hydroxide form in water. Therefore, t h e following ion exchange mechanism may also be conceivable:
vinylpyridine-divinylbenzene copolymer was in t h e pulverized form a n d t h e XAD resins were in t h e macroporous form. Further research is required to determine t h e mechanism of t h e interaction of phenol with polyvinylpyridine. Literature Cited (1) Anderson, R. E., Hansen, R. D., Ind. Eng. Chem., 47, 71-5
However, this ion exchange mechanism appears to be unfavorable because t h e capacity of t h e copolymer for phenol adsorption was scarcely affected by t h e presence of acid, similarly to t h e case of adsorption of phenols o n activated carbon a n d contrary t o t h e cases with anion exchange resins (4). Polymeric adsorbents with n o ion exchange functional group such as Amberlite XAD resins may adsorb phenol by physical adsorption. However, such a mechanism would not wholly explain t h e adsorption of phenol by t h e vinylpyridine-divinylbenzene copolymer, because t h e copolymer showed a remarkably higher breakthrough capacity than those observed with the nonionic resins, in spite of t h e fact t h a t the
(1955). (2) Chasanov, M. G., Kunin, R., McGarvey, F., Ind. Eng. Chem., 48, 305-9 (1956). ( 3 ) Pollio, F. X., Kunin, R., Enuiron. Sci. Technol., 1, 160-3 (1967). (4) Kim, B. R., Snoeyink, V. L., Saunders, F. M., J . Water Pollut. Control Fed., 48,120-33 (1976). ( 5 ) Crook, E. H., McDonnell, R. P., McNulty, J. T., Ind. Eng. Chem., Prod. Res. Deu., 14,113-8 (1975). (6) Brown, H. C., Mihm, X. R., J . A m . Chem. SOC.,77, 1723-6 (1955). (7) Maclay, W. N., Fuoss, R. M., J . Polym. Sei., 6, 511-21 (1951). (8) Katchalsky, A,, Rosenheck, K., Altmann, B., J . Polym. Sci., 23, 955-65 (1957). (9) Gottlieb, S., Marsh, P. B., Ind. Eng. Chem.,Anal. Ed., 18,16-9 (1946). Received for reuieu. February 7,1979. Accepted July 31, 1979. Work supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan (No.303045).
Organophosphate Insecticide Disappearance from Leaf Surfaces: An Alternative to First-Order Kinetics James H. Stamper*, Herbert N. Nigg, and Jon C. Allen University of Florida, Institute of Food and Agricultural Sciences, Agricultural Research and Education Center, P.O. L a k e Alfred, Fla. 33850
Box 1088,
A new model of organophosphate insecticide disappearance from leaf surfaces is presented. Excellent agreement ( R L= 0.963) with observed insecticide residue decline has been achieved. No statistically determined arbitrary constants appear in t h e model, and only t h e insecticide concentration a t one time is required to predict its concentration a t any other time. T h e model appears to be valid over a wide range of organophosphate types and environmental conditions. Expensive monitoring studies might now be done more efficiently and a t less cost. T h e fundamental process governing such disappearance may be diffusion.
secticide disappearance, researchers have customarily regarded each individual process that might lead to its loss as being essentially first order (1-4, 9). This assumption leads t o exponential decay of insecticide concentration with time, provided other variables t h a t might affect the rate constant ( e g , temperature, moisture, wind, solar radiation, microbial population) d o not vary appreciably over time. T h a t such exponential decay were present could be detected by plotting t h e logarithm of the observed concentration vs. time. If a straight line results, t h e decay is properly attributable to a first-order process whose rate constant is the slope of the line (without t h e minus sign).
T o register one insecticide for agricultural use requires environmental monitoring studies in a variety of crops. These studies include residue behavior in and on soil, in and on t h e plant, and in air. Additional monitoring may be required depending on speculative effects on the environment or transfer of‘ the chemical between environmental components. In short, little basic science is used in these studies and enormous resources are consumed in empirically monitoring every conceivable environmental situation. I t was t h e purpose of this study to obtain a better representation of t h e mathematical form taken by these monitoring data, and thereby enhance t h e predictability of residue persistence.
Analysis a n d Obseruations
M o d e l i n g Attempts
Modeling of insecticide disappearance from foliage and soil surfaces has been undertaken by several authors (1-21). A review of the presumed mechanisms leading to insecticide loss has been presented by Ebeling (12). In order to predict in1402
Environmental Science & Technology
Unfortunately, such semilog plots d o not, in general, yield straight lines (13).T h a t this is t h e case is well known and is depicted in Figure 1 (see below). One could argue that two first-order processes with different rate constants, one dominant early and t h e other later, are present (11, 1 4 ) . Primary evidence for this explanation is lacking. Also, t h e supposed change-over time from one process to t h e other is highly variable as are the two “fitted” rate constants themselves, rendering the a priori prediction of insecticide residue decline with time most uncertain. Such a treatment seems rather arbitrary and unjustifiably contrived to yield decay rates (exponential) t h a t have been largely assumed in t h e beginning. Our first thought was that insecticide disappearance might depend primarily upon chemical reactions taking place on the leaf surface. Hydrolysis or photolysis might serve to degrade t h e insecticide. Whatever their time rates, these processes 0013-936X/79/0913-1402$01.00/0
@ 1979 American Chemical Society
+4.00
+4.08
+3.00
+3.80
+2.00
A= 0.830 B = 0.098 +1.00
+ I .e0 I
R 2 = 0.884
T1
/ / x
/‘/
I
;,/’
A=-0.1 2 1 B = 1.18 R 2 = 0.973
/
I / 0.00
*I.BB
*2.m
*3.m
L.00
Figure 1. Regression lines for sample (no. 11) data set. Left: -In C = A
should vary with such environmental variables as leaf wetness, radiant energy absorption, or temperature. B u t when we monitored these variables, together with insecticide concentration, no perceptible dependence upon individual environmental variables resulted. Insecticide losses appeared to proceed temporally but with a decidedly nonexponential character throughout. A new model of insecticide disappearance from surfaces is presented here. We have observed from data taken in t h e field hy ourselves and others (9, 14-1 7) that a conspicuously linear relationship consistently results from plotting t h e logarithm of insecticide residue concentration vs. t h e logarithm of t h e time. This result obtains over a wide range of organophosphate insecticides (experimental d a t a being scanty for nonorganophosphate compounds), leaf surfaces to which it has been applied, geographic regions, weather conditions, insecticide formulation a t application, and dislodgment method a t removal. I n order to compare t h e two a priori alternatives, 41 separate sets of field d a t a were analyzed graphically in each of the two ways described above. For convenience, all concentrations, in a particular d a t a set and corresponding times, t , have heen expressed in units of C1 and t l , respectively, with C1 t h e concentration a t t l , the earliest time after insecticide application that data were taken (usually 1 or 2 days). T h e first data point ( t , , C , )then becomes (1,l) in these units. Figure 1 shows a sample d a t a set (no. 11) fairly representative of t h e entire 41. T h e left graph is a plot of y = -In C vs. x = t . T h e right graph is t h e same except t h a t t h e abscissa represents x = In i. All logarithms are natural, Le., base e . T h e regression lines, J’ = A H x , obtained from a least-squares analysis, are shown for each, together with the square of the correlation coefficient, H. Dotted lines represent 95% confidence limits. Table I summarizes t h e complete results. Were first order, C = Co. exp(-kt), operative, one should find -In (C/Cl) = -htl ht. O r , in t h e units chosen, -In C = -ht, ( h t l ) t .T h a t is, for a particular d a t a set, A should be negative a n d B t h e same a m o u n t positive. In fact, all A’s for t h e semilog fits t u r n out positive a n d bear no consistent relationship with t h e corresponding H . Conversely, Table I shows the In-ln plot to be a far superior ( I ,
+
+
+
*1.00
+ Bt. Right: -In
+2.m
C= A
+ B In t
representation of t h e data. R? values average 0.963 vs. only 0.854 for t h e semilog treatment. Furthermore, t h e slopes ( B ) of t h e regression lines of t h e In-In plots show a certain uniformity (Figure 2) not present in t h e semilog plots a n d tend to distribute themselves normally about a mean of 1.43 with a standard deviation of 0.36.’If the alternative regression lines, x = (1/H)y - A/B, are constructed to minimize x deviations, H is found to be normally distributed about a mean of 1.50 with a standard deviation of 0.37. T h e intercepts ( A )are, as anticipated, quite small with a mean of -0.19. It would appear, then, t h a t t h e primary process governing insecticide loss from surfaces may be expressed: -In (C/CJ = (3/2) In ( t l t i )
(1)
or
Th c’orj Why Equation 3 is a better representation of available d a t a i i , of course, a separate question. We tentatively propose a n explanation suggested by t h e mathematical form of Equation 3. I t has recently been established (18)t h a t even for so-called “nonvolatile” insecticides, volatilization can be t h e dominant pathway for insecticide loss from surfaces. Once insecticide has reached t h e leaf in irregularly positioned small volumes, diffusion of insecticide molecules from each volume now commences. Some work on t h e diffusion of insecticides has been carried out already, mainly in a n effort t o model insecticide movement in soils ( 7 , 8, 19, 20) For a single volume of insecticide with center at r = 0, t h e initial ( t = 0 ) distribution of insecticide molecules would be somewhat as depicted in Figure 3. How C ( r , t )develops in time is governed by Fick’s second law of diffusion: C2C = ( l / D ) ( d C / d t )
(4)
with D t h e diffusion constant of t h e insecticide vapor. D is Volume 13, Number 11, November 1979
1403
Table I a data set no.
1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 mean
semilog fit: -In C = A 11,
+ Bt
In-in fit: -in C = A R l t.. .k. = -.
+ B In t
I,
day
R2
A
B
day-’
R2
A
B
2 2
0.938 0.779 0.887
0.145 0.761
0.375 0.249 0.244
0.187 0.124
0.958 0.961 0.984
-0.489 0.109 0.195 -0.097 -0.147 0.145
2.058 1.597 1.381
0.073 -0.541 -0.638 -0.309 -0.121 -0.643 -0.436
1.494 1.631
2 2 2 2 2 2 1
1 1 1 1 2 2 2 2 2 2 2 2 1 1 1
1 1 1
1 1 1 1 1 1 1 1 1 1 3 3 3 1 1.54
0.572 0.502
0.876 0.837 0.788
0.640 0.723
0.246 0.310 0.191
0.827 0.930
0.770 0.301
0.242 0.236
0.910 0.879 0.884 0.877 0.887
0.612 0.918 0.830 0.474
0.138 0.123 0.098 0.120 0.104
0.962 0.958 0.776 0.804 0.872 0.875 0.882 0.846 0.887 0.853 0.873 0.864 0.788 0.956 0.934 0.761 0.770 0.829 0.871 0.839 0.918 0.721 0.906 0.907 0.776 0.768 0.720 0.798 0.854
0.509 0.224 0.304 0.804 0.907 0.615 0.475 0.492 0.655 0.619 1.090 0.449 0.782 1.349 0.189 0.053 0.633 0.934 0.453 0.756 0.665 0.491 0.480 0.064 0.817 0.873 0.545 1.043 0.777
0.465 0.299 0.278 0.262 0.37 1 0.203 0.194 0.166 0.133 0.132 0.112 0.131 0.108 0.214 0.090 0.130 0.165 0.135 0.212 0.343 0.083 0.245 0.094 0.134 0.141 0.105 0.169 0.126
0.122 0.123 0.155 0.095 0.121 0.118 0.138 0.123 0.098 0.120 0.104 0.233 0.150 0.139 0.131 0.186 0.101 0.097 0.083 0.133 0.132 0.112 0.131 0.108 0.214 0.090 0.130 0.165 0.135 0.212 0.343 0.083 0.245 0.094 0.134 0.070 0.052 0.084 0.126 0.134
0.992 0.967 0.968 0.993 0.942 0.951 0.986 0.973 0.936 0.932 0.954 0.961 0.982 0.989 0.985 0.963 0.977 0.993 0.934 0.991 0.944 0.968 0.962 0.917 0.91 1 0.949 0.992 0.963 0.982 0.998 0.963 0.912 0.869 0.942 0.993 0.991 0.981 0.986 0.963
-0.505 -0.232 0.078 0.159 -0.285 -0.032 0.014 -0.105 -0.595 -0.277 -0.610 -0.514 0.153 -0.493 -0.244 0.006
0.100 -0.136 -0.129 -0.038 -0.208 -0.083 -0.636 -0.295 0.088 -0.044 0.029 -0.045 -0,190
1.481 1.885 1.222
1.618 1.496 1.177 1.419 1.216 2.519 1.692 1.722 1.646 2.232 1.226 1.151 1.241 1.561 1.622 1.33 1 1.581 1.367 1.451 0.617 1.005 1.300 1.011 1.560 1.893 0.873 1.393 0.949 1.401 1.176 0.877 1.454 1.181 1.432
a Data sets 1-13: Data of Popendorf and Leffingwell ( 74) taken from parathion applied to California orange leaves with residue removal by vacuum techniques only. 14-26: Same, with greater residue removal by dislodgment with a detergent solution. 27, 28: Data of Thompson and Brooks ( 75) taken from dioxathion applied to Florida orange leaves during hot, wet and cool, dry periods, respectively. 29, 30: Same, with ethion applied during hot, wet and cool, dry periods, respectively. 31, 32: Same, with carbophenothion applied during hot, wet and cool, dry periods, respectively. 33, 34: Data of Nigg et al. ( 9 )taken from carbophenothion applied to Florida orange leaves during hot, wet and cool, dry periods, respectively. 35, 36: Same, with ethion applied during hot, wet and cool, dry periods. respectively. 37: Same, with parathion applied during a cool, dry period. 38-40: Data of Winterlin et al. ( 76) taken from parathion applied to California peach leaves in formulations of emulsified concentrate, encapsulated and wettable powder, respectively. 41: Data of Leffingwell et al. ( 77) taken from ethion applied to California grape leaves.
taken here to be constant in space a n d time. At high concentrations, however, this approximation is not valid (211. T h e solution to Equation 4, of course, depends upon t h e precise functional form of t h e initial concentration represented in Figure 3. B u t if t h e drop-off of C(r,O)with r is sufficiently rapid (small initial volume), the solution of Equation 4 is independent of t h a t form a n d is a t r = 0, from a straightforward generalization to three dimensions of t h e solution presented by Laidler (22): C ( 0 , t )= M”/(477Dt)3’2, t > VO”J/D (5) 1404
Environmental Science & Technology
where Mo and Vo are t h e initial mass and volume of insecticide. T h e validity of Equation 5 demands t h a t each initial pesticide volume be smaller t h a n (Dt).j”, t h e latter being a n a p proximate measure of the cube of the molecular displacement in time t . T h a t such might be the case is suggested by the fits to data provided by Equation 5; a precise determination of D, however, for these insecticides under t h e conditions which prevailed has not yet been attempted. Equation 1, of course, follows from Equation 5.
t
n
ar LL
4 t
a
r-!h
I
I
I I I I I
Distance
0 6 0.8 I O I 2 1 4 I 6 I 8 2 0 2.2 2 4 2 6
SLOPE Figure 2. Histogram of regression line slopes (6) for the 41 In-In graphs of Figure 1
A g r e e m e n t u ) i t hE x p e r i m e n t
T h e statistic:
r
Figure 3. Initial distribution of insecticide molecules a t a n y other time, t , t h e concentration can be predicted by Equation 2. And a single measurement of C1 a t t l is t h e minimum information any solution t o t h e problem requires. Furthermore, no arbitrary constants, common in other models, appear in Equation 2. All insecticides and surfaces we have so far examined seem to follow Equation 2 well within t h e confines of experimental error. Literature Cited
was determined both for t h e “semilog approach” with C,caIcd = ClohSdexp z ( t , - t ) and t h e mean h from Table I, and also for each for the “ln-ln approach” with Cicalcd= Cl(1hsd(tl/t):3/2, of the 41 data sets. T h e median value of P is 2.37 in the former case and 0.545 in t h e latter. T h e superiority of Equation 2 as a representation of‘ observed d a t a is demonstrated by this statistic. However, t h e source of t h e average percent error of 0.545 with Equation 2 is not clear. T h e error may derive in part from Equation 2 itself. B u t even if Equation 2 were exact, experimental errors alone in measuring Ci a n d ti would lead to (AC,/C,)‘ (ACi/C,)2 ( 3 / 2 ) 2 ( A t l / t 1 ) 2 (3,’ 2 ) 2 ( A t , / t i ) 2 where , the A symbol denotes “error i n . . .”. Since t l is customarily reported by researchers only to t h e nearest day, ( A t l l t l ) may average 0.10. More importantly, (ACJCi) is commonly quite large. If ( A C i I C i ) averaged 0.376, not a n uncommon estimate, t h e entire P could be attributed to measurement error. Such measurement errors could also lead to average errors in calculated regression line slope of 0.36 as suggested by Figure 2. But until more careful measurements of residue persistence are made, one cannot be sure. I t may be t h a t a process secondary to diffusion serves to modify Equation 2. Three sources of possible variability stand out. First, rapid enough air movement (wind) a t t h e leaf surface might periodically alter t h e diffusion process. Loss of insecticide would perhaps prot h a n by diffusion ceed a t a faster rate (similar to a larger )”,“ alone. Second, t h e diffusion constant, D , of t h e insecticide vapor may not properly be regarded as constant in space a n d time. At sufficiently high concentrations, D can be a n appreciable function of space (21) rendering Equation 4 invalid. T h e time dependence of D , through its dependence upon temperature in t h e field, is evident; a tendency for molecular movement along a negative temperature gradient, as well as t h e negative concentration gradient, can result. Certainly, though, a considerable improvement is rendered in t h e predictability of organophosphate insecticide residue levels on leaf surfaces. Such predictions are crucial to t h e estimation of worker reentry time, harvesting schedules, a n d atmospheric contamination. T h e major advantage in viewing insecticide losses from t h e perspective outlined here is t h a t i l ’ a single measurement of surface insecticide concentration, ( ‘ I , is taken a t a known time, t 1 , following application, t h e n
-
+
+
+
(1) Hamaker, J. W., Ado. Chem. Ser., No. 60,122-31 (1966);Goring, C. A. I., Laskowski, D. A., Hamaker, J. W., Meikle, R. W., in “Environmental Dynamics of Pesticides”, Hague, R., Freed, V. H., Eds., Plenum, New York, 1975, pp 135-72; Hamaker, J. W., Goring, C. A. I., ACS S y m p . Ser., No. 29,219-43 (1976). (2) Hamaker, J. W., in “Organic Chemicals in the Soil Environment”,
Goring, C. A. I., Hamaker, J. W., Eds., Marcel Dekker, New York, 1972, pp 253-339. (3) Hamaker, J. W., Proc. Br. Crop Protect. Conf., 181-99 (1976). (4) Walker, A,, Proc. Eur. Weed Res. Coun. Symp., 240-50 (1973); J . Enuiron. Qual., 3,396 (1974). ( 5 ) Guenzi, R. D., Beard, W.E., J . Enuiron. Qual., 5,243 (1976). ( 6 ) Freed, V. H., Chiou, C. T., Hague, R., Enuiron. Health Perspect., 2 0 , 6 5 (1977). (7) l,eistra, M., Agric. Eni’iron., 3, 325 (1977). ( X I Mayer. R., Letey, J., Farmer, W. J., SoilSci. Soc. A m . Proc., 38, ,-)6:3 ( 1974). ($1) Nigg, H. N., Allen, J. C., Brooks, R. F., Edwards, G. J., Thompson, N. P.. King, R. R.,Blagg, A. H., Arch. Enuiron. Contam. Toricol., 6 , “37 (1977);Nigg, H. N., Allen, J. C., King, R. W,, Thompson, N. I’., Edwards. G. J., Brooks, R. F., Bull. Enuiron. Contam. Toricol., 19,578 (1978). 1 10) Hague, R., Freed, V. H., in “Environmental Dynamics of Pesticides”, Plenum, New York, 1975, 367 pp. (11) Gunther, F. A., Blinn, R. C., “Analysis of Insecticides and Acaracides”, Interscience, New York, 1955,696pp; Gunther, F. A,, Residue Reu., 28,l (1969); 67,l (1977). i 1 2 ) Eheling, IV.,Residue Reu., 3, 3 (1963). i 1 :i)Sutherland, G. L., n’idmark, G., J . Assoc. Off, Anal. Chem., 54, 1:116 (1971). ( 1.3) I’opendorf’, I+ J., : Leffingwell, . J. T.,J . Agric. Food Chem., 26, 4:17 (1978). i 15) Thompson, K.P., Brooks, R. F., Arch. Enuiron. Contam. ToxiC,Ci/., 5 , 55 (1976). i 16) LVinterlin, LV., Bailey, J. B., Langbehn, L., Mourer, C., Prstic. M i i n i t . J., 8, 263 (1975). ( 17) 1,ef’f‘intrwell.J. T.. Suear. R. C.. Jenkins., D.., Arch. Enciron. ( ‘ o n t a r n . .Toxi;,o/., 3, 40’(1975). ( 18) Spencer, IV.F., Farmer, W. J., Cliath, M. M., Residue R P L ~49, ., 1 (1973). i 19) Ehlers, R.,Letey, J., Spencer, W. F., Farmer, I+ J., Soil ’. Sci. Soc. A m . Proc., 33, 501 (1969). ( 2 ) )Collins, R. L., Doglia, S., Weed Sci., 21, 343 (1973). i 2 1 ) Margenau, H., Murphy, G . M., “The Mathematics of Physics and Chemistry”, D. Van Nostrand, New York, 1956, p 2:38. ( 2 2 ) Laidler, K. J., “Physical Chemistry with Biological Applicationd”, Benjamin-Cummings, Menlo Park, 1978, 587 pp. Receiued for reuieu March 26, 1979. Accepted August 15, 1979. Florida Agricultural Experiment Stations Journal Series No. 1553.
Volume 13, Number 11, November 1979 1405
