Radon and Its Decay Products - American Chemical Society

Chapter 24

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A Model for Size Distributions of Radon Decay Products in Realistic Environments F. Raes, A. Janssens, and H. Vanmarcke Nuclear Physics Laboratory, State University of Gent, Proeftuinstraat 86, B-9000 Gent, Belgium A model has been developed to calculate the size distributions of the short lived decay products of radon in the indoor environment. In addition to the classical processes like attachment, plate out and ventilation, clustering of condensable species around the radioactive ions, and the neutralization of these ions by recombination and charge transfer are also taken into account. Some examples are presented showing that the latter processes may affect considerably the appearance and amount of the so called unattached fraction, as well as the equilibrium factor.

This paper is the third chapter of our theoretical investigations of the size distribution of radon decay products. In all of the work we concentrated more particularly on the behavior of the so called unattached fraction under different environmental conditions. In a first paper (1), we have applied the theory describing the clustering of mixtures of condensable vapors around ions, offering a conceptual framework to cope with the broad spectrum of experimental data on the size of unattached -RaA and ThB particles. It was shown that the observations could largely be explained by ion cluster formation and growth, looking at the radioactive ions as though they were normal positively charged ions. As a second step we investigated the impact of ion clustering and growth on the form of the active size distribution in different environmental conditions (2). The key question was whether the description of airborne activity in terms of an "unattached fraction" with a single diffusion coefficient and an "attached fraction" described by a unimodal lognormal distribution, is appropriate in all conditions. We showed that the composition of the atmosphere determines the physical appearance of radioactive particles in two ways: 1) the presence of condensable products may broaden the size distribution of the free radioactive fraction either by clustering or by forming an ultra fine aerosol to which the free fraction can become attached; and 2) the neutralization of 0097-6156/87/0331-0324$06.00/0 © 1987 American Chemical Society

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A Model for Size Distributions of Radon Decay Products

325

radioactive ions, mainly by charge transfer with appropriate gases quenches clustering and influences the deposition of airborne a c t i v i t y , especially i n rooms with d i e l e c t r i c walls. Whereas i n the second paper, we considered a rather general system of ions that were continuously being formed by radioactive decay of a gaseous mother isotope, we w i l l now consider radon and a l l of i t s short lived decay products, and we w i l l calculate size distributions for each decay product.

Ion C l u s t e r F o r m a t i o n and Growth

The c l a s s i c a l theory of charged cluster formation, and i t s application to radon decay products i s given extensively i n (1). The theory demonstrates that when an ion ( i n our case the radioactive decay product) i s exposed to a super-saturated vapor, or to some binary mixture of condensable vapors (both under-saturated), the ion may start growing spontaneously, when i t passes some c r i t i c a l size. The main conclusions regarding the size of the unattached fraction, and the comparison with the experimental findings are summarized i n Table I. It i s shown that the consideration of the clustering of binary mixtures of condensable products (H2SO4 and H2O i n our case) rather than the clustering of H2O alone i s essential to account for the observed range of d i f f u s i o n c o e f f i c i e n t s of radon decay products and for the observed growth of these products.

C o m p e t i t i v e Removal P r o c e s s e s

It takes some time for an ion to grow from the molecular size to the c r i t i c a l cluster size (1). When the ion becomes neutralized or i s scavenged from the gas phase within that period of time, obviously no growth w i l l occur. The ion removal processes are neutralization by recombination or charge transfer, deposition on surfaces, attachment to aerosol p a r t i c l e s , v e n t i l a t i o n and radioactive decay. The description of these processes i s given i n (2). Table II summarizes the mean ion lifetime corresponding to the mentioned removal processes and compares them with the time an ion needs to become a c r i t i c a l H2O-H2SO4 cluster. The growth time i s calculated for two d i f f e r e n t H2SO4 concentrations at a r e l a t i v e humidity of 75%, considering the kinetics of H2SO4 c o l l i s i o n s with ( s u b c r i t i c a l ) H2OH2SO4 ion clusters (1). Table II shows that ion growth w i l l be inhibited i n the most stringent conditions of neutralization, deposition or attachment, but also that there may be situations where the time an ion needs to become a stable p a r t i c l e i s comparable to or smaller than the ion lifetime c h a r a c t e r i s t i c for each removal process. The N u m e r i c a l Model AER01A

The model used here i s similar to the one used i n (2), except that i t is now extended to calculate the evolution i n time of RaA, RaB and RaC containing p a r t i c l e s . The core of the model i s the code AER01, which was developed for the description of photolytic and r a d i o l y t i c

326

RADON AND ITS DECAY PRODUCTS

Table I. Comparison of the experimental findings and t h e o r e t i c a l predictions of the size of free radon decay products

Experimental Findings

Diffusion Coefficient (cm s

)

Occurence of Growth

E f f e c t of Relative Humidity on D i f f u sion C o e f f i c i e n t

(0.55 «-)

Theory : Clustering of HO

Theory : Clustering of H 0 and H S 0 2

2

4

0.1 - 0.08

0.1 - 0.03 +

impossible

possible i n "polluted" atmospheres

D \ when r.h.t

D Ψ when r.h.t

0.08 - 0.03 (+ 0.003)

on some occasions

inconsistent

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Table I I .


327

Comparison of the time an ion cluster needs to reach the c r i t i c a l size with the c h a r a c t e r i s t i c lifetimes corresponding with d i f f e r e n t competitive removal processes

Process

ion c l u s t e r i n g

Time of Reach the C r i t i c a l Size (s)

Conditions

H S0 = 0 HSC>4 = 10 molec cm" H2SO4 = l0 molec cm 2

00

4

8

3

2

10

-3

300 3 ion mean l i f e t i m e (s)

recombination

charge transfer

260 10 0.06

3

Rn Rn Rn

= 37 Bq m" = 3.7 10 Bq m" =3.7 1 0 Bq n f 4

3

1 0

3

3

NC>2 = 0 molec cm" N0 = 1 0 molec cm" 11

3

00

0.2

2

deposition

1

S/V = 0.02 cm" , D = 0.04 cm s" conductive wall dielectric (surface charge density = 8 1 0 " C cm" ) 2

13

1

2

2500

7 420 2

attachment

aged aerosol fresh nucleation aerosol

ventilation

1 h"l

3600

radioactive decay

RaA RaB RaC

265 2320 1710

328


formation of H2O-H2SO4 aerosol from the gas phase. description of AER01 i s given i n (3).

The f u l l

The S i z e D i s t r i b u t i o n o f S t a b l e P a r t i c l e s This size d i s t r i b u t i o n i s approximated by two modes: a nucleation mode containing p a r t i c l e s with a diameter between the c r i t i c a l size (~ 1 nm, depending on the conditions) and 0.4 ym; and an accumulation mode between 0.01 and 1 ym. The accumulation mode i s described by a lognormal d i s t r i b u t i o n with a fixed median diameter, geometric standard deviation and t o t a l number concentration and i s considered here as a background aerosol that does not change i n size i t s e l f , but plays a role i n scavenging radon daughters, ions and H2SO4 molecules. H2O-H2SO4 p a r t i c l e s enter the nucleation mode at the c r i t i c a l size by homogeneous or ion-induced aerosol formation from the gas phase, and they further grow by condensation. The rate of aerosol formation i s very much dependent on the H2O and H2SO4 concentratons i n the gas phase. The H2O concentration i s held constant at 75% r.h. at 25°C. Contrary to our calculations i n (2), where the H2SO4 concentration was fixed i n the course of the calculation, we now have solved the balance equation for H2SO4, simultaneously with the balance equations for the p a r t i c l e s . Hence we are able to keep track of variations i n p a r t i c l e formation and growth rates due to variations i n the H2SO4 concentration. It i s assumed that the charge of the p a r t i c l e s i n both modes i s given by the Fuchs equilibrium charge d i s t r i b u t i o n (5), and a l l p a r t i c l e s are subject to deposition and v e n t i l a t i o n .

The S i z e D i s t r i b u t i o n o f RaA C o n t a i n i n g P a r t i c l e s This size d i s t r i b u t i o n i s approximated by three modes: a free a c t i v i t y mode; a nucleation mode; and an accumulation mode. The free a c t i v i t y mode contains the s u b c r i t i c a l clusters and i s confined between the diameter of the pure water ion cluster and the c r i t i c a l s i z e . Free RaA ions are formed continuously by radioactive decay of radon. Each radioactive decay w i l l produce 3.4 10^ gaseous ions (positive and negative) that w i l l play a role i n the recombination process, or may induce aerosol formation. Free radioactive ions may become uncharged by recombination or charge transfer, but only the charged ones are able to grow from the free a c t i v i t i y mode to the nucleation mode at a rate given by ion induced nucleation theory (3). Both charged and uncharged free RaA p a r t i c l e s may become attached to stable p a r t i c l e s i n the nucleation and accumulation mode. For the nucleation and accumulation mode, Fuch's equilibrium charge d i s t r i b u t i o n i s assumed.

The S i z e D i s t r i b u t i o n o f RaB and RaC C o n t a i n i n g P a r t i c l e s RaB and RaC size distributions are calculated i n the same way. Recoil of RaB ions from aerosol p a r t i c l e s i s taken into account i n the way proposed by Mercer (6). I f RaA ions or molecules are attached to aerosol p a r t i c l e s i n the accumulation mode, i t i s assumed that they remain on the surface of the p a r t i c l e s ; for RaA

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329

attached to or grown into the nucleation mode, i t i s assumed that the RaA i s submersed in the middle of the H2O-H2SO4 droplet.

Comments The decay of RaA, RaB and RaC w i l l also contribute to the formation rate of positive and negative gaseous ions, and this contribution w i l l change in time along with the concentration of the airborne radon daughters. Although i t i s straightforward to incorporate balance equations for the gaseous ions, this was not done i n the present version of AER01A. The ionization rate i s calculated considering only the radon concentration, and this w i l l lead to a s l i g h t underestimation of the growth process. Although AER01A contains the necessary coagulation algorithms, coagulation was not taken into account i n the present calculations, because of the r e s u l t i n g excessive c a l c u l a t i o n times. Hence, radon daughters that enter the nucleation mode by growth or attachment are not allowed to interact with the accumulation mode any more. However, since in our examples the p a r t i c l e concentrations are rather low, i t i s not expected that omission of coagulation w i l l induce large errors. One test c a l c u l a t i o n showed that the attached fraction i s underestimated by 1% i n conditions similar to Case 1 (see below). In cases of high p a r t i c l e concentrations no nucleation mode of radioactive p a r t i c l e s w i l l exist and the problem becomes irrelevant (see e.g. Case 5 below). By using the c l a s s i c a l theory of ion induced nucleation to describe the growth of radon daughters from the free a c t i v i t y mode to the nucleation mode, we loose information about the size of the s u b c r i t i c a l c l u s t e r s . These clusters are a l l lumped together between the size of a pure H2O ion cluster at 75% r.h. and the size of the c r i t i c a l H2O-H2SO4 c l u s t e r . The model only does keep track of the growth by condensation of the radon daughters once they arrived i n the nucleation mode. The prediction made by the model calculations should be taken with some care for two reasons: 1) H2O and H2SO4 are considered to be the condensing species, whereas other species may be active i n experimental or domestic environments; 2) the model uses c l a s s i c a l nucleation theory, which i s the only workable theory, but which i s also to be c r i t i c i z e d because i t applies macroscopic e n t i t i e s to clusters that contain only a few molecules (3).

R e s u l t s and D i s c u s s i o n s The environmental conditions for each of the cases considered below are summarized i n Table I I I ; a l l these parameters are constant i n time. The b u i l d up of the nucleation mode of the stable p a r t i c l e s and the build up of both the nucleation and accumulation modes of the radon decay products is calculated, and the results are given after a process time of one hour. Figures 1 to 5 show the size d i s t r i b u t i o n s of stable and radioactive p a r t i c l e s , and Table IV gives the disequilibrium, the equilibrium factor F, the "unattached f r a c t i o n " f and the plate-out rates for the d i f f e r e n t daughters.

330


Table I I I

D e s c r i p t i o n o f t h e c o n d i t i o n s f o r which t h e s i z e b u t i o n s were c a l c u l a t e d

N 0

w

2

molec cm

Case Case Case Case Case

1 2 3 4 5

Ο 10 Ο 10 10

a

l

1

distri

N

accum 3

characteristics

cm""

conductive conductive dielectric dielectric dielectric

1 1

1 1

1 1

100 100 100 100 10.000

In a l l o f t h e c a s e s : Rn = 12 Bq πΓ- ; H2SO4 f o r m a t i o n r a t e = 5 10" molec cm~3s-l ; v e n t i l a t i o n r a t e = 3 l O ^ s " ; s u r f a c e t o volume r a t i o = 0.02 c m ~ l . The a c c u m u l a t i o n mode i s l o g n o r m a l w i t h a median d i a m e t e r o f 0.1 ym and a g e o m e t r i c s t a n d a r d d e v i a t i o n o f 1.8. 3

1

T a b l e IV

D i s e q u i l i b r i u m between radon and i t s d a u g h t e r p r o d u c t s , e q u i l i b r i u m f a c t o r (F) and u n a t t a c h e d f r a c t i o n ( f ) w i t h r e s p e c t t o t h e p o t e n t i a l α energy and p l a t e o u t r a t e s o f the u n a t t a c h e d RaA, RaB and RaC f r a c t i o n s f o r t h e d i f f e r e n t c a s e s c o n s i d e r e d . The v a l u e s p r e v a i l a f t e r one hour p

f

plate out^ ) (h" ) RaB

RaC

0.31 1.47 520. 1.8 3.7

0.11 1.47 520. 1.8 3.7

1

Case

disequilibrium (Rn; RaA; RaB; RaC)

F

f

1 2 3 4 5

1 0.89;0.44;0.23 1 •0.86;0.36;0.17 1 •0.02; 0.00;0.00 1 •0.54;0.07;0.02 1 •0.81;0.37;0.20

0.40 0.34 0.003 0.10 0.35

0.76 0.46 0.93 0.85 0.06

RaA

0.61 1.47 520. 2.1 4.0

24.

RAES ET AL.


Diameter. Dp

331

(urn)

F i g u r e 1. Size distributions of the stable partie les ( ) of RaA ( ), RaB ( ) and RaC ( ) containing p a r t i c l e s , after 1 hour, Case 1.


332

Diameter,Dp (jum)

Figure 2. Size distributions of the stable p a r t i c l e s ( ) of RaA ( ), RaB ( ) and RaC ( ) containing p a r t i c l e s , after 1 hour, Case 2.

RAES ET AL.


333


334



RAES ET AL.


D i a m e t e r , Dp (urn)


335

336

RADON AND

ITS DECAY PRODUCTS

From Table I we can infer that growth of radioactive ions may be expected in a steel room operated at low radon concentrations, low concentrations of primary aerosol p a r t i c l e s , low concentrations of gases that induce charge transfer ( l i k e N0 >NO), and with some formation of condensable products. These conditions are simulated in Case 1 (Figure 1). The stable aerosol size d i s t r i b u t i o n i s bimodal. The RaA size d i s t r i b u t i o n turns out to be trimodal: the mode at the smallest sizes contains the free and nucleated RaA p a r t i c l e s and can be called the unattached f r a c t i o n ; the second and third mode contain the RaA that i s attached to the stable nucleation and accumulation mode respectively. It should be noticed that the a c t i v i t y contained in the attached f r a c t i o n i s more than 10 times smaller than i n the unattached fraction, such that only one mode, the unattached fraction, w i l l probably be detectable. The mean d i f f u s i o n c o e f f i c i e n t of that f r a c t i o n i s 0.013 cm s~l. The RaB and RaC size distributions are bimodal, again only the mode i n the lower size range w i l l probably be detectable. S t r i c t l y speaking, this mode cannot be called "unattached fractions", since they contain both nucleated RaB (or RaC) and RaB (or RaC) that i s attached to the stable nucleation model. The mean d i f f u s i o n c o e f f i c i e n t s of these modes are 0.007 and 0.002 cm" s" for RaB and RaC respectively. In Cases 2, 3 and 4, we focus attention on the e f f e c t of e l e c t r i c a l parameters l i k e the charge of the radon daughter and the conductivity of the walls. Both a high radon concentration ( i . e . , high ionization rate of the a i r ) and a high N0 concentration can affect the charge of the radon daughters; however, since high N0 concentrations w i l l more r e a d i l y occur, and since neutralization by N0 goes linear with the N0 concentration whereas n e u t r a l i z a t i o n by recombination goes only with the square root of the radon concentration (2) we changed only the N0 concentrations in our calculations. Calculations were performed considering both conducting and d i e l e c t r i c walls, the l a t t e r having a surface charge density of 8 10" C cm" (2). The size d i s t r i b u t i o n s for Case 2 are shown in Figure 2. In this case, N0 i s present at 4 ppb; the radon daughters get uncharged by charge transfer, hence are not available for nucleation anymore, and we end up with a well defined unattached fraction. Charge transfer does not affect the amount of gaseous ions in the a i r , such that nucleation s t i l l occurs around these ions, and a stable nucleation mode develops Radon daughters attach to these p a r t i c l e s as well as to the preexisting accumulation mode, and a broad bimodal attached f r a c t i o n i s formed. In the following cases we deal with d i e l e c t r i c walls, which largely enhance the deposition of ions and charged p a r t i c l e s by electrophoresis (2). In Case 3 no N0 i s present and the radon daughters remain charged, but a l l ions, stable and radioactive, are scavenged by the walls before they can grow or even attach to the preexisting aerosol. The nucleation modes collapse and v i r t u a l l y no airborne a c t i v i t y i s l e f t ( F i g . 3). In Case 4, N0 i s present; most parts of the radon decay products become neutral, such that they are not susceptible to electorphoretic deposition anymore. They remain airborne for a longer time and can attach to the preexisting aerosol (Fig. 4). The plate out rates of the unattached f r a c t i o n of the d i f f e r e n t daughters are s l i g h t l y d i f f e r e n t (Table IV). This i s because a d i f f e r e n t f r a c t i o n of each of the daughters remains 2

2

2

1

2

2

2

2

2

13

2

2

2

2

24.

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337

charged, and this i n turn i s due to their different radioactive l i f e t i m e , hence a different exposure time to Ν0 · Case 5, i n which the concentration of the preexisting aerosol is raised to 10,000 cm~ , can be considered as a simulation of a domestic environment. The resulting size distributions are given i n Figure 5. The increase of the aerosol concentration d r a s t i c a l l y affects the p a r t i t i o n i n g of the r a d i o a c t i v i t y between the attached and unattached fraction, as was to be expected. However, the increase in the aerosol concentration also results i n an increase of the plate out rate (Table IV). Normally this i s attributed to the smaller residence time of the unattached fraction, resulting i n smaller clusters. However, this cannot be the reason here since the model predicts the absence of growth, and cannot keep track of changes i n size of s u b c r i t i c a l clusters (see above). Again the reason i s that the r a t i o of charged to uncharged unattached daughters is higher i n Case 5 than i n Case 4. This time this i s due to the shorter residence time of the unattached daughters (controlled by the attachment process i n this case), such that neutralization by charge transfer i s not as complete as i n Case. 4 2

3

Conclusions We have developed a model that allows calculation of the evolution in time of the size distributions of the short lived decay products of radon. A l l relevant processes (including clustering and growth, and neutralization of the decay products) were taken into account, except different patterns of a i r c i r c u l a t i o n and different degrees of turbulence which may also affect the deposition of airborne material. Application of the model i n some selected conditions showed that the active size distributions and the amount of airborne a c t i v i t y i s largely affected not only by the aerosol content of the atmosphere, but also by i t s chemical composition, as well as by the dielectric/conductive characteristics of the surfaces i n the room. These factors have not been taken into account i n previous models (7,8). Case 1 showed that clustering and growth of radon decay products i s to be considered especially in experimental environments ( i . e . , steel rooms and partly treated atmospheres). From Cases 2 to 5 we may infer that clustering and growth i s not too relevant i n domestic environments because of important competitive removal processes l i k e neutralization by charge transfer and/or attachment and/or deposition by electrophoresis. On the other hand, the charge properties of the radon daughters seem to be very important i n the domestic environment. We believe that the calculations presented here give a better understanding of the many factors that determine the behavior of radon decay products, and that they explain why such a large range of values i s being found of d i f f u s i o n c o e f f i c i e n t s of the unattached fraction, of equilibrium constants, plate out rates, etc. (see (1) for a review, (9) for experiments i n steel rooms and (10), (11), (12) for f i e l d studies i n domestic environments). It i s d i f f i c u l t to use the model as a predictive model, since this would imply the knowledge of the chemical composition of the indoor atmosphere, as well as the formation rates of some relevant condensable products, which i s hard to achieve. Linking

338

RADON AND ITS DECAY PRODUCTS the radon problem with the general problem of indoor pollution becomes necessary here. However, the model is a powerful tool in the assessment of the risk caused by radon and in the assessment of the effectiveness of remedial actions in widely different environments.

Acknowledgments This work is supported by the Communion of the European Committees, contract number B10-F-496 and by the Interuniversity Institute for Nuclear Physics. R.F. greatly acknowldeges the School of Engineering and Applied Science of the University of California, Los Angeles, for the many C.P.U. hours that were made available for this work, and Maureen Kronish for typing the manuscript. Literature Cited Fuchs, N.A., On the stationary charge distribution on aerosol particles in a bipolar ionic atmosphere, Pure and Applied Geophysics 56 : 185 (1963) George, A.C., Knutson, E.O. and Tu, K.W., Radon daughter plateout-I, Health Physics 45 : 439 (1983) Israeli, Μ., Deposition rates of Rm progeny in houses, Health Physics 49 : 1069 (1985) Jacobi, W., Activity and potential α-energy of Rm-222- and Rm-220 daughters in different air atmospheres, Health Physics 22 : 441 (1972) Mercer, T.T., The effect of particle size on the escape of recoiling RaB atoms from particulate sur faces, Health Physics 31 : 173 (1976) Porstendorfer, J., Wicke, A. and Schraub, Α., The influence of exhalation, ventilation and deposition processes upon the concentration of Rn-222, Rn-220 and their decay products in room air, Health Physics 34 : 465 (1978) Raes, F., Description of the properties of unattached RaA and ThB particles by means of the classical theory of cluster formation, Health Physics 49 : 1177 (1985a) Raes, F., Janssens, A. and Vanmarcke, Η., A closer look at the behaviour of radioactive decay products in air, The Science of the Total Env. 45 : 205 (1985b) Raes, F. and Janssens, Α., Ion induced nucleation in a H2O-H2SO4 system : extension of the classical theory and search for experimental evidence, J. Aerosol Sci. 16 : 217 (1985c)

24. RAES ET AL.

339 Produc A Model for Size Distributions of Radon Decay

Raes, F. and Janssens, Α., Ion induced aerosol formation in a H2O -H2SO4 system : numerical calculations and conclusions, J. Aerosol Sci. (1986), to be published Reinking, A. Becker, K.H. and Porstendorfer, J., Measurements of the unattached fractions of radon daughters in houses, The Science of the Total Env. 45 : 261 (1985) Vanmarcke, Η., Janssens, A. and Raes, F., The equilibrium of attached and unattached radon daughters in the domestic environment, The Science of the Total Env. 45 : 251 (1985) RECEIVED

August 20, 1986

Radon and Its Decay Products - American Chemical Society

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