Environ. Sci. Technol. 2005, 39, 3826-3832
(E)-5-[2-(Methoxycarbonyl)ethenyl]cytidine as a Chemical Actinometer for Germicidal UV Radiation C H E N G Y U E S H E N , † S H I Y U E F A N G , ‡,§ D O N A L D E . B E R G S T R O M , ‡,§ A N D E R N E S T R . B L A T C H L E Y I I I * ,† School of Civil Engineering, Purdue University, West Lafayette, Indiana 47907-2051, Department of Medicinal Chemistry and Molecular Pharmacology and the Purdue Cancer Center, Purdue University, West Lafayette, Indiana 47907, and the Walther Cancer Institute, Indianapolis, Indiana 46208
(E)-5-[2-(Methoxycarbonyl)ethenyl]cytidine (S) was examined for use as a chemical actinometer for germicidal UV radiation. Its photoproduct, 3-β-D-ribofuranosyl-2,7dioxopyrido[2,3-d]pyrimidine (P), is strongly fluorescent with excitation and emission maxima at 330 and 385 nm, respectively. Experiments were conducted to characterize the dynamic behavior of aqueous solutions of S and P when subjected to UV radiation. UV sources used for these experiments included a low-pressure mercury lamp, a XeBr excimer lamp, and a KrCl excimer lamp; all three sources were mounted in collimating devices to provide incident beams that could be easily and accurately characterized by radiometry. These three sources each yielded essentially monochromatic output with characteristic wavelengths of 254, 282, and 222 nm, respectively. At practical concentrations, it was found that the absorbance of the actinometer solution was neither high enough to make the actinometer solutions optically opaque nor low enough to be optically transparent to UV. In addition, the photoproduct displayed a molar absorption coefficient that was similar in magnitude to that of the parent compound, thereby resulting in competitive absorption of UV energy between S and P during irradiation. For purposes of evaluation of the results of irradiation, a mathematical model was developed to account for the nonideal optical characteristics of the system. The model is based on a description of local photochemical kinetics; predictions of overall reactor performance were developed by spatial and temporal integration of model results. The model was used to analyze the dynamic behavior of actinometer solutions during UV irradiation and to estimate the quantum yield for photoproduction of P from S. This modeling approach is potentially applicable to other photochemical processes in which multiple compounds are present that absorb photoactive radiation; however, general application of this modeling approach to photochemical reactor systems will require inclusion of other terms to describe relevant transport behavior within the system. * Corresponding author phone: (765)494-0316; fax: (765)496-1107; e-mail:
[email protected]. † School of Civil Engineering, Purdue University. ‡ Department of Medicinal Chemistry and Molecular Pharmacology and the Purdue Cancer Center, Purdue University. § Walther Cancer Institute. 3826
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Introduction Chemical actinometry is commonly used in photochemistry as a relatively simple and accurate method for radiation measurement (1). Actinometry has been employed for characterization of photochemical reactor systems, including those used for ultraviolet (UV) disinfection. Common actinometers that have been used in studies of UV photoreactor systems include potassium ferrioxalate (2-4), potassium peroxodisulfate (5, 6), potassium iodide (7-9), and uridine (10, 11). The characteristics of these actinometers have been thoroughly described in the literature. For radiation in the germicidally active portion of the UV spectrum, these actinometers function well. However, important limitations or disadvantages of these actinometers exist. For example, potassium ferrioxalate may require reagent preparation through crystallization; the actinometer solution must be prepared daily because of its inherent instability (1). Potassium peroxodisulfate has been reported to be somewhat more stable than potassium ferrioxalate, but solutions have been reported to require fresh preparation every day or two (5). Moreover, the photoproducts of this actinometer are protons (H+); therefore, quantification of absorbed radiation is susceptible to interference by pH buffers (5). The photoproduct of the iodide/iodate actinometer (I3-) exists in equilibrium with many other forms of iodine (12) and has been observed to be unstable, requiring analysis within minutes of exposure (13). The uridine actinometer is characterized by a quantum yield (Φ) that is quite low relative to the other actinometers listed above. The quantum yield of the uridine actinometer has been observed to vary by more than 100% across the germicidal range and has also been reported to vary as a function of irradiance (10, 11). Although some of these actinometers depend on measurements of photoproduct formation using analytical methods that require no sample workup, none have been developed for on-line, real-time analysis or monitoring. Collectively, this set of characteristics indicates a need for development of alternative actinometer systems. When subjected to UV irradiation, the nonfluorescent compound, (E)-5-[2-(methoxycarbonyl)ethenyl]cytidine (MW 327.3, hereafter referred to as S) is transformed to a bright violet fluorescent product, 3-β-D-ribofuranosyl-2,7-dioxopyrido[2,3-d]pyrimidine (MW 295.26, hereafter referred to as P) (14). The phototransformation process is illustrated in Figure 1. It is presumed that the transformation occurs by way of trans to cis isomerization, in line with the well-known photochemistry of substituted alkenes (15). However, the cis isomer has never been observed because of the rapid ring closure to yield P. Consequently, unlike other photonmediated trans to cis isomerizations, the phototransformation of S is irreversible. The stable photoproduct, P, has an excitation maximum at 330 nm and an emission maximum at 385 nm. In the absence of UV radiation, these compounds are extremely stable. Chromatographic analysis of samples of both compounds, after being stored in the dark for more than 10 yr, showed no evidence of decay or transformation (results not shown). An important advantage of S for its application as an actinometer is that it is highly sensitive to UV radiation in aqueous solution. This provides the potential for development of methods to be used in the analysis of photochemical reactor systems. In addition, P is photochemically stable, once produced. However, it should be recognized that the high photosensitivity of S to long wavelength UV radiation also represents a potential shortcoming in its application as an actinometer in that experiments must be conducted under conditions of limited 10.1021/es049120n CCC: $30.25
2005 American Chemical Society Published on Web 04/13/2005
FIGURE 1. Scheme of S phototransformation to P by UV irradiation (14). exposure to ambient UV radiation. Experience in handling this actinometer has revealed that it is possible to conduct experiments under conditions of low ambient light, such that instruments and experiments can be seen, but little or no detectable P formation results. On the basis of this information, experiments were undertaken to further define the characteristics of S as a chemical actinometer for germicidal UV radiation. In addition, a mathematical model was developed to describe the dynamic behavior of aqueous solutions of S and P. The model will be useful in practical applications of aqueous S solutions as an actinometer. More generally, this model and the approach used to develop it will be useful in the analysis of photochemical reactor systems where photon energy is absorbed by target molecules and other dissolved constituents.
Materials and Methods At present, S and its photoproduct P are not commercially available. Both compounds were prepared in the laboratory as needed (see ref 14 for details) and stored in the dark at room temperature until use. All other chemicals used were reagent grade and commercially available. Nanopure water was used for all solution preparations. Aqueous-phase concentrations of S and P were both quantified by HPLC (Varian HPLC, model 9012, solvent delivery and 9050 UV-visible detector, set at λ ) 330 nm). Aqueous standards were prepared gravimetrically and by dilution, followed by HPLC analysis. This method yielded a stable, linear response (peak area as a function of aqueousphase concentration) over the range of actinometer and photoproduct concentrations used in this study. Detection limits for S and P were roughly 0.4 and 0.2 µM, respectively, based on a signal:noise ratio of 5:1. The HPLC column used was an Econosphere C18 3 µm (Alltech, Deerfield, IL). Eluent composition for these analyses was 45% water, 35% methanol, and 20% ammonium acetate buffer (25 mM). An Aminco-Bowman series 2 luminescence spectrometer (Thermo Spectronic, Rochester, NY) was used to measure the fluorescence of the actinometer product. Fluorescence intensity was measured for aqueous solutions of P ranging in concentration from 0 to 0.34 mM. Fluorescence intensities of aqueous actinometer solutions with an initial S concentration of 0.14 mM were also quantified after irradiation under a collimated beam for UV254 doses ranging from 0 to 20 mJ/ cm2. The sensitivity of the luminescence spectrometer (sprectrofluorometer) was adjusted to yield detector high voltage of 600 V and auto range of 70% full scale. Excitation was performed at 330 nm, while emission was measured from 370 to 430 nm in 1.0 nm increments at a scan speed of 1.0 nm/s. Excitation and emission shutters were both closed prior to data acquisition due to the photosensitivity of S. Absorbance measurements were conducted using a Perkin-Elmer Lambda 20 UV-visible spectrophotometer using a quartz cuvette (1.0 cm path length) and scanned over the wavelength range of 400-200 nm against Nanopure water as a blank.
A series of experiments was conducted to characterize the fundamental photochemical behavior of S. UV254 radiation was delivered to aqueous solutions of S using a flat-plate collimator (16) that housed a low-pressure mercury lamp (Trojan Technologies Inc., London, ON, Canada). Similar collimating devices were constructed to house XeBr and KrCl excimer lamps; these lamps yield essentially monochromatic output at characteristic wavelengths of 282 and 222 nm, respectively. The relative spectral output of these lamps was measured at the bottom of the collimating device using an Ocean Optics USB2000 fiber optic spectrometer. Results of these measurements for the XeBr and KrCl systems indicated bandwidths (at half-maximum power) of 2.46 and 2.05 nm, respectively. Corresponding wavelengths of maximum output were 281.61 and 221.88 nm, respectively. Measurements conducted using a fiber optic radiometer detector (model P2 fiber optic with model IL1400A radiometer, International Light, Newburyport, MA), mounted on a micropositioning device (W. H. Kessel, Chicago, IL) indicated spatially uniform and temporally stable output beams from these devices. UV irradiance from each collimator was monitored by a radiometer (model IL1400A, International Light Inc., Newburyport, MA) with a model SEL240 detector. The detector had been calibrated against a NIST standard for wavelengths ranging from 400 to 200 nm. An opaque shutter was used to control exposure time under the collimated beam. Aqueous actinometer solutions (3.7 mL) were placed in small Petri dishes (diameter 3.5 cm) and irradiated in the center of the collimated beam. The solution surface was 2 cm below the end of the collimator. Radiometric measurements were collected at the same location. Actinometer solutions were mixed by the use of a small magnetic stir bar to promote uniformity of UV exposure. Aqueous actinometer solutions with a range of initial S concentrations were subjected to UV irradiation from each source using this method, and the concentrations of S and P were monitored as a function of exposure time using the HPLC method described above.
Results and Discussion Molar Absorption Coefficients of S and P. The molar absorption coefficients of aqueous S and P are illustrated in Figure 2 for wavelengths ranging from 400 to 200 nm. The data presented in Figure 2 indicate that S and P are both fairly strong absorbers of germicidal UV radiation. For the UV wavelengths that were examined in this study, three different absorbance situations were displayed. At 222 nm, the molar absorption coefficients of S and P were nearly identical. At 254 nm, P was a stronger absorber than S, whereas the opposite situation was observed at 282 nm. Under conditions of similar molar concentration of S and P in solution, the two compounds will absorb UV radiation with similar effectiveness at all three wavelengths. As such, any assessment of the photochemical dynamics of an aqueous solution containing these compounds will need to account for competitive absorption of applied radiation. Fluorescence Intensity of P. The fluorescence intensity of aqueous P as a function of its molar concentration is illustrated in Figure 3. For the range of concentrations VOL. 39, NO. 10, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Molar absorption coefficients of aqueous S and P as a function of wavelength. Vertical dashed lines indicate wavelengths at which photochemical behavior was examined in this study.
FIGURE 3. Fluorescence intensity as a function of concentration for aqueous solutions of P. The solid line represents a linear fit to the data, forced through the origin. examined and the conditions of fluorometry employed, a highly linear relationship between the concentration of P and fluorescence intensity was observed. Also included in Figure 3 is a linear fit through these data, forced through the origin, to illustrate the validity of the linear relationship between P concentration and fluorescence intensity for this concentration range. An initial experiment was conducted to define, in a qualitative sense, the basic photochemical behavior of S as an actinometer. Aqueous solutions of S (initial concentration ) 0.14 mM) were subjected to UV254 irradiation under a collimated beam. Subsamples of these solutions were collected after being subjected to applied UV254 doses (i.e., applied dose defined as the product of incident irradiation, at the free surface, and exposure time) ranging from 0 to 20 mJ/cm2 and analyzed for fluorescence intensity using the fluorometer. The results of these analyses are illustrated in Figure 4. These data illustrate a trend of a roughly linear increase in fluorescence intensity as a function of UV254 dose in the limit of low doses, followed by a gradual decline in the rate of fluorescence intensity increase at higher doses. This behavior is consistent with photoproduction of P, thereby leading to a condition of competitive absorption of the incident UV radiation and a decrease in the rate of photoproduct formation. Collectively, these data illustrate several important features of the actinometer based on S. First, the actinometer is sensitive to UV254 radiation, such that quantifiable changes in actinometer and photoproduct concentration are observed at UV254 doses that are relevant in disinfection operations. Second, the (stable) photoproduct of this actinometer displays strong fluorescence character. As such, the response of this actinometer system can be characterized using 3828
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FIGURE 4. Fluorescence intensity of aqueous actinometer solutions as a function of applied UV254 dose. Initial S concentration ) 0.14 mM. fluorometry, an analytical method that is well-suited to online, real-time analysis or monitoring applications. With regard to the use of fluorometry as an analytical method for quantification of P, the data presented in Figure 4 also illustrate another interesting characteristic of this actinometer system. While the change in fluorescence intensity resulting from UV exposure was essentially identical in the two experiments for which results are provided, the absolute values of fluorescence intensity in the two tests (at any given dose) were different. The differences in observed fluorescence between tests 1 and 2 in Figure 4 are believed to be attributable to differences in the initial concentration of P (i.e., in the “unirradiated” solution, dose ) 0). Although the starting concentrations were different, changes in the concentration of P through these two experiments were virtually identical. The observed changes in P concentration were attributed to the imposed UV radiation. Since changes in P concentration can be measured by HPLC or fluorometry, it is then possible to use the data from each of these tests to quantify photon delivery to the actinometer solution; however, accurate quantification of photon delivery requires that competitive photon absorption in solution be accounted for. Photochemical Production of P from S. Aqueous solutions of S were subjected to UV irradiation from each of the collimated beam systems described above in well-mixed, shallow, batch reactors. As a result of the sensitivity of S to long wavelength UV radiation from laboratory lighting, low concentrations of P were always present, even in the initial, unirradiated solutions. The initial conditions of these experiments were such that the molar concentration of P was never more than 4% of the molar concentration of S. For each of the UV sources, a range of initial concentrations of S and P were applied, and their concentrations were monitored as a function of irradiation time by HPLC. For each UV source, experiments were conducted for a range of exposure times to allow actinometer solutions to be subjected to UV doses ranging from (nominally) 0-40 mJ/cm2, based on the product of incident irradiance and exposure time. This dose range was selected because it is representative of the doses delivered in many disinfection applications. However, it should be noted that since the output irradiances from the three UV sources were different, the periods of irradiation required to deliver these doses were different for each UV source. The results of these experiments are illustrated in Figures 5-7 for exposures conducted at 254, 282, and 222 nm, respectively. For each of the experiments, a steady, zeroorder decline in the molar concentration of S was evident in the early parts of the experiment, with a corresponding increase in the molar concentration of P. However, the rate of P production deviated from a zero-order process (with respect to time) at larger values of exposure time. This
FIGURE 5. Time-course measurements of the aqueous concentrations of S and P in experiments involving UV254 irradiation under a collimated beam. Solid lines represent model fits to data. observation was consistent with the data illustrated in Figure 4 and was attributed to the competitive absorption of UV254 radiation by S and its photoproduct P. Mathematical Model to Describe Dynamic Behavior of Actinometer System. The dynamic behavior of the actinometer system based on aqueous solutions of S and its photoproduct P are complicated by competitive photon absorption that evolves during the course of the reaction. All available evidence suggests that this reaction proceeds exactly as illustrated in Figure 1; therefore, for purposes of modeling, it is assumed that the relevant chemistry is described by this figure. For the photochemical process described by Figure 1, the rate of reaction can be represented as:
dCS ) - ΦλRλ,S dt
(1)
where CS is the concentration of S (mol/L), t is the time (s), Φλ is the quantum yieldλ for photochemical production of P from S (mol of P/einstein), and Rλ,S is the rate of photonλ absorption per unit volume by S (einstein/L‚s). The subscript λ is used to indicate wavelength-specific or wavelengthdependent behavior. The reactor system used in the experiments that represent the focus of this modeling effort was assumed to be wellmixed. For purposes of modeling, the well-mixed assumption implies that the rate of transport attributable to mixing was large relative to the rate of reaction. In other words, transport as a result of mixing was sufficiently rapid to limit the development of substantial spatial gradients in reactant or product concentration over the course of the experiment that would otherwise have developed as a result of reaction.
FIGURE 6. Time-course measurements of the aqueous concentrations of S and P in experiments involving UV282 irradiation under a collimated beam. Solid lines represent model fits to data. In a system wherein only the starting material (S) absorbs incident radiation, the rate of photonλ absorbance per unit volume by S (Rλ,S) is defined as:
(1 - 10-λ,SCSH) ∀
Rλ,S ) IλA
(2)
where Iλ is the photon irradianceλ (einstein/cm2‚s), A is the surface area normal to the incident photon beam (cm2), λ,S is the molar absorption coefficientλ of S (L/mol‚cm), H is the solution depth (cm) ) optical path length (cm), and ∀ ) irradiated solution volume (L). At the beginning of each experiment, Rλ,S would have been essentially constant, because S was the only compound in solution that absorbed incident UV radiation, and as described above, the incident irradiance (photon flux) delivered by the collimated-beam system was spatially and temporally uniform. However, as the reaction proceeded, photon absorption by P increased, thereby resulting in a deviation from zero-order kinetics. In theory, knowledge of Φλ and Rλ,S is sufficient for accurate estimation of the photochemical reaction rate. Unfortunately, the physical conditions of many photochemical processes are such that Rλ,S is difficult to calculate. However, for two limiting conditions, calculation of Rλ,S is greatly simplified. These conditions have a clear physical interpretation for the batch reactor used in these experiments (see Figure 8). The first condition is one in which the solution is opaque to incident radiation as a result of photon absorption by the target compound (S, in this case) only. For the reaction of interest, this would correspond to a condition in which all incident photons are absorbed by S (i.e., the solution is opaque to incident UV radiation as a result of photon absorption by S). Referring to Figure 8 and the terms described VOL. 39, NO. 10, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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to the product of incident photon flux (irradiance), molar absorption coefficient, and molar concentration. Mathematically, the condition of transparency would be met in these experiments when λ,SCSH f 0 and λ,PCPH f 0. Although solution depths were small in these experiments (approximately 0.37 cm), the second limiting condition was also not satisfied when examining the entire system. However, it was possible to apply the second limiting condition to small (differential) portions of the reactor system. In particular, a model was developed around small, differential elements of thickness ∆h and cross-sectional area A (see Figure 8). For these small elements, the condition λ,SCSH f 0 and λ,PCPH f 0 can be met, depending on the magnitude of ∆h. A series expansion can be used to demonstrate that in the limit as x f 0:
10x ≈ 1 - ln(10)x
(3)
Therefore, in the limit as λ,SCSH f 0, the volumetric rate of photon absorbance (RS) is defined by:
(1 - [1 - ln(10)λ,SCS∆h]) ∀i
Rλ,S ) Iλ,iA
(4)
where Iλ,i is the irradianceλ incident on ith differential control volume (photons/cm2‚s), and ∀i is the volume of ith differential control volume (L). For this simulation, all differential volumes were assigned the same dimensions. Since ∀i ) A‚∆h, eq 4 was further simplified:
Rλ,S ) Iλ,i[ln(10)λ,SCS] FIGURE 7. Time-course measurements of the aqueous concentrations of S and P in experiments involving UV222 irradiation under a collimated beam. Solid lines represent model fits to data.
FIGURE 8. Schematic illustration of conditions of irradiation used in experiments to measure photochemical dynamics of aqueous actinometer solutions. above, this condition is met for large values of the product λ,SCSH and when no other compounds are present in solution that absorb the incident radiation. In other words, this condition is met under conditions of relatively high CS, relatively large λ,S, long optical path length (or some combination of these factors), and when competitive photon absorption does not take place in the system. While S is fairly effective at absorbing UV radiation at the wavelengths of interest in this study, it is clear that competitive photon absorption will develop as a result of the photochemical reaction of interest. Therefore, an analysis of the system based on the assumption of complete photon absorption by S would be possible only for the initial conditions of irradiation (i.e., before P concentration has increased substantially), or more generally for conditions that simultaneously yielded large values of λ,SCSH and small values of λ,PCPH, where λ,P is the molar absorption coefficientλ of P (L/mol‚cm) and CP is the concentration of P in solution (mol/L). The latter condition was not met in the experiments described herein. The second limiting condition is one in which the solution is optically transparent to incident radiation. Under these circumstances (as will be demonstrated below), the rate of photon absorbance by the target compound is directly related 3830
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(5)
Equation 5 indicates that on a local basis (e.g., within solution volumes of differential optical depth, ∆h), the rate of photon absorbance by the target compound is directly related to the local photon flux (irradiance), the molar absorption coefficient of the target compound, and the concentration of the target compound. Moreover, this derivation allows for the presence of other compounds in solution that could represent absorptive competition for incident photons. Therefore, it is possible to define the local rate of a photochemical reaction as follows:
dCS,i ) - ΦλIλ,i[ln(10)λ,SCS,i] dt
(6)
where the subscript i refers to a characteristic that applies within the ith differential control volume. Figure 1 indicates a 1:1 stoichiometric relationship between S and P; each mole of S consumed in the reaction yields 1 mol of P. It was assumed that the intermediate in the reaction sequence (Figure 1) did not accumulate within the system and was never present at a concentration high enough to influence photon absorbance by either S or P. Therefore
dCP,i dCS,i )dt dt
(7)
where CP,i is the molar concentration of P within ith control volume. For practical application of this model, it is necessary to define the spatial variation in irradiance within the system, because the term Iλ,i refers to irradiance incident on the differential control volume. Under the conditions employed in these experiments, competitive absorption of UV radiation occurred. Therefore, photon absorption by both S and P was accounted for in representing local irradiance. Beer’s law was applied for this purpose under the assumption of additive absorption. It was also necessary to account for spatial
TABLE 1. Summary of Refractive Indexes (λ) and Reflection Coefficients for Air-Water Interface (Rλ) for UV Wavelengths Used in This Study
TABLE 2. Estimates of Quantum Yield for Photoproduction of P from S
λ (nm)
nλ,air
nλ,water
Rλ
λ (nm)
Φλ (mol/einstein)a
SD (mol/einstein)
no. of replicate experiments
222 254 282
1.00031 1.00030 1.00029
1.3980 1.3764 1.3651
0.0275 0.0250 0.0238
222 254 282
0.693 0.732 0.850
0.037 0.064 0.049
3 5 3
a
variations in irradiance attributable to reflection of incident radiation at the air:water interface as well as decreases in irradiance as a result of divergence of the incident beam. Collectively, these terms were grouped, as shown in eq 8, to represent the irradiance incident on a slice of actinometer solution:
Iλ,i ) Iλ,0(10-(λ,SCS+λ,PCP)x)(1 - R)
(L +L x)
2
(8)
where Iλ,0 is the photon irradianceλ at free surface of aqueous solution (photons/cm2‚s), λ,P is the molar absorption coefficient of P (L/mol‚cm), x is the vertical distance from free surface (cm), Rλ is the reflectionλ coefficient, and L ) distance from lamp axis to free surface (cm). The first term in parentheses on the right-hand side of eq 8 accounts for absorption of UV radiation by S and P (i.e., Beer’s law). The second parenthetical term accounts for reflection of radiation at the free surface due to a change in refractive index of the two media through which the radiation was transmitted, namely, air and water. Under circumstances when radiation is imposed normal to the interface of two media with differing refractive indexes (e.g., air and water), the Fresnel equation reduces to
Rλ )
(
)
nλ,air - nλ,water nλ,air + nλ,water
2
(9)
where nλ,air is the refractive indexλ for air and nλ,water is the refractive indexλ for water. Refractive index varies among media but is also a function of other parameters, including wavelength and temperature. For air and water, detailed characterizations of the refractive index have been developed as a function of wavelength and temperature by Edle´n (17) and Schiebener et al. (18), respectively. Table 1 provides a summary of the refractive indexes for air and water at each of the wavelengths used in this study (at 20 °C), as well as the corresponding reflection coefficients for an air:water interface (oriented normal to incident radiation) at each wavelength. For purposes of these simulations, it was assumed that the refractive index of the actinometer solution was identical to that of pure water. In the absence of an absorbing medium, irradiance within the beam from a flat-plate collimator beam drops off roughly as the square of distance from the source (16). This decline is attributable to slight divergence of the beam from the source. The last term in eq 8 accounts for beam divergence. For the system illustrated in Figure 8, eqs 6-9 represent a model to describe the dynamic behavior of the system during these experiments. The model was implemented in a finite difference format, based on the following approximations of eqs 6 and 7:
∆CS,i ≈ - ΦλIλ,i[ln(10)λ,SCS,i] ∆t
(10)
∆CP,i ∆CS,i ≈∆t ∆t
(11)
and
Mean of estimates from replicate experiments at each wavelength.
where ∆CS,i and ∆CP,i represent the changes in the concentrations of S and P, respectively, within the ith control volume. Values of Iλ,i were calculated using eqs 8 and 9. Time steps used in these simulations were 1.0 s, and modeling was based on a differential slice thickness (∆h) of 0.01 cm. During each time step, photochemical transformations were modeled as if each differential slice existed in (temporary) isolation from all other slices. The condition of complete mix was simulated by redefining the concentrations of S and P in each slice at the end of each time step as the spatial average of the concentrations of each compound within the entire system. Calculations of changes in the concentrations of S and P in the next time step were based on the spatially averaged concentrations of these compounds that existed at the end of the preceding time step. This procedure was repeated for each time step, through an irradiation time at each wavelength that allowed for the delivery of a dose of roughly 40 mJ/cm2 (imposed at the free surface), corresponding to the conditions used in the experiments. Input parameters for the model included the initial concentrations of S and P as well as measured values of λ,S, λ,P, Iλ,0, and H. For the conditions used in these experiments, the maximum value of absorbance within any differential control volume, based on a control volume thickness of 0.01 cm, was
maximum absorbance ) (λ,SCS + λ,PCP)∆h|max ) 0.0271 (12) Therefore, the maximum error that could be ascribed to the assumption of an optically transparent solution (as defined by eqs 3-5) was roughly 0.2%. Calculated changes in the concentrations of S and P within any time increment (∆t ) 1.0 s) were less than 0.4% of the respective concentrations that existed within the reactor at the beginning of each time step. These small changes in concentration, combined with the smoothing of spatial variations in concentration at the end of each time step, were assumed to adequately represent the mixing conditions used in these experiments. To reiterate, the complete mix assumption is valid under conditions where the rate of transport (by mixing) is sufficiently large to eliminate spatial concentration gradients that result from reaction. The model was fit to each of the data sets illustrated in Figures 5-7 using nonlinear regression, subject to an optimization criterion of minimization of the sum of residual squared errors. Independent estimates of the quantum yield were developed for each data set based on these fitting operations. Table 2 provides a summary of the estimates of Φλ, along with a representation of the error in estimates of Φλ. At all three wavelengths examined in this study, the quantum yield for the reaction was quite high; the high value of the quantum yield for radiation is indicative of the sensitivity of S as an actinometer. The quantum yield for this actinometer was similar in magnitude to those of commonly applied actinometers for characterization of UV photoreactors at room temperature. Rahn et al. (9) reported an estimate of Φ ) 0.73 mol/einstein for the iodide/iodate actinometer for UV254. Hatchard and VOL. 39, NO. 10, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Parker (2) reported Φ ) 1.26 mol/einstein for the potassium ferrioxalate actinometer for UV254; however, this value has recently been called into question (9). Mark et al. (5, 6) reported Φ ) 1.8 mol/einstein for the potassium peroxodisulfate actinometer for UV254 based on H+ production (based on production of 2 mol of H+/mol of peroxodisulfate consumed by reaction). In general, the numerical model did a good job of representing the dynamic behavior of the actinometer system. Model predictions of the time-course behavior of S and P were in close agreement with measured values. The largest absolute difference between model predictions and measurements was seen in the experiments involving the highest initial concentration of S and the longest irradiation times. For the case of UV254, the model predicted a concentration of P that was roughly 8% higher than the measured value. Competitive absorption of photoactive photons is a common situation in photochemical reactor systems. The modeling approach described by eqs 8-11 represents a method by which the dynamic behavior of such a system may be simulated. Estimates of overall reactor performance are developed from this modeling approach by temporal and spatial integration of local photochemical reaction rate representations by the model. It should be recognized that the validity of this model is strongly dependent on the assignment of an appropriate mixing assumption and proper simulation of this mixing condition within the model. Virtually all photochemical reactors that are used in treatment applications are operated in a continuous-flow mode, and most operate in the turbulent regime. These reactors also are characterized by much longer optical paths than were used in these experiments. More specifically, fullscale photochemical reactors are generally characterized by complex fluid mechanics and strong spatial gradients in their radiation intensity fields; consequently, the assumption of complete mix cannot be applied to most photochemical reactor systems. Therefore, this model is not directly applicable to continuous-flow systems but may be useful in the analysis of photochemical dynamics in small, laboratory systems, such as shallow batch reactors that are often used to quantify intrinsic kinetics of photochemical reactions. However, models of field-scale (continuous-flow) photochemical reactor systems can be developed based on the concept of local reaction rate if transport behavior and the irradiance field are adequately described and properly incorporated into the model.
Acknowledgments This work was funded by the Water Environment Research Foundation (Grant 99-CTS-2-UR) and the National Science Foundation (Grant BES 0210350). Excimer lamps were made available by Ushio America, Inc.
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Literature Cited (1) Kuhn, H. J.; Braslavsky, S. E.; Schmidt, R. Chemical actinometry. Pure Appl. Chem. 1989, 61, 187-210. (2) Hatchard, C. G.; Parker, C. A. A new sensitive chemical actinometer. II. Potassium ferrioxalate as a standard chemical actinometer. Proc. R. Soc. London, Ser. A 1956, 235, 518-536. (3) Demas, J. N.; Bowman, W. D.; Zalewski, E. F.; Velapoldi, R. A. Determination of the quantum yield of the ferrioxalate actinometer with electrically calibrated radiometers. J. Phys. Chem. 1981, 85, 2766-2771. (4) Harris, G. D.; Adams, V. D.; Moore, W. M.; Sorensen, D. L. Potassium ferrioxalate as chemical actinometer in ultraviolet reactors. J. Environ. Eng., ASCE 1987, 113, 612-627. (5) Mark, G.; Schuchmann, M. N.; Schuchmann, H. P.; von Sonntag, C. A chemical actinometer for use in connection with UV treatment in drinking-water processing. J. Water SRT-Aqua 1990, 39, 309-313. (6) Mark, G.; Schuchmann, M. N.; Schuchmann, H. P.; von Sonntag, C. The photolysis of potassium peroxodisulphate in aqueous solution in the presence of tert-butanol: A simple actinometer for 254 nm radiation. J. Photochem. Photobiol. A 1990, 55, 157168. (7) Rahn, R. O. Use of potassium iodide as a chemical actinometer. Photochem. Photobiol. 1993, 58, 874-880. (8) Rahn, R. O. Potassium iodide as a chemical actinometer for 254 nm radiation: Use of iodate as an electron scavenger. Photochem. Photobiol. 1997, 66, 450-455. (9) Rahn, R. O.; Stefan, M. I.; Bolton, J. R.; Goren, E.; Shaw, P.-S.; Lykke, K. R. Quantum yield of the iodide-iodate actinometer: Dependence on wavelength and concentration. Photochem. Photobiol. 2003, 78, 146-152. (10) Linden, K. G.; Darby, J. L. Estimating effective germicidal dose from medium-pressure UV lamps. J. Environ. Eng., ASCE 1997, 123, 1142-1149. (11) Zhang, J.-Y.; Boyd, I. W.; Esrom, H. UV intensity measurement for a novel 222 nm excimer lamp using chemical actinometer. Appl. Surf. Sci. 1997, 109/110, 482-486. (12) Gottardi, W. Iodine and disinfection: Theoretical study of the mode of action, efficiency, stability and analytical aspects in the aqueous system. Arch. Pharm. 1999, 332, 151-157. (13) Gong, W. Long-Term Effects of Disinfection on Wastewater Effluents. Ph.D. Dissertation, Purdue University, 2002. (14) Bergstrom, D. E.; Inoue, H.; Reddy, P. A. Pyrido[2,3-d]pyrimidine nucleosides, synthesis via cyclization of C-5-substituted cytidines. J. Org. Chem. 1982, 47, 2174-2178. (15) Turro, N. J. Modern Molecular Photochemistry; BenjaminCummings: Menlo Park, CA, 1987. (16) Blatchley, E. R., III. Numerical modelling of UV intensity: Application to collimated beam reactors and continuous-flow systems. Water Res. 1997, 31, 2205-2218. (17) Edle´n, B. The refractive index of air. Metrologia 1966, 2, 71-80. (18) Schiebener, P.; Straub, J.; Levelt Sengers, J. M. H.; Gallagher, J. S. Refractive index of water and steam as a function of wavelength, temperature and density. J. Phys. Chem. Ref. Data 1990, 19, 677-715.
Received for review June 10, 2004. Revised manuscript received March 3, 2005. Accepted March 21, 2005. ES049120N
