and, if the latter is sufficiently large, mobility is inferred. Such criteria may be ambiguous in actual practice, to the point of uselessness.’ This is especially true if even minor surface heterogeneity is present. The thermodynamic criteria, moreover, are inconsistent with the concept of mobility as used in three-dimensional systems. Here, mobility is a rheological or a kinetic quantity. A fluid is mobile; a solid is not. Kinetic mobility implies that diffusional encounters between molecules are fast enough to permit a bimolecular processes to be important on the time scale studied. Surface mobility in a film adsorbed at a liquid interface can be established through surface viscosity measurements and in the case of liquid or gaseous monolayers kinetic mobility is generally assumed as a matter of c0urse.l The problem becomes more difficult if the interface is solid (and therefore itself not usually at thermodynamic equilibrium). Dielectric and nuclear resonance relaxation times have been informative as to mobility on a relatively short time scale; thus submonolayer adsorbed water typically appears to be immobile, and multilayer water, to be mobilea2v3 In special cases, surface diffusion rates can be obtained, such as by using deposited films of 14C-labeled fatty acid,4 or in field emission and field ion emission studies.K The question of kinetic surface mobility is of some importance in heterogeneous catalysis since many mechanisms appear to require bimolecular surface reactions. Experimental rate laws do not distinguish, however, between a Rideal-type process, whereby a species that is in (1) A. W. Adamson, “The Physical Chemistry of Surfaces”, 3rd ed, Wiley-Interscience, New York, 1976. (2) J. R. Zimmerman and J. A. Lasater, J. Phys. Chem., 62, 1157 (1958). (3) E. McCafferty and A. C. Zettlemoyer, Discuss. Faraday SOC.,239 (1971). (4) See D. E. Beischer, J. Phys. Chem., 57, 134 (1953). (5) G . Ehrlich and F. G. Hudda, J. Chem. Phys., 35, 1421 (1961);E. W. Muller and T. T. Tsong, “Field Ion Microscopy”,American Elsevier, New York, 1969. 0022-365418112085-0116$01.OO/O
the vapor phase makes a reactive collision with a surface adsorbed one, and a Langmuir-Hinshelwood type mechanism. In this last case, both species are regarded as surface adsorbed and possessing sufficient two-dimensional mobility to permit reactive surface encounters. Even the conceptual distinction between the two kinds of process can be cloudy. In the case of a solid surface, two-dimensional mobility likely is activated in that some vibrational excitation or weakening of the adsorption bond is required for site-to-site movement. Further excitation, to the point of breaking the adsorption bond, would again allow surface movement through evaporation and readsorption. At this point the distinction becomes one of how closely the activation energy approaches that of desorption and whether single hopping between nonadjacent sites is important. Our own interest in the question of surface mobility arises from studies on the autoxidation of unsaturated fatty acids adsorbed on silica gel. The adsorption isotherms are of the Langmuir type, which suggests localized adsorption, but, as noted earlier above, isotherm fitting is not diagnostic of molecular mobility in reaction kinetics. Kinetically, such adsorbed films do appear to be mobile. Autoxidation rates can be comparable to those in neat liquid or solution phase and singlet oxygen inhibitors are effective, an observation implying bimolecular reactivity.6 Further, the nature of the chemiluminescence accompanying such autoxidations strongly implied the occurrence of surface bimolecular reactions.’ Part of the emission was assigned to excited-state carbonyl-containing molecules, the formation of which likely is through radicalradical reactions. A component around 630 nm, corresponding to singlet oxygen emission, again requires a bimolecular reaction. Thus surface mobility, in some kinetic sense of the word, seems to be required. There have been some studies of the diffusional mobility of adsorbed saturated fatty acids. Fatty acids adsorbed on mica or on various metal plates have been observed to transfer to a second plate pressed against the first.8 One explanation is that of true surface mobility, adsorbed molecules migrating by site-to-sitemotion to the occasional points of actual plate-to-plate contact and transferring via such bridges. The alternative is that of direct vapor transport, as suggested by Young.g Stearic acid films (6) G. Wu, R. A. Stein, and J. F. Mead, Lipids, 14, 644 (19791,and preceding papers. (7) V. Slawson and A. W. Adamson, Lipids, 11, 472 (1976); A. W. Adamson and V. Slawson, Colloid Interface Sci., 6, 193 (1976). (8)E. Rideal and 3. Tadayon, Proc. R. SOC. London, Ser. A, 226,346, 357 (1954).
0 1981 American Chemlcal Society
Mechanism of Surface Mobility
The Journal of Physical Chernistty, Vol. 85,No. 1, 198 1
117
TABLE I: Transport of Labeled Palmitic Acid between Spaced Silica Gel Chromatographic Platesa teomp,
C 100
spacing, mm 0.2
time, h 0
1.0 1.83 5.0 24.0
100
noneb
o
1.0 Figure 1.
Physical arrangement for the vapor transport studies.
deposited on quartz, mica, and glass are, for example, appreciably volatile.1° The present, essentially qualitative study was undertaken to see whether, in the case of fatty acids adsorbed on silica gel, an experimental indication could be obtained as to the viability of vapor-phase hopping as a mechanism for “surface” bimolecular reactions. Silica gel is notoriously heterogeneous,ll and, amorphous, should not present the smooth, lattice plane type surfaces possible with a crystalline adsorbent. Low activation energy, site-to-site hopping thus seemed unlikely, a priori, but would have to be considered seriously if vapor-phase transport could be ruled out. Palmitic rather than an unsaturated fatty acid was chosen to avoid complication by autoxidation products.
Experimental Section Method and Procedures. The basic observation was one of transfer of 14C-labeledpalmitic acid from one silica gel coated chromatographic plate to a second one positioned a small distance away by means of a spacer. The schematic arrangement is shown in Figure 1. The plates were 2.5 X 9.0 mm thin-layer chromatographic slides, with a 250-pm thick coating of silica gel G. This type was chosen because it has calcium sulfate rather than organic materials as a binder. Calcium sulfate has little effect on the autoxidation of fatty acids and appears to have negligible adsorption capacity for them.l2,l3 Its presence should only be that of an inert diluent to the adsorption layer. The total material in the coating was 9.6 mg cm-2. The procedure was as follows. A chloroform solution of the labeled palmitic acid was prepared with a concentration such that a 3-pL drop, free falling from a syringe tip, would, in spreading to give a circular spot, leave on evaporation an amount of palmitic acid corresponding to the desired degree of monolayer coverage. The typical solution contained about 40 pg of palmitic acid per microliter, and the spot diameter was about 0.5 cm. The reported BET specific surface area of the silica gel is about 400 m2 g-lJ4 and our measured BET area is 370 f 12 m2 g-l for one lot and 393 f 2 m2 g-l for the other (courtesy of Calsicat Division, Mallinckrodt Chemical Co.). These were samples taken from the chromatographic plates and so were mixed with about 13% low surface area binder. We take the silica gel area itself to be about 400 m2 g-l. The average area of surface per palmitic acid molecule would be, in this case, about 180 A2, or about twice that for a compact monolayer of molecules lying flat on the (9)J. E.Young, Aust. J. Chem., 8, 173 (1955). (10)G.L. Gaines, Jr., and R. W. Roberts, Nature (London),111,787 (1963). (11)J. W. Whalen, J . Phys. Chem., 71, 1557 (1967). (12)G.Wu,R.A. Stein, and J. F. Mead, Lipids, 12, 971 (1977). (13)G.Wu, private communication. (14)(a) G. Wu,R. A. Stein, and J. F. Mead, Lipids, 12,965 (1977).(b) L. R. Snyder, “Principles of Adeorption Chromatography”,Marcel Dekker, New York, 1968.
2.0 5.0
% spactrans- teomp, ing, time, h C mm fer 0 0.85 1.20 2.23 6.56 0 12.3 14.7
18.1
100
0.1c
0
0
1.0
1.81
2.0
3.31 5.36 16.4 0 1.27 2.02 4.01 11.3
5.0
100 0.2c
% transfer
24.0 0
1.0 2.0 5.0 24.0
a About half-monolayer coverage for spot on source plate Sink plate set directly o n unless otherwise indicated. About one monolayer coverage. top of source plate.
surface. The achieved degree of monolayer coverage, half in the above example, was not sensitive to the exact drop volume used since separate testa showed that the spot area and drop volume were approximately proportional. After deposition of the drop of solution, the plate was allowed to air dry overnight. A Teflon sheet with a 14-mm diameter hole cut out was positioned over the prepared plate, as a spacer, and a second, clean chromatographic slide was placed on top of the spacer. The sandwich-like assembly was carefully clamped together, and the unit placed in a temperature-regulated oven. After the desired elapsed time, the plates were disassembled, and an area greater than that of the spacer hole was scraped off from both the lower, source, plate and the upper, sink, plate. The silica gel from each was transferred to separate scintillation vials, and 10 cm3of a Dimilume scintillation mixture added to each vial. The samples were dark adapted for 30 min before counting. A Beckman LS 8100 scintillation counter was used. Palmitic acid is soluble in Dimilume (which is mainly aromatic hydrocarbon such as toluene or xylene), and it was evident that desorption from the silica gel occurred. The silica gel, of course, settled to the bottom of the vial; its presence was determined not to affect the correctness of the radioactivity measurement. The counts from the source and the sink plates were added, and the transfer is reported as the percent of this total. Materials. Reagent grade materials were used throughout. The chromatographic plates were obtained from Analtech, Newark, DE. Palmitic acid, >99%, was from NuChek Prep. Inc., Elysian, MN, and palmitic-l-14C acid, from ICN, Irvine, CA. The scintillation fluid used was Dimilume-30 from Packard, Downer’s Grove, IL. Other Measurements. Scanning electron microscope (SEM) pictures were obtained by J. Worall by means of a Cambridge 54-10 stereoscan instrument.
Results and Discussion A number of experiments were made, and the principal data are given in Table I and Figure 2. Qualitatively, the transport rate increased exponentially with temperature, increased with increasing surface coverage, and decreased with increasing spacing between the source and sink plates. To proceed further, however, a determination of the nature of the rate law governing the transfer is needed. A possible kinetic model is that of rate-limiting diffusion across the vapor space between the source and sink plates. For a linear diffusion gradient dn/dt = -ADdC/dx = -ADP/RTG (1) where A is the area of the source, D, the diffusion coef-
110
The Journal of Physical Chemistry, Vol. 85, No. 1, 1981
Adamson and Slawson I
Figure 3. Concentration profiles for linear dlffusion from a slab source, for two plate separations, d , and d p . 0
2
4
6
S
IO
fi
12
14
16
IS
20
22
hrs'"
Flgure 2. Transport of palmitic acid between thin-layer chromatographic plates spaced 0.1 mm apart. The coverage was half-monolayer.
ficient for gaseous palmitic acid, P, the vapor pressure in equilibrium with the source, 6, the spacer thickness, and C, the gas-phase concentration. We assume for the moment that the vapor pressure in equilibrium with the sink is always negligible. We can estimate D from gas kinetic theory as D = XC/2, where F is the mean molecular velocity and A, the mean ! molecular diameter, u, free path, X = k T / 2 1 / 2 ~ a 2 PThe should be about 5 A,15and we take the ambient pressure, P', to be 1 atm. For 85 O C , X = 4.4 X cm and I?= 1.7 X lo4 cm s-l, whence D N 0.038 cm2 Equation 1becomes dn/dt = -1.7 X 10-9AP/6
(2)
mechanism. Examination of the SEM photographs suggests another rate model. We see a jumble of silica gel particles of about 1 pm in dimension, or of external surface area of about 3 ms g-l. Comparison with the 400 m2 g-l adsorption capacity thus indicates that only about 1 % of the surface is external. Since the transfer was followed up to several percent, most of the material must have come from internal surface. The interior of the particles is porous, the surface area corresponding to channels of 60 8, in diameter. The internal transport mechanism could still be essentially a vapor phase one, but occurring within the pore structure. The model is now that of Figure 3, showing diffusion from a slab source into an infinite slab, that is, the air space. One-dimensional diffusion of this nature typically leads to an equation of the form Q/Qo = f(Dt/x2) where Q is amount remaining in the source slab and x is a characteristic dimension, such as the thickness of the slab. For the simple case of diffusion from a slab source into a slab sink, one finds (1 - Q/Qo)proportional to (Dt)1/2.Our data do indeed give linear plots of percent transferred vs. t1l2,within the experimental error of about 10%. This is illustrated in Figure 2. If the actual mechanism of transport within the source slab is one of vapor diffusion through pores, the effective diffusion coefficient becomes the value in air reduced by the distribution ratio k, where k = equilibrium concentration in air/equilibrium concentration in source slab. For the case of an infinite source, approximately valid in our case since transport was not followed to high percentages of transfer, a simple form is1'
mmHg at 85 with P in mmHg. This last is ca. 2 X O C , I 6 so that for a spot area of 0.2 cm2 and 6 = 0.1 mm, or 2.4 X lo4 mol h-l. For dn/dt becomes about 1.2 X 10-5P mol total were dehalf-monolayer coverage, 4.7 X posited, so the calculated rate becomes 5.2% h-'. The observed rate is about one tenth of the above, suggesting that simple vapor transport is not rate limiting. However, the calculated rate is a maximum one since the actual vapor pressure in equilibrium with the source could be less than that of the bulk palmitic acid. Further analysis does tend to confirm the above conclusion. According to eq 1,the percent transferred should be linear with time. The data do not conform to this prediction. There is curvature even at short times. A slightly more sophisticated approach adds the assumption of surface heterogeneity, so that P, the equilibrium vapor pressure, varies with amount adsorbed in such a manner as to account for the curvature; allowance may be made at this point for back-diffusion across the vapor space as material accumulates in the sink. While the data for any one temperature could be fit by means of an empirically chosen variation of P with amount adsorbed, no single such choice could also accommodate the data at other coverages and temperatures. Further, eq 1 predicts that the transfer rate should be inversely proportional to 6. While the rate does indeed decrease with increasing 6, the dependence is less than that predicted. On several grounds, then, rate-limiting diffusion across the air space seems to be an only marginally acceptable
where x: is the thickness of the actual slab, about 0.004 cm. We estimate k to be 7.6 X 10-5P,16 where P is the vapor pressure in mmHg, and hence a = 4.2 X 10-3Pcorresponding to 25Pt1/2 in percent per hour. At 85 "C,the slope of the plot in Figure 2 should thus be 0.050 h-ll2. The observed rate is about ten times faster than the above estimate and is thus bracketed by the two extremes of infinite slab diffusion and diffusion along a linear gradient between a source and a sink. Equation 3 assumes an infinite (unmixed) air space, and the actual situation must be more like the alternative shown in Figure 3, where the air space is of thickness 6, and bounded by the sink slab. The solution for the complete situation is complicated and it seems unwarranted to try to fit the data to it. Qualitatively, the result should lie between the ex-
(15)Air is a poor solvent and we assume the molecule to be coiled. (16) E. Jantzen and W. Erdmann, Fette Seifen, 54, 197 (1952).
(17)R. M. Barrer, "Diffusion in and Through Solids", Cambridge University Press, London, 1941.
(1 - Q/Qo) = ( 2 k / ~ ~ / ~ ~ ) = ( Dat1/' t ) ~ / ~ (3)
The Journal of Physical Chemistry, Vol. 85, No. 1, 1981 119
Mechanism of Surface Mobility
I00"C
ks
S5OC
70°C
2;:
2:;
\ 3:O
3,;
38'-C
3:;
I
j.3
IO'/T
Figure 4. Temperature dependence of the slopes of Figure 2. Dashed line: vapor pressure of liquid palmitic acid (ref 19).
tremes, and would include some dependence on 6, as observed. The temperature dependence of a should be essentially that of the vapor presure of palmitic acid in equilibrium with the silica gel, that is, the apparent activation energy should correspond to the heat of adsorption. Figure 4 shows the Arrhenius plot of our data for 6 = 0.1 mm and half-coverage, the slope of the line drawn corresponding to 18 kcal mol-l. Vapor pressure data for bulk palmitic acid are also those from Jantzen and Erdmann16 are similar although somewhat lower in absolute values and giving a slightly larger slope. Qualitatively, however, the temperature dependence of the rate of transport and of vapor pressure are the same. This last result is somewhat surprising since a reasonable expectation is that the heat of adsorption should be somewhat larger than that of bulk condensation. A possible rationalization is that the pores are small enough that normal vaporization does not occur. If molecules in the middle region of a pore still experience some adsorption potential then, in effect, they are only partially desorbed. The experimental arrangement used here is an artificial one, but one that did allow the unambiguous conclusion (18) Calculated as vapor concentration divided by moles adsorbed per unit pore value of the silica gel. (19) "Handbook of Chemistry and Physics", 57th ed, CRC Press, Cleveland, Ohio, 1976.
that vapor transport occurs at a significantrate. The more generally important case is that of transport of molecules between particles and within a particle of porous adsorbent. For nonporous adsorbents, it seems clear that vapor transport of adsorbed fatty acids such as palmitic should be kinetically important. The air space across which diffusion would occur is now of the order of a particle dimension or less. Analysis shows that the fraction transferred per unit time should be inversely proportional to the particle size. For 1pm or smaller particles, vapor transfer rates would be fast enough to sustain rapid reactions. For a high surface area, porous adsorbent, such as silica gel, the important transport is not between particles, in the case of chemical reaction, but within and along pores. In the studies of autoxidation of unsaturated fatty acids adsorbed on silica gel, the specific surface area was 300 m2 g-' so that the average pore diameter in the silica gel was about 60 A. We see from eq 2 that vapor transport over distances of the order of a pore diameter should be quite rapid indeed. As an approximate calculation for palmitic acid at 85 "C, molecules should exchange across a pore diameter at the rate of 4 X lo4 fractions s-l. Typical autoxidation studies were conducted in the range of 50 to 100 "C and over times of minutes to hours, so that even much less volatile species than palmitic acid should have a large enough encounter rate via vapor transport to make reasonable a Rideal-type mechanism. The temperature dependence of a reaction involving vapor-phase hopping might be expected to be at least that for vaporization. This need not be so, however, if chain reactions are involved or if preequilibria are present so that the rate-determining step is not that of vaporization. The point of our discussion, however, is not to argue that vapor-phase hopping is the transport mechanism but rather that the process is fast enough that it could account for bimolecular reactions in surface autoxidations. What is gained is reassurance that it is permissible to invoke such reactions.
Acknowledgment. These studies were supported in part by a grant from the US. National Science Foundation to the University of Southern California. The authors are greatly indebted to Dr. James Mead and Dr. Robert Stein of the Laboratory of Nuclear Medicine and Radiation Biology of UCLA for use of the scintillation counter as well as their generous contribution of encouragement and constructive criticism.
