Environ. Sci. Techno/. 1986, 20, 895-904
General Purpose Adsorption Isotherms David G. Kinniburgh Hydrogeology Research Group, British Geological Survey, Wallingford, Oxon OX10 855, U.K.
The fitting of adsorption isotherm equations to experimental data is often an important aspect of data analysis. If the Langmuir and Freundlich isotherms are used, then consideration must be given to the proper weighting of the observations. Preferably nonlinear regression (nonlinear least squares) should be used since this enables these isotherms to be fitted directly and also enables other isotherms to be tested with little extra effort. Isotherms described here which are likely to show a wide range of applicability include the Tbth, modified Dubinin-Radushkevich, and multisite Langmuir isotherms. These can also describe competitive adsorption (binary exchange) reactions and are well suited for heterogeneous exchangers such as soils and sediments. Specific examples discussed are the adsorption of P and K by soils, Na-Cu exchange by montmorillonite, and Zn adsorption by ferrihydrite. Introduction Although the Langmuir and Freundlich isotherms were first introduced about 70 years ago, they still remain the two most commonly used adsorption isotherm equations. Their success undoubtedly reflects their ability to fit a wide variety of adsorption data quite well, but it may also partly reflect the appealing simplicity of the isotherm equations and the ease with which their adjustable parameters can be estimated. Both isotherm equations can be transformed to a linear form and so their two adjustable parameters are easily estimated either by graphical means or by linear regression. This ease of fitting may have led to the Langmuir and Freundlich isotherms enjoying rather more “success”than they deserve since closer examination of the data often reveals systematic deviations from the fitted isotherms. For many isotherms, including those with three or more adjustable parameters, it is no longer possible to estimate the adjustable parameters by ordinary linear regression or by any reliable graphical means, and so it is necessary to use nonlinear regression. This usually involves the minimization of the residual sums of squares and is often called nonlinear least squares (NLLS). Many NLLS algorithms are now widely available in easy-to-use computer programs, and so the fitting of complicated nonlinear isotherms is no longer difficult. An important advantage of the NLLS approach is that, once set up, it is relatively straightforward to fit a wide range of adsorption isotherm equations with little extra effort. In this paper, it is shown how just a few “general purpose” isotherms can be made to fit a wide variety of adsorption data. Various aspects of the fitting of adsorption isotherms to experimental data are also discussed. While NLLS methods are preferred even for fitting the Langmuir and Freundlich isotherms, it is likely that linear regression methods will continue to be used. The usual way of fitting the Langmuir and Freundlich isotherms involves fitting one of the transformed forms of the original isotherm equation either by graphical means or by unweighted linear regression. This conveniently ignores the particular distribution of error implied and, as has been repeatedly pointed out for the Langmuir isotherm, cab lead to biased estimates of the isotherm parameters. This is perhaps not so critical when adsorption data are confined to a narrow range of adsorption densities, but it becomes 00 13-936X/86/0920-0895$0 1.50/0
increasingly important as the range increases. Therefore, the question of the proper weighting of the observations when linear regression is used is also briefly discussed. The most promising extensions to the Langmuir and Freundlich isotherms are based on the generalized Langmuir and Generalized exponential isotherms (1). Several special cases of these two isotherms are potentially interesting (Table I), but this paper concentrates on three: the multisite Langmuir, Tbth, and modified DubininRadushkevich isotherms. These can reasonably be called “general purpose” isotherms since each shows great flexibility and is able to fit a wide variety of adsorption data. They are particularly suitable for describing adsorption on heterogeneous surfaces (1). The Langmuir-Freundlich (LF) and Redlich-Petersen (RP) isotherms are also interesting because they are essentially Freundlich isotherms but with different asymptotic properties-that is, both give linear log n-log c plots over part of the isotherm, but the LF isotherm approaches an adsorption maximum at high concentrations while the RP isotherm approaches a linear isotherm (Henry’s law) at low concentrations. The Tbth isotherm has both asymptotic properties, but unlike the LF and RP isotherms, its log n-log c plot gives a continuous, smooth curve throughout the intermediate range of concentrations. The Dubinin-Radushkevich (DR) isotherm is a parabola in log n-log c space that often fits data well in the intermediate range of concentrations but in its basic form has unsatisfactory asymptotic properties. These are removed in the modified DR isotherm which, in terms of fitting ability, closely resembles the Tbth isotherm. The Tbth, LF, and RP isotherms reduce to the Langmuir isotherm when the “heterogeneity parameter”, p, is set to unity, and the modified DR isotherm is close to Langmuirian when is 0.25. These isotherms can also be used to describe binary (competitive) adsorption. When, as is usual, all the adsorption sites remain occupied all the time, this can be done quite simply by replacing the concentration term in the isotherm equation by a concentration (or activity) ratio. Using Linear Regression To Estimate the Adjustable Parameters in the Langmuir and Freundlich Isotherms The adjustable parameters in the Langmuir and Freundlich isotherms are normally estimated by linear regression. The Langmuir isotherm can be linearized in at least three different ways (Table 11), and simple linear regression will result in different parameter estimates depending on which of the linearized forms is fitted. This is because each of these transformations changes the original error distribution (for better or worse). The choice of the “best” transformation has been most widely discussed in the biochemical literature where equations analogous to the Langmuir isotherm are important for describing drug binding and enzyme kinetics (2-8). The best transformation is not necessarily that which gives the highest correlation coefficient but rather that in which the resulting error distribution most closely matches the “true” error distribution. The preferred transformation may therefore vary from data set to data set (4). Dowd and Riggs (3) favored the distribution coefficient (n/c vs. c) plot since, unlike the double-reciprocal plot, this
@ 1986 American Chemical Society
Environ. Sci. Technot., Voi. 20, No. 9, 1986 895
Table I. Some Useful Adsorption Isotherm Equations'
isotherm
no. of adjustable parameters
equation
Langmuir (Ll) Freundlich (F) Langmuir-Freundlich (LF) Redlich-Peterson (RP) Tdth multisite Langmuir (Lk) sum of Freundlichs (Fk) Dubinin-Radushkevich (DR) modified Dubinin-Radushkevich (ModDR)"
n = KcM/(l + Kc) n = KC)^ n = (Kc)@M/[l+ KC)^] n = KcM/[I + KC)^] n = KcM/[[l + (Kc)@]1/,9] n = ~ ~ = , [ K , c M , /+( IK,c)l n = Ll(KLc)8i log n = -@[log2(Kc)] + log M log n* - log c* + log c c < c* log = { -p log2 [Kc/(l + Kc)] + log M c
asymptotic properties linear adsorption max a t low c a t high c
2 2 3 3 3 2k 2k 3 3
Yes no no Yes Yes yes no no Yes
c*
yes = M no yes = M no yes = M yes = E M i no no yes = M
On is the amount adsorbed, c is the equilibrium solution concentration, M is the adsorption maximum, k is an affinity parameter, and ,9 is an empirical parameter which varies with the degree of heterogeneity. "Where (n*,c*) is the point where d log n/a log c = 1. c* cannot be calculated explicitly but is given to a good approximation by log c* = (-1/2,9) - log K . This estimate can be refined by a modified Newton using log c*,+, = log c*, (b, - 1)/2@where b, = [-2,9/(1 + Kc*,)] log [Kc*,/(l + Kc*,)] and i is the iteration number.
+
Table 11. Linear Transformations of the Langmuir Isotherm: n = KLcM/(l
+ KLC)
parameters
plot
l / n = 1 / M + (l/KLM)(l/c)
1/11 vs. l / c
(n,fiiY
nz4
c/n = ~ / K L M + (l/M)c
(ii) Reciprocal (Langmuir) c/n vs. c KL = slope/intercept M = l/slope
(n,fii/ci)*
n,4/c,2
n = M - (l/KL)(n/c)
n vs. n/c
fii2
n;2
n/c = KLM - KLn
(iiib) Distribution Coefficient (Scatchard) n/c vs. n KL = -slope M = -intercept/slope
it:
ni2
(i) Double Reciprocal (Lineweaver-Burk) KL = intercept/slope M = l/intercept
(iiia) Eadie-Hofstee KL = -l/slope M = intercept
iterative
weights" single pass
transformation
'The weights shown are the weights that each of the residuals must be multiplied by so that the parameters derived from a weighted linear regression will be close to the parameters derived from a unit weighted NLLS. The 'hats" signify estimated values. fi, is not known a priori and therefore must be estimated iteratively (iterative weights) or approximatted by the observed values (single pass weights). For a constant relative error, each of the above weights should be divided by fi?.
tends to exaggerate deviations from the fitted equation, highlighting outliers and guarding against an overoptimistic interpretation of the goodness of fit. In 1965, NLLS routines were not widely available and so Dowd and Riggs were not able to compare results from the three linear transformations with those from NLLS. However, Colquhoun ( 4 ) extended the work of Dowd and Riggs by including such a comparison and found that NLLS (unweighted) was the best method (i.e., it gave unbiased parameter estimates with minimum variance) for data with constant variance and a normally distributed error. In recent years, specialized curve fitting programs incorporating NLLS have become available in biochemistry (6, 7). Although much well-founded criticism of the various linearized forms of the Langmuir isotherm has appeared in the environmental chemistry literature, the lessons to be learned seem to go largely unheeded. For example, Harter (8) discusses the shortcomings of the Langmuir plot but does not mention the use of weighting or of NLLS. The benefit of the NLLS approach, when propertly weighted, is subtle and not to be seen in statistics such as R2;rather, the benefit is in the assurance that the best parameter estimates have been obtained. All the transformations of the Langmuir isotherm tend to weight low n observations more than high n observations. In addition, the EadieHofstee and Scatchard plots suffer the disadvantage that they have n,which is usually assumed to contain all the measurement error, in the in896
Environ. Sci. Technol., Vol. 20,
No. 9, 1986
Table 111. Zinc Adsorption by Ferrihydrite at pH 5.5 (in 1 M NaN03)'
observation 1 2 3 4 5 6 7 8
9 10
amount adsorbed, n mmol of Zn/mol of Fe
equilibrium concentration, c, mmol of Zn/L
0.75 1.40 1.95 2.51 3.03 3.53 4.02 4.41 4.79 5.22
0.030 0.069 0.118 0.166 0.217 0.270 0.325 0.388 0.453 0.512
From Kinniburgh and Jackson (9).
dependent variable which in conventional regression analysis is assumed to be error free. If due attention is given to proper weighting, then weighted linear regression of any linear form of the Langmuir isotherm will provide estimates of the parameters close to those obtained by NLLS (see next section). To demonstrate this, Table I11 shows data for the adsorption of zinc by ferrihydrite (iron hydrous oxide gel) at pH 5.5. Table IV compares the Langmuir parameters estimated by weighted and unweighted linear regression using the GENSTAT statistical package (distributed by
Table IV. Regression Estimates of the Langmuir Isotherm Parameters for the Zn Adsorption Data Given in Table 111 parameters adsorption adsorption maximum, M , maximum, M , mmol of objective function Zn/mol of Fe mmol of Zn/mol of Fe method nonlinear regression (=NLLS) constant absolute error constant relative error log transform dependent variable linear regression
x ( n i - fiJP
E[(ni - f i i ) / f i i 1 2 x(log ni - log fiJ2 weights, wi, used”
l l n vs. l / c c/n vs. c n vs. nlc n l c vs. n l / n vs. l / c c/n vs. c n vs. n/c n l c vs. n l l n vs. l / c c/n vs. c n vs. n/c n/c vs. n l / n vs. l / c c/n vs. c n vs. n/c n/c vs. n Units are c in mmol/L and n in mmol of Zn/mol of Fe.
2.10 3.10 3.04
9.90 7.98 8.03
4.23 2.62 3.30 2.97 2.20 2.20 2.30
6.53 8.77 7.65 8.16 9.64 9.64 9.41 9.81 7.98 7.98 7.65 8.16 9.82 9.82
error distribution variable error
constant absolute error
2.14
constant relative error
constant absolute error
3.10 3.10 3.30 2.97 2.13 2.13 NCb NC
* NC, no convergence.
Numerical Algorithms Group Ltd., 256 Banbury Road, Oxford OX2 7DE, U.K., or in North America by Numerical Algorithms Group Inc., 1101 31 St, Suite 100, Downers Grove, IL 60515-1263). The results using NLLS are also included for reference and comparison. Both a constant absolute error and a constant relative error have been assumed. Note the relatively large variation and bias in the estimates of KL and M when ordinary unweighted linear regression was used and their close agreement when appropriately weighted. If no weighting is used, then the reciprocal (Langmuir) transformation will give parameter estimates that lie somewhere between those obtained by assuming a constant absolute error and a constant relative error-often this may not be an unreasonable assumption and can perhaps be used to justify the common use of this transformation. If the assumption of a constant absolute error is more appropriate then the l / n vs. l / c (or equivalently, the c/n vs. c ) , regression with weights involving n and ii gave the parameter estimates that came closest to those obtained by NLLS. However, since this involves weights that include ii, the estimated adsorption, iterative weighting must be used. Alternatively, ii can be replaced by n without introducing a serious bias in the parameter estimates, e.g., as in the single pass estimates (Table IV). If iterative weighting is used, then the l / n vs. l / c (or equivalently the c/n vs. c), regressions must be used because the mixing of dependent and independent variables in the n vs n/c and n/c vs. n regressions can lead to a failure to converge. If weighted linear regression is not feasible, then the unweighted n vs. n/c and n/c vs. n regressions will give estimates of KL and M that bracket those obtained by NLLS assuming constant relative and absolute errors. In constrast, when a constant relative error is assumed, the weighted l / n vs. l / c regression gives identical parameter estimates with those produced by NLLS. Variable weighting of individual observations can be applied when one of the linear transformations is used by first multiplying by the weights given in Table I1 and then by the variable weights.
The Freundlich isotherm parameters are commonly estimated from the linearized form log n = 6 log K + 6 log c e (1)
+
where e is the error term. This is equivalent to n = (Kc)be
(2)
rather than n = KC)^
+e
(3)
Equation 2 assumes a constant relative error while eq 3 assumes a constant absolute error. Often the former assumption is more appropriate, and so linear regression based on eq 1can give reliable estimates of the Freundlich isotherm parameters. If an assumption of constant absolute error is more reasonable, then either NLLS or linear regression with weights equal to n14should be used. Use of Nonlinear Regression Background. Rather than attempting to correct the deficiencies of the linearizing transformations, a more direct (and versatile) approach is to use nonlinear regression. (Nonlinear least squares, NLLS, is used here synonymously with nonlinear regression). This involves finding the set of parameters that minimizes the weighted residual sum of squares (WRSS)which for m observations is given by rn
WRSS = Xw,(n, - iiJ2
(4)
1=1
where ii, is the fitted value for observation i calculated from a particular isotherm equation and w, is the associated weighting factor. Most of the large statistical packages available for medium to large computers (e.g. BMDP, SAS, GENSTAT) have suitable NLLS programs, and similar routines are also widely available in scientific subroutine libraries. Some of these larger packages (or subsets of them) have already been converted for use on personal computers, a trend Environ. Sci. Technol., Vol. 20,
No. 9, 1986 897
likely to continue. In addition, various more or less specific optimizing programs already exist for personal computers (10, 11). Nash (12)discusses NLLS algorithms that have minimal storage requirements and are therefore particularly suited for small computers. Ideally the weights in eq 4 should be inversely proportional to the variance of each observation and can be estimated by replicate measurements or from prior knowledge of the size of the likely component sources of error. If such estimates are not available, as frequently happens, then the choice is usually between a constant absolute error and a constant relative error. The latter assumption can be conveniently introduced by log transforming the dependent variable, ni,and applying unweighted NLLS (Table 11). Most comprehensive NLLS routines also provide useful ancillary information (e.g., the approximate standard errors of the adjustable parameters and their correlations) which give an indication of the reliability of the parameter estimates. This helps to prevent over interpretation of the data. Sometimes, as in GENSTAT, advantage can be taken of the linearity of one or more of the adjustable parameters. For example, the multisite Langmuir isotherm is linear in the M ibut nonlinear in the Ki(13). Therefore, in any iteration, once the Kivalues have been fixed, the M, values can estimated directly by multiple linear regression. This effectively halves the number of adjustable parameters to be estimated by nonlinear regression. Most general purpose NLLS routines only require the user to provide the appropriate weights and a subroutine or set of program statements for calculating the fitted values. They are therefore very flexible. Normally n can be written explicitly in terms of the independent variable(s), i.e., concentration, but it is also possible to estimate n iteratively. This arises if, for example, the amount of adsorption itself depends on the amount of adsorption (as happens when lateral interactions are included), or if iterative weighting is used. Ross (14) describes the use of NLLS. All the NLLS results in this paper are derived from a program called ISOTHERM (15) which incorporates an unconstrained, derivative-free NLLS routine, EOIFCF, from the NAG subroutine library (16). Among the useful features of ISOTHERM are a library of the more commonly used adsorption isotherm equations (which can be easily extended), an option for obtaining tabular output suitable for plotting theoretical of fitted isotherms, and the ability to (i) flag isotherm parameters as either adjustable or fixed, (ii) add an “initial adsorption” parameter to any isotherm, (iii) consider competitive adsorption of two species by using as the independent variable a concentration ratio with adjustable exponent, and (iv) change easily between linear and logarithmic scales for both the independent variable(s) and the isotherm parameters. A general difficulty not frequently addressed, concerns the optimal distribution of experimental data points. Normally data points should not be clustered at discrete points on the concentration scale since this introduces an unintended and probably undesirable weighting of the fit at these points. Should the data points be uniformly distributed along a linear or logarithmic (or some other) concentration scale? There is no general answer, but a reasonable approach is to attempt to space the data points uniformly along a linear concentration scale if the error term is more or less independent of concentration and along a logarithmic scale if the error term tends to increase with concentration. The latter option usually applies when 898
Environ. Sci. Technol., Vol. 20, No. 9, 1986
the data cover a wide range of concentrations. It can often prove revealing to replicate some data points so that the residual s u m of squares can be resolved into ita “pure error” and “lack of isotherm fit” components (17). Goodness-of-Fit. When the fit of different isotherms is compared for the same set of data, it is necessary to have some measure of the goodness-of-fit. Many criteria have been proposed, but the principle criterion adopted here is the residual root mean square error (RMSE) which for m observations and p adjustable parameters is defined by
where RSS in the residual s u m of squares computed from eq 4 with all the weights, w,,set to unity. When unit weighting is used during the parameter estimation, the RMSE is the estimated standard deviation of the errors and should be similar in size to any independent estimates of the measurement errors. If the RMSE is much larger, then some other source of error in n is indicated-perhaps a serious lack of fit to the model being tested. Note that the appearance of m - p in the denominator implies the RMSE can increase when an extra adjustable parameter is added to the model. Clearly when this is the case, the addition of the extra parameter is not jusitified, but this may also be true even when the RMSE decreases. A better test for the effectiveness of adding extra adjustable parameter is provided by the “extra sum of squares principle”. The coefficient of determination, R2, can also be a useful measure of the goodness-of-fit since it is dimensionless. When multiplied by 100, it gives the percentage of the variance (about the mean) explained by the model. Extra Sum of Squares Principle. Inevitably, as extra adjustable parameters are added to a model, the residual sum of squares will decrease because of the increased flexibility. Provided that one model is a generalization or specialization of another, it is possible to apply the extra sum of squares principle (7,17)to test the significance of the addition or removal of adjustable parameters. For example, if model 2 is a generalization of model 1, then the F ratio may be calculated from (RSSi - R S S J / h - P I ) (6) F(P2 - P1, m - Pz) = RSSZ/(m - P A where m is the number of observations, p is the number of adjustable parameters, and the subscripts refer to the model number. This F ratio can then be tested against the appropriate F statistic. The following isotherms can be compared in this way: L1 and L2; L1 and Tbth; linear and Freundlich; Freundlich and Redlich-Peterson; Freundlich and Langmuir-Freundlich. Error in the Independent Variable. One of the assumptions of both the linear and nonlinear regression methods is that the independent variable is measured without error; it has been tacitly assumed that the measured equilibrium solution concentration, c , is the independent variable and therefore implicitly error free. This is rarely the case. Estimates of c are invariably subject to measurement error since adsorption is usually measured by difference; both n and c will contain errors. These errors will be negatively correlated. There is no easy, general solution to this difficulty, but where the experimental procedure means that that initial (total) concentration (cT)is known relatively accurately and the main source of error is in measuring c, then the objective function may be redefined in terms of c (18)by using the equation
fi = (CT - 2)V/S = f(x;2)
(7 )
where V is the total volume of solution, S is the solid/ solution ratio, f(x;2)is the adsorption isotherm equation, x is the vector of adjustable parameters, and the hats signify fitted values, If, for example, the Langmuir isotherm is assumed, then eq 7 gives (CT - 2)
‘ ” 1 Freundlich: -F’6Ok l o q K = I L 1 3 01 p =0.160 Y 1501 nc=18.8 mmol kg-’
1
i
V K2M -=S 1+K?
which may be solved for (in this case, this involves solving a quadratic equation). 2 can then be used in the optimizing routine to estimate the adjustable parameters, i.e., minimize Cwi(ci - 2J2. Constraints on Parameter Values and Scaling. Freqently physical, chemical, or other considerations mean that valid parameter estimates must fall within a restricted range of values. The most frequent and important case is when a parameter value is constrained to be positive. Here, simply reparameterizing to the log of the parameter will achieve the required constraint. Other transformations are possible. In the general case, constrained optimization routines may be used. In practice, if the model chosen accurately represents the data and if the initial parameter estimates are reasonable, then an unconstrained routine will normally suffice. Although there are several ways of obtaining reasonable initial estimates, a trial and error approach usually involves the least effort. The choice of initial estimates can greatly affect the speed of convergence and even whether the best solution is found. This is particularly true for the multisite Langmuir isotherm, and for which a stepwise fitting procedure is recommended: first, fit the data to the L1 isotherm (this should present no difficulty); then use these estimates as the initial estimates for site 1of the L2 isotherm. For site 2, increase the affinity by 2 orders of magnitude, decrease the number of sites likewise, and then refit; repeat as necessary. In practice, the quantity and quality of most experimental data mean that no more than two, or exceptionally three, classes of sites can be justifiably included. Most optimization procedures work best when a fixed change in each of the parameters produces a similar change in the weighted residual sum of squares and when the parameters are not strongly correlated. Scaling and reparameterizing to provide these characteritics can therefore increase the speed of convergence. Some Applications of the General Purpose Isotherms to Real Data Selection of Data. Four sets of previously published adsorption data are analyzed. All the data are for isotherms carried out at room temperature. These include adsorption by soils, clays, and oxides. One small set is for phosphorus adsorption while the other three are for competitive adsorption (binary exchange) with somewhat larger data sets. These represent a typical selection of adsorption and exchange data and demonstrate the flexibility of the various isotherms. The particular data sets selected illustrate a range of different treatments of “raw” adsorption data in terms of the presence/absence of initial adsorption, the choice of independent (solution) variable, and the weighting used. The discussion will center around the treatment of the data per se rather than its detailed interpretation-in this respect, the actual data values are themselves unimportant. A proper statistical analysis is just as necessary with poor quality and/or small data sets as it is with large, high-quality data sets. Indeed, the correct weighting tends to become more important the greater the errors in the data (4).
Flgure 1. Change in phosphorus adsorption by a soil derived from a basic igneous till as a function of the equilibrium (18 h) solution P concentration (after Bache and Williams (79)). Positive changes signify a net uptake of P by the soil. Experimental points and fitted curves for the Freundlich, modified Dubinin-Radushkevich, and T6th isotherms are shown. Units for K are L mol(’@-’) kg-’@ (Freundlich) and L mol-’ (modified DR and T6th); units for M are mmol kg-’ in all cases.
Phosphorus Adsorption by Soils. Phosphorus adsorption isotherms for soils and sediments are usually of the high-affinity type and are poorly described by the Langmuir (Ll) isotherm. Unfortunately, retrieving reliable P adsorption data from published isotherms is often difficult because they are usually plotted unsatisfactorily, i.e., with a linear concentration scale. Critical low concentration data tend to be clumped close to the zero concentration axis leading to serious loss of information. However, Bache and Williams (19) plotted P adsorption isotherms for four acidic Scottish soils using a log c scale, thus making their data amenable for further analysis. They obtained the isotherms by adding varying amounts of P (in 0.02 M KC1) to essentially untreated soils; i.e., the soils already contained an unknown amount of labile P. Therefore, the isotherms reported were An vs. log c plots, i.e. An = f(x;c) - no
(9)
where An is the change in the amount of adsorption and no is the amount of initial adsorption. In this example, as is usual, the isotherm was described in terms of the total concentration of soluble P species. No explicit account is taken of the actual P species present in solution. Figure 1shows a typical P adsorption isotherm for one of the soils reported by Bache and Williams (19). The data vary over 3 orders of magnitude in P concentration, but it is difficult to get a feel for the shape of the adsorption isotherm because of the way in which the data have been plotted. The smooth spread of the seven data points suggested that the major source of error in An was likely to lie in the estimation of An from the published graph rather than from its experimental determination. Therefore, in fitting the data to the various isotherms, a constant absolute error in An was assumed. Three isotherms (Table I),namely the Freundlich (0.633),modified DR (0.584)and T6th (0.5721, fitted the data almost equally well providing an initial adsorption parameter was included as an additional adjustable parameter (RMSE’s in parentheses, all in mmol of P kg-l) (18,20). The Freundlich isotherm fitted the data as well as the other two isotherms; with one fewer adjustable parameters, it seems preferable. However, it is more likely to overestimate P adsorption if applied to concentrations outside the observed concentration range. This is reflected in the relatively high estimate of the initial adsorption parameter, no, given by the Freundlich isotherm. Note that because no has been included as an adjustable parameter, it is no longer possible to esitmate the Freundlich parameters by linear regression. Environ. Sci. Technol., Vol. 20, No. 9, 1986
899
7
0
M 815-d
kg
OOL
001 0.02 003 A R ( = a,/o::+M,J
Flgure 2. Potassium-calcium (pius magnesium) exchange on a Lower Greensand sol1 plotted as the change in potassium adsorption, An, vs. the “equlllbrium” activity ratio, AR (after Beckett (27)). Experimental points and fhed curves for the two-site Langmulr (L2 = double Gapon), modifled DubininRadushkevich,and T6th isotherms (the last two curves are almost coincident). I n each case, the maximum possible potassium adsorption was fixed at 81.5 mmoi kg-‘.
The L2 isotherm also fitted the data well (RMSE = 0.627 mmol of P kg-l), but with five adjustable parameters and only seven data points, this was considered to be a case of overfitting! Potassium Adsorption by Soil. Ion-exchange reactions in temperate soils are largely governed by the presence of clay minerals with a permanent negative charge. Calcium and magnesium tend to dominate the exchange complex in these soils; thus, any change in the amount of potassium (K+) adsorbed leads to the desorption of an equivalent amount of calcium plus magnesium (the exchange behavior of calcium and magnesium is so similar in most mineral soils that they can be treated as a single equivalent species). The K+-(Ca2+ Mg2+) exchange isotherm can conveniently be studied by adding different weights of untreated soil to a series of calcium solutions containing graded amounts of potassium. After equilibration, the supernatant is analyzed for K+, Ca2+,and Mg2+ and the gain or loss of adsorbed K+ calculated by difference. Beckett (21) described such an experiment for a loamy sand soil derived from the Lower Greensand (U.K.), plotting the change in potassium adsorption, A n , as a function of the calculated activity ratio (AR = aK/ aCa+Mp1/2) after a 12-h equilibration (Figure 2). These data were analyzed in the same way as the phosphorus data except that the independent variable was an activity ratio rather than a concentration. The Langmuir (Ll) isotherm then becomes numerically equivalent to the Gapon isotherm. Although no measurement errors were given in the original paper, it has been assumed that these were independent of the amount of K adsorbed. In each case, the maximum adsorption was fixed at 81.5 mmol of K kg-’ since this was the measured cation-exchange capacity of the soil. The best-fitting sets of parameters and the fitted curves are shown in Figure 2. The RMSE’s (in mmol of K kg-l) were 0.211 (L2 = double Gapon), 0.240 (Modified DR), and 0.242 (Tbth), so the double Gapon isotherm just gave the best fit although all three fits are good. The double Gapon parameters (Figure 2) agree well with those derived by Bolt (see note at the end of Beckett (21)) and suggest that about 3% of the sites have a high affinity for K, an affinity some 160 times greater than for the other 97% of sites. These high-affinity K sites are probably located at the weathered edges of mica-like minerals. Neither the Gapon (Ll) nor Vanselow isotherms describe the data well. The value of the AR for which A n = 0, ARo, is the estimated activity ratio of the soil solution in its initial
+
900
Environ. Sci. Technol., Voi. 20, No. 9, 1986
(undisturbed) state. ARo can either be estimated graphically or by solving the appropriate isotherm equation for n = no;it is about 0.012 in the present case. no is minus the value of A n at AR = 0 and corresponds to the estimated amount of labile, exchangeable K adsorbed by the soil in its initial state. Variation of no merely shifts the exchange isotherm vertically up or down. Therefore, the three (or four in the case of the double Gapon isotherm) basic isotherm parameters define the intrinsic exchange characteristics of the soil while the initial adsorption parameter defines the particular state of the soil when sampled. This set of parameters seem preferable to that normally chosen for such “Q/I”curves (21,22). An advantage of measuring isotherms in this way is that by starting with the soil in its near natural state and not moving too far from it, the exchange isotherm can readily be defined over the relevant range of exchanger compositions without any drastic pretreatments which might result in a significant change to the soil exchange properties. Of course, exchange data can also be treated in terms of the classical thermodynamic approach (23), but this requires data over the entire range of exchanger compositions and does not overcome the problem of describing the nonidealities involved. Copper Adsorption by Sodium Montmorillonite. Sposito et al. (24) presented data (their Table 11) for Na+-Cu2+exchange by a sodium montmorillonite (Wyoming bentonite) in a perchlorate background medium maintained at a total concentration of about 0.01 N and in the pH range 5.0-6.0. Data were presented for the variation in exchanger composition (qCu,qNa) as a function of the equilibrium concentrations of Cu2+and Na+ in solution and were analyzed as follows: solution concentrations were converted to activities (aCu,aNa),and the Vanselow selectivity coefficient, Kv, was calculated for each of the 17 exchanger compositions available (an anomalous sample at pH 4.14 was excluded). The average Kv was estimated to be 1.32 f 0.26, and the individual values showed no systematic variation with exchanger composition. Therefore, the Sposito’s terminology, the montmorillonite was behaving as an “ideal” exchanger (23). The total adsorbed charge, which in this case is equal to the certain exchange capacity (CEC), was estimated to be 0.92 f 0.05 equiv kg-l and showed no systematic variation. The constancy of Kv implies that it is unlikely that any other simple isotherm could fit the data as well as the Vanselow isotherm. However, it was of interest to (i) see how well (or badly) other isotherms fitted the data and (ii) fit the isotherms assuming that only the amount of Cu adsorbed was known (as would be the case if Cu had been added to a Na-montmorillonite suspension and the amount of adsorbed Cu estimated by difference). In each case, the activity ratio, aCu/aN?,was treated as the independent variable. Since estimates of the standard deviations, u,, of each of the measurements of adsorbed Cu were given, each observation was weighted by the factor 1/u?. (The measurement errors in the solution concentrations have been ignored although they should also be considered in a thorough analysis.) The five isotherms fitted were Vanselow (0.00481), L1 (0.00889),L2 (0.00570),modified DR (0.00811), and Tbth (0.00693) (RMSE’s in parentheses in mol of Cu kg-l). The form of the Vanselow isotherm fitted was ncu = &fCu(l - 1/[1 + 4Kv(ac~/aN,2)]”~] (10)
-
where the exchange reaction is written in the direction 2NaX CuXz and Mcu is the maximum number of moles of Cu per kilogram that can be adsorbed. The fitted curves for all but the L2 isotherm are plotted in Figure 3. The
0
w- v
i
-
u(
fiz1.70
log K,: -7.70 lagM,=-1.01 logK2=- 4 8 9
log M I = -2,645 -Li
‘Mad DR
-ab
M = 0 372 mol Cu kg-’
2
i
6
I B l ‘ o
log c t fipH
Flgure 4. Zinc adsorption by ferrihydrite in 1 M NaNO, as a function of the logarithm of the zinc concentration-hydrogen ion activity ratio in solution. A total of 151 data points is plotted, and V i e d curves for the two-site Langmuir, modified Dubinin-Radushkevich, and T6th isotherms are shown.
adsorption can be represented by a single variable, namely, the activity ratio, uZn/uHn,or its logarithm, log uzn f rtpH. In 1M NaN03, the activity coefficient of zinc is constant so that the zinc activity can be replaced by its concentration. When the amount of Zn adsorbed was plotted vs. log c rtpH (ti = 1.70), then all of the Zn data were reduced to a single curve irrespective of the individual variation in log c and pH (Figure 4). Furthermore, this curve is fitted well by L2, modified DR, and TBth isotherms (Figure 4). In each case, C(log ni - log fi,)’ was minimized; i.e., a constant relative error in ni was assumed. The RMSE’s in terms of log n were 0.0699 (L2), 0.0779 (TBth), and 0.0627 (modified DR). Many years ago, Schofield proposed what is now generally known in soil science as the Ratio Law (22): “...if a soil is in equilbrium with a large volume of a dilute solution, the equilibrium will not be upset if the activities of the monovalent ions are altered in one ratio, of the divalents in the square root and the trivalents in the cube root of that ratio”. The power terms arise from the stoichiometry of the exchange reaction. The Ratio Law describes how the ratio of cation activities must be varied so as not to change the cation composition of the exchanger. It does not describe how the exchanger composition would vary with an arbitrary change in solution activities-this more demanding requirement is the aim of exchange isotherms. The Ratio Law has been confirmed many times, but Schofield noted that it was obeyed for Ca2+-H+ exchange by a variable charge Natal soil (29). This can now be rationalized since an analysis of the pH dependence of calcium adsorption by ferrihydrite has shown that the value of the apparent H+-Ca2+exchange stoichiometry coefficient is closer to 1 than to 2 (28). Therefore, the appropriate independent variable should be closer to pH-pCa than to the pH-l/2pCa applicable to permanent charge dominated soils and implicit in the Ratio Law as stated above. Standard Errors of the Adjustable Parameters. Although summary statistics such as the RMSE or the coefficient of determination give a good idea of the overall goodness-of-fitof an isotherm to experimental data, these statistics give no indication of the errors associated with individual parameter estimates. These errors are often quite large because of the high correlation between adjustable parameters. Table V summarizes the parameter estimates, their standard errors, and their correlation coefficients for the isotherms plotted in Figures 1-4. Most of the data sets contain at least one pair of very highly correlated parameters. The phosphorus adsorption data illustrate the problem well. All three isotherms illustrated in Figure 1show a very good degree of fit (R2> 0.999) and yet many of the parameter estimates have relative stand-
+
Environ. Sci. Technol., Vol. 20, No. 9, 1986
901
Table V. Fitted Parameters, Their Standard Errors, and the Correlation Coefficients between the Adjustable Parameters for the Isotherms Plotted in Figures 1-4" (A) Phosphorus Adsorption by Soil, m = 7 (Figure 1)
log K
P
no
log K
P
log M no
log K
P
log M
no
(i) Freundlich Isotherm (RMSE = 0.633; R2 = 0.99904) log K P 14.10 f 1.28 1.000 0.160 f 0.0161 -0.999 1.000 18.79 f 3.82 0.990 -0.985 (ii) Tbth Isotherm (RMSE = 0.572; R2 = 0.99941) log K P 7.338 f 2.575 1.000 0.1427 f 0.0809 -0.997 1.000 2.323 f 0.387 0.986 -0.996 4.95 f 3.96 0.976 -0.957
no 1.000 log M
no
1.000 0.933
1.000
(iii) Modified DR Isotherm (RMSE = 0.584; R2 = 0.99939) log K P log M -0.693 f 2.56 1.000 0.0256 f 0.0184 0.996 1.000 2.028 0.269 -0.999 -0.992 1.000 6.14 f 4.31 -0.940 -0.965 0.929
no
*
(B)Potassium Adsorption by Soil, rn = 61 (Figure 2)
(C) Copper Exchange by Sodium Montmorillonite, m = 17 (Figure 3)
(i) Double Gapon Isotherm (RMSE = 0.211; R2 = 0.99355) K1 K2 M2 no
K1 K2
2.71 f 0.10 1.000 4 2 4 f 138 0.781 1.000 2.36 0.20 -0.869 -0.623 1.000 M2 0,491 0.812 -0.128 1,000 no 4.32 f 0.12 M, 8195 M2 (fixed) (ii) Tbth Isotherm (RMSE = 0.242; R2 = 0.99136) K P no K 10.66 f 1.44 1.000 P 0.406 f 0.020 -0.989 1.000 no 4.07 f 0.076 0.779 -0.781 1.000 M 81.5 (fixed) (iii) Modified DR Isotherm (RMSE = 0.240; R2 = 0.99151) K P no K 0.0166 f 0.0035 1.000 R 0.0932 f 0.0053 0.996 1.000 no 4.07 f 0.083 -0.712 -0.765 1.000 M 81.5 (fixed)
-
1.000
(i) Vanselow Isotherm (RMSE = 0.00481; R2 = 0.99797) KV M Kv 1.356 f 0.033 1.000 M 0.459 f 0.0028 -0.855 1.000 (ii) Tbth Isotherm (RMSE = 0.00693; R2 = 0.99608)
K K
P
M
3.100 f 0.083 0.911 f 0.042 0.3956 f 0.0076
1.000 -0.586 0.398
P
M
1.000
-0.966
1.000
(iii) Modified DR Isotherm (RMSE = 0.00811; R2 = 0.99463) K P M K 0.239 f 0.027 1.000 0.233 f 0.012 0.981 1.000 M 0.372 f 0.004 -0.943 -0.891 1.000
(D) Zinc Adsorption by Ferrihydrite, rn = 151 (Figure 4)
(i) Two-Site Langmuir Isotherm (RMSE = 0.0699; R2 = 0.99849) 1% K1 log Mz log Kz log Kl 1% MI 1% K2 1% Mz fi
log K
P
log M ri
log K
P
log M fi
-7.699 f 0.033 -1.015 f 0.019 -4.889 f 0.035 -2.645 f 0.032 1.70 (fixed)
1.000
-0.830 0.477 -0.527
1.000 -0.179 0.202
(ii) Tbth Isotherm (RMSE = 0.0779; R2 = 0.99812) log K P -7.097 f 0.062 1.000 0.202 f 0.007 0.864 1.000 -0.187 f 0.0078 -0.963 -0.962 1.70 (fixed)
1.000 -0.954
log M
1.000
(iii) Modified DR Isotherm (RMSE = 0.0627; R2 = 0.99878) log K P log M -12.54 f 0.19 1.000 0.0463 f 0.0011 0.992 1.000 -0.318 f 0.062 -0.988 -0.963 1.000 1.70 (fixed)
rn is the number of observations; RMSE is the root mean square error. R2is the coefficient of determination (dimensionless); units for isotherm parameters and variables are the same as in Figures 1-4.
ard errors greater than 10%; no is particularly poorly estimated. This reflects the restricted range of adsorption 902
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densities covered, the small number of data points, and the very high correlations between the adjustable param-
eters. For example, if, in this case, the value for the initial adsorption parameter, no, is fixed at 4.95 mmol of P kg-l, the value estimated by fitting the Tdth isotherm (Table V, A(ii)), then refitting the Tdth isotherm does not change R2 or the parameter estimates but the standard errors are reduced by a factor of between 3 and 6 times. Similar reductions in the standard errors are found by fixing other parameters and by fitting other isotherms. The basic problem in fitting adsorption isotherms is that a given amount of adsorption can often be nearly as well explained by assuming that there are a small number of high-affinity sites or that there are a large number of low-affinity sites. For example, consider the Langmuir isotherm. The affinity parameter ( K ) is best estimated from the slope of the adsorption isotherm at very low concentrations, However, this slope gives the product KM, not just K. In order to separate these two parameters, it is necessary to know the adsorption maximum (M), and this can only be estimated with precision from data at very high concentrations where the slope of the isotherm approaches zero. If data are restricted to an intermediate range of concentration, then they may be fitted very well, but it will be difficult to separate K and M; K and M will show a high negative correlation and correspondingly high standard errors. Similar problems arise with other isotherms. This does not detract from their ability to back-calculate adsorption at a given solution concentration providing the data are within the range covered by the original experimental data, but it does caution against the over interpretation of the parameters. In particular, when the parameters are to be interpreted in a physical sense (as free energies of adsorption, surface areas, etc.), it is highly desirable to have estimates of the associated standard errors. For numerical reasons, the standard errors calculated by NLLS routines are only approximate, and more importantly, they assume that the underlying model is basically correct. This often is not the case, or at least, it is often not known with certainty that it is. The best approach is to test the model thoroughly by careful experimental design. If the experimental data cover a wide range of concentrations, then examination of the residuals should reveal any systematic deviations from the model. In any case, the standard errors of the parameter estimates should be treated with caution; if anything, they may be too small; Le., the errors may be larger than indicated. Conclusions In a sense, the search for a general purpose adsorption isotherm is likely to remain an elusive goal. However, the multisite Langmuir, modified Dubinin-Radushkevich, and Tdth isotherms are able to describe a wide variety of adsorption data of interest to environmental chemists. They offer more flexibility than the Langmuir and Freundlich isotherms and so should enable the concentration (or activity) range over which adsorption can be accurately described to be extended. These isotherms are particularly suitable for describing adsorption on heterogeneous surfaces and are able to fit data showing a gentle change of slope in their log n-log c plots. The greater flexibility of the two-site Langmuir isotherm (it has four adjustable parameters as opposed to the three of the modified DR and Tdth isotherms) sometimes can cause problems in the location of a unique set of best-fitting parameters. This does not detract from its fitting (and descriptive) ability but means that extra care must be taken when interpreting the fitted parameters. Nonlinear least-squares (NLLS) methods, appropriately weighted, are the best way of estimating isotherm parameters-even for the Langmuir and
Freundlich isotherms. The flexibility of NLLS makes it easy to compare different isotherms, and this should encourage a more critical approach to the fitting of isotherm data. All three isotherms are “well behaved” in the sense that they approach an adsorption maximum at high concentrations and a linear isotherm at low concentrations. They should therefore be suitable for modeling and computer simulation studies. It is true that the parameters describing this asymptotic behavior may not always be well-defined because of the limited range of experimental data available, but their presence in the isotherm equations makes it a simple matter to define reasonable values. This may not be as good as storing alongside each set of isotherm parameters its valid range but it is simpler. Provided that the independent (solution) variable is replaced by a suitable activity (or concentration) ratio, the flexibility of the above general purpose isotherms can also be successfully used to describe ion-exchange reactions. Of course, well-known exchange isotherms such as the Vanselow isotherm should also be tested. All the isotherms discussed here might reasonably be called “empirical” because they are not derived from molecular or thermodynamic principles. They are purely descriptive, and description is not the same as explanation. However, there are sound reasons why such empirical isotherms can be expected to continue to play an important role in environmental chemistry. Acknowledgments I thank John Barker and Jon Hosking for helpful discussions. Literature Cited (1) Jaroniec, M. Adu. Colloid Interface Sci. 1983,18,149-225. (2) Wilkinson, G. N. Biochem. J . 1961, 80, 324-332. (3) Dowd, J. E.; Riggs, D. S. J. Biol. Chem. 1965,240,863-869. (4) Colquhoun, D. J. R. Stat. SOC.Ser. C 1969,18, 130-140. (5) Parker, R. B.; Waud, D. R. J. Pharmacol. Exp. Ther. 1971, 177, 1-12. (6) Mannervik, B. Methods Enzymol. 1982,87C, 370-390. (7) Munson, P. J.; Rodbard, D. Anal. Biochem. 1980, 107, 220-239. (8) Harter, R. D. Soil Sci. SOC.Am. J. 1984, 48, 749-752. (9) Kinniburgh, D. G.; Jackson, M. L. Soil Sci. SOC.Am. J. 1982, 46, 56-61. (10) Westall, J. “FITEQL. A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data”; Report 82-01; Department of Chemistry, Oregon State University: Corvallis, OR, 1982. (11) Christian, S. D.; Tucker, E. E. Am. Lab. 1982,14(9), 31-36. (12) Nash, J. C. Compact Numerical Methods for Computers: Linear Algebra and Function Minimization; Adam Hilger: Bristol, 1979. (13) Holford, I. C. R.; Wedderburn, R. W. M.; Mattingley, G. E. G. J. Soil Sci. 1974, 25, 242-255. (14) Ross, G. J. S. In Mathematics and Plant Physiology;Rose, D. A.; Charles-Edwards, D. A,, Eds.; Academic: London, 1981; Chapter 15, p p 269-282. (15) Kinniburgh, D. G. “ISOTHERM. A Computer Program for Analyzing Adsorption Data”; Report WD/ST/85/02; British Geological Survey: Wallingford, 1985. (16) Numerical Algorithms Group NAG Fortran Manual, Mark 10; Numerical Algorithms Group Ltd: Oxford, 1983. (17) Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd ed.; Wiley: New York, 1981; Chapters 1-2. (18) Barrow, N. J. J . Soil Sci. 1978, 29, 447-462. (19) Bache, B. W.; Williams, E. G. J. Soil Sci. 1971,22,289-301. (20) Fitter, A. H.; Sutton, C. D. J. Soil Sci. 1975,26, 241-246. (21) Beckett, P. H. T. Soil Sci. 1964, 97, 376-383. (22) Russell, E. W. Soil Conditions and Plant Growth, 10th ed.; Longmans: London, 1973; pp 90-101. Environ. Sci. Technol., Vol. 20, No. 9, 1986
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Environ. Sci. Technol. 1986, 20, 904-911
(23) Sposito, G. The Thermodynamics of Soil Solutions; Oxford University Press (Clarendon): New York, 1981; Chapter 5. (24) Sposito, G.; Holtzclaw, K. M.; Johnson, C. T.; LeVesqueMadore, C. S.Soil Sci. Soc. Am. J. 1981, 45, 1079-1084. (25) Kinniburgh, D. G.; Jackson, M. L. In Adsorption of Inorganics at Solid-Liquid Interfaces;Anderson, M. A.; Rubin, A. J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981; Chapter 3, pp 91-160. (26) Schindler, P. W. In Adsorption o f Inorganics ut SolidLiquid Interfaces;Anderson, M. A.; Rubin, A. J., Eds.; Ann
Arbor Science: Ann Arbor, MI, 1981; Chapter 1, pp 1-49. (27) Kinniburgh, D. G. J. Soil Sei. 1983, 34, 759-769. (28) Kinniburgh, D. G.; Barker, J. A.; Whitfield, M. J. Colloid Interface Sei. 1983, 95, 370-384. (29) Schofield, R. K.; Taylor, A. W. Soil Sei. Soc. Am. h o c . 1955, 19, 164-167.
Received f o r review June 21, 1985. Accepted March 19, 1986. This research is published with the permission of the Director of the British Geological Survey (NERC).
Limitations in the Use of Commercial Humic Acids in Water and Soil Research Ronald L. Malcolm” US. Geological Survey, Box 25046, M.S. 408, Federal Center, Denver, Colorado 80225
Patrick MacCarthy Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, Colorado 80401
Seven samples of commercial “humic acids”, purchased from five different suppliers, were studied, and their characteristics were compared with humic and fulvic acids isolated from streams, soils, peat, leonardite, and a dopplerite sample. Cross-polarization and magic-angle spinning 13C NMR spectroscopy clearly shows pronounced differencesbetween the commercial materials and all other samples. Elemental and infrared spectroscopic data do not show such clear-cut differences but can be used as supportive evidence, with the 13CNMR data, to substantiate the above distinctions. As a result of these differences and due to the general lack of information relating to the source, method of isolation, or other pretreatment of the commercial materials, these commercial products are not considered to be appropriate for use as analogues of true soil and water humic substances, in experiments designed to evaluate the nature and reactivity of humic substances in natural waters and soils. W
Introduction Extraction and isolation of humic and fulvic acids from soils and sediments are time-consuming and laborious processes. Humic substances in natural waters are considerably more difficult to isolate, primarily due to the low concentration of humic substances in waters as compared to concentrations in soils and sediments. In addition to extensive labor and time requirements, the purchase of and familiarity with specialized equipment and procedures usually are necessary in order to isolate humic substances. Most researchers are anxious to conduct experiments that test various hypotheses concerning the diverse nature and reactivities of humic substances, but many researchers apparently decide that the initial process of extracting, isolating, and purifying humic substances from the waters, soils, or sediments that are to be investigated, is not necessary. Some researchers may consider the extraction process to be more of an annoyance, or a menial task, as well as causing an unnecessary delay of weeks or months before real and meritorious experimentation can begin. In reality, these steps usually constitute some of the most essential prerequisites to meaningful studies on humic substances and comprise an indispensable part of the experimental design. 904
Environ. Sci. Technol., Vol. 20, No. 9, 1986
For reasons cited above and others, many researchers have used commercially available so-called “humic acids” in their studies. The use of these commercial humic acids has been mildly criticized by some researchers in the past, but these materials are still commonly used in research. The purposes of this paper are (1)to show that several common commercial humic acids are not representative of soil or aquatic humic or fulvic acids, (2) to demonstrate that use of commercial humic acids may be of limited value in terms of understanding the nature and reactivity of natural humic substances in waters and soils, and (3) to present evidence that many of the commercial humic acids purchased from different suppliers possibly come from the same stockpile. For this paper, humic acids from a variety of commercial sources were characterized and their properties are compared to humic substances from soil and stream sources. The humic acids from five commercial suppliers that were investigated for this paper (Table I) are the most common commercial humic products used in the United States during the last decade. The use of other commercial humic acids such as Ega Chemie sodium humate ( I ) , Merck humic acid (2,3),Light humic acid (3),Wako Ltd. humic acid (4))Riedel and de Haen humussaure (5-7), leonardite humic acid from American Humates (8), and Carbonox from a North Dakota lignite (9-12) also has been reported in the literature. Some of the commercial humic acids cited in the older literature above may no longer be available. Fulvic acid is available commercially from Contech, Inc., but was not evaluated in this study. The use of brand names in this r e p o r t is for identification purposes only and does not constitute endorsement by the US.Geological Survey or the Colorado School of Mines. One of the major limitations in working with commercial humic acids is the lack of information on their origin and method(s) of extraction. Without this information it is impossible to attach any geochemical or environmental significance to data obtained by using these materials. These problems are compounded by the evident lack of consistency from batch to batch even with samples from the same supplier. This undesirable situation is well illustrated by letters received from various suppliers of commercial humic acids in response to requests for in-
Not subject to US. Copyright. Published 1986 by the American Chemical Society
