Volatile Organic Compound Determinations Using Surrogate-Based Correction
for Method and Matrix Effects

Table of Contents

The principal properties that are related to analyte recovery in a vacuum distillate are boiling point and relative volatility. The basis for selecting compounds to measure the relationship between these properties and recovery for a vacuum distillation is presented. Surrogates are incorporated into samples and their recoveries are shown to accurately predict experimental recoveries of other analytes. The accuracy of the surrogate-based recovery predictions, as compared to experimental results, typically exceeds 95 percent for water and soil test samples and can be used to correct analytical results for matrix effects.

INTRODUCTION

The U. S. Environmental Protection Agency (EPA) has reported that vacuum distillation can be used to determine the concentration of volatile organic compounds (VOCs) in various matrices.¹ A formal method incorporating this procedure is currently in the Resource Conservation and Recovery Act (RCRA) promulgation process as an alternative method for determining VOCs in hazardous waste.²

Vacuum distillation is performed on a variety of matrices using the same experimental conditions.¹ Grouping the analyses of differing matrices for quantification is efficient when the quantifying procedure does not employ a matrix-specific calibration. However, the accurate determination of an analyte's concentration in the final vacuum distillate (or extract) requires a correction for losses of analyte if a matrix-independent calibration is used. This study investigates an approach to predict and correct for analyte losses.

Alternative EPA methods used to determine VOC concentrations require separate calibrations for soil and water samples, with the assumption that such calibrations generally compensate for both method losses and matrix effects.^3,4 In this paper, we are recommending an instrument calibration independent of method losses and matrix effects (i.e., direct injection of standards) when determining VOC's using vacuum distillation. Surrogate compounds can be incorporated into samples for vacuum distillation analyses and their measured recoveries accurately predict the actual recoveries of other analytes. The establishment of analyte recovery allows the analyst to compensate for method and matrix losses, and therefore, a matrix-independent calibration is viable.

This study was conducted to identify properties that impact analyte recovery when a sample matrix is vacuum distilled and to identify the bases for selecting surrogate compounds to measure method and matrix effects. We have adopted the term, relative volatility (a)⁵, to describe the potential of a compound to be extracted from a matrix and use the term, boiling point, to describe the potential of a compound to condense (related to its vapor pressure). We are introducing the term, a-surrogate, to identify compounds used to assess relative volatility effects and the term, b-surrogate, to identify compounds used to assess condensation effects. We have not tried to differentiate method losses from matrix effects and use matrix effects to describe both categories of losses.

EXPERIMENTAL SECTION

Vacuum Distillation Apparatus.  The vacuum distillation apparatus previously described¹ was used with several modifications (see Figure 1). For this study, a six-port Valco valve (0.03 in. orifice) was used as the sample chamber valve. Two additional modifications were made so that mass balance data could be collected for each analysis. The first modification was the incorporation of Luer fittings to replace the gas chromatograph (GC) interface fittings at the sampling valve. The added Luer fittings enabled the flushing of the cryoloop with methanol and the collection of the resulting methanol-distillate solution using two 5 mL Luer-tip syringes. The second modification was the addition of a cryotrap between the distillation apparatus and the vacuum pump. This new cryotrap enabled the transfer and isolation of the condensate present on the condenser column after a vacuum distillation.

GC/MS Apparatus.   A Finnigan Magnum Ion Trap GC/MS, equipped with a 30 m x 0.2 mm i.d., 1-mm film thickness, DB-624 capillary column (J&W Scientific, Folsom, CA), was used for the determination of VOCs in the vacuum distillation fractions. Gas chromatograph operating conditions were 3 min. at 40 °C, 3 °C/min. ramp to 230 °C, and isothermal at 230 °C for 1 min.

Samples.  The samples which were vacuum distilled for this study were primarily distilled water. When it was necessary to investigate variations of water matrices the desired mixtures were prepared directly in the sample chamber. Samples were spiked with a 20 mL methanol solution containing 10 mg of each analyte. The analytes are listed in Table 1. Analytes were obtained from Supelco (Bellfonte, PA). Methanol was the only solvent used to prepare standards and spiking solutions.

Procedure.  The vacuum distillation of samples was performed using recommended conditions.¹ Mass balances were routinely performed for each vacuum distillation by analyte. This was accomplished by analyzing the cryoloop fraction, the condenser column fraction and the sample residues. Determinations were performed using direct aqueous injections of the collected fractions on the ion trap GC/MS. The mass balance was typically greater than 70 percent. A loss bias that could be correlated to water solubility or boiling point was not observed. Mass balances were not attempted when the sample residue contained material such as oil, since such a fraction was not amenable to direct injection analysis.

The cryoloop fraction was collected by flushing the cryoloop with 5 mL methanol, using two 5 mL Luer-tipped gas-tight syringes to push the solvent back and forth through the valve and loop. The methanol flush solution contained an internal standard (d₄-1,2-dichlorobenzene) to quantify and compensate for any losses of flush solution.

The sample residue fraction was collected by removing the material with a 10 mL syringe. A 2 mL aliquot of methanol, spiked with the d₄-1,2-dichlorobenzene internal standard, was used to rinse the sample chamber. The rinsate was combined with the sample residue.

The condenser column fraction was collected by performing a 10 minute vacuum transfer, of the material collected on the condenser column during a vacuum distillation, to a liquid nitrogen collection trap. The condenser column was heated to a temperature greater than 30 °C to assist in transfer of material.

RESULTS AND DISCUSSION

For vacuum distillation, a compound's recovery is related to its boiling point.¹ When an analyte's water solubility exceeds approximately 5 mg/L, boiling point is no longer the only factor governing analyte recovery. The gas/water partition coefficient is the chemical property that most accurately describes analyte losses unrelated to boiling point.

Gas/Liquid Partitioning. The partitioning between gas and liquid is described⁶ as

ln(°C_L/C_L) = V_g/(KV_L)     (1)

where °C_L is the initial concentration of analyte in the liquid phase, C_L is the resultant concentration in the liquid phase after equilibrium, V_g is the volume of headspace, V_L is the volume of liquid and K is the gas/liquid partition coefficient.

Equation 1 is for a closed system at equilibrium. Testing its ability to describe our vacuum distillation system requires an assumption in order to obtain a value for V_g. The assumption is that V_g is the volume that would contain, as a gas (at 760 mm Hg and 25 °C), the amount of water vaporized during a vacuum distillation. The amount of water vaporized was experimentally found to be 0.108 g. Using Boyle's law, the volume of gas, V_g, is calculated to be 1.8 L.

When solving eq 1 using the vacuum distillation data, we find that the partition coefficient values do not agree with published values. However, the values generated through our experiments demonstrate a relationship between analytes that remains consistent for each vacuum distillation. This relative partitioning is described for batch distillation and identified as the relative volatility (a).⁵ We now investigate the reliability of using relative volatility to describe the separation of an analyte from a matrix for trace determinations.

To simplify discussion of relative volatilities, a reference system is necessary to assign a constant relative volatility value to each analyte. Our reference system establishes values reflecting six vacuum distillations performed over a three week period. Using the amount of analyte recovery for the six vacuum distillations, eq 1 is solved to obtain values of V_g/KV_L for each analyte by vacuum distillation. As we are interested in the relative differences between analyte gas/liquid partition coefficients (V_g and V_L being constants for a given vacuum distillation), the resultant V_g/KV_L values are normalized. This normalization is accomplished by dividing each analyte V_g/KV_L value by the sum of all the analyte V_g/KV_L values. We then average the six sets of normalized values to obtain the relative volatility values identified in Table 1.

Having established relative volatility values for each analyte and assuming the relationship between V_g/KV_L and relative volatility is linear, then

V_g/KV_L = aa+b     (2)

The constants a and b describe the slope and intercept of the linear relationship and c is the value for relative volatility. For each vacuum distillation the constants a and b can be determined utilizing two analytes with established a values and measuring their percent residue (C_L/°C_L X 100%). Equation 1 can be expressed as

ln(°C_L/C_L) = V_g/KV_L = aa+b     (3)

Figure 2 demonstrates the comparison of the relative volatility to the percent residue for each of the six vacuum distillations used to generate Table 1. Each curve follows a general natural log pattern as expected. The variation between curves demonstrates that for a given vacuum distillation the relationship between relative volatility and percent residue cannot be described without some measurements.

Figure 3 illustrates that a relationship between the relative volatility and the percent of analyte in the residue exists for aqueous samples when the matrix is modified. Line A represents the average of the percent residue-to-relative volatility relationships presented in Figure 2. The addition of sodium chloride to water (Line C) demonstrates a difference in the sample residue composition that is consistent with the variation observed between vacuum distillations (Figure 2). The addition of methanol to water produced a much greater variation to the relationship (Line B) and suggests that methanol, as an additive, assists the separation of analytes from an aqueous matrix.

Figures 2 and 3 demonstrate that for each vacuum distillation the curves describing the relationship of percent analyte in the residue to the relative volatility are uniform but not identical. The fact that such a relationship consistently exists suggests that compounds (designated as a-surrogates), can be selected to give relative volatility reference values. The measurement of the percent of these -surrogates remaining in the sample residue can be used to solve eq 3 and describe the percent of other analytes remaining in the residue.

Table 2 is a list of compounds where experimental literature values for K are compared to our relative volatility values. Figure 4 furthur illustrates the relationship of partition coefficients to relative volatility values, and can be used to predict an approximate relative volatility value for a compound if its gas partition coefficient is known.

Condenser Factors and Cryoloop Recovery. The previous discussion describes the extent of removal of an analyte from a matrix by measuring the amount of analyte remaining in the sample residue after vacuum distillation. For ease of discussion, this material removed from a sample during vacuum distillation is referred to as sample vapor (°C_L-C_L). The vacuum distillation procedure results in a distillate to be analyzed, which contains the portion of sample vapor not subsequently trapped on the condenser column. Therefore, prior to describing factors that affect recovery of analytes in the cryoloop, the impact of the condenser column must be assessed.

The condenser column only impacts analytes present in the sample vapor. We use the condenser efficiency to describe the percent of analyte removed from the sample vapor. The average percent of analytes trapped on the condenser (six vacuum distillations) is presented in Table 3. Efficiencies for some of the listed compounds (2-pentanone, pyridine, 4-methyl-2-pentanone, and 2-picoline) are affected by factors other than boiling point.

Plotting the condenser efficiencies of 2-pentanone, pyridine, 4-methyl-2-pentanone, and 2-picoline, presented in Table 3, against their respective relative volatilities indicates that the amount of analyte trapped on the condenser is closely related to relative volatility (see Figure 5). The plot suggests there is minimal condensation related to relative volatility for analytes with relative volatility values less than 2. Comparing Figures 2 and 5, it is evident that the trapping efficiency compared to relative volatility and the percent residue compared to relative volatility are similar relationships. Therefore for the analytes only affected by their relative volatility, presence of the analytes in the cryoloop should be closely related to relative volatility.

In fact, such a uniform relationship exists between percent of the analyte recovered in the cryoloop and the analyte's relative volatility (Figure 6). The multiple curves presented in Figure 6 were generated using the same vacuum distillations used to generate the curves in Figure 2. These figures illustrate that there are similar variations between vacuum distillations for analyte content in both the sample residue and cryoloop distillate.

The relationship between relative volatility and analyte recovery in the cryoloop exists even when the aqueous sample is altered (Figure 7). The addition of l g salt, 1 mL methanol, 1 g glycerol, or 2 percent soap (by volume) demonstrates the loss of analyte remains consistent with the relative volatility-to-recovery relationship. The consistent relationship between analyte recovery and relative volatility indicates that -surrogates can be used to characterize the relationship of analyte recovery-to-relative volatility for the vacuum distillation of aqueous samples.

An additional phase can impact the relationship of analyte recovery-to-relative volatility (Figure 8). Line A represents the average of the data presented in Figure 6. Line B illustrates the impact to this relationship when 5 g of soil is added to 5 mL water. The similarity of Lines A and B indicates that soil does not disrupt the percent recovery-to-relative volatility relationship. The differences between the two lines is within the variation observed for replicate vacuum distillations of water samples (Figure 6).

The addition of 1 g cod liver oil to 5 mL water, however, introduces a major matrix effect that significantly lowers analyte recoveries (Figure 8, Line C). While the introduction of the organic phase results in decreased analyte recoveries, a relationship to relative volatility remains. A better understanding of how the oil impacts analyte recovery was complicated by experimental limitations. The low recoveries of analytes in the cryoloop introduced significant measurement errors, and the oil-water sample residue was not amenable to the direct injection analyses required for mass balance. The matrix effects introduced by the addition of oil will be explained further in future studies.

While analyte recoveries from oil suggest that high-organic-content matrices will have poor recovery for many analytes, the poorer recoveries are predictable by measuring the losses of -surrogates. The measurement of severe analyte losses ensures that the analyst is aware of extreme matrix effects and exercises precaution using surrogate-based corrections which would inherently magnify instrument measurement errors. These relationships between analyte recovery and relative volatility for aqueous and mixed-phase samples indicate that -surrogates can characterize relative volatility relationships for the vacuum distillation of samples. However any use of such relationships to correct analyte data for losses should address the potential of magnifying errors when analytes are poorly recovered.

The relationship of analyte condensation to its boiling point is another important component for vacuum distillation. Excluding those analytes in Table 3 where condensation is primarily attributed to relative volatility (2-pentanone, pyridine, 4-methyl-2-pentanone, and 2-picoline), the remaining data are represented in Figure 9 as a uniform relationship of condenser trapping to analyte boiling point. The data points represent average values, and the curve suggests that either selected compounds or the efficiency factors presented in Table 3 could describe the relationship of condensation-to-boiling point for a given vacuum distillation.

Figure 10 shows the relationship between percent condensation of the analytes on the condenser column to their boiling point for a set of vacuum distillations. This figure illustrates that while for a given vacuum distillation this relationship is uniform, it varies between vacuum distillations. The data further illustrate that the variation between curves was not closely related to the condenser column temperature range between -7 °C and -12 °C. Such variations indicate the curve presented in Figure 9 can not be used to predict the relationship for a given vacuum distillation. In fact, the presence of methanol in a sample was found to induce an even greater variation in the condensation of analyte on the condenser column (Figure 11). The variation between vacuum distillations requires that prediction of analyte losses related to boiling point be assessed for each vacuum distillation.

Figures 8-10 indicate that it would be possible to select compounds where the measurement of their condensation would describe the boiling point-to-condensation relationship. We have identified these selected compounds as b-surrogates. The variation of curves presented in Figures 8-10 indicate that the recovery of b-surrogates is critical information required to accurately predict the cryoloop recovery of many analytes.

Predicting Analyte Recovery Using Relative Volatility and Boiling Point Surrogates. The recovery of analytes in the cryoloop during vacuum distillation depends on both a compound's relative volatility and its boiling point. An analyte's recovery in the cryoloop can be described as

Recovery (%) = 100% - %loss (a) - %loss (b).     (4) 

where %loss (a) is the sum of percent losses related to an analyte's relative volatility and %loss (b) is the percent loss related to an analyte's boiling point. The %loss (b) is independent of %loss (a) and only impacts the fraction of analyte that remains after loss (a). Equation 4 can also be described as

%Recovery = 100% [1-f (a)] [1-f (b)]       (5)

where f (a) is the function describing the relationship of analyte lost due to relative volatility and f (b) is the function describing the relationship of analyte lost related to boiling point.

Using eq 3 to solve for f (a), where %loss (a) = C_L/°C_L we obtain

f (a) = 1/e^(a+b)      (6)

For analytes where losses related to boiling point can be considered negligible, eq 4 can be reduced to

%Recovery = 100% [1-1/e^(a+b)]      (7)

The eq 5 constants a and b for a given vacuum distillation can be solved using experimentally determined recoveries for two compounds with known values for a (a-surrogates). The solution can then be used to predict the recovery of any analyte if a relative volatility value is known and if its boiling point suggests a negligible loss (b).

To further simplify our discussion, we assume the function describing any significant analyte loss related to boiling point f (b) is linear. The linear function f (b) can be described as

f (b) = cD°T+d      (8)

where the term D°T is the amount that a boiling point exceeds the temperature where loss (b) is measurable (the data in Figure 9 suggests 170 °C as an estimated limit). Constants c and d are solved using the recoveries for two b-surrogates, after compensating their recoveries for losses predicted by their relative volatility values as described by eq 5.

Substituting for f (a) and f (b) in eq 5 and using eqs 6 and 7, eq 5 becomes

Recovery = 100% [1-1/e^(a+b)][1-cD°T+d]      (9)

Equation 9 incorporates the assumptions that f() and f() are defined using two data points. Experimentally we find that these assumptions are valid for segments of f (a) which are bracketed by a-surrogate values.

Table 4 presents the accuracy of surrogate-based corrections as the ratio of an analyte's predicted recovery divided by the analyte's measured recovery for test samples. The surrogate-pair column was obtained using eq 9 to calculate the predicted analyte recovery. The multi-surrogate column was obtained using all a-surrogates to describe the function, f (a), used to calculate the predicted analyte recovery. Two b-surrogates were used to describe f (b) for both columns of data. The similarity of the ratios contained in both columns demonstrates that the f (a) solutions are equivalent. It is evident when reviewing Figures 9-11 that more than two b-surrogates are necessary to describe f (b) accurately, which would improve the prediction of analyte recoveries in the cryoloop.

The data in Table 4 demonstrate that -surrogates and -surrogates can accurately define the relationships for analyte recovery when a sample is vacuum distilled. Predictions are less accurate when the actual recoveries of analytes fall below ten percent, as the precision of measurement for surrogates and analytes becomes significant (generally when a compound's boiling point is greater than 210 °C or its relative volatility value exceeds 6).

Selection of Surrogates. It appears that gas/liquid partitioning is well-defined using relative volatility values and, therefore, only a few a-surrogates are required to predict such analyte losses for a given vacuum distillation. However, when predicting recovery for an analyte, the relative volatility value of an analyte should be bracketed by values of a-surrogate. 

As stated earlier, a number of b-surrogates are required to accurately predict the recovery of analytes in the cryoloop. This is especially true for analytes that have boiling points between 150 °C and 220 °C, where the relationship between boiling point and condenser trapping efficiency can produce dramatic effects on recovery predictions. Actual selection of surrogates would have to depend on the analyst's required accuracy and the analyte's boiling points.

Figure 8 illustrates the attenuating effects caused by the addition of an oil phase to a water sample. While the recovery of analyte compared to relative volatility is much lower for oil matrices than for the other matrices studied, it is important to emphasize that a-surrogates can still be applied. The use of -surrogates to monitor the partitioning will document such severe matrix effects and will predict other analyte recoveries when the analyst can accept magnified measurement errors inherent with poor recoveries. We did not attempt in this study to reduce losses of analyte due to the severe matrix effects of oil, but we would expect that extending vacuum distillation time and heating the sample would improve recoveries.

CONCLUSION

The surrogate-based correction of analytical data obtained using vacuum distillation is practical and can provide accurate analyte concentrations. The variables which affect recoveries are measured individually by using surrogate compounds specific to each variable, making it unnecessary to group determinations by matrix. This ability to analyze different matrices in the same sample analytical batch is beneficial, as the number of calibrations and the resulting documentation are greatly reduced. Surrogate-based corrections also negate the need to assess matrix effects using separate matrix spike analyses. Incorporating surrogate-based corrections with vacuum distillation of samples results in a very effective and efficient method for environmental analyses.

ACKNOWLEDGMENT

The EPA, through its Office of Research and Development (ORD), funded and performed the research described here. It has been subjected to the Agency's peer review and has been approved as an EPA publication. The U.S. Government has the right to retain a non-exclusive, royalty-free license ina and to any copyright covering this article.

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