Lindane Diffusion in Soils: I. Theoretical Considerations and Mechanism of Movement1

WILFRIED EHLERS, J. LETEY, W. F. SPENCER, AND W. J. FARMER2

ABSTRACT

Equations are developed to describe the combined vaporand "nonvapor" phase diffusion of a volatile insecticide in soilsand compared with the diffusion of lindane in a Gila silt loamin a transient state system. The quantity of diffused lindaneappears to increase linearly with increased lindane concentra-tion in the treated soil up to about 20 ppm but deviates fromlinearity at higher concentrations. The diffusion coefficient oflindane is independent of time until 22 ppm of the initial 80ppm lindane concentration in the treated soil have diffusedinto the formerly untreated soil. The diffusion rate then de-creases rapidly. The dependency of the diffusion coefficient onconcentration and time may be explained by the fact thatlindane will reach maximal vapor density in the range of 20 to30 ppm. After these concentrations are built up in the initiallyuntreated half-cells by diffusion, vapor diffusion approacheszero and all the diffusion is in the "nonvapor" phase. At aJ.0% soil water content, 50% of the lindane diffuses in thevapor phase and 50% in the "nonvapor" phase. At near satu-ration, total diffusion is in the "nonvapor" phase. Lindane dif-fusion in soils can easily change from "nonvapor" to vaporphase and back to "nonvapor" phase.

Additional Key Words for Indexing: pesticide residues, vaporand "nonvapor" phase diffusion, liquid scintillation analysis.

CHLORINATED hydrocarbon insecticides may persist insoils for several years (8). Their persistence is influ-

enced by properties of the insecticides themselves, by prop-erties of soils, by the climate and by the microbial environ-ment. Diffusion is one of the mechanisms for movementand, hence, a factor affecting the persistence of chlorinatedhydrocarbons in soils.

Little is known about the diffusion of lindane (7-hexa-chlorocyclohexane) in soils with the exception of thestudies of adsorption and diffusion of this insecticide inUganda mud blocks by Barlow and Hadaway ( 1 ) . Theaim of the present investigation was to obtain an insightinto the mechansim of lindane diffusion, to determine theinfluence of varying conditions on diffusion and to evaluateparameters for predicting lindane diffusion in soils. Theresults of this study are reported in this and a followingpaper (3).

1 Contribution of the Department of Soils and Plant Nutrition,University of California, Riverside, and the Soil and WaterConservation Research Division, ARS, USDA. This work hasbeen supported in part by USDA Cooperative Agreement No.12-14-100-9016 (41). Received Oct. 30, 1968. ApprovedFeb. 27, 1969.

2 Former Postgraduate Research Soil Scientist and Professorqf Soil Physics, University of California, Riverside; Soil Scien-tist, USDA; and Assistant Soil Chemist, University of Cali-fornia, Riverside. Present address of senior author: Institut furPflanzenbau und Pflanzenziichtung, 34 Gottingen, von Sieboldstr. 8, Germany.

THEORY

A volatile compound can diffuse through soil in both vaporand "nonvapor" phases. The term "nonvapor" diffusion is usedto denote diffusion in any form other than the vapor phase.Equations developed to describe the diffusion must allow forthe movement in these phases. Jackson (5) developed equa-tions to describe water movement through the soil in the com-bined vapor and liquid states. A development similar to theone of Jackson (5) will be used.

Steady-state vapor diffusion is described by

q, = -( (dp/dx) [1]

where <?„ is the vapor flux (g cm-Ssec-1), Dv is the vapor diffu-sion coefficient in air (cmSsec-1), 5 and ST are the air-filled andtotal porosity of the soil respectively (cm3cm-3), and p is thevapor density (g cm-3). This assumes the ratio of apparent totrue vapor diffusion coefficient is SW'3/ST

2 (9).Combination of the continuity equation, dp/dt = —1/5

(dqv/dx), and equation [1] leads to the transient-state equation

dp/dt = d/dx (dp/dx)]. [2]

Equation [2] is valid for nonadsorbing media. Sorption by themedia can be accounted for by adding a source term on theright-hand side of equation [2]. The source term is — (p/S)(dc/dt) where /3 is the soil bulk density (g cm-3), and c is thetotal "nonvapor" concentration of the compound in question(g per g soil).

Addition of the source term to equation [2] and rearrangingleads to

dc/dt + (S/P) (dp/Bt) =

d/dx[(DvSw/a/l3ST2) ( d p / d x ) ] . [3]

Since pS/p is extremely low (10~5 or less) as compared with theequilibrium "nonvapor" concentration, it will be assumed that(S//3) (dp/dt) is negligible as compared with dc/dt in equation[3] and can be eliminated.

The vapor flux can be expressed in terms of "nonvapor" con-centration gradients by using the following relation

dp/dx = (dp/dc) (dc/dx). [4]

Combination of equation [3] and [4] leads to

dc/dt = d/dx {[(DVS™'3/I3ST2) ( d p / d c ) ] dc/dx}. [5]

Equation [5] accounts for vapor diffusion and the associatedvaporization and condensation expressed in terms of "nonvapor"concentration.

Diffusion will also occur in the "nonvapor" phase. The fol-lowing treatment will assume that the "nonvapor" diffusionthrough soil can be described like ionic diffusion. This is prob-ably only an approximation because the organic compoundwould have limited solubility and tend to concentrate atinterfaces.

The steady-state linear diffusion is given by

qc = - -y)Ds (dc/dx) [6]

501

502 SOIL SCI. SOC. AMER. PROC., VOL. 33, 1969

where qc is the flux (g crrr2 seer1) in the "nonvapor" phase, 6is the volumetric water content, (L/Le)z is the tortuosity fac-tor, 7 is the interaction term between the organic compoundand soil, and Ds is the "solution" diffusion coefficient of thecompound. The bulk density is necessary in this equation be-cause the concentration is expressed as grams per gram ofdry soil.

Combination of equation [6] with the law of continuity,flc/dt = —1//3 (5qc/dx) leads to

dc/dt = d/dx [6(L/Le)2 (1 -y) Ds ( d c / d x ) ] . [7]

Equation [7] accounts for the "nonvapor" diffusion.The total diffusion will be equal to the summation of the

vapor and "nonvapor" diffusion. The total can be accounted forby combining equations [5] and [7] into

dc/dt = d/dx {[(Dt)510/3//35T2) (dp/de)

+ 8(L/Le)* (1 -7)Ds]dc/dx}. [8]

For simplicity in notation, some new terms will be defined.The apparent vapor phase diffusion coefficient, £)„', will bedefined as

£>„' = T2) (dp/ de). [9]

The apparent "nonvapor" diffusion coefficient, Ds' will bedefined as

D.' = 6(L/Le)*(l -y)Ds. [10]

The apparent total diffusion coefficient, Dvs, will be defined as

Dvt = D,' + D,'. [H]

If /)„' and O, can be considered to be constants for theconditions of a given study, equation [8] can be written as

dc/dt - Dvsd*c/dx2 [12]

which is Pick's second law of diffusion.Equation [12] can be solved for the specific boundary con-

ditions imposed by an experiment and Dvs calculated. Therelative diffusion in the vapor and "nonvapor" phases can bedetermined by conducting the diffusion experiment under dif-ferent ambient pressures because vapor diffusion is influencedby ambient pressure, whereas "nonvapor" diffusion is not.According to the development of Jackson (6), Dvs would berelated to the pressure by

Dvs = D' + D' (P0/P) [13]

where P is the ambient pressure and P0 is the reference pressure.A plot of £>„,, versus P0/P should yield a straight line with theslope equal to Dv' and the intercept at Ds'.

MATERIALS AND METHODS

Diffusion of lindane through soil was measured in diffusioncells under laboratory conditions using the method of Farmerand Jensen (4). The diffusion system consisted of a half-cellcontaining soil treated with 14C-labeled lindane in contact witha half-cell filled with untreated soil. After a given time thehalf-cells were separated and the 14C-labeled lindane contentdetermined in each half-cell.

The diffusion cells were constructed of acrylic plastic with

an inner cylindrical cavity of 15-mm diameter and 9-mm totaldepth. The cell consists of two parts and, unless specified other-wise, the upper part (depth 4.5 mm) contained the soil treatedwith labeled lindane. The lower part of the cell (depth 4.5 mm)contained soil without lindane.

Solution of equation [12] for this system is reported in Crank(2).

ML/2/ML = - - —Z> 7T

exp [-(2n - Dvst/L2] [14]

where ML/2 is lindane activity in the initially untreated half-cell after the half-cells had been united for time, t, ML is thetotal lindane activity in the cell, Dm is the diffusion coefficientas defined by equations [9, 10 and 11], and L is the depth ofthe diffusion cell.

The less than 1-mm fraction of Gila silt loam soil used forthe experiments contained 0.58% organic matter and 17.6%clay, predominantly montmorillonite (4). The surface area ofthe soil is approximately 90 m2/g (A. J. Mackenzie and E. R.Ferrier, Brawley, Calif., unpublished data).

The lindane-treated soil was prepared by mixing the air-dried soil with a hexane solution containing dissolved lindanein labeled and unlabeled form. The lindane concentration inhexane was calculated to give a theoretical lindane concentra-tion in the soil of 100 ppm with a specific activity of 10,000cpm/g of soil except where stated otherwise. The hexane wasevaporated overnight. During this evaporation period the initiallindane concentration was reduced to about 80 ppm by vola-tilization of the insecticide.

A soil water content of 10% (weight basis) was establishedby mixing with a spatula the air-dried soil for each cell withthe appropriate water quantity. A water content of 35% wasachieved by adding water to the soil while filling the cell.

A water content of about 2% was established by equilibrat-ing the soil with 53% relative humidity using a saturatedMg(NO3)2 solution. A small gain of water occurred duringpacking of the soil into the cell. The exact water content wasdetermined in parallel samples.

The bulk density of the soil in the cell was 1.26 g/cm3. Thediffusion period was 48 hours except in the diffusion-timestudies. The temperature was SOC ± 0.5C. After the diffusionperiod the cells were separated with the aid of a sharp metalshim and the soils were placed directly into counting vials.

Two scintillation solutions were used. The first solution con-sisted of 5 g of PPO in 1 liter of toluene. It was used to measurethe lindane content of soils at 2% water content. The secondsolution consisted of 10.4 g of PPO and 166 g naphthalene dis-solved in a solution of 800 ml of xylene, 800 ml of dioxane,and 473 ml of absolute ethanol. This solution was used withsoils of 10 and 35% water content.

To avoid a special procedure of extraction of lindane fromthe soil the 14C-lindane activity was determined in the presenceof the soil (4). Thus lindane adsorption, liquid occlusion andthe counting efficiency of the scintillation solution may lowerthe observed activity of the labeled insecticide as compared withits actual activity. In the case of a nonvolatile pesticide, a cali-bration curve can easily be established by plotting the knownactivity of the pesticide in a constant quantity of soil againstthe measured counts per minute. As lindane volatilizes veryeasily, we determined the total activity actually in the soil bya successive extraction with the scintillation solution using soilsamples with different lindane contents. The activity determinedby successive extraction of the samples was plotted against thecounts per minute determined in the presence of the soils. Inthe range between 10 and 10,000 dpm a straight line resulted,indicating that there is no adsorption effect. Only occlusionlowers the counting efficiency of the first scintillation solutionfrom 89 to 85% and of the second solution from 85.5 to 81%.

EHLERS ET AL.: LINDANE DIFFUSION IN SOILS: I 503

The equations developed assume that Dvs is a constant for agiven soil condition at a specific temperature. Since Dvs con-sists of several components which cannot be proved a priori tobe constant, a study was established to determine the validityof assuming Dvs a constant. The effect of lindane concentrationon Dvs was determined by using 1, 10, 100, and 1,000 ppm oflindane in the treated half-cell arid measuring the quantitydiffused. The value of Dvs should also be independent of thetime that the half-cells are left united before separation. Thisfactor was checked by separating the half-cells at various timesand analyzing for 14C-labeled lindane. All of these experimentswere conducted at a soil water content of 10%. Farmer andJensen (4) have previously shown that for dieldrin arid lowwater content (soil equilibrated at 53% relative humidity) thediffusion coefficient is independent of the time the half-cellsare together.

Two procedures were followed to determine whether appre-ciable diffusion would occur in the vapor phase. In one case,an air gap was left between the soils contained in the half-cells,whereby any movement from one half-cell to the other wouldhave to cross the gap in the vapor phase. This procedure indi-cates whether movement can occur in the vapor phase, but noquantitative estimate can be made of vapor and nonvapor phasemovement in the soil. For a quantitative analysis of the vapordiffusion coefficient, the diffusion experiments were conductedunder various ambient pressures at 10 and 35% water content.The latter is near water saturation. Equation [13] was used todetermine D' and D'.

RESULTS AND DISCUSSION

The amount of diffused lindane is plotted against variousinitial concentrations of lindane present in the cell in Fig.1. If less than about 30% of the lindane in the cell isallowed to diffuse to the initially untreated half-cell, diffu-sion can be considered to have occurred in an infinite sys-tem. Under these conditions the quantity of lindane diffus-ing from one half-cell to the other in a given time is pro-portional to the initial concentration in the treated half-cellif Dvs is constant (7, eq. 1.91). The relationship foundappears to be linear at the lower concentration range butnot at the high concentration range. These data suggestthat Dvs is independent of concentration at the lower con-centration range but not at the higher concentrations.

In Fig. 2, the fraction of diffused lindane is plottedagainst the time that the half-cells were united. The figureadditionally shows theoretical curves for different Dvsvalues calculated from equation [14]. Up to one-half weekand up to approximately 28% diffused lindane, the experi-mental data fit quite well between the curves drawn for Dvsvalues of 10 and 12 mm2/week. Beyond these limitsthe experimental curve indicates that the Dvs value isdependent on time or probably more significantly depen-dent on the fraction of lindane diffused. Thus we concludethat equation [14] adequately describes lindane diffusionin the system until approximately 28% of the lindane hasbeen transferred.

There are, therefore, limitations to the valid use of con-stant Dm in equations describing lindane diffusion in soil.Since Dvs is a composite of several factors (equations [9]and [10]), any one or more of these factors could con-tribute to deviations from theory when deviations areobserved. These factors are Dv, dp/de, Ds and y. WhereasDv, Ds, and y are conceivably concentration dependent

"O.I I 10 100 1000CONCENTRATION OF TREATED SOIL (ppm)

Fig. 1—Effect of concentration on the diffusion of lindane inGila silt loam at 30C and 10% water content during a 48-hour diffusion period.

ML

0.35

0.30

0.25

0.20

0.15

0.10

0.05-0.00 -̂

Dvs=IOmm2/week 0

Dvs= I mm2/week

8 10 DAYS

Fig. 2 — Effect of time on the fraction of diffused lindane inGila silt loam at SOC and 10% water content. Theoreticalcurves for various Dva values are included.

and could cause behavior as indicated in Fig. 1, the resultspresented in Fig. 2 cannot be readily explained on the samebasis. On the other hand, deviations of dp/ de from a con-stant can be used to explain the observations reported inFig. 1 and 2.

No data are presently available on the relationshipbetween P and c for lindane in soil. Spencer, Cliath andFarmer (10) have presented data on P and c for dieldrin.They found that p for 100 ppm dieldrin in soil was thesame as for pure dieldrin. Therefore, for concentrationsgreater than 100 ppm, dp/ de = 0. They found, further-more, that p at 10 ppm was much less than at 100 ppm.Although these data are limited in extent and probably arenot the same as for lindane, they do provide orders ofmagnitudes upon which estimations can be made on ourpresent problem with lindane.

For high concentrations, dp/de may be zero, which hasthe effect of causing vapor diffusion, £>'„, to be zero eventhough dc/dx is not zero. However at lower concentra-tions (when the vapor is not saturated with respect to lin-dane), dp/ Be has a finite value and vapor diffusion willoccur.

504 SOIL SCI. SOC. AMER. PROC., VOL. 33, 1969

0.25

0.20f

2.0

Fig. 3—Effect of pressure on the diffusion coefficient of lindanein Gila silt loam at 30C and 10% water content.

From Fig. 2, note that Dvs appears to be relativelyconstant until 28% of the lindane has been transferred.At this stage D,,s decreases. Since there was about 80 ppmin the cell originally, there is about 22 ppm in the originallyuntreated half-cell when Dvs starts to decrease. This sug-gests that at concentrations greater than about 22 ppm,dp/Sc is no longer a constant but starts to approach zeroas the concentration increases. Note in Fig. 1 that thedeviation from linearity also occurs at a concentration ofabout 20 ppm. As the dp/ de approaches zero, the entirediffusion will occur in the "nonvapor" phase.

Values of Dvs are plotted as a function of PJP forsoil with 10% water content in Fig. 3. The correlationcoefficient of the data is highly significant. D'v is 5.6 mm2

week"1; D's has almost the same value (5.8 mm2 week-1).This means that both vapor and "nonvapor" diffusion areof the same order of magnitude in Gila soil with 10%water. At 35% water content Dvs is 10 mmVweek whichis approximately the same as that at 10% water content.However at 35% water content the D,,s value remainedconstant with increasing pressure indicating that Ds' = Dvs.

Figure 4 shows the relationship between the gap widthand the fraction of lindane diffused after 48 hours at 30Cfor soils of three different water contents. The relationshipis essentially linear indicating the effect of the gap on diffu-sion is mainly a distance effect. The lindane is able tochange from "nonvapor" phase to vapor phase when leav-ing the treated half-cell and will partially revert to "non-vapor" phase when reaching the untreated half-cell. Vapor

ML0.15-

0.10-

THICKNESS OF GAP (mm)Fig. 4—Effect of gap thickness on the diffusion of lindane in

Gila silt loam at 30C and 10% water content during a 48-hour diffusion period.

phase diffusion in the gap was sufficient to compensate forthe absence of nonvapor phase diffusion.

ERRATAAn error occurs in the papers entitled "Lindane Diffu-

sion in Soils: I and II" which appeared in the SSSA Pro-ceedings, 33:501-508 (1969). B should be eliminatedfrom equations 6, 7, 8 and 10 of paper I and in equations1 and 3 of paper II. The reason for eliminating 0 fromequation 6 is that c times /3 in the units given result inconcentration being expressed in terms of grams/unittotal volume rather than per unit volume of solution, asis commonly used for ionic diffusion through soil. For-tunately, this error does not affect any of the results pre-sented except the last column of Table 2 on page 507should be eliminated. The authors express appreciation toDr. R. C. Shearer for calling this error to their attention.—W. EHLERS, J. LETEY, W. F. SPENCER, and W. J. FARMER