Predicting the Emission Rate ofVolatile Organic Compounds fromVinyl FlooringS T E V E N S . C O X , †

J O H N C . L I T T L E , * , † A N DA L F R E D T . H O D G S O N ‡

Virginia Polytechnic Institute & State University,418 Durham Hall, Blacksburg, Virginia 24061, andE. O. Lawrence Berkeley National Laboratory,1 Cyclotron Road, Berkeley, California 94720

A model for predicting the rate at which a volatileorganic compound (VOC) is emitted from a diffusion-controlled material is validated for three contaminants(n-pentadecane, n-tetradecane, and phenol) found invinyl flooring (VF). Model parameters are the initial VOCconcentration in the material phase (C0), the material/airpartition coefficient (K), and the material-phase diffusioncoefficient (D). The model was verified by comparing predictedgas-phase concentrations to data obtained during small-scale chamber tests and by comparing predicted material-phase concentrations to those measured at the conclusionof the chamber tests. Chamber tests were conductedwith the VF placed top-side-up and bottom-side-up. Withthe exception of phenol and within the limits of experimentalprecision, the mass of VOCs recovered in the gas-phasebalances the mass emitted from the material phase. Themodel parameters (C0, K, and D) were measured usingprocedures completely independent of the chamber test.Gas- and material-phase predictions compare well to thebottom-side-up chamber data. The lower emission ratesfor the top-side-up orientation may be explained bythe presence of a low-permeability surface layer. Thesink effect of the stainless steel chamber surface was shownto be negligible.

IntroductionVarious building materials and consumer products (examplesinclude adhesives, sealants, paints, wood stain, carpets, vinylflooring (VF), and manufactured wood products) are sourcesof volatile organic compounds (VOCs) in the indoor envi-ronment. These materials typically contain residual quantitiesof VOCs that can be important sources of air contamination.Understanding the source characteristics of these materialsis crucial if indoor air quality problems are to be solved (1).For example, an improved understanding of mass-transfermechanisms could facilitate the reformulation of buildingmaterials to minimize VOC contamination of indoor air (2).

Characterizing the source behavior of building materialstypically involves chamber studies, which are time-consum-ing, costly, and subject to several limitations (3). Of the variousmechanisms governing VOC source behavior, diffusion is

one of the most important (4-6). Chamber-based sourcecharacterization studies have frequently neglected the roleof diffusion in emission processes. Furthermore, modelsbased on chamber-derived data are often empirical in natureand are of limited value when extrapolating to otherconditions. For those indoor sources controlled by internaldiffusion processes, a mechanistic diffusion model holdsconsiderable promise for predicting emission characteristicswhen compared to empirical models (3, 4, 7).

The primary objective of this study is to demonstrate thatVOC emissions from VF, an exemplary diffusion-controlledsource, are described by well-established mass-transfertheory and are predictable using a simple mathematicalmodel. A secondary objective is to examine whether adsorp-tion to the stainless steel chamber surface represents asignificant VOC sink.

Emissions ModelA model describing emissions from a homogeneous, diffu-sion-controlled source (3, 4, 7) is briefly reviewed and thenextended to include the chamber wall sink effect. Withreference to Figure 1, the transient diffusion equation is

where C is the concentration of a VOC in the slab of material(in this case, VF), D is the material-phase concentration-independent diffusion coefficient, t is time, and x is distancefrom the base of the slab. The initial condition assumes auniform material-phase concentration of the VOC, C0. Thefirst boundary condition assumes that there is no flux fromthe base of the slab. The second boundary condition isimposed via a mass balance on the VOC in the chamber airor

where yin and y are the concentrations of the VOC in theinfluent and effluent chamber air, respectively; Q is thevolumetric air flow rate; V is the well-mixed chamber volume;A is the exposed surface area of the slab; and L is the thicknessof the slab. A linear and instantaneously reversible equilib-rium relationship is assumed to exist between the slab surfaceand the chamber air or

where K is a material/air partition coefficient with units of

* Corresponding author telephone: (540)231-8737; fax: (540)231-7916; e-mail: jcl@vt.edu.

† Virginia Polytechnic Institute & State University.‡ E. O. Lawrence Berkeley National Laboratory.

FIGURE 1. Schematic representation of a homogeneous source inroom or chamber.

∂C∂t

) D∂

2C

∂x2(1)

∂y∂t

V ) Qyin - DA∂C∂x

|x)L - Qy (2)

K )C|x)L

y(3)

Environ. Sci. Technol. 2002, 36, 709-714

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mass per volume/mass per volume. The instantaneouslyreversible assumption implies that resistance to mass transferbetween the material surface and the bulk chamber air isnegligible. For a 0.01-m stagnant boundary layer and a gas-phase diffusion coefficient of 10-5 m2 s-1, the characteristicdiffusion time is about 10 s. As will be shown, this is fastrelative to the time scale over which gas-phase chamberconcentrations change. Combining eqs 2 and 3 and assumingyin is zero, yields

A solution to these equations was given by Little et al. (4):

where

and the qn values are the roots of

Equation 5 gives the contaminant concentration in theslab as a function of time and distance from the base of theslab. The gas-phase concentration of the VOC in the chamberat any time t is obtained by first finding the concentrationat the slab surface (x ) L) and then applying the equilibriumcondition defined by eq 3. Finding the roots of eq 8 isstraightforward because the function approaches infinity atwell-defined intervals. The first root occurs between zeroand π/(2L), the second occurs between π/(2L) and (3π)/(2L),the third occurs between (3π)/(2L) and (5π)/(2L), and so on.With the roots conveniently bracketed, they can be foundusing the method of bisection.

To evaluate the importance of the chamber sink effect fora given VOC, a linear and instantaneously reversible equi-librium relationship is also assumed to exist between thestainless steel chamber surface and the chamber air or

where q is the adsorbed surface concentration and Ks is thesurface/air partition coefficient. Ks has units of mass persurface area/mass per volume. With reference to Figure 1,As is the exposed surface area of stainless steel within thechamber. Now, assuming there is no VF in the chamber andyin ) 0, a mass balance on the VOC in the chamber (bothadsorbed to the walls and in the gas-phase) yields

If the gas-phase concentration in the chamber air at timezero is y0, then combining eqs 9 and 10 and integrating resultsin

Equation 11 can be used to determine the value of Ks from

experimental data, as will be described. A similar analysismay also be applied to the situation where the VF slab ispresent in the chamber. In that case, eq 2 must be modifiedto include the accumulation of the adsorbed VOC on thechamber walls, in an analogous fashion to eq 10. Fortunately,as shown in eq 11, the incorporation of the adsorbed phasemay be expressed as a simple increase in the chamber volumeequal in magnitude to KsAs. The foregoing solution maytherefore be applied with eq 7 modified as follows:

An analytical expression for the mass emission rate into thechamber air, E, may be derived from the expression for C(x,t)given in eq 5, as follows:

where J(x,t) is the mass-transfer flux as a function of distancefrom the base of the slab and time.

Experimental ApproachA commercial grade sheet VF material was selected for studybecause VF is present in many residential and commercialbuildings, is relatively homogeneous, and has been shownto emit hazardous organic chemicals (8). A small-scalechamber study was used to generate data for model valida-tion. The model parameters (C0, K, and D) were measuredcompletely independently of the chamber experiments.Additional experiments were conducted to measure thechamber surface partition coefficient, Ks. The model isvalidated by comparing experimental measurements to (i)the predicted gas-phase concentration in the chamber as afunction of time during the chamber experiment and (ii) thepredicted material-phase concentration in the VF as afunction of depth after completion of the chamber experi-ments.

The VF used in this study is a monolayer sheet vinyl (1.8m wide) manufactured for the medical facilities market. Inaddition to poly(vinyl chloride), the VF contained ap-proximately 50% (by weight) CaCO3 as well as plasticizers,pigments, and stabilizers (9). The nominal thickness was 2mm with a density of approximately 1.5 g cm-3. The VF wasmanufactured 4 months prior to the investigation. Uponreceipt, six 30 cm × 30 cm squares were cut from the centerof the specimen, stacked, wrapped in multiple layers ofaluminum foil, and stored at below -5 °C. Squares from thecenter of the stack were removed as needed for experimentalwork. Experiments were completed within 2 months of receiptof the specimen.

In all experiments, gas samples for VOCs were collectedon Tenax-TA sorbent tubes. The sampling flow rate of 0.10L min-1 was regulated with a mass flow controller. Samplevolumes were 0.5-3.0 L with the smaller volumes used onlyduring the initial experimental period. The tubes wereanalyzed for individual VOCs by thermal desorption gaschromatography/mass spectrometry using a modificationof U.S. EPA Method TO-1 (10). The target compounds weren-tetradecane, n-pentadecane, phenol, and 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate (TMPD-MIB). For TMPD-MIB, the 1 and 3 isomers were individually quantified, andthe results were combined. Six-point calibrations wereprepared for all compounds using 1-bromo-4-fluorobenzeneas the internal standard.

The VF was tested for VOC emissions in small-scalechambers following standard practice (11). The 10.5-Lchambers were constructed of 316 stainless steel and operatedat 0.98 ( 0.5 L min-1 with N2, 23 ( 1 °C, and 50 ( 5% relative

( VAK)∂C

∂t|x)L + D

∂C∂x

|x)L + ( QAK)C|x)L ) 0 (4)

C(x,t) )

2C0∑n)1

∞ { exp(-Dqn2t)(h - kqn

2) cos(qnx)

[L(h - kqn2)2 + qn

2(L + k) + h] cos(qnL)} (5)

h ) QADK

(6)

k ) VAK

(7)

qn tan(qnL) ) h - kqn2 (8)

Ks ) qy

(9)

dqdt

As + dydt

V ) -Qy (10)

ln( yy0

) ) -( QV + KsAs

)t (11)

k )V + KsAs

AK(12)

E ) AJ(x,t)|x)L ) -AD∂C(x,t)

∂x|x)L (13)

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humidity (RH). The exposed surface area of the VF specimenswas 0.0195 m2. This resulted in a flow rate/area ratio of 3 (m3

h-1)/m2, which equals the ratio for a 3 m high space finishedwith VF and ventilated at 1 h-1. The edges of the specimenswere sealed, and the backs were covered with stainless steel.Because there was evidence that mass-transfer properties ofthe top were different than the bottom, the top surface of theVF was exposed in one experiment, and the bottom surfacewas exposed in another. The chamber effluent gas wasperiodically sampled over a period of 30 days. During thefirst day, effluent samples were collected at 1, 3, 6, and 24h elapsed time.

Independent measurements of C0 were obtained using anovel method of cryogenic milling followed by VOC extractionduring fluidized bed desorption (FBD) at room temperature.C0 was measured at room temperature because the physicalstructure of a polymeric material is significantly modifiedwhen heated to above the glass transition temperature (Tg).According to the dual-mobility conceptual model of diffusionin polymers, at temperatures below Tg, one fraction of thetotal VOC concentration is considered mobile while the otherfraction is considered partially immobilized within micro-voids frozen into the polymer structure (12). Althoughadditional work is needed to more completely describe themass-transfer characteristics of common polymeric materials,C0 determined by FBD is thought to approximate the mobilefraction of VOCs. The theory, methodology, and equipmentused to assess C0 is described elsewhere (13, 14). Independentmeasurements of K and D were based on transient sorption/

desorption data obtained from tests conducted using a high-resolution dynamic microbalance. The microbalance appa-ratus and methodology used to determine K and D are alsodescribed elsewhere (15, 16).

Material-phase VOC concentration as a function of depthin the VF samples was measured before and after chamberexperiments (14). A microtome was used to cut successivethin slivers (∼0.2 mm thick with a mass of 15-30 mg) froma VF specimen. Each VF sliver was transferred to a glass tube,which was then inserted into the sleeve heater of a thermaldesorption apparatus. The inlet flow of humidified N2 (∼10%RH) to the sample tubes was regulated at 100 cm3 min-1. Aportion of the outlet gas stream (1/25) was sampled for VOCs.The remainder of the flow was vented. At the start ofdesorption, the heater temperature was quickly ramped fromambient to 60 °C and held for 10 min. Next, the temperaturewas ramped over 20 min to 150 °C and then held constant.Gas samples were collected successively over periods from0 to 60, from 60 to120, and from 120 to 180 min after initiatinga test. Two replicate tests with blanks were conducted.

A procedure to evaluate Ks, the stainless steel chambersurface/air partition coefficient, was developed. Two 10.5-Lstainless steel chambers were connected in series using 0.64-mm Teflon tubing. The chambers were held in an incubatorat 23 ( 1 °C. The first “source” chamber was supplied 1.0 (0.2 L min-1 with nitrogen humidified at 50 ( 5% RH. After1 h, background samples for the analysis of VOCs werecollected from the inlet and the outlet of the second “target”chamber. Next, a 15 × 15 cm square of new VF was attachedto a stainless steel plate with the bottom surface exposed.The exposed surface area of the specimen was 0.02 m2. Thisspecimen was placed into the source chamber. VOC sampleswere collected from the inlet and the outlet of the targetchamber at 48 h elapsed time. Then, the source chamberwas removed. The nitrogen supply gas was connected directlyto the inlet of the target chamber. This established time zerofor the decay period. The flow rate was immediately reducedto 0.46 ( 0.2 L min-1 to lengthen the decay period and allowfor the collection of multiple VOC samples. These wereobtained from the chamber outlet at average elapsed timesof 7.5, 20, 35, 50, 67.5, 90, 120, 180, 270, and 360 min.

Results and DiscussionMass Balance. As summarized in Table 1, VOC mass balancecalculations were performed by comparing material-phaseconcentration data collected from VF slivers before and afterchamber testing with gas-phase concentration data collected

TABLE 1. Mass Balance Summary

compdameasd in material-phasebefore chamber testb (µg)

measd in material-phaseafter chamber testb (µg)

measd material-phaseloss (µg)

measd in gas-phaseeffluentb,c (µg)

difference(µg)

n-pentadecane, T 2 770 ( 40 2 540 ( 150 240 240 ( 20 0n-pentadecane, B 2 770 ( 40 2 210 ( 130 560 420 ( 30 140n-tetradecane, T 2 530 ( 40 2 320 ( 200 200 270 ( 20 70n-tetradecane, B 2 530 ( 40 1 920 ( 160 600 470 ( 40 130phenol, T 18 600 ( 900 16 400 ( 400 2 200 1 800 ( 120 400phenol, B 18 600 ( 900 13 900 ( 300 4 800 2 500 ( 160 2 300

a T, top-side-up. B, bottom-side-up. b Mean and standard deviation. c Uncertainty based on prior work in which ∼25 pairs of collocated sampleswere collected and analyzed using identical methods and materials.

FIGURE 2. Measured initial material-phase concentration profiles.

TABLE 2. Model Parameters C0, K, D, and Ks for Selected VOCs

compd C0a (µg m-3) K a (µg m-3)/(µg m-3) D a (m2 s-1) Ks (µg m-2)/(µg m-3)

n-pentadecane (4.3 ( 0.9) × 107 420 000 ( 40 000 (6.7 ( 1.1) × 10-14 0.13n-tetradecane (4.4 ( 0.4) × 107 120 000 ( 1 000 (12 ( 0.1) × 10-14 0.043phenol (20 ( 0.4) × 107 120 000 ( 3 000 (12 ( 0.1) × 10-14 0.065

a Mean and standard deviation.

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during tests. With the exception of phenol in the bottom-side-up tests, VOC mass transfer between the material andthe gas phases balanced within measurement uncertainty.One possible reason for the discrepancy is that two differenttechniques were used to measure the material-phase con-centrations. Those measured before the chamber experimentwere based on composite samples taken over a larger anddifferent piece of the same VF. The post-chamber measure-ments were based on a series of thin slivers taken over arange of depths from a small piece of the exposed VF.Measured material-phase concentrations of phenol in VFshow greater variability than the other VOC concentrationmeasurements (13, 14). This suggests that phenol is lessuniformly distributed in VF than other residual VOCs or thatphenol, unlike the alkane hydrocarbons, may be a degrada-tion product of another chemical contained in the VF ratherthan a manufacturing residual.

Independent Measurement of Model Parameters. Theinitial material-phase concentration profiles of the four targetcompounds are shown in Figure 2. The error bars expressuncertainty based on the coefficient of variation estimatedfrom concentrations measured in three replicate slivers takenat the VF surface. Although the initial concentrations ofn-tetradecane, n-pentadecane, and phenol are all relativelyuniform, the TMPD-MIB concentration varied strongly withdepth and could not be used in model validation because eq5 requires a uniform initial concentration. Values of the modelparameters (C0, K, and D) for n-pentadecane, n-tetradecane,and phenol are summarized in Table 2. In related work (16),the K and D values of these three compounds were shownto be independent of concentration as required for the model.

Sink Effect. Values for the stainless steel chamber surface/air partition coefficient, Ks, are also shown in Table 2. Thesewere obtained by plotting the data collected according to eq11 (as shown in Figure 3) and then calculating Ks from theslope of the graph and the known values of V, Q, and As. Theplotted data follow reasonably linear relationships, support-ing the assumption of a rapidly reversible linear adsorptionisotherm. In all cases, the magnitude of KsAs is greater thanthe magnitude of V (see eq 11), indicating that the rate ofdesorption from the stainless steel surface is significant ascompared to the rate of dilution. Nevertheless, mathemati-cally incorporating the sink effect in the emissions modelmade less than 1% difference to the predicted gas-phasechamber concentrations, indicating that the rate of desorp-tion from the stainless steel surfaces is insignificant ascompared to the rate of emission from the vinyl flooring.

Validation of Model. Figures 4-6 show predicted gas-phase concentrations as compared to measured concentra-tions of n-pentadecane, n-tetradecane, and phenol for thetop-side-up and bottom-side-up VF chamber experiments.

Although the model predicts gas-phase VOC concentrationsvery well for the bottom-side-up scenario, it tends tooverpredict for early times and slightly underpredict at longertimes. A possible cause of the overprediction is that D andK were measured at 26 °C while chamber tests were con-ducted at 23 °C. It has been shown for VOCs in polymers thatD increases with temperature while K decreases withtemperature. The model predicts relatively higher gas-phaseconcentrations as D grows larger and K grows smaller. Inaddition, as previously mentioned, the mass balance forphenol in the bottom-side-up experiment indicates lowerthan expected gas-phase concentrations.

FIGURE 3. Plots to determine stainless steel chamber surface/airpartition coefficients, Ks.

FIGURE 4. Predicted and measured chamber gas-phasen-pentadecane concentration.

FIGURE 5. Predicted and measured chamber gas-phasen-tetradecane concentration.

FIGURE 6. Predicted and measured chamber gas-phase phenolconcentration.

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The VOC concentrations from the top-side-up VF may belower than predicted due to different mass-transfer propertiesat the top surface. The steep concentration gradient of TMPD-MIB in the VF (Figure 2) suggests that TMPD-MIB may havebeen applied in some form to the VF surface during manu-facturing. The functionality of the flooring material wouldpresumably be improved by the presence of a low-perme-ability surface layer.

Figures 7-9 show the measured material-phase concen-trations of n-pentadecane, n-tetradecane, and phenol after722 h of chamber exposure. The model predicts the material-phase concentrations well, but consistent with the existence

of a top surface diffusion barrier, underpredicts the con-centrations in the top-side-up VF after chamber testing.

Implications for Source Characterization. The goodmodel predictions are very encouraging because the modelis based entirely on fundamental mass-transfer mechanismsand the model parameters were measured using procedurescompletely independent of the chamber test. This suggeststhat relatively homogeneous diffusion-controlled buildingmaterials can be characterized in a way that is more directthan the traditional chamber study. In addition, the modelpresented here can also be used to evaluate the impact indoormaterials have on indoor contaminants when acting as aVOC sink (17, 18).

The source characterization process would be greatlyfacilitated if the values of K and D could be predicted, asopposed to being measured, each time a new contaminantis identified. Although not explored in this paper, the limitedresults shown in Table 2 suggest that D and K tend to correlatewith molecular weight and vapor pressure, respectively, asshown previously (16). If such correlation equations can bededuced for the typical diffusion-controlled materials foundin buildings, perhaps based on the different classes of organiccompounds, all that would be required is the identificationand measurement of the initial concentration of individualVOCs in the material phase. Once the VOCs have beenidentified and quantified (i.e., C0 is determined), values forD and K could be obtained from appropriate correlationequations and used to predict the emission rates withoutfurther effort (3).

Future work in this area includes assessing the uniformityof K, D, and C0 within a particular material and across differentspecimens and brands of building materials. Quantifying thetemperature dependency of K and D is also necessary tomaximize the utility of the model. Extending this work toother homogeneous building materials is needed to furthervalidate the overall strategy. In addition, construction andvalidation of similar models for nonuniform initial concen-trations and multilayer building materials would extend theusefulness of the approach.

AcknowledgmentsFinancial support for the work at VT was provided by theNational Science Foundation (NSF) through an NSF CAREERAward (Grant 9624488). Work at LBNL was sponsored by theU.S. Department of Energy, Assistant Secretary for EnergyEfficiency and Renewable Energy, Office of Building Tech-nology, State and Community Programs under Contract DE-AC03-76F00098.

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(5) Christiansson, J.; Yu, J.-W.; Neretnieks, I. Indoor Air ’93.Proceedings of the 6th International Conference on Indoor AirQuality and Climate, Helsinki, Finland, July 4-8, 1993; Vol. 2,pp 389-394.

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(7) Cox, S. S.; Little, J. C.; Hodgson, A. T. In Healthy Buildings 2000Proceedings, Espoo, Finland, August 6-10, 2000; SIY Indoor AirInformation: Oy, Finland, 2000; Vol. 4, pp 169-174.

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FIGURE 7. Predicted and measured material-phase n-pentadecaneconcentration profiles (after chamber test).

FIGURE 8. Predicted and measured material-phase n-tetradecaneconcentration profiles (after chamber test).

FIGURE 9. Predicted and measured material-phase phenol con-centration profiles (after chamber test).

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(9) Tshudy, J. A. Environmental Research and Consulting, Ephrata,PA, personal communication, 1998.

(10) Method TO-1, Revision 1.0: Method for the Determination ofVolatile Organic Compounds in Ambient Air Using TenaxAdsorption and Gas Chromatography/Mass Spectrometry (GC/MS); U.S. Environmental Protection Agency, Center for Envi-ronmental Research Information, Office of Research andDevelopment: Washington, DC, 1984.

(11) Standard Guide for Small-Scale Environmental Chamber De-terminations of Organic Emissions From Indoor Materials/Products; ASTM D5116-97; American Society for Testing andMaterials: Philadelphia, 1997.

(12) Vieth, W. Diffusion in and through Polymers; Hanser Publish-ers: Munich, 1991; pp 29-38.

(13) Cox, S. S.; Hodgson, A. T.; Little, J. C. J. Air Waste Manage. Assoc.2001, 51, 1195.

(14) Cox, S. S.; Hodgson, A. T.; Little, J. C. Proceedings of EngineeringSolutions to Indoor Air Quality Problems Symposium; Air andWaste Management Association: Raleigh, NC, July 17-19, 2000;pp 65-75.

(15) Zhao, D. Y.; Cox, S. S.; Little, J. C. Indoor Air ’99. Proceedings ofthe 8th International Conference on Indoor Air Quality andClimate; Construction Research Communications Ltd.: Edin-burgh, Scotland, August 8-13, 1999; Vol. 1, pp 408-413.

(16) Cox, S. S.; Zhao, D. Y.; Little, J. C. Atmos. Environ. 2001, 35 (22),3823.

(17) Zhao, D. Y.; Rouques, J.; Little, J. C.; Hodgson, A. T. Indoor Air’99. Proceedings of the 8th International Conference on IndoorAir Quality and Climate; Construction Research Communica-tions Ltd.: Edinburgh, Scotland, August 8-13, 1999; Vol. 5, pp264-269.

(18) Zhao, D. Y.; Little, J. C.; Hodgson, A. T. Modeling the reversible,diffusive sink effect in response to transient contaminantsources. Indoor Air, in press.

Received for review March 29, 2001. Revised manuscriptreceived August 30, 2001. Accepted November 2, 2001.

ES010802+

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