Environ. Sci. Technol. 2007, 41, 1194-1199
Relationship between Micellar and Hemi-Micellar Processes and the Bioavailability of Surfactant-Solubilized Hydrophobic Organic Compounds DERICK G. BROWN* Department of Civil & Environmental Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
In a landmark study on surfactant-enhanced biodegradation of hydrophobic organic compounds (HOCs), Guha and Jaffe´ demonstrated that a fraction (f) of micellar-phase HOC is directly bioavailable to bacterial cells. They developed a theoretical description of f which provided an excellent model of the experimental results. However, a mass transfer term describing the transport of the HOC through the cell wall (mc) was found to vary over an order of magnitude for the different surfactants examined, and a theoretical description of it remained elusive. This elusivity also resulted in the model not being able to describe a priori why f was zero for the non-ionic surfactant C12E23. Here, the results of a recent study on surfactant sorption are used to develop an alternative mechanism describing mc, where hemi-micellar formation on the cell surface is incorporated into the pathway describing micellar HOC bioavailability. The revised model is validated against HOC bioavailability data for five different C12Ey surfactants, and it is shown that a single value for the mass transfer coefficient describing transfer of the hemi-micellar HOC into the bacterial cell is able to replicate the complete C12Ey dataset, including that of C12E23 which eluded the original model. Overall, the results indicate that surfactant sorption and hemi-micelle formation are important parameters governing surfactant-enhanced bioavailability.
Introduction Surfactants are molecules that have both hydrophobic and hydrophilic moieties. The hydrophobic moiety is often an alkyl chain while the hydrophilic moiety is typically either a charged group or a polar non-ionic group (Figure 1). Surfactants form micelles in aqueous systems when present at concentrations above their critical micelle concentration (CMC). In their simplest form, micelles are spherical or ellipsoidal surfactant aggregates with the hydrophobic portion of the surfactant molecules oriented into the center of the micelle. Hydrophobic organic compounds (HOCs), such as petroleum hydrocarbons and chlorinated solvents, will partition into the hydrophobic core of the micelles. This results in an increased apparent aqueous solubility of the compound (Capp, mg L-1) which is the sum of the * Corresponding author phone: 610-758-3543; fax: 610-758-6405; e-mail:
[email protected]. 1194
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FIGURE 1. Nonionic surfactants examined in this study, expressed as CxEy, where x is the number of carbons in the alkyl chain and y is the number of ethylene oxide units in the polyoxyethylene (POE) chain. For this study the alkyl chain was fixed at x ) 12 and the POE chain was varied, with y ) 4, 7, 9, 10, and 23. aqueous (Caq, mg L-1) and micellar (Cmic, mg L-1) HOC concentrations:
Capp ) Caq + Cmic
(1)
The micellar-phase HOC concentration is typically modeled using a linear partition relationship of the form (1-3):
Cmic ) kmicSmicCaq
(2)
where kmic is the HOC-micelle partition coefficient (L mg-1) and Smic is the micelle concentration (mg L-1) which is the difference between the total surfactant concentration (Stot, mg L-1) and the critical micelle concentration (Scmc, mg L-1):
Smic ) Stot - Scmc
(3)
The ability of surfactants to increase the apparent aqueous HOC concentration has led numerous researchers to investigate the potential for surfactants to enhance the biodegradation rate of HOCs. A significant number of studies can be found in the literature on surfactant-enhanced biodegradation. The results of these studies have been mixed, with some indicating enhanced biodegradation of HOCs in the presence of surfactants (e.g., refs 1, 2, 4-7), whereas others observed inhibition of HOC biodegradation (e.g., refs 8-11). In a landmark study on phenanthrene biodegradation, Guha and Jaffe´ (1, 7) demonstrated that a fraction of the micellar HOC is directly bioavailable to bacterial cells (i.e., the micellar HOC can be directly transferred to the bacterial cell, rather than indirectly bioavailable where it must be released into the aqueous phase prior to being taken up by the bacterial cell). They defined the bioavailable HOC concentration (Cbio, mg L-1) as the following (1, 7):
Cbio ) Caq + f Cmic
(4a)
where f (unitless) is the fraction of micellar HOC that is directly bioavailable. Substitution of eq 2 into eq 4a gives the bioavailable HOC concentration written as a function of the aqueous HOC concentration:
Cbio ) (1 + f kmic Smic)Caq
(4b)
Using phenanthrene as the HOC, Guha and Jaffe´ experimentally determined bioavailability factors for the non-ionic surfactants Triton X-100, Triton N-101, Brij 30 (C12E4), and Brij 35 (C12E23) (1, 7), and in a following study, Sriwatanapongse obtained the bioavailability factors for the nonionic surfactants C12E7, C12E9, and C12E10 (12). The notation CxEy refers to alkyl polyethoxylate surfactants, where x represents the number of carbons in the alkyl group and y represents the number of ethylene oxide groups (Figure 1). The bioavailability factors were found to decrease with increasing surfactant concentrations and this is shown in Figure 2 for the C12Ey surfactants. Using this formulation for micellarphase HOC bioavailability, Brown et al. (2) then demonstrated the range of surfactant concentrations that enhance HOC 10.1021/es061558v CCC: $37.00
2007 American Chemical Society Published on Web 01/09/2007
FIGURE 2. Bioavailability factor plotted as a function of surfactant structure and concentration for the C12Ey surfactants (see Figure 1) with phenanthrene used as the HOC. Solid symbols are data from Guha and Jaffe´ (7) and hollow symbols are data from Sriwatanapongse (12). Lines are best-fit model results using mc as the single fitting parameter for each surfactant. bioavailability and through reactor mass balances showed how surfactants can lower the bioavailable concentration such that their presence would decrease the biodegradation rate. Guha and Jaffe´ developed a theoretical description of f based on the pathway for transport of micellar-phase HOC into the cell and they validated this model against experimental data using phenanthrene as the HOC and Triton X-100 as the surfactant, for which required model parameters were available in the literature (7). While this provided an excellent model of their experimental results, a mass transfer term describing the transport of HOC through the cell wall was found to vary over an order of magnitude for the different surfactants examined, and a theoretical description of this term remained elusive. This elusivity also resulted in the model not being able to describe a priori why f was zero for C12E23 while it was nonzero for the other C12Ey surfactants (Figure 2). The purpose of the current study is to provide an alternative mechanism describing the transport of micellarphase HOC into the cell and to validate this mechanism with existing datasets. Specifically, the original model assumed that the surfactant formed a complete hemi-micelle layer on the bacterial cell surface and that mass transfer of micellar HOC into the cell is driven by Cmic. However, results of a recent study on sorption of C12Ey surfactants on the bacterial cell surface indicate that varying levels of hemi-micellar sorption occur as a function of the number of ethylene oxide units, y (13). For the revised model developed here, this hemimicellar sorption is incorporated into the pathway describing micellar HOC bioavailability and the gradient of HOC into the cell is written in terms of the hemi-micellar HOC, rather than the micellar HOC. The revised model is validated against the C12Ey data of Guha and Jaffe´ (7) and Sriwatanapongse (12), and it is shown that the model is capable of replicating all the experimental data, including that of C12E23 which eluded the original model. With this revised model, the single fitted parameter for the entire C12Ey dataset is one describing the mass transfer of the hemi-micellar HOC into the bacterial cell.
Model Development Original Bioavailability Model. The original model developed by Guha and Jaffe´ assumed two parallel pathways for HOC to enter into the bacterial cell, followed by biodegradation
FIGURE 3. Pathways for a hydrophobic organic compound (HOC) to enter the bacterial cell. Pathway (a) is transport of aqueous HOC into the cell. Pathway (b) is direct transfer of micellar HOC to adsorbed surfactant hemi-micelles, with subsequent transport into the cell. Pathway (c) depicts a limiting case where no hemi-micelles are formed, resulting in micellar HOC not directly bioavailable. Note that the micellar HOC is always indirectly bioavailable via partitioning into the aqueous phase and subsequent transport into the cell through pathway (a). of the internal HOC. The first pathway is transfer of aqueousphase HOC into the cell and the second is direct transfer of micellar-phase HOC into the cell. These are depicted as pathways (a) and (b) in Figure 3. The first pathway is considered for the case when biodegradation is controlled by the aqueous-phase HOC transfer into the cell. In this case, the specific mass transfer-limited growth rate (µmt, s-1) can be written as follows (7, 14):
µmt ) msYCaq
(5)
where ms is the mass transfer rate of the bulk HOC into the bacterial cell (L mg-1 s-1) and Y is the biomass yield coefficient (unitless). The assumption here is that the concentration of HOC in the cell is sufficiently small such that it can be considered zero and the mass transfer is completely controlled by Caq. Application of eq 5 ultimately leads to the overall biodegradation rate described by the well-known Monod equation (7, 14). The second pathway representing the micellar-phase transport into the bacterial cell is composed of two mass transfer processes. The first is the transport of the micelles containing HOC from the bulk fluid to the cell, followed by dynamic transfer of the micellar HOC to adsorbed hemimicelles on the cell surface upon micelle breakdown due to micellar relaxation kinetics. This process is described by the -1 equivalent specific growth rate µbreak mic (s ) when biodegradation is completely controlled by micellar transport and breakdown (7):
µbreak mic ) YPrmmicCmic
(6)
where mmic is the mass transfer rate of micelles from the bulk solution to the cell (L mg-1 s-1), which is a function of the reactor mixing and biomass concentration (7, 15, 16), and Pr is the probability of a micelle breaking down when adjacent to the cell surface (described below). The second mass transfer process is the transport of the HOC from the hemi-micelles into the bacterial cell, and Guha and Jaffe´ modeled this process as shown (7):
µc ) Y
mcCmic ) YmckmicCaq Smic
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where µc is the specific growth rate (s-1) when biodegradation is completely controlled by this transport process and mc is the mass transfer rate through the cell wall (s-1). The specific -1 growth rate for the micellar pathway (µmic mt , s ) is then (7)
1 µmic mt
)
1 µbreak mic
+
1 µc
(8)
Substitution of eqs 6 and 7 into eq 8 leads to the following solution for µmic mt :
µmic mt ) msY f Cmic
(9)
where the bioavailability factor, f, is
f)
mc P ms r mc + PrSmic mmic
(10)
Given this formulation, the inclusion of the micellar HOC pathway (eq 9) in the total biodegradation kinetics results in the overall biomass growth rate being described by the Monod equation with Cbio as the substrate concentration (7). Now, the probability of a micelle breaking down adjacent to the cell surface can be calculated from the kinetics of micellization. It is defined as the ratio of the micellar diffusion relaxation time to the relaxation time of demicellization (τ1, s) (7):
Pr )
∆2 2Dmicτ1
(11)
where Dmic is the micelle diffusion coefficient (m2 s-1) and ∆ is the micelle equivalent diameter (m). The demicellization relaxation time, also known as the fast relaxation time of micellization kinetics, has been studied extensively by Aniansson et al. and can be calculated as follows (17):
1 k- k- Stot - Scmc ) + τ1 σ2 N Scmc
(12)
where k- is the stepwise micelle dissociation rate constant (s-1); N is the average micelle aggregation number (number of surfactant molecules that make up a micelle); and σ is the standard deviation of the micelle aggregation number. Inclusion of eqs 11 and 12 into eq 10 allows the bioavailability factor to be written as follows (7):
f)
a1 + a2Smic 1 + b1Smic + b2S2mic
a1 )
∆2mmic k2msDmic σ2
a2 )
∆2mmic k2msDmicScmc N
b1 )
∆2mmic k2mcDmic σ2
b2 )
∆2mmic k (14b) 2mcDmicScmc N
(14a)
Guha and Jaffe´ (1, 7) demonstrated the validity of this approach for the biodegradation of phenanthrene in the presence of the surfactant Triton X-100, for which k-, σ2, N, ∆2, and Dmic values were available in the literature. They experimentally determined the terms ms, mmic, a1, a2, b1, and b2, and then compared the experimental values to a1 and a2, calculated via eq 14a, with excellent results. They could not 9
µc ) m′cYChm
(15)
where m′c is the mass transfer coefficient describing transfer of the hemi-micellar HOC into the cell (s-1) and Chm is the hemi-micellar HOC concentration (mg HOC per mg biomass), which itself can be defined by the partition function
Chm ) khmShmCaq
(16)
Here Shm is the sorbed surfactant in the form of hemi-micelles (mg surfactant per mg biomass) and khm is the partition coefficient of aqueous HOC into the hemi-micelles (L mg-1). The hemi-micelle concentration can be calculated following the formulation of Brown and Al Nuaimi (13) as
Shm )
Γmax ,2MWsurf Aomcell
(17)
(13)
where
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obtain theoretical values for b1 and b2, however, as mc remained unknown. They also performed experiments with the surfactants Triton N-101, Brij 30 (C12E4), and Brij 35 (C12E23), and noted through the ratio of a1/b1 and a2/b2 that mc varied over an order of magnitude for the different surfactants. Additionally, the model was not able to describe a priori the results for the surfactant C12E23, where the bioavailability factor was found to be effectively zero for all surfactant concentrations examined. Revised Bioavailability Model. The model described above assumes that for the micellar pathway (Figure 3b) all micellar HOC transferred to the cell upon micellar breakdown is bioavailable and that the HOC gradient across the cell wall is driven by the micellar HOC concentration (i.e., eqs 6 and 7). However, the results of a recent study by Brown and Al Nuaimi on the sorption of nonionic surfactants onto the bacterial cell surface indicate that varying levels of hemimicellar sorption occur as a function of surfactant structure (13), which may impact the bioavailable concentration of HOC at the cell surface. A limiting case is shown in pathway (c) in Figure 3, where no hemi-micelles form on the cell surface and thus the micellar HOC cannot be directly transferred to the cell. Independent of whether hemi-micelles form on the surface, the first mass transfer process describing transport of the micelles containing HOC from the bulk fluid to the cell would remain the same, defined by µbreak mic (eq 6). However, the second mass transfer process describing micellar HOC transport into the cell would vary as a function of the hemimicelle formation on the cell surface and the ability of those hemi-micelles to partition the HOC. When the gradient across the cell wall is due to the hemi-micellar HOC concentration, µc can be written as
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where Γmax,2 is the sorbed concentration of surfactant in the form of hemi-micelles (molecules per bacterium); MWsurf is the surfactant molecular weight (g mol-1); Ao is Avogadro’s number (6.022 × 1023 molecules mol-1); and mcell is the mass of a single bacterium (g). The one parameter in eqs 16 and 17 that is not well understood is khm. A few studies have shown that HOC partitioning into hemi-micelles occurs (18, 19), however, no data are available for C12Ey surfactants. To provide an estimate of khm variation with y, one may argue that it should be related to kmic. However, micellization in the aqueous phase is controlled by interactions between the surfactant and water molecules and is a very different process than hemi-micelle formation, which is controlled by interactions between the surfactant and water molecules, surfactant interactions with the bacterial cell surface components, and lateral interactions between the adsorbed surfactant molecules (13, 20). The variability in aqueous versus sorbed surfactant properties
TABLE 1. Surfactant Properties and Experimental Data.
surfactant C12E4 C12E7 C12E9 C12E10 C12E23 a
Scmca (mg L-1)
MWsurf (g mole-1)
14.3 32.4 39.8 25.2 46.7
362 494 581 626 1198
Brown and Al Nuaimi (13).
b
(107 molecules/ bacterium) Γmax,2a Γmaxa
kmic (L mg-1)
mmic (L mg-1 s-1)
31.5 18.4 18.2 7.93 0.543
0.0144b 0.0287c 0.0280c 0.0456c 0.0165b
0.016b 0.108c 0.024c 0.145c 0.016b
Guha and Jaffe´ (1) and Guha (16). c Sriwatanapongse (12).
can be seen in the data in Table 1, where the Scmc and kmic values for the C12Ey surfactants vary by a factor of approximately three, while the hemi-micellar sorption, which on a mass basis can be considered as MWsurf‚Γmax,2, varies by over a factor of 20. Here, the variation of khm with y is considered to be proportional to the strength of the surfactant interactions that form the hemi-micelles, which following the surfactant adsorption model of Brown and Al Nuaimi (13) is taken as the ratio of the maximum sorption concentration of surfactant as hemi-micelles (Γmax,2) to the total maximum sorbed surfactant concentration (Γmax, molecules per bacterium). The hemi-micellar partition coefficient can then be written as
khm ) k′hm
Γmax ,2 Γmax
(18)
where k′hm is the normalized partition coefficient defining HOC partitioning into the hemi-micelles on the cell surface (L mg-1) for a given surfactant class (e.g., C12Ey). With this formulation, hemi-micelles formed with surfactants having a low Γmax,2/Γmax ratio would weakly partition HOCs while those with Γmax,2/Γmax approaching unity would have a partition coefficient of k'hm. Substitution of eqs 16-18 into eq 15 then gives
µc ) Y
[
]
2 m′ck′hm Γmax,2 MWsurf Caq Aomcell Γmax
(19)
Comparison of eq 19 to eq 7 shows that µc in the formulation of Guha and Jaffe´, which was originally written as a function of the aqueous surfactant concentration, now includes the sorbed surfactant concentration on the bacterial cell surface. Equating eqs 19 and 7 provides the mass transfer coefficient of Guha and Jaffe´, mc, written as a function of the sorbed surfactant concentration:
mc )
[
37.0 22.1 19.8 10.1 4.98
]
2 2 m′ck′hm Γmax,2 MWsurf Γmax,2 MWsurf ) m′′c Aomcell Γmax kmic Γmax kmic
Thus, where the original formulation (eq 10) had the bioavailability factor solely as a function of the aqueous surfactant concentration, here it is a function of both the aqueous and sorbed surfactant concentrations. Calculation of Required Parameters for C12Ey Surfactants. To apply these equations to the bioavailability data for the C12Ey surfactants, a number of terms must be calculated, including k-, N, σ, and Dmic. First, the demicellization rate has been described by Aniansson et al. (17) as a function of the monomer diffusion coefficient (Dmon, m2 s-1) and the length of the surfactant alkyl chain (Lalkyl, m):
k- ) N
Dmon (1.1 × 10
-10
m)
2
(
exp -
Lalkyl 1.1 × 10-10m
)
(22)
The alkyl chain length can be calculated from the equation of Tanford (21):
Lalkyl ) [1.5 + 1.265nc] × 10-10
(23)
where nc is the number of carbons in the alkyl chain. For C12 chains, eq 23 gives an alkyl chain length of 1.67 × 10-9 m. The monomer diffusion coefficient for C12Ey surfactants can be obtained from a curve fit to the data of Eastoe et al. (22):
Dmon ) [6.05 - 1.16ln(y)] × 10-10 (R2 > 0.999) (24) and the average aggregation number for C12Ey surfactants can be estimated following Becher (23) as:
N)
1025 - 5.1 y
(25)
Finally, studies on nonionic surfactant micellization indicate that σ is approximately 20% of N (17, 24, 25). Thus, eqs 2225 allow calculation of τ1 (eq 12) for C12Ey surfactants. Now, the equivalent micelle diameter of C12Ey surfactants can be determined from the micellar volume (Vmic, Å3), which can be obtained from the following curve fit to the data of Becher (23):
(20)
Vmic ) (268.48 - 2.5221y) × 103 (R2 ) 0.993) (26)
where m′′c is a lumped mass transfer term accounting for both the partitioning of the HOC into the hemi-micelles and transfer of the hemi-micellar HOC into the bacterial cell. Here, m′′c is assumed constant and the variability in mc observed by Guha and Jaffe´ (7) is accounted for by the remaining terms in eq 20. Finally, substitution of eq 20 into eq 10 gives
The equivalent micelle diameter can then be determined as
m′′c P ms r f) m′′c Smickmic Γmax + Pr mmic MWsurf Γ2
max,2
(
∆)2
1/3
(27)
Then, the micelle diffusion coefficient can then be approximated using the Stokes-Einstein equation (26, 27):
Dmic ) (21)
)
3 Vmic 4 π
kT 3πη∆
(28)
where k is Boltzmann’s constant, T is the temperature, and η is the viscosity of water. Equations 27 and 28, along with τ1 from eq 12, allow determination of Pr for C12Ey surfactants VOL. 41, NO. 4, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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(eq 11). The only unknown in the above model, which is used as a fitting parameter in the parameter estimation process, is either mc when using the original µc formulation given by eq 7, or m′′c when using the revised formulation of µc developed here as eq 19.
Materials and Methods Experimental Datasets. Two sets of data were used in this study. The first was the data relating the bioavailability factor (f) to surfactant concentration (Stot) for biodegradation of phenanthrene in the presence of C12Ey surfactants. Data for y ) 4 and 23 was obtained from Guha and Jaffe´ (1, 7) and that for y ) 7, 9, and 10 was obtained from Sriwatanapongse (12). Both of these studies used the same mixed bacterial culture and experimental apparatus. The bioavailability factors are shown in Figure 2, values for kmic and mmic are given in Table 1, and ms was 8.7 × 10-6 L mg-1 s-1 (1, 7). The second dataset was Γmax and Γmax,2 from Brown and Al Nuaimi (13) for the sorption of C12Ey surfactants on the bacterial cell surface, with y ) 4, 7, 9, 10 and 23 (Table 1). The bacterial culture used in this study was a Sphingomonas sp. which was isolated from the same mixed culture used by Guha and Jaffe´ (1, 7) and Sriwatanapongse (12) and was identified as a phenanthrene degrader. Parameter Estimation. The equations described above were coded in C and run in conjunction with the nonlinear parameter estimate code PEST (Version 6.0.5, Watermark Numerical Computing). Two parameter estimation series were performed. The first examined each surfactant individually and determined the best-fit values of mc from eq 10 for each surfactant along with the associated 95% confidence intervals. The second parameter estimation process fit the data from all five surfactants simultaneously to eq 21, with the single fitted parameter being m′′c.
Results and Discussion Bioavailability Model. The best-fit model results using f defined by eq 10 are presented in Figure 2, where mc was used as the fitting parameter to the data of Guha and Jaffe´ (solid symbols) and Sriwatanapongse (hollow symbols). It is seen that the bioavailability factor decreases as a function of the ethylene oxide chain length, with the largest values for C12E4 and dropping down to effectively zero for C12E23. The corresponding mc values dropped from 8.1 × 10-4 L mg-1 s-1 for C12E4 to e10-6 L mg-1 s-1 for C12E23. While Guha and Jaffe´ were unable to directly calculate mc, they estimated it based on the ratios of their fitted parameters as described above and found that mc ranged from 8.7 × 10-5 L mg-1 s-1 to 8.7 × 10-4 L mg-1 s-1 for the surfactants C12E4, Triton X-100 and Triton N-101 (7). As discussed above, the model developed here for the micellar phase bioavailability suggests that this variation in mc is due to surfactant sorption on the bacterial cell surface. Specifically, eq 20 indicates that mc should be linearly related to the term (Γ2max,2MWsurf)/(Γmax kmic) with the slope equal to m′′c and an intercept of zero. This is plotted in Figure 4 and, as indicated by eq 20, a strong linear relationship is observed with a slope of 1.34 × 10-9 and an intercept of zero (R2 ) 0.916). A more rigorous value of m′′c was obtained with PEST by simultaneously applying the bioavailability data for all five surfactants to eq 21 using m′′c as the single fitting parameter, and the resulting best fit value is 1.37 × 10-9 ( 0.28 × 10-9 (95% confidence interval). These results indicate that surfactant sorption and the formation of hemi-micelles on the bacterial cell surface have a strong influence on the surfactant-enhanced bioavailability of HOC and that the variability in mc observed in the original model of Guha and Jaffe´ (7) is likely due to this surfactant sorption. By incorporating the data from the surfactant 1198
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FIGURE 4. Plot of mc calculated from the data of Guha and Jaffe´ (7) and Sriwatanapongse (12) shows the linear relationship indicated by eq 20, with the slope equal to m′′c and a zero intercept. Error bars depict ( 95% confidence intervals. sorption study of Brown and Al Nuaimi (13), the revised bioavailability model presented here in eq 21 is able to replicate the data of Guha and Jaffe´ (1, 7) and Sriwatanapongse (12) utilizing the single fitted mass transfer parameter m′′c. Most importantly, the revised model was able to replicate the data for Brij 35 (C12E23), which eluded the original model, indicating that surfactant sorption is indeed an important parameter governing surfactant-enhanced bioavailability. Interrelationships between Bioavailability Processes and Biodegradation Kinetics. In addition to the relationship between surfactant sorption and HOC bioavailability, two points must be made about applying surfactants to enhance the biodegradation of HOCs, both of which if not well understood can readily result in surfactants reducing or inhibiting HOC biodegradation. First, the interplay between Cmic and f on Cbio (eq 4) has a very strong impact on the overall HOC bioavailability enhancement with surfactants. Examination of eq 2 shows that Cmic increases with increasing Smic, while the data in Figure 2 shows that f decreases as Smic increases. This interplay results in a range of surfactant concentrations that provides enhanced bioavailability, and surfactant concentrations outside of this range can reduce the overall HOC bioavailability. This aspect of surfactantenhanced bioavailability has been studied in detail by Brown et al. (2) and the relationship between Cbio and Smic in this optimal surfactant concentration range has been termed the “bioavailability curve.” In this study it was also shown that both the presence of soil and the total mass of HOC in the system can strongly affect the bioavailability curve and that the addition of surfactants can reduce HOC bioavailability, even when f is nonzero (2). Second, it is important to note that bioavailability alone is not an indicator of the ability of surfactants to enhance the HOC biodegradation rate. The biodegradation rate is also a function of the ability of the bacterial culture to utilize this enhanced bioavailability. This can be readily demonstrated with the Monod equation written in terms of the bioavailable concentration (2, 7):
dCaq µmax Cbio X )dt Y Ks + Cbio
(29)
where µmax is the maximum specific growth rate (s-1) and Ks is the half-saturation constant (mg L-1). When no surfactant is present Cbio ) Caq (see eq 4) and if Caq . Ks then the bacteria
are already growing close to their maximum growth rate. In this case, the addition of surfactant may increase Cbio, but it will have negligible effect on the biodegradation rate. This relationship between Ks and Cbio must be determined for the specific bacterial culture being used in order to assess the potential for surfactants to enhance the HOC biodegradation rate. Overall, these results highlight the complex relationships that occur between surfactant sorption on the bacterial cell surface; solubilization of the HOC by both micellar and hemimicellar surfactant; bioavailability of the micellar HOC; and HOC biodegradation kinetics. Neglecting any of these processes may result in poor predictions of the bioremediation system’s performance. As such, these processes must be understood both individually, as with the study here on hemi-micelle formation and HOC bioavailability, and as a system as a whole in order to successfully apply surfactants to enhance the biodegradation of HOCs.
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Acknowledgments The author gratefully acknowledges the support of the National Science Foundation under grant no. 0134362.
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Received for review June 30, 2006. Revised manuscript received November 15, 2006. Accepted November 22, 2006. ES061558V
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