(13) Mackay, D., Leinonen, P . J., Enuiron. Sci. Technol., 9,1178-80 (1975). (14) Chiou, C. T., Freed, V. H., Schnedding, D. W., Kohnert, R. L., 11,475--8 (1977). (15) Kummert, R., Ph.1). Thesis, Swiss Federal Institute of Technology, 1979 (in German). ( 16) Matter, C., Ph.D. Thesis, Swiss Federal Institute of Technology, 1979 (in German). (17) Zepp, R. G., Cline, D. M., Enuiron. Sci. Techno/., 11, 359-66 (1977). (18) Zepp, R. G., Enuiron Sei. Technol., 12.327-9 (1978). (19) Cohen, Y., Cocchio, W., Mackay, D., Enuiron. Sei. Technol., 12, 553-8 (1978). (20) Zimmermann, U., Gas- Wasser-Abwasser, 9, 473-80 (1975) (in German). (21) Groh, K., J . Chromatogr., 84,255-73 (1973). (22) Groh, K., Zurcher, F.,J . Chromatogr., 117, 285-94 (1976). (23) Schwarzenbach, R. P., Bromund, R. H., Gschwend, P. M., Zafiriou, 0. C., Org. Geochem., 1, 93-107 (1978). (24) Grob, K., Grob, G., Grob, K., Jr., Chromatographia, 10,181-7 (1977). (E?) Grob, K., Jr., Grob, K., J . Chromatogr., 40,257-9 (1977). (26) Groh, K., Chromatographia, 8,423-33 (1975). (27) Schwarzenhach, R. P., Molnar, E., Giger, W., Wakeham, S.G., unpublished data. (28) Imbuden, D. M., Lerman, A., in “Lakes: Chemistry, Geology, Physics”, Lerman, A,, Ed., Springer Verlag, New York, 1978. (29) Buhrer, H., Ambuhl, H., Schweiz. 2. Hydro/., 37,347-69 (1975)
(in German). (30) Nydegger, P., Beitr. Geol. Schweiz-Hydrol., 9, 8 (1957) (in German). (31) Hoehn, E., EAWAG, private communication, 1979. (32) Giger, W., Roberts, P. V., in “Water Pollution Microbiology”, Vol. 2, Mitchell, R., Ed., Wiley, New York, 1978, pp 135-75. (33) Gay, E. W., Jr., Hanst, P. L., Bufalini, J. J., Noonan, R. C., Enuiron. Sei. Technol., 10,58-67 (1976). 134) Dilline. W. L.. Bredewee. C. J.. Tefertiller, N. B., Enuiron. Sci. ,~ Techno/.,’lO, 351-6 (1976): (35) Liss, P . S., Slater, P. G., Nature (London), 247,181-4 (1974). (36) Broecker. W. S.. Pen&.! T.-H.. Tellus. 26.21-35 (1974). (37) Emerson, S., Liknol.-bceandgr., 20,’754-61 (1975). (38) Grob, K., Grob, G., J . Chrornatogr., 62,l-13 (1971). (39) Grob, K., EAWAG, unpublished data, 1978. (40) Li, Y.-H., Schweiz. Z. Hydrol., 35,l-7 (1973). (41) Zimmermann, U., Zurich-Waterworks, private communication, 1979. (42) Sturm, M., EAWAG, private communication, 1979. (43) Buhrer, H., EAWAG, private communication, 1979. (44) Kunz, W., Vierteljahresschr. Naturforsch. Ges. Zuerich, 3, 250-337 (1977) (in German). (45) Irmann, F., Chem. Ing. Tech., 37,789 (1965). Received for review April 16,1979. Accepted July 9,1979. This worh was funded in part by the Swiss Department of Commerce (Project COST 646) a n d the swiss National Research Foundation.
Use of Frequency Distributions of Potential Ozone in Evaluating Oxidant Controls Neil J. Daly Department of Chemistry, Australian National University, P.O. Box 4, Canberra, ACT, 2600, Australia
A method for combining photochemical models and real airshed data to provide frequency distributions of potential ozone is discussed together with a mechanism for examining the effects of alternative proposals for emission controls. The method is exemplified by analysis of airshed data measured in the Sydney basin. The analysis leads to the conclusion that although hydrocarbon control has been urged as the optimum control strategy for oxidant, less stringent controls on both hydrocarbons and nitrogen oxide appear equally effective in limiting ozone formed in 1-day irradiations and offer additional advantages during multi-day irradiations due to the NO, controls they incorporate. The formulation of policies to control the concentrations of oxidants in city airsheds remains a controversial problem. The objective is the reduction of the quantities of ozone, peroxyacyl nitrates, aerosols, and other secondary pollutants that form as a result of the solar irradiation of mixtures of nonmethane hydrocarbons (NMHC) and nitrogen oxides (NO,). The controversy is over whether the optimum control strategy is control of NMHC emissions, control of NO, emissions, or control of both NMHC and NO, emissions. The various national policies can be seen to differ. Thus, the Japanese Government has adopted a policy of NO, control, while the United States Government has sought to limit oxidant through control of NMHC emissions. More recently, the Japanese Government has been reported to be examining the case for some accompanying NMHC control and the lJnited States the need for some NO, control ( I ). In Europe, the case has been argued for NO, control with some accompanying control of NMHC emissions (2).In Australia, control of NMHC only has been proposed ( 3 , 4 ) ,as has control of both NMHC and NO, (5). Many of the key issues that require resolution before the optimum control strategy can be de0013-936X/79/0913-1373$01.00/0
veloped have been reviewed by Dimitriades and Altshuller ( 6 ) and Pitts (7). A recent analysis of isopleth diagrams that relate ozone formation to NMHC and NO, concentrations has led to a renewal of the proposal that control of NMHC emissions is the optimum strategy for control of photochemical oxidants (8).The paper seeks to evaluate the relative merits of alternative control strategies by using the technique of comparing the frequency distributions of potential ozone that the alternative policies could generate in an airshed (9). U s e of F r e q u e n c y Distributions
In Australia, no legal standard has been set for oxidant, although there is the tendency to adopt the goals recommended by the World Health Organization ( 3 ) .The appropriate goal for ozone is the “1-h” average concentration not to be exceeded more than once per year, which is a frequency of about 0.1%of the year. An implication of such a goal is that the concern is not only with maximum values, but also with how often the goal is exceeded. Accordingly, the task of developing the optimum control strategy is one of determining which set of fractional reductions in emissions minimizes the frequency with which the stated oxidant concentration is exceeded. A useful method for evaluating the likely effects of the alternative proposals for emission controls involves calculating the oxidant forming potential of the alternative distributions of NMHC and NO, in the airshed. An airshed has a potential for forming oxidant because of the various concentrations of NMHC and NO, which occur. This potential is realized only when the necessary conditions of atmospheric stability and clear skies occur simultaneously. If the necessary meteorological conditions are treated as occurring a t random intervals, the task of controlling oxidant becomes one of controlling the ambient concentrations of
@ 1979 American Chemical Society
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NMHC and NO, in such a way as to minimize the frequency with which oxidant has the potential for exceeding the stated goal. In principle, the oxidant potential of an airshed can be calculated using a suitable photochemical model. In practice, the oxidant concentrations predicted by photochemical models are valid only within the limits implicit‘ in the assumptions of each particular model. In general, the major variables which influence the oxidant dependence upon precursor concentrations are: (a) the nature of the hydrocarbon mixture; (b) the ratio of nitric oxide to nitrogen dioxide in the NO, mixture; (c) the intensity of the solar irradiation assumed; (d) the values assigned to the individual ?ate constants for the elementary reactions used in the reduced mechanism of the model; (e) the rate of atmospheric dilution; (f) the reaction time for which the mixture undergoes irradiation. Accordingly, the results obtained for an analysis based on any particular photochemical model are valid only within the limits with which the chosen model describes t h e airshed of interest. Where the model of Dodge ( I O , I I ) is used, the oxidant potential is obtained as an ozone potential, which is valid within the conditions stipulated by Dodge ( I O ) . In sensitivity tests, Dodge has shown that the absolute dependence of the ozone isopleths upon the concentrations of nonmethane hydrocarbons and nitrogen oxides varies as factors such as the mixture of the hydrocarbons, the diurnal variations of 1-h average values of the photolytic rate constants, the period of irradiation, the atmospheric dilution rate, and the admixture of fresh emissions are varied. However, the ozone isopleths hold their relative positions on the hydrocarbons and nitrogen oxides scale as these Conditions are varied, and the model is considered to be of use in developing oxidant strategies for various airsheds (11). Following Dodge ( I O , 1 1 ) , it is assumed that the average of the 0600 to 0900 h concentration of NMHC and NO, gives the ozone peaks observed-albeit a t a different location-later in the day. Thus, for a chosen year, the 365 sets of the averaged 0600 to 0900 h concentrations of NMHC and NO, represent the annual ozone potential of the element of the airshed represented by the monitoring station. The maximum 1-h average concentration of ozone that can potentially be formed from each set of NMHC and NO, data is calculated from the photochemical model, and the annual frequency distribution of these ozone concentrations is prepared. Such a distribution is taken as defining the ozone potential of the existing ambient concentrations of NMHC and NO, in the airshed for 1-day irradiations under the conditions set by the model. The absolute values in the distributions will differ from the distributions observed in the airshed because of the limits implicit in the model, and because such necessary conditions as the simultaneous occurrence of atmospheric stability and clear skies are not always met. The distributions are of use, however, in making relative judgments on the merits of alternative controls. If it is assumed that fractional reductions in emissions of NMHC and NO, lead to the corresponding fractional reductions in ambient levels of each precursor, it is possible to assume a planned reduction in concentrations of each of the NMHC and NO, sets and to recalculate the distribution of potential ozone from the new set of precursor concentrations. Such a procedure gives a method for evaluating the likely relative impacts of alternative control strategies. An examination of the use of such frequency distributions is given for data measured in the Sydney airshed. Frequency Distributions o f Potential Ozone Figure 1 shows the cumulative distribution of potential ozone concentrations calculated from about 400 sets of NMHC and NO, data said (12) to be typical of the morning airshed 1374
Environmental Science 8 Technology
uu
z“
ou
0 08
90 80 60 40 20 10 5 I PERCENT OF VALUES WHICH EOUAL OR EXCEED STATED OZONE CONCENTRATION
01
Cumulative distribution of potential ozone calculated for Sydney using the Dodge model: (A)existing concentrations of precursors; (0)33% reduction in NO, emissions;( 0 )33% reduction in NMHC emissions; ( 0 )33% reduction in both NO, and N M H C emissions Figure 1.
in Sydney for days of high oxidant or precursor concentrations. The ozone values were calculated from the Dodge model ( I O ) using photolytic constants for the summer solstice a t 34’N. The constants are suitable for Sydney, which is about 34”s. The rate of atmospheric dispersion, the length of irradiation, and the nature of the mixture of NMHC and NO, were those used by Dodge. The magnitudes of the ozone concentrations are not absolute, but the relative effects of the controls shown in the figure are informative. Figure 1shows the distribution of potential ozone for each of the alternative pol’icies: (a) a reduction of NMHC emissions to 67%of initial levels; (b) a reduction of NO, emissions to 67% of initial levels; and (c)’areduction of both NMHC and NO, emissions to 67% of initial levels. The distributions in Figure 1 show that for these Sydney airshed data there is little difference between the distribution of potential ozone resulting from the same fractional reduction in either NMHC or NO, emissions. The simultaneous reduction of both NMHC and NO, has greater effect in lowering the range of potential ozone values right through the range of ozone concentrations. The comparable effectiveness of these alternative policies has its origins in the range of the sets of NMHC and NO, values that occur in a real airshed and shows the difficulties of deciding control strategies on the basis of the “dividing line” eoncept proposed by Dodge ( I O ) and reevaluated by Bilger (8). Originally Dodge positioned a line described by the equation NMHC = 5.6N0, to locate the “apex” points of the ozone isopleths (10).This line was believed to divide the diagram into two regions for control purposes. The first of these regions is described as predominantly NMHC-rich and is characterized by values of the ratio NMHC/NO, exceeding 5.6. In this region, reduction of NO, levels was seen to offer the most effective means of ozone control. The second region is described as predominantly NO,-rich and is characterized by values of the ratio NMHC/NO, less than 5.6. In this region, reduction of NMHC was seen to offer the most effective means of ozone control (IO). Bilger reexamined the “dividing line” concept and proposed that the criterion for selecting the dividing line be that the line describe the points for which fractional reductions in NMHC yield the same reductions in ozone concentrations in, the corresponding fractional reduction in NO, (8) Using this more satisfactory criterion, the dividing line has the equation NMHC = 9N0,. On this basis it is concluded that, where NMHC and NO, controls are equally costly, the oxidant control strategies required are control of NMHC emissions for an airshed characterized by a ratio below 9.0 and control of NO, emissions for an airshed characterized by a ratio in
5 IO 20 40 60 80 90 95 PERCENT OF VALUE OF THE RATIO L E S S THAN OR EOUAL TO STATED VALUE
Figure 2. Cumulative distribution of ratios of NMHC/NO, observed in the Sydney airshed
-0
8u
30
1
1
1
1
1
1
,
,
I
I
I
90 80 60 40 20 IO 5 I P E R C E N T OF V A L U E S WHICH E Q U A L OR EXCEED STATED OZONE CONCENTRATION
, 01
Figure 3. Cumulative distribution of potential ozone calculated for Sydney using the modified (see text) Dodge model: (A)existing concentrations of precursors; (0)33% reduction in both NMHC and NO, emissions; (0) 55 % reduction in NMHC emissions
tween the distributions for the alternative controls are insignificant and within the uncertainty (ca. 15%)in ozone values calculated from the Dodge model (10). Thus, in terms of the maximum 1-h average concentrations of ozone formed in 1-day irradiations, the distributions of potential ozone for Sydney from the Dodge model show that a 33% reduction in both NMHC and NO, has the same relative effect as a 55% reduction in NMHC. The choice as to which represents the better policy depends upon factors such as the relative cost of controls and the relative effectiveness in dealing with problems such as those of multi-day irradiations, aerosol, and PAN formation. This result challenges the finding that NMHC controls represent the optimum control strategy for oxidants.
Discussion The use of distributions of potential ozone enables the evaluation of alternative control strategies to be based upon the distributions of real airshed data. Additionally, in comparison with strategies based upon the “dividing line” concept (8, IO),it has the advantage of being able to evaluate the effectiveness of combinations of NMHC and NO, controls as well as those of either NMHC or NO, control for given airsheds. The technique depends upon the reliability of the photochemical model used to calculate oxidant concentrations. As with all approaches, the absence of suitable cost models remains a barrier to choosing the optimum control strategy. Recent evaluations of the parameters of certain elementary processes such as:
+ NO RO + NO:! HO + NO:! H02 + NO RC03 + NO RO:! + NO:! + CO RO2
+
+
+
excess of 9.0. A major weakness in the “dividing line” concept is that the optimum control strategy is treated as either control of NMHC emissions or control of NO, emissions. The difficulty of applying the dividing line concept is shown by examining sets of airshed data. Figure 2 shows the cumulative frequency distribution of NMHC/NO, ratios based upon about 400 sets of NMHC and NO, data measured’:! during the Sydney Oxidants Study. The figure shows plots of the percentage of values of the ratio that are equal to or less than the stated value. The result shows that about 60% of values are less than 9.0, and about 40% exceed 9.0. Such a straddling of the line shows the difficulties in choosing either NMHC control or NO, control and justifies an examination of the effects of alternative policies in reducing potential ozone. Post and Bilger proposed that the ozone values measured in Sydney are well described by the Dodge model if the ozone concentrations calculated by the model are arbitrarily reduced to 67% of the calculated values (12).The reduction is said to be due to the dilution effect in the atmosphere brought about by the lifting of the morning inversion, although the effect of post 0900-h emissions of NO, could also be important (11,13). Figure 3 presents distributions of potential ozone calculated for Sydney using this modified version of the Dodge model. The cumulative frequency distributions in Figure 3 examine the relative effectiveness of alternative policies for emission controls. The distributions show the ozone potential in the Sydney airshed for three sets of conditions: (a) existing ambient concentrations of NMHC and NO,; (b) 33% reduction in emissions of NMHC and NO,; and (c) 55% reduction in emissions of NMHC. The results show that each of the sets of emission controls leads to the same distribution of ozone. The differences be-
have shown that the rate constants may have values up to 10 times those previously accepted (14).Use of such new values in the Dodge model may have the effect of increasing the values of the ozone isopleths to almost double previous values. It is not yet clear whether the isopleths would continue to hold their relative positions as before. Despite this evidence, it remains pertinent to evaluate the relative effects of alternative strategies upon the distributions of ozone calculated from the Dodge model, since this has been used as the basis for the proposal that control of NMHC emissions is the optimum strategy for control of oxidants (8) and since the empirically corrected model is said to describe ozone values measured in Sydney (12). Recently, from consideration of theDodge model, and assumptions on the relative costs of NMHC and NO, controls, Bilger proposed that control of NMHC emissions is the optimum strategy for control of photochemical oxidant (8).This proposal appears to be sound in choosing between either NMHC control or NO, control, provided that (a) the oxidants problem is that of ozone formed during 1-day irradiations and (b) NO, controls are twice as costly as NMHC controls, but it does not consider the possibility of simultaneous controls on both NMHC and NO, emissions or the distribution of NMHC and NO, concentrations encountered in a real airshed. The analyses described in this work show that less stringent controls in both hydrocarbons and NO, emissions can be as effective in reducing the ozone potential in a real airshed as more stringent controls on NMHC only. The appreciation that NMHC controls form the optimum oxidant control strategy assumes some cost model. Costs of emissions controls are generally believed to increase with some form of exponential or power series dependence of the degree of fractional reduction ( 2 5 ) .Where this is the case, or more Volume 13, Number 11, November 1979
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generally, where the dependence of the rate of increase of costs upon the degree of fractional reduction is greater than a zero-order dependence, an important result holds. The result is that for any fractional reduction of one precursor there is a corresponding smaller fractional deduction in emissions of both precursors obtainable for the same cost. For example, where the rate of increase of cost of emissions control is assumed to have a first-order dependence upon the degree of fractional reduction, and the Bilger assumption that the cost of NO, controls is twice that of NMHC controls for the same degree of fractional reduction used, it follows that the cost of 55% reduction in NMHC .missions equals that of 33% reduction in both NMHC and NO, emissions. The data of Figure 3 show each strategy to be equally effective in controlling ozone formed in 1-day irradiations. To the extent that these assumptions are true, it follows that the relative merits of the alternative strategies are determined by their effectiveness in controlling downwind ozone and oxidants other than ozone. In general, the higher the degree of controls required, the more favored becomes the use of less stringent combined controls. The problem of oxidants is more complex than is represented by the simple criterion of the ozone formed in 1-day irradiations ( 6 ) ,and the dependence of oxidants other than ozone on precursor concentrations has yet to be quantified for the range of precursor concentrations encountered in the airshed. Pitts (7) summarized a number of factors that make the reduction of emissions of NO, appear important in terms of the following observations: (a) although NO, emissions decrease ozone levels in the immediate area, they seem to raise ozone levels in areas downwind; (b) control of NO, reduces ambient levels of toxic Nos; (c) reduction of NO, emissions will lower ambient levels of secondary nitrate aerosols; (d) NO, is changed into many compounds such as PAN. The desirability of including some NO, controls in the program as well as hydrocarbon controls is further established by the results of Ripperton et al. (16)and Jeffries et al. ( 17), who showed that the effectiveness of control of hydrocarbons only in reducing ozone when fresh emissions are irradiated on the first day is not carried over to the second day of irradiation. Reductions in NO, emissions are needed to reduce the ozone formed under these conditions. Dimitriades ( 1 8 ) examined the likely results of control of NO, and proposed the possibility of two opposing effects. (a) I t (NO, control) will cause increased oxidant levels during the first day-a part of the increment to be carried into the downwind areas during subsequent days; (b) it will result in an aged mixture containing less NO, and, therefore, with less potential for oxidant formation in downwind areas. He concluded the net result to be neither known nor predictable. The results of the analysis of data from the Sydney airshed show that for calculations based on both the Dodge model (Figure 1)or the modified Dodge model (Figure 3), the control of both hydrocarbons and nitrogen oxides can be as effective in limiting the ozone formed in 1-day irradiations as some more stringent control of hydrocarbons alone. This result, together with the conclusion that control of downwind oxidant will result from control of NO, along with hydrocarbons (18), makes a policy, which includes some controls of NO, as well as hydrocarbons, appear t o have several advantages over one that does not. Thus, where the analyses of frequency distributions of potential ozone show that alternative policies of reducing NMHC and simultaneously reducing both NMHC and NO, have comparable effects in limiting ozone formed in 1-day irradiations, it appears that control of both NMHC and NO, is the optimum strategy for airsheds in which transport and
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recirculation meteorology are significant. In the particular case of the Sydney basin, Hyde, Hawke, and Heggie have shown that transport and recirculation of photochemical smog are important factors both inland and along the coast. Within the inland region they conclude that three mechanisms are important (19):(a) transport of oxidant precursors from the city and coastal source regions into the southwest of the region by the afternoon sea breeze; (b) transport from the inland source area by north-northeasterly gradient winds; and (c) recirculation of oxidants and precursors into the Sydney basin by nocturnal drainage flows. Along the coastal region two main mechanisms were considered to be important (20): (a) horizontal transport and recirculation of air advected offshore by westerly drainage flow and then back inland within the sea breeze; and (b) vertical recirculation of air within a shallow, slow moving sea breeze. If these transport and recirculation effects are important, the inclusion of some NO, control along with hydrocarbon controls in oxidant controls for Sydney seems desirable.
Literature Cited (1) Guicherit, R. “Proceedings of the Symposium on Occurrence and Control of Photochemical Pollution”; Clean Air Society of Australia and New Zealand: Sydney, 1976. (2) Guicherit, R.; Blokzijl, P. J.; Plasse, C. J. “Some Notes on the Abatement of Photochemical Ozone Production”; T N O Research Institute for Environmental Hygiene: Delft, The Netherlands, 1977. (3) State Pollution Control Commission “Report on Air Pollution Constraints in the Sydney Region”; Sydney, NSW, 1977. (4) Bilger, R. “Optimum Control Strategy for Photochemical Oxidants”, Charles Kolling Research Laboratory Technical Note ER-23; University of Sydney: Sydney, N.S.W., 1977. (5) Daly, N. J. “Photochemical Pollution in Australian Airsheds”; Australian Government Printing Service: Canberra, 1977. (6) Dimitriades, B.; Altshuller, A. P. J. Air Pollut. Contr. Assoc. 1977, 27, 299-307. (7) Pitts, J. N., Jr. Enuiron. Sei. Technol. 1977,11, 456-61. (8) Bilger, R. W. Enuiron. Sci. Technol. 1978, 12, 937-40. (9) Daly, N. J. “International Clean Air Conference, Clean Air-the Continuing Challenge”; White, E. T., Hetherington, T., Thiele, B. R., Eds.; Ann Arbor Science Publishers: Ann Arbor, 1978; p p 659-68. (10) Dodge, M. C. “International Conference on Photochemical Oxidant Pollution and Its Control”, EPA-600/3-77-001b; U.S. Environmental Protection Agency: Research Triangle Park, 1977. (11) Dodge, M. C. “Effect of Selected Parameters on Predictions of a Photochemical Model”, EPA-600-3-77948; US.Environmental Protection Agency: Research Triangle Park, 1977. (12) Post, K.; Bilger, R. W. “Ozone Precursor Relationships in the Sydney Airshed”, Charles Kolling Research Laboratory Technical Note ER; University of Sydney: Sydney, N.S.W., 1977. (13) Daly, N. J.; Steele, L. P. “Proceedings of the Symposium on Occurrence and Control of Photochemical Pollution”; Clean Air Society of Australia and New Zealand: Sydney, 1976. (14) Smith, M. “Research on Air Pollution a t CSIRO”, Short Course on Air Quality Technology; Sydney University: Sydney, N.S.W., 1979. (15) Pierrard, J. N. Innouation 1974,5, 6-9. (16) Ripperton, L. A,; Eaton, W. C.; Sickles, J. E. “Final Report to the Environmental Protection Agency”, EPA 68-02-1296; Environmental Protection Agency: Research Triangle Park, 1976. (17) Jeffries, H. E.; Fox, D. L.; Kamens, R. M. “Outdoor Smog Chamber Studies”, EPA-650/3-75-001; Environmental Protection Agency: Research Triangle Park, 1975. (18) Dimitriades, B. “International Conference on Photochemical Oxidant Pollution and Its Control”, EPA-600/3-77-001b; Environmental Protection Agency: Research Triangle Park, 1977. (19) Hyde, R.; Hawke, G. S.; Heggie, A. C. “International Clean Air Conference, Clean Air-the Continuing Challenge”, White, E. T., Hetherington, T., Thiele, B. R., Eds.; Ann Arbor Science Publishers: Ann Arbor, 1978; p p 119-34. (20) Hyde, R.; Hawke, G. S.; Heggie, A. C. In ref 19, pp 157-66.
Received for review December 19, 1978. Accepted July 11, 1979
