Environ. Sci. Technol. 1994, 28, 2278-2285
Modeling the Mass Transfer of Semivolatile Organics in Combustion Aerosols Jay R. Odum,+ Jianzhen Yu, and Richard M. Kamens'
Department of Environmental Sciences and Engineering, School of Public Health, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7400
The atmospheric transport and fate of airborne organic compounds are highly dependent upon the phase or phases (i.e., gas or particle or gadparticle) in which the compound exists. Semivolatile organic compounds (SOCs) partition into both the gas and particle phases, and this partitioning is a function of the compound's vapor pressure,the amount of available surface area, and the ambient temperature. Over the last 10 years, efforts to predict atmospheric SOC partitioning have been primarily based on the equilibrium theory advanced by Pankow, Yamasaki, and Bidelman (1-6). These efforts have substantially increased the understanding of the partitioning process and produced predictive capabilities that are generally within a factor of 3 (i.e.,0.33 < predictediobserved < 3.00) (7,8). In other cases though, predictions can be off by as much as a factor of 10 (7, 8). Reasons for such variability have been characterized by Pankow and Bidelman, and they range from sampling artifacts to equilibrium nonattainment (9, 10). A recent paper by Rounds et al. (11) implies that attainment of full partitioning equilibrium in the atmosphere may be the exception rather than the norm. This suggests that dynamic mass transfer models rather than equilibrium models may be better suited to predict semivolatile partitioning. The ability to accurately predict the atmospheric transport and fate of SOCs will become increasingly important with the gradual implementation of the control measures laid out in the 1990 Clean Air Act Amendments. As the control requirements for many hazardous SOCs become more stringent, a factor of 3 may no longer be considered a suitable predictive capability. Furthermore, if these predictions are to be used as inputs for other
atmospheric chemistry models, then a factor of 3 at the input may be grossly amplified in the model output. If the predictive capability of equilibrium partitioning models is limited by the occurrence of nonequilibrium behavior in the atmosphere, it would seem that a more dynamic partitioning model is needed if atmospheric chemists will be required to make accurate predictions on the fate of SOCs. A significant improvement in the modeling of dynamic semivolatile partitioning was made in 1990 by Rounds and Pankow (12). They developed aradial diffusion model to describe the mass transfer of SOCs into and out of atmospheric aerosols. The model aerosol that was used consists of a spherical particle that is composed of a nonporous, nonsorbing inner core that is surrounded by a uniformly, porous sorbing outer shell. Diffusion into and out of the particle was assumed to be the only ratelimiting process (i.e., mass transfer at the particle surface is instantaneous). Sorption within the pores was assumed to be instantaneous, reversible, and described by a Llangmuirian isotherm, and gas-phase pore diffusion was assumed to be the predominant mechanism for intraparticle transport (i.e.7surface transport is negligible). Rounds et al. (I 1)later used this model to see if it could accurately describe the loss of SOCs from automotive exhaust particulate. They were able to successfully model several polycyclic aromatic hydrocarbons and long-chain alkanes, but their efforts produced an interesting result: the experimentally observed diffusion coefficients were 6 orders of magnitude smaller than those that were predicted by gas-phase pore diffusion theory. Assuming that the experimental procedure did not contain artifacts due to preferential desorption flow paths, it was suggested that strict gas/particle equilibrium with airborne particulate matter may rarely be achieved for SOCs. Diffusion through a liquid-like organic material inion the particle was suggested as a possible explanation for the observed discrepancy. In fact, there is mounting evidence that many types of combustion aerosols may have a liquid-like phase associated with them: (a)the impaction of wood and diesel soot particles on a metal foil produces a viscous liquid slick that retains little or no particle integrity (13);(b) subcooled liquid rather than solid vapor pressures yield better fits in Langmuirian partitioning models ( I , 3);and (c) as much as 50-90 5% (by weight) of the carbon associated with some combustion aerosols is extractable organic carbon (14). In light of this evidence, it seems that a radial diffusion model that includes diffusion through a viscous, liquid-like7organic layer and evaporation/absorption at the surface of this layer might more accurately describe the mass transfer of SOCs into and out of many types of combustion aerosols. This paper discusses such a model.
* To whom correspondence should be addressed. E-mail address: Kamensa SOPHIA.SPH.UNC.EDU. + Present address: California Insititute of Technology, Pasadena, CA 91125.
Radial Diffusion Model Development. The model used in this study begins with a model combustion particle. The particle is assumed
A radial diffusion model was developed to describe the dynamic mass transfer of semivolatile organics into and out of combustion aerosols. The model combustion aerosol consists of a solid carbon core that is surrounded by a viscous, liquid-like, organic layer. Diffusion takes place only within the organic layer and is controlled by mass transfer a t the particle surface. Modeling of semivolatiles requires the tuning of two separate parameters: a diffusion coefficient (D)and a surface mass transfer coefficient (a). Preliminary testing of the model on the uptake of deuterated pyrene by diesel exhaust aerosol at a temperature of 25 "C suggests that diffusion coefficients for PAH are of the order of cm2is and that surface mass transfer coefficients for pyrene are of the order of cmis.
Introduction
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0 1994 American Chemical Society
to be a composite sphere composed of a solid carbon core, with radius a,, that is covered with a liquid-like organic coating with radius from a, to a. It is also assumed that no diffusion into or out of the solid carbon core occurs. Thus at a,, D = 0 where D is the diffusion coefficient of the analyte. It is also assumed that the organic layer thickness is constant and diffusion through the organic media is isotropic (Le., diffusion is only a function of r). This behavior is described by Fick’s second law:
aciat = D(a2C/ar2+ ( z / r ) a c / a r )
(1)
(2)
where Jsurf (mass cm-2 s-l) is the flux at the surface (i.e., at r = a), C, (mass/cm3 of liquid organic layer) is the concentration of the analyte at the surface, C, (mass/cm3 of liquid organic layer) is the concentration at the surface that would be at equilibrium with the gas phase, and a is the surface mass transfer coefficient. For concentrations of C, greater than or less than C,, a gradient is established at the surface that drives diffusion out of or into the particle. Initially, the physical significanceof a may seem obscure. However, examining (Y in the context of a simple kinetics model can lend it an understandable physical interpretation. Considerthe followingequilibrium situation for some SOC:
where G is the gas-phase concentration, P is the intraparticle concentration, TSP is the mass concentration of suspended particulate,P , is the particle-phase equilibrium concentration, Geq is the gas-phase equilibrium concentration, k’on is the absorption rate constant, koff is the evaporation rate constant, and Kp is the equilibrium constant. Initially, it is also assumed that the on- and off-gassing (Le., the absorption and evaporation) rates can be approximated to be pseudo-first-order processes. This is an oversimplification, but the exercise has instructional merit. Furthermore, it is assumed that no extraneous sources or sinks exist (i.e., P + G = Peg + Geq). Given the above assumptions, it can be shown that the rate of change in P is given by
- w t = (koff+ k 0 , v - peq)
.+ Model Output
- - Analytical Solution 0.1 0.099 0.08 0.07 i 0.11
.
0.06 -
003 0.020.01 -
0.05
0.04
where C (mass/cm3 of the liquid organic layer) is the concentration at radius r (cm) and D (cm2/s)is the diffusion coefficient in the organic media. The surface condition that describes evaporation/condensation at the surface as described by Crank (15) is
Jsurf = -DaC/ar = a ( ~- ,c,)
I
0.13I
(4)
where k,, = k’,,*TSP. Multiplying eq 2 by the surface to volume ratio of the organic layer (S/Vorgin cm2/cm3of organic layer) yields the following:
Comparison of eqs 4 and 5 shows that they are very similar. In fact, if the system is at equilibrium so that on- and off-gassing rates are equal, or if the system is only limited by evaporation and absorption at the surface (i.e., intra-
0
2
4
6
8
I
rime)’R (min)’I2
Flgure 1. Comparison of numerical and analytical solutions for a 0.1pm monodispersed aerosol with an diffusion coefficient of 1 X 10-16 cm2/sandno Inner particle core. W/Mmis the fractional mass approach to equilibrium.
particle diffusion is either instantaneous or nonexistent), then eqs 4 and 5 are the same. Thus, a is approximately equal to
The approximation assumes that absorption/evaporation is a simple first-order process. This is certainly not the case if diffusion is limiting mass transfer. However, when the system is close to equilibrium, the approximation is reasonable. Furthermore, if the functional dependencies of koffandk,, are known, then determining the functional dependencies of a will be a much easier task. SolutionTechnique. Analytical solutions exist for eqs 1and 2 for a monodispersed aerosol size distribution and have been documented by Crank (15). Yet real atmospheric combustion aerosols do not generally have monodispersed size distributions, so the equations must be solved numerically. The model developed in this study was initially implemented with an Euler explicit finite difference method to solve eqs 1 and 2 because of the relative ease with which the method may be applied. Furthermore, if the time step is kept small, the global error for the explicit Euler method remains small. The numerical method used here was tested against the analytical solution given by Crank to ensure that the model was performing correctly. A monodispersed 0.1-pm diameter aerosol with an intraparticle diffusion coefficient (D)of 1 X cm2/sand no inner carbon core (Le., a, = 0) was used for the simulation. The surface mass transfer coefficient was 1 X 10-lo cm/s, and the number of nodes was 50. I t can be seen in Figure 1 that the agreement between the numerical and analytical solutions is excellent. The plot shows the fractional approach to equilibrium (MJM,) as a function of the square root of time. The number of nodes can actually be decreased to less than 5 before there is any discernible disagreement between the analyticaland numerical solutions. This was an important observation because it allowed application of the model to a polydispersed aerosol using a constant spatial step (dr). This permitted the larger particle sizes to have a large number of nodes and the smaller particle sizes to have a smaller number of nodes without losing significant accuracy in the predictive capability of the model. Envlron. Scl. Technol., Vol. 28, No. 13, 1994 2279
0 ' 9O
r
0 3 02
01 0 0
Tiwe in Hours (EDT)
Flgure 2. Chamber particle concentration (TSP) over time.
m
E 2 -
3001 250
01
14
21
'
4
I
23
01
03
05
I
Time in Hours (EDT)
Flgure 3. Changes in deuterated gas-phase pyrene (dlO-py) concentration with time.
Experimental Section Outdoor Smog Chamber Experiment with Diesel Soot. Diesel exhaust from a 1967 Mercedes sedan (200D) engine was injected a t night into a 190-m3outdoor Teflon film smog chamber located in Pittsboro, NC ( I 6). Exhaust was injected into the chamber for 5 min. The particle concentration in the chamber after the injection of diesel exhaust ranged from 0.929 to 0.704 mg/m3(Figure 2). Over the course of the experiment, the chamber temperature ranged from 25 to 22 "C. Approximately 2 h prior to the injection of diesel exhaust, deuterated pyrene (dlO-py) was volatilized into the chamber through a hot (200 "C) injector. A graph of the gas-phase concentration of d10py is shown in Figure 3. One can see that initially there was a rapid loss of dl0-py from the gas phase followed by amore gradual decline. This was due to the establishment of equilibrium with the chamber walls and entrainment of outside air into the chamber. Sampling. Samples were collected using the following sampling train: a 40-cm, 5-channel annular denuder (i.d. = 2.4 cm with 0.1-cm spaces) followed by a 47-mm Teflon impregnated glass fiber filter (T60A20, Pallflex Products Corp., Putnam, CT) and another 40-cm, 5-channel annular denuder (16, 17). The walls of the denuders had been coated with a fine XAD-4 resin [as originally developed by Gundel et al. ( 1 7 ) l that allows the denuders to be extracted and reused multiple times in the field (16). Immediately after sampling, an internal standard was added directly to the annulus, and the denuders were 2280
Environ. Sci. Technol., Vol. 28, No. 13, 1994
extracted four times with 30-mL aliquots of a 20:30:50 dich1oromethane:acetone:hexane (Optima Grade, Fisher D151-4:A929-4:H303-4)mixture. The denuders were then dried with pure nitrogen gas and reused. The extracted mixture (total volume = 120 mL) was placed into a round bottom flask that was wrapped in aluminum foil and transported back to the laboratory at 0 "C. These samples were later rotary evaporated to 5 mL, solvent exchanged to pure dichloromethane, then concentrated to 50 p L with dry nitrogen, and stored in the dark at 0 OC until quantification was performed. Collection and extraction efficiencies for pyrene and other PAH for the denuder system have been characterized and are greater than 95 % for the sampling conditions used in this experiment (16). Filter samples were immediately removed from the sampling train after sampling and placed in brown, glass jars equipped with Teflon airtight lids. They were transported back to the lab a t 0 "C. Samples were reweighed, and internal standards were added. They were soxhlet extracted in approximately 20 mL of dichloromethane for 8-12 h. Extracts were concentrated with micro-Snyder columns to 5 mL and then blown down with dry nitrogen to 50 pL. Extraction and workup efficiencies for pyrene on U S . National Bureau of Standards standard reference material (SRM) 1650 have been characterized previously by members in this group (18). When deuterium-labeled internal standards were later used to account for workup and volatility losses, greater than 90% of the reported pyrene mass was accounted for on SRM1650. Quantification. All quantitative analyses were conducted on a Hewlett-Packard 5890 gas chromatograph (GC) equipped with a 5971A mass selective detector (MSD). All injections were performed on a split/splitless injector with a Hewlett-Packard 7673 autoinjector. The data acquisition mode was selected ion monitoring (SIM). A J&W, DB-5 (30 m X 0.32 mm i.d.; 0.25 wm film) fused silica column was used. The GC temperature program was as follows: 60 "C for 0.2 min, 60-250 "C a t 20 "C/min, 250-300 "C at 6 "C/min, and hold a t 300 "C for 5 min. The initial injection port temperature was 300 "C. The error associated with the acquisition and quantitation of the data has been estimated to be f20%. Experimental/Model Parameters The following parameters are used as inputs for the model. The chamber volume is 190 m3. Particle concentrations (TSP) in the chamber are converted into the total number of particles in the chamber ( N d from a combination of size distribution data collected with an electrical aerosol analyzer and filter particle mass (TSP) measurements. The number of particle bins (Nb = 7), the fraction of particles in the ith bin (f;),and the radius of the particles in those bins (ai)are taken from EAA data. TSP measurements made throughout the course of an experiment yield a first-order TSP loss rate constant. The thickness of the organic liquid layer ( a - a,) can be estimated from percent extractable measurements. Percent extractable measurements are made by weighing filter samples on a three place milligram microbalance (Sartorious, Model 4503-MP6) both before and after soxhlet extraction. Filter samples are folded and placed in an upright position in the soxhlets to ensure that nonextractable mass is not lost during the extraction. The difference in the before and after extraction weights is considered to be the extractable organic mass. Since this
characteristic “S”shape indicative of surface limited mass transport. Vapor Pressure Dependence of Dand a. If the time required for uptake or release of a compound by a combustion aerosol is a function of the surface mass transfer coefficient, then it is of interest to know how a varies among compounds. From the derived functional relationship for a (eq 6),predictions of mass transfer rates within a group of compounds could be possible. The rate of desorption of a compound from the surface of a solid ( 4 , 19) may be described by
-
. i i
ratedesorb = [ ( 1 / ~ ) e - Q 1 C, /~~1
(Time)”‘ (min)”‘
Figure 4. Fractional approach to equilibrium using different values for the surface mass transfer parameter a.
model assumes that the particle is comprised of only two phases, the elemental carbon core and the liquid organic coating, all the extractable mass is considered to comprise the liquid organic layer, and the nonextractable mass is considered to comprise the elemental carbon core. Very little data exist on combustion particle morphology, and therefore, it is difficult to know if all the extractable mass is actually in the liquid phase. Hence, in the absence of adequate data on the heterogeneity of the organic layer, all extractable mass is attributed to the liquid organic layer to avoid adding another level of complexity to the model. The time step (dt) is chosen to satisfy the stability condition for a given simulation. Initial particle and gasphase concentrationsare measured by taking samples from the chamber. The surface equilibrium concentration can either be measured directly if the system is at equilibrium or be estimated from partitioning equilibrium theory (eq 3). The diffusion coefficient (D) and the surface mass transfer parameter ( a )are compound dependent and are used as the compound fitting parameters. Results and Discussion Initially, several model simulations of SOC loss from the particles were run in order to examine how the surface mass transfer parameter ( a ) affected the rates of SOC loss. In Figure 4, all parameters except a, whose value corresponds to the number next to each line, were held constant. In this plot, the y-axis (Mt/M,) is the fractional mass approach to equilibrium (i.e., MJM, = 1 at equilibrium), and the x-axis is the square root of time. The value for the diffusion coefficient in the simulation was 1 X 10-15 cm2/s,and the particle radius is 0.1 pm. It can be seen that for smaller values of a , the time to equilibrium is a strong function of a. Yet as a approaches larger values, the time to equilibrium ceases to be a function of a. This is because for very large values of a the maximum gradient between the surface and the interior of the particle is established shortly after time zero and is maintained throughout the simulation. Therefore, the time to equilibrium is simply limited by the maximum rate of diffusion through the particle, and the fractional approach to equilibrium curves has a more parabolic shape. However, when the surface mass transfer time scale (4*a/(30*a))is similar to or greater than the diffusion time scale ( ( a aOl2/D),the approach to equilibrium curves have the
(7)
where 7 is a characteristic molecular vibration time, Q1 is the heat of desorption from the surface, R is the ideal gas constant, T is the absolute temperature, and C, is the surface concentration of the compound of interest. Given this relationship, it is reasonable to assume that the rate of evaporation from aliquid surface will have the following form: rate,,,,
= (ke-Qa/RT)Cs = koffCs
(8)
where k is a constant and Qe is the heat of evaporation from the liquid surface. Furthermore, the equilibrium vapor pressure of a compound (p) over some solution is related to the vapor pressure over the pure liquid ( P L O ) of the compound by o -(Qe-Qv)/RT (9) P = XPLe where x is the mole fraction of the compound and Qv is the heat of vaporization for the subcooled liquid of the compound. The exponential term in eq 9 represents the nonideality of solution and is equivalent to an activity coefficient. The above relationships (i.e., eqs 8 and 9) imply that within a class of compounds koff should be directly proportional to the subcooledliquid vapor pressure of the compound. On the other hand, it can be shown from the kinetic theory of gases that kon is only mildly compound dependent since it is inversely proportional to the square root of the compounds molecular weight (M). Therefore, for SOCs with small partitioning equilibrium constants (i.e., koff >> KO,), a should be directly proportional to the compound’s vapor pressure. This implies that the rate of uptake or loss of an SOC can be a function of its vapor pressure. For example, consider the following class of compounds-polycyclic aromatic hydrocarbons (PAH). If two compounds such as pyrene and chrysene both have values of koff that are much larger than k,,, then the rate of evaporation of chrysene from the model aerosol will be slower than the rate of pyrene evaporation. It is doubtful that this difference would be due to any difference in diffusion coefficients. It can be shown from the WilkeChang (20) equation that values for the liquid diffusion coefficients of pyrene and chrysene should differ by less than 10%:
Dli, = (7.4 x 10-a(4M)1’2T‘)/pP6
-
DpyrenJDchyysene - ( Vchrysenel Vpyene) o.6 = (178.96/158.93)0.6(10) DpyrenelDchrysene = 1.07 where 4 is the solvent association term, M is the molecular Environ. Sci. Technol., Vol. 28, No. 13, 1994 2281
1
to equilibrium are related to the compound's vapor
then should be related to the compound's vapor Ac"""hv7 I pressure, pressure as suggested above. CY
If a is indeed directly related to the subcooled liquid vapor pressure of SOCs whose value of k,ff >> k,, and their liquid diffusion coefficients are fairly compound independent within a class of compounds, then fitting experimental data with the model discussed in this paper will be relatively easy for such compounds. If one has experimental diffusion data for just two compounds of the same class, then converging on a diffusion coefficient and surface evaporation parameters can be accomplished. Therefore, for a class of compounds, unique values of CY can be determined for each compound, and a unique value of D can be determined for the class of compounds for diffusion through a given type of combustion aerosol a t a given temperature. Having empirical values of D and a at various temperatures for a given aerosol type would allow one to model the dynamic partitioning of SOCs at those temperatures. However, if one could determine the functional temperature dependence of D and CY, then modeling those compounds a t any temperature would be possible. Temperature and Humidity Functional Dependence. Equation 10 suggests that D will be directly proportional to temperature. However, the viscosity of the particle liquid layer has its own temperature dependence and is most likely described by the following:
-21 0 C25
-22
' -7.5
I
i
1
-6.5
-5.5
-4.5
I
l0g(P03
Figure 5. Association of Rounds and Pankow effective diffusivitiesDen and subcooled vapor pressures PL;C16-C24 in the bottom graph refers to the identity of normal alkanes by carbon number.
weight of the solvent, 1 is the solvent viscosity, T is the temperature, and V is the molar volume of the diffusing molecule. This relationship suggests that if pure diffusion were controlling the rate of evaporation from the particle, then pyrene and chrysene would have similar times to equilibrium. However, Rounds et al. observed that the time to equilibrium for chrysene is much slower than that for pyrene for diffusion out of automotive exhaust particulate (11). The gas-phase pore diffusion model used in that study attributes the difference in times to equilibrium to a difference in the effective diffusion coefficients of the two compounds (11). A graph (see Figure 5) of the effective diffusion coefficients measured by Rounds et al. (D,ff)vs subcooled liquid vapor pressures shows that the measured diffusion coefficients are highly correlated with the vapor pressure of the compound as sorption retarded gas-phase pore diffusion theory suggests (11). However, the magnitudes of the effective diffusion coefficients are on the order of 10-14-10-1acm2/s(11). These values yield molecular diffusion coefficients that are of the order of viscous liquid or solid-phase diffusion coefficients. However, the calculation performed in eq 10 suggests that the liquid diffusion coefficients for PAH with very dissimilar vapor pressures should be almost identical. Thus, if diffusion through a liquid layer is occurring and the difference in diffusion times for pyrene and chrysene cannot be attributed to a difference in their liquid diffusion coefficients, then the factor controlling their times to equilibrium must be their surface evaporation parameters ( C Y ) . Furthermore, since Rounds et al. found that the times 2282
Envlron. Sci. Technol., Vol. 28, No. 13, 1994
I.1 =
beE8IT
-3.5
(11)
where b is a preexponential constant, E, is the activation energy needed by a solvent molecule to escape the potential well of its neighbors, R is the ideal gas constant, and T i s the absolute temperature. Each type of combustion aerosol (i.e., wood soot, diesel particulate, etc.) will most likely have its own unique preexponential factor and activation energy. Therefore, the complete temperature dependence of D should look like the following: D
0:
Te-EaIRT
(12)
Equation 11 generally describes the temperature dependence of viscosity for most liquids over reasonably small temperature ranges. However, this form assumes that the density of the liquid is changing very little over the temperature range of interest. If this is not the case, then the temperature dependence will be more complicated than that given by eq 12. Despite the fact that the diffusion coefficient seems to vary exponentially with temperature, data from Kamens et al. (21) suggest that temperature may not be the most important factor controlling intraparticle diffusion for certain types of aerosols. They conducted several experiments in which the rates of PAH photodegradation inlon wood soot particles were measured under various conditions. Kamens et al. concluded that absolute humidity had a larger influence on the rate than did temperature and that rates of PAH photodegradation were directly related to the atmospheric water vapor concentration (21). Furthermore,McDow et al. (22)observed that the amount of H 2 0uptake by wood soot is directly proportional to the relative humidity over a large range of humidities. Therefore, rates of PAH photodegradation in wood soot particles seem to be directly related to the amount of water absorbed by the aerosol. If the reaction responsible for
PAH degradation is a bimolecular, diffusion-controlled reaction and absorption of water into the organic layer increases this rate, then uptake of water by wood soot may decrease the viscosity of the liquid layer and thereby increase the value of the diffusion coefficient. Combining this with eq 10 suggests the following relationship:
4.5 4
g -m
3.5 3
2.5
where D is the diffusion coefficient in the organic layer, poorgis the viscosity of the organicliquid layer in the absence of H20, ~ H , Ois the viscosity of H20, Voorgis the volume of the liquid organic layer in the absence of H20, and VH,O is the volume of H2O taken up by the particle. If the viscosity of the organic layer is larger than that of water by more than a factor of 5 and uptake of water is less than 25 % ,then the diffusion coefficient is relatively linearly related to the amount of water uptake by the particle as Kamens et al. (21) suggest. The conclusion drawn from the argument above assumes that uptake of water within the aerosol has only a physical effect on the reaction and not a chemical one. This assumption seems reasonable in light of data reported by McDow et al. (22). Therefore, if the above reasoning is correct, then diffusion coefficients may have a larger dependence on relative humidity than on temperature for certain types of combustion aerosols such as wood soot. This is probably not the case with diesel exhaust however since its liquid layer is composed of mostly nonpolar organics and, therefore, has very little affinity for atmospheric H2O (22, 23). As the argument above points out, the functional dependence of D on temperature and humidity can be quite complex. However, the diffusion coefficient is not the only parameter influenced by temperature in a liquid diffusionlevaporation model. The surface evaporation parameter will most likely have a complex temperature dependence as well. For compounds whose value of k,ff >> k,,, the temperature dependence of a should resemble that of eq 8: a = ke-Qe/RT for kOff>> k,,
(14)
This suggests that a is highly dependent on temperature. As temperature decreases, a will decrease exponentially. However, a is related to the sum of the k,ff and kon rate constants, and k,, is temperature dependent as well. According to the kinetic theory of gases, k,, is directly related to the square root of temperature. Therefore, as temperature decreases, a will initially decrease exponentially for compounds having values k,ff >> ken. However, as temperature continues to decrease, values of kon will begin to exceed values of koff, and the temperature dependence of a will become less significant (see Figure 6). Once again referring to the data of Rounds et al. ( I l ) , it can be discerned that around 295 K (i.e., the temperature at which Rounds et al. performed their desorption experiments) most PAH have values of k,ff 2 k,, for evaporation at the surface of automotive exhaust particulate. If this were not the case, then times to equilibrium would most likely not appear to be a function of the compound's vapor pressure as argued above (see Figure 5). However, at colder temperatures values of ken, which are not vapor pressure dependent, may begin to exceed values of k,ff and times
2 1.5 1O O O K A
Figure 6. Temperature dependence of a.
to equilibrium for several of the least volatile SOCs may cease to be a strong function of temperature or of the compound's subcooled liquid vapor pressure. Functional Dependence on Particle Size. If the functional dependence of k,ff defined in eq 8 is correct, then k,ff should not have a strong dependence on particle size. However, if the Kelvin effect becomes important at very small particle sizes (Le., d < 0.1 pm), then this may not be the case. The rate constant for absorption (k,,,) has a strong dependence on particle size for particle sizes in the transition regime (24):
k,, = ~ T ( U ) ~ ( ~ R T / T M ) ' / ~ N ~(15) where a is the particle radius, R is the ideal gas constant, T i s the temperature, M is the molecular weight, N is the number of particles per unit volume, and cp is the accommodation coefficient. This equation suggests that each particle size will have its own absorption rate and that this rate decreases sharply with particle size. If this is the case, it will only be possible to measure a bulk average value for ken. It should be noted that the equilibrium theory developed up to this point (2-10) does not address this problem of k,, being a function of particle size. It simply uses a bulk equilibrium constant for the whole aerosol distribution. It would be interesting to sample urban aerosols on size basis and determine whether or not each size truly has its own equilibrium constant as eq 15 predicts. Uptake of Pyrene by Diesel Particulate. To test the ability of the model outlined above to describe mass transfer of SOCs into and out of combustion aerosols, a preliminary outdoor smog chamber experiment was conducted. Fresh diesel emissions were injected into a 190m3 outdoor Teflon film smog chamber at night. The particle size distribution for the experiment is shown in Figure 7. Two hours prior to the injection of diesel exhaust, deuterated pyrene (dlO-py) was volatilized into the chamber through a hot injector. A graph of the gas-phase dlo-pyrene concentration is shown in Figure 3. Initially there is a steep decline in the gas-phase concentration of dl0-py because it must first come to equilibrium with the chamber walls. After the initial decline, there is a slower decline of the gas-phase concentration which is due to dilution of the chamber air, Before the injection of diesel exhaust, it can be seen that the particle-phase concentration of dl0-py is essentially zero (see Figure 8). The slight nonzero (1 ng/ Environ. Sci. Technol., Vol. 28, No. 13, lQ94 2283
0 40
n
D i a m e t e r (urn)
Figure 7. Electrical aerosol size distributions experiment.
for July 1, 1993,
300 280 260 240 220
. I
m E
01
zoo
5
180
7
160
2
140 120
2
T
e
100 80 60 40 20 0
0
2
4
6
8
(Time)
10
12
14
16
18
'" (mt n)'"
Figure 8. Model fit to particle dl0-py data.
mg) concentration is due to the partitioning of dl0-py to background aerosols in the chamber. Shortly after the injection of diesel emissions, the dl0-py particle-phase concentration (i.e., [dlO-pyPart])increases dramatically as shown in Figure 8. This is due to the uptake of dl0-py by the diesel particulate. The line through the data in Figure 8 is output from the model. The model simulation used the seven bins and the fraction of particles in each bin that were obtained from the electrical aerosol analyzer. The initial number of particles (Nto= 6.30 X in the chamber and the first-order decay rate constant (q = 1.66 x 104 s-l) describing the loss of the particles in the chamber with time were obtained from sample mass and size distribution data. The same decay rate constant ( 4 ) was used for all size bins. This seems reasonable considering that the surface to volume ratio, calculated from the electrical aerosol analyzer data, remained relatively constant throughout the experiment. The ratio of liquid organic carbon to elemental carbon used in the simulation was 40% (Vratio = 0.4). If all the organic carbon is attributed to an outer liquid layer, then this ratio yields an organic layer that is 1 nm thick for the 0.0133 pm diameter particles and an organic layer that is approximately 60 nm thick for the 0.750 pm diameter particles. The initial gas- and particle-phase concentrations were obtained by direct measurement on the system at time zero using the denuder/filter/denuder sampling train outlined in the Experimental Section. The equilibrium particle-phase concentration (1.2 X 106 ng/cm3) used in 2284
Environ. Sci. Technol., Vol. 28. No. 13, 1994
this simulation was estimated by calculating an equilibrium constant for pyrene using the concentrations measured in the chamber over the course of the experiment and then back-calculating a value of C, for dl0-py. The diffusion coefficient used in the simulation was 6 X lO-'5 cm2/s, and the mass transfer coefficient was 4 X cm/s. A time scale analysis suggests that the diffusion time scale (i.e., (a - aOl2/D)is W O O that of the mass transfer time scale (Le., (4*a)/(30*a)) for the smallest particles. While for the largest particles (i.e., a = 0.375 pm), the diffusion time scale is approximately 1/2 of the mass transfer time scale. For the bulk number of the particles (i.e., a = 0.05-0.1 pm), the diffusion time scale is of the order of 1-10 min, and the mass transfer time scale is of the order of 1h. This suggests that the rate limiting process is the mass transfer at the surface and that diffusion is only limiting for the larger particles. The best model fit was chosen by minimizing the sum of the square of the residuals for every data point other than the second one (Le., the point a t 5 min1I2). A line through all six points could not be obtained using reasonable values of D and a. As indicated previously, our dl0-py measurements can vary by as much as f20% from the actual concentrations. If error bars are added to all the points in Figure 8, then fits with a range of values are possible. This range for D and cy vary from the values used in Figure 8 by less than an order of magnitude. However, the fit shown in Figure 8 is excellent for the first and the last four points, suggesting that the second point may be in error. This group has also acquired more recent data that suggest this conclusion as well. Conclusions A model was developed to describe the mass transfer of semivolatile organics in and out of combustion aerosols. The theoretical discussions suggest that mass transfer may be highly dependent upon ambient temperatures and humidities. Furthermore, times to sorption equilibrium may be a function of particle size as well as the vapor pressure of the sorbing compounds. A preliminary experiment was conducted in order to test the validity of the model. An excellent fit was obtained if the second point was ignored. This experiment suggests that the diffusion coefficient for PAH in diesel particles a t 25 "C is of the order of 10-15cm2/sand the surface mass transfer coefficient for deuterated pyrene is of the order of 10-lo cm/s. Future experiments conducted by this group will concentrate on collecting more samples in the early part of the experiment using shorter sampling times so that a better experimental curve can be obtained. Acknowledgments This work was supported by a contract from the North Carolina Super Computing Center (Kenneth Galluppi, Project Officer) and by a gift from the Ford Motor Co. (Paul Killgoar, Project Officer). Literature Cited (1) Bidleman, T. F.; Billings, W. N.; Forman, W. T. Enuiron. Sci. Technol. 1986,20, 1038-1043.
(2) Bidleman, T. F. Enuiron. Sci. Technol. 1988,22, 361-367. (3) Bidelman, T. F. Workshop Report; Shepson, P. B., Ed.; CIRAC: Toronto, Canada, Nov 26-28, 1991. (4) Pankow, J. F. Atmos. Enuiron. 1987, 21, 2563-2571.
(5) Yamasaki, H. K.; Kuge, Y. Nippon Kagaku Kaishi 1984,8, 1324-1329. (6) Yamasaki, H. K.; Kawata, Y.; Miyamoto, H. Environ. Sci. Technol. 1982,16, 189-194. ( 7 ) Pankow, J. F. Atmos. Environ. 1991,25A, 2229-2239. (8) Pankow, J. F. Atmos. Environ. 1992,26, 2489-2497. (9) Pankow, J. F.; Bidelman, T. Atmos. Environ. 1991, 25A, 2241-2249. (10) Pankow, J. F.; Bidelman, T. Atmos. Environ. 1992, 26A, 1071-1080.
(11) Rounds, S . A,; Tiffany, B. A.; Pankow, J. F. Environ. Sci. Technol. 1993,27, 366-377. (12) Rounds, S. A.; Pankow, J. F. Environ. Sci. Technol. 1990, 24, 1378-1386. (13) McDow, S. R.; Sun, Q.; Vartiainen, M.; Hong, Y.; Yao, Y.; Fister, T.; Yao, R.; Kamens, R. M. Environ. Sci. Technol. 1994,28, 2147-2153. (14) Japar, S. M.; Szkarlat, A. C.; Gorse,R. A.; Heyerdah1,E. K.; Johnson, R. L.; Rau, J. M.; Huntzicker, J. J. Environ. Sci. Technol. 1984, 18, 231-234. (15) Crank, J. The Mathematics ofDiffusion;Oxford University Press, Amen House: London, 1964. (16) Kamens, R.; Fan, Z.; Yao, Y.; Chen, D.; Vartiainen, M. Chemosphere 1994,28, 1623-1632.
(17) Gundel, L. A.; Lee, V. C.; Mahanama, K. R. R.; Daisey, J.; Stevens, R. K. Submitted to Atmos. Environ. Also Lawrence Berkeley Lab Report 34862, 1 Cyclotron Road, Berkeley, CA 1994. (18) Kamens, R. M.; Guo, J.; Guo, Z.; McDow, S. R. Atmos. Environ. 1990,24A, 1161-1173. (19) Adamson, A. W. Physical Chemistryojsurjaces;John Wiley and Sons: New York, 1982. (20) Wilke; Chang. Am. Inst. Chem. Eng. J . 1955, 265. (21) Kamens, R. M.; Guo, Z.; Fulcher, J. N.; Bell, D. A. Environ. Sci. Technol. 1988, 22, 103-108. (22) McDow, S. R.; Sun, Q.; Hong, Y.; Yao, Y.; Vartiainen, M.; Hayes, E.; Kamens, R. M. Atmos. Environ. Accepted for publication. (23) Schuezle, D.; Lee, F. S. C.; Prater, T. J.; Tejada, S. B. Int. J. Environ. Anal. Chem. 1981, 9, 93-144. (24) Wexler, A. S.; Seinfeld, J. H. Atmos. Environ. 1992, 26A, 579-591.
Received for review February 2, 1994. Revised manuscript received August 1, 1994. Accepted August 16, 1994." @
Abstract published in Advance ACS Abstracts, September 15,
1994.
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