Concurrent Solution and Adsorption Phenomena in Gas-Liquid Chromatography-A Comparative Study Hsueh-Liang Liao and Daniel E. Martire Department of Chemistry, Georgetown University, Washington, D.C. 20007
A study is made of three methods for obtaining bulk liquid-gas partition coefficients ( K L ) from GLC retention measurements on solute-liquid phase systems where a multiple sorption mechanism leads to sample size-dependent peak maximum retention times and asymmetric peak shapes. The methods compared all involve retention measurements on several columns differing only in liquid phase weight per cent, followed by extrapolations to give infinite dilution bulk retention volumes. The test solutes studied on four n-octadecane columns at 40.0 O C gave the following average K Z values: n-propanol, 110.3; see-butanol, 55.8; and methylisopropylamine, 106.8. Evidence is found for adsorption of the alcohols on the solid support and at the gas-liquid interface. The relative merits of the three approaches, which yield K L values in excellent agreement with each other, are compared. The implications of this study are discussed. SOLUTE ADSORPTION at the carrier gas-liquid phase interface and/or on the solid support in gas-liquid chromatography (GLC) usually leads to peak asymmetry, to sample size dependent peak maximum retention times, and to retention parameters which depend on the weight per cent of liquid phase in the column packing. This hinders separations, the assignment of meaningful retention parameters, and the determination of bulk solution thermodynamic quantities (1-5). Recently, two methods have been proposed for dealing with chromatographic peaks which are the result of concurrent solution and adsorption partitioning mechanisms (2-6). I n these studies the problem of extracting meaningful bulk solution partition coefficients (or retention volumes) was treated. The approaches will be briefly described in the next section. The purpose of the present study is to compare the two methods, and to suggest an alternative approach which involves the production and analysis of solution dominated elution peaks. BACKGROUND
With many compounds, particularly alcohols, solute adsorption on the solid support is a well-known and troublesome factor in GLC separations and in quantitative GLC studies of solution thermodynamics. More recently, Martin (7,8) and others (3-5,9-13) have shown that solute adsorption (1) D. E. Martire in “Progress in Gas Chromatography,” J. H. Purnell, Ed., Interscience Publishers, New York, N.Y., 1968. pp 93-i20. (2) J. R. Conder. J . Chromaton. 39. 273 (1969). (3) J. R. Conder,’D. C. Locke,&d J.’H. Purnell, J. Phys. Chem.,73, 700 (1969). (4) . , D. F. Cadogan. - . J. R. Conder, D. C. Locke. and J. H. Purnell, ibid., p 708. (5) D. F. Cadoean and J. H. Purnell. ibid.. v 3489. (6j D. E. Martire and P. Riedl, ibid.,’72,3478 (1968). (7) R. L. Martin, ANAL.CHEM., 33, 347 (1961). (8) Zbid., 35, 116 (1963). ( 9 ) R. L. Pecsok, A. de Yllana, and A. Abdul-Karim, ibid., 36,452 (1964). (10) D. E. Martire, R. L. Pecsok, and J. H. Purnell, Nature, 203, 1279(1964). 498
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
at the gas-liquid interface can also contribute to solute retention for certain systems. The effect of this latter phenomenon on the assignment of retention parameters and on the determination of thermodynamic solution quantities has been discussed in a recent review chapter ( I ) . Most recently, a comprehensive treatment of concurrent solution and adsorption phenomena in GLC (3, 4 ) has established that ut infinite dilution the fully corrected net retention volume ( V N ) takes the general form Vx
=
KLVL
+ K I A I + KsAs
(1)
where KL is the liquid-gas bulk partition coefficient, V Lis the total column liquid volume, K I and Ks are, respectively, the partition coefficients relevant to liquid-gas and solid support interfacial adsorption, and AI and A s are the corresponding total surface areas. If Equation 1 is rewritten in the form
and measurements are made on several columns differing only in the liquid phase weight per cent in the total packing, then a plot of V.v/VL against VL-I should give a curve extrapolating to KL at VL-I = 0. Alternatively, in terms of the measured specific retention volume ( V , ” ) ,one could write (12)
where p L is the liquid phase density at T , frefers to the liquid weight fraction (weight of liquid phase/weight of packing), and the prime superscripts refer to the surface areas per gram of packing. Therefore, KL may also be determined from a plot of V,” against 0 - 1 extrapolated to = 1, where the surface terms become negligibly small. Both of these plotting procedures for obtaining KL require knowledge of infinite dilution retention volumes. The finding of symmetrical (Gaussian) peaks guarantees that infinite dilution has been achieved for all of the retention mechanisms that are operating (2). However, the observation of peak asymmetry implies that the samples sizes are too large, so that the condition of effective infinite dilution has not been attained for one or more of the distribution mechanisms contributing to retention. Since retention measurements on peak maxima are unreliable in this latter case, the problem of a rational method of peak analysis presents itself. Adsorption at the gas-liquid interface and on the solid support in GLC most often follows Langmuir type isotherms (2, 3, 14). The consequences of this, for small sample sizes, are: asymmetrical peaks, with sharp leading boundaries and
a-1
(11) D. E. Martire, R. L. Pecsok, and J. H. Purnell, Trans. Faraday Soc., 61,2496(1965). (12) D. E. Martire, ANAL.CHEM.,38, 244 (1966). (13) R. L. Pecsok and B. H. Gump, J . Phys. Chem., 7 1 , 2202 (1967). (14) J. R. Conder in “Progress in Gas Chromatography,” J. H. Purnell, Ed., Interscience Publishers, New York, N.Y., 1968, pp 207-270.
diffuse trailing boundaries, that persist at even the smallest sample sizes that can be conveniently handled and detected ; and retention times that increase with decreasing sample size. The asymmetry results from the fact that, at these sample sizes, the distribution isotherms for the adsorption processes have greater curvature than the bulk partition isotherm (which may even be linear). In other words, while the absorption process may have reached infinite dilution, the adsorption processes have not (1-3). We refer to these low sample size asymmetrical peak shapes as “adsorption dominated.” Solubility in the bulk liquid, on the other hand, usually follows anti-Langmuir isotherms. [The only exceptions occur in solutions with pronounced negative deviations from Raoult’s law--i.e., solute activity coefficients much less than unity-in which cases the isotherms are of the Langmuir type (2)]. The usual characteristics for large sample sizes, even when adsorption is also taking place, are: asymmetrical peaks with diffuse leading edges and sharp trailing edges; and retention times that increase with increasing sample size. We refer to these high sample size asymmetrical peak shapes as “solution dominated.” At these larger sample sizes, coverage of the available adsorption sites has been attained and the contribution of the surface terms to the retention time has levelled off, while solution capacity is still maintained. Hence, at some large sample size, anti-Langmuir solubility isotherms will lead to solution dominated peaks shapes which are skewed in the opposite sense of adsorption dominated peaks. Two approaches have been devised for obtaining infinite dilution bulk retention volumes from asymmetric peaks for a multiple sorption system. One utilizes a diffuse leading edge (solution dominated peak), while the other employs a diffuse trailing edge (adsorption dominated peak). Martire-Riedl Method (6). In their GLC study of hydrogen bonding, the above authors obtained the previously described elution peak behavior for alcohol solutes on the liquid phases n-heptadecane, di-n-octyl ether and di-n-octyl ketone. They observed that, with decreasing sample size: the initial retention time remained constant down to about 0.2 pl and then increased; the peak maximum retention time decreased linearly, reached a minimum, and then increased again as the initial retention time began to increase; and the peak shape went from solution dominated to adsorption dominated. They argued that the region of initial retention time constancy reflected saturation of active adsorption sites on the solid support by the peak front. Further, that the entire peak shifted at smaller sample sizes because of progressively incomplete saturation, and that the retardation of the peak maximum at larger sample sizes was due to solubility isotherm nonlinearity. Consequently, the infinite dilution peak retention time was obtained by plotting the observed peak maximum retention time against sample size and extrapolating to zero sample size. Only those peaks were used that exhibited constant initial retention times-i.e., solution dominated peaks. Specific retention volumes obtained by this approach were independent of liquid phase weight percentage (10% and 15% columns were studied), suggesting that solute adsorption at the gas-liquid interface was either negligible for these systems or was accounted for by the extrapolation procedure, and that bulk V”, values had been obtained. In agreement with other studies ( 4 , 13), large positive deviations from Raoult’s law were observed for the alcohol solutes, thus supporting the concept of anti-Langmuir solubility isotherms.
Conder Method (2). A solute is eluted in turn from each of a set of columns of identical length but of differing liquid weight percentage (hence, differing VL). Small sample sizes (less than 0.1 p1) are used to produce a large asymmetrical adsorption dominated peak on each column under identical recorder attenuation and detector operating conditions. The columns are arbitrarily numberedj = 0, 1 , 2 , 3..., where the zero value is designated for the most heavily loaded column. Conder shows that a set of retention volumes corresponding to elution at a fixed solute gas phase concentration from all columns can be obtained by finding corresponding points on the diffuse (tailing) side of each peak for which hi/VN, (the ratio of the height of a point above the base line to the net retention volume) is the same. This involves choosing an h,, and finding sets of hj which fit (4)
Calculating sets for different values of h, yields values of V,, for each column as a function of gas phase concentration. Then, curves for the sets of VNicalculated for each h, are generated by plotting VN,/VLagainst VL-l (see Equation 2.) Since, at VL-l = 0, all practical sample sizes correspond to infinite dilution, the curves for all h, should extrapolate to the - KL] same value of KL. The difference quantity [(VN,/VL) then measures the contribution of the adsorption terms. This approach has been successfully applied by Purnell et a[. ( 4 , 5 ) . EXPERIMENTAL
Apparatus. The GLC apparatus used in this study has been described before (6, 15). A Perkin-Elmer hotwire thermal conductivity detector (P-E part No. 008-0686) and a Sargent SR-G, 1-mV recorder were employed. All external tubing connections were wrapped with heating tape to prevent solute condensation. Chemicals. The liquid phase used, n-octadecane, was obtained from Humphrey Chemicals. High temperature GLC analysis confirmed the quoted minimum purity of 99.0%. The density of n-octadecane at the temperature of the experiment (40.00 =t 0.05 “C) was p~ = 0.7683 gram/ml. The solutes used: n-propanol, secondary butanol, and methylisopropylamine, were obtained in the purest available grade from commercial sources. Subsequent studies indicated that no major impurities were present and that minor impurities were sufficiently removed from the solute peak so as to offer no complications. Procedure. Four n-octadecane columns, each exactly 4.00 ft long, were prepared in the usual manner from 0.25in. 0.d. copper tubing. The solid support was Johns-Manville Chromosorb W, 60-80 mesh, AW-DMCS treated. The amount packed in each column was determined by the difference in weight of the coated support material before and after packing. The exact liquid phase weight percentage was determined by a combustion or ashing method (6). The salient column characteristics are summarized in Table I. Because of the requirements of the peak analysis methods, the detector block temperature (210 “C), the detector current, and the recorder setting were held constant for all experiments. To study the Martire-Riedl approach at least seven elution curves, corresponding to sample sizes ranging from 3 pl to 0.5 pl, were recorded with each column. Solution dominated peak shapes were observed for the alcohols, while the amine had a near Gaussian peak shape with a constant peak maximum retention time that persisted up to about 6 pl. The (15) Y.B. Tewari, D. E. Martire,and J. P. Sheridan, J . Phys. Chem., 74, 2345 (1970). ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
499
Table I. Column Characteristics Column Properties A B C D Weight per cent of liquid phase 7.17 9.99 14.98 24.48 Weight of packing (8) 6.0198 5.2422 6.0564 7.2312 Weight of liquid phase (g) 0.4318 0.5232 0.9073 1.7703 Volume of liquid phase (ml/gpacking) x 102 9.335 12.99 19.49 31.86 (ml) 0.5620 0.6809 1.1809 2.3041 Liquid surface area" (mz/gpacking) 0.72 0.67 0.66 0.66 a Values interpolated from Figure 2 of Reference (9). (The original data were kindly loaned to us by R. L. Pecsok).
Table 11. Comparison of Liquid-Gas Bulk Partition Coefficients ( K L ) in n-Octadecane at 40.0 "C Modified" Conder New Solute M-R method method method n-Propanol 111.8 108.5 110.7 sec-Butanol 57.7 55.0 54.8 Methylisopropylamine 107.5 105.5 107.5
1
100
; -
I
IO
5
15
(fr'
Modified to include extrapolation of infinite dilution V," values tof = 1 (see Figure 1). a
Figure 1. Infinite dilution specific retention volume (V,") us. reciprocal liquid phase weight fraction 0 - 1 for solutes in n-octadecane at 40.0 "C 0
peak areas needed for the extrapolation to zero sample size were measured with a planimeter. One of the elution curves (at about 2 pl) for each solute on each column was used in the application of our new approach (to be described later). For the sample sizes used (less than 3 pl), the peak maximum concentrations were sufficiently small to satisfy the condition with respect to the time-averaged velocity at the rear of the peak boundary (2). To study the Conder approach, a sample of less than 0.05 p1 was injected into each of the columns. Adsorption dominated peaks were observed for all of the solutes. Several n-alkane solutes were used as internal standards to check for column bleeding and constancy of operating conditions. Finally, retention times were converted into accurate retention volumes in the usual manner
n-Propanol Methylisopropylamine A sec-Butanol
0
160 -
140-
RESULTS AND DISCUSSION
Using the M-R approach, least squares linear regression was performed on the linear plots of peak maximum retention time against peak area to yield extrapolated zero sample size (Le., infinite dilution) retention times. For each column, the corresponding specific retention volumes were calculated and plotted against 0 - 1 in accordance with the following modified form of Equation 3 V,"
KL 273.2
= ___
PLT
+
fT
0.5
1.0
1.5
I
NJ-1
(5)
which is consistent with the M-R assumption of a negligible solid support adsorption contribution for a solution dominated peak. The results are illustrated in Figure 1. The K L values at 0-l = 1 are given in Table 11. Note that the V g ovalues for methylisopropylamine show no dependence on the liquid phase loading, while the alcohols clearly do; this is an indication of the presence of alcohol adsorption at the gas-liquid interface. This V," dependence on column loading is in direct conflict with our earlier findings (6) that a given alcohol-liquid phase system had the same V g ovalue on the 10% and the 15% columns with both n-heptadecane and di-n-octyl ether. A likely explanation for this discrepancy is a small systematic error in our earlier measurements 500
I
0
KZAr'273.2
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
Figure 2. n-Propanol in n-octadecane at 40.0 "C Plots of V N ~V /L against V L - for ~ various values of h, (in chart inches) according to Conder's method. The lower (dashed) curve is based on the infinite dilution V N values obtained by the Martire-Riedl extrapolation.
on either the 10% columns, the 15% columns, or both. This is plausible if one notes that the V," values on the 10% and 15 n-octadecane columns studied here agree with each other to within 5 % for both n-propanol and sec-butanol. Hence, the presence of a surface effect was overlooked, resulting in a probable error of up to 10% in the alcohol infinite dilution bulk specific retention volumes quoted in reference (6). The
.. -
160 -
Figure 3. sec-Butanol in n-octadecane at 40.0 "C (see sublegend of Figure 2)
Figure 4. Methylisopropylamine in n-octadecane at 40.0 "C (see sublegend of Figure 2)
V O ovalues reported there are undoubtedly on the high side. Fortuitously, however, the reported association constants (which depend on the ratios of Yo0for a given solute on two liquid phases) should be virtually unaffected by this error. As Cadogan and Purnell (5) have noted, the liquid surface effect contributions should be comparable on the n-heptadecane and the electron donor solvents (di-n-octyl ether and di-n-octylketone) at comparable liquid loadings. Nevertheless, these earlier measurements are being redone in light of our current findings, which are now in agreement with those of others ( 4 , 13) with respect to the existence of liquid surface effects for alcohol solutes on nonpolar liquid phases. In fact, from the slopes of the plots in Figure 1, we obtain through Equation 5 (using a mean value of AI' = 0.68 mz/g packing) values of KI = 380 X cm for sec-butanol and K I = 280 X cm for n-propanol. These KI values are in the same general range as those found by Pecsok and Gump (13) for alcohol/squalane systems. The Conder approach is illustrated in Figures 2 to 4. The h, values correspond to chart peak heights, in inches, on the diffuse side of the adsorption dominated peak at a fixed detector attenuation setting of 2. The plots of VN/VLagainst VL-I for a given ho are in accordance with the form of Equation 2 and the recommended procedure ( 2 , 5). As predicted by Conder, the curves for a given solute converge to approximately the same point as VL-I approaches zero. We find, however, that the method suffers from the limitation imposed by the nonlinear extrapolation, which can be subject to human prejudice. Values of KL of up to 2 units higher or lower could have been obtained by judicious curve fitting. Nevertheless, the agreement with the M-R approach shown in Table I1 is satisfactory, given the approximations and assumptions involved in the two methods. Furthermore, in Figures 2 to 4 are shown plots based on the infinite dilution V, values obtained by the M-R extrapolation to zero sample size. As expected the amine gives a straight line of zero slope, whereas the alcohols give curves falling well below the Conder curves since they have already been corrected for solute adsorption on the solid support. As a further check on the M--R assumption that at large sample sizes the peak front saturates the
Tables 111. Comparison of Retative Merits of the Three Approaches for Obtaining Infinite Dilution Bulk Partition Coefficients Method Modified M-R Conder New One One Number of peaks Several required on each column AI 1 All Required conSingle columns columns stancy of deteccolumn tor and recorder operating conditions Linear Nonlinear Linear Extrapolation to obtain K L Shortest InterExperimental and Longest mediate computational time None Gas-liquid Complicating sur- Gas-liquid interface interface face effects in and solid peak analysis support None Primary source of Peak maximum Extrapolaobvious tion proretention error cedure time and peak area measurements available solid support adsorption sites, experiments were conducted on a 4-ft blank column (Le., one packed with uncoated solid support). The results showed that at sample sizes above 1 pl, the initial retention times were virtually zero for the three solutes studied. During the course of this comparative study, a simple alternative approach based on Conder's general method, but utilizing solution dominated peaks instead, was developed. A large solution dominated peak (corresponding to a sample size of about 2 ~ lis)produced on each of the four columns. Using computer iteration, a set of hj values on the diffuse side of the peak are found which both satisfy Equation 4 and give the best fit to the bulk solution expression
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
501
In effect, this iteration method apparently seeks out those peak heights where the adsorption terms are negligible and the solubility isotherms are linear, thus yielding infinite dilution bulk solution retention volumes. The resulting KL values are listed in Table 11. They each represent unique solutions to the sets of equations solved. Interestingly, the hj values found for the amine were the values at the peak maxima, as would be expected. In view of the simplicity of this method, the observed agreement with the other approaches is encouraging. CONCLUSIONS
The relative advantages and disadvantages of the three approaches are summarized in Table 111. The new approach measures up very well against the other two. However, all three are capable of giving consistent KL results for solutes which exhibit multiple sorption mechanisms. The implications of this study and, largely, the earlier studies of Conder
and Purnell (2-5, 14, 16, 17) are evident. In particular, bulk solution thermodynamic quantities for testing theories of nonelectrolytic mixtures (15) or for determining hydrogenbond association constants (5, 6 ) can now be obtained with greater confidence for systems which were previously considered to be too troublesome and error prone. Also, meaningful bulk solution retention parameters can be confidently assigned for such compounds as alcohols. Finally, analytical and preparative scaie GLC separations of mixtures where one or more of the compounds is a multiple sorber can be approached with a better understanding of the effect of sample size and column loading on peak shape and retention.
RECEIVED for review September 13,1971. Accepted November 30, 1971. This work was supported by a grant from the National Science Foundation. (16) J. R. Conder and J. H. Purnell, Trans. Faraday Soc., 64, 3100 (1968). (17) Zbid.,65,824(1969).
Short Cut Fused Peak Resolution Method for Chromatograms S. M. Roberts IBM, Data Processing Division, Palo Alto, Calv. 94304 This paper describes a simple, fast, and effective computation method for resolving fused peaks of chromatograms. If the underlying curves are Gaussian, the method has a sound theoretical basis and can produce in practice fits comparable to least squares approximations. If the underlying curves are not Gaussian, the user can still apply the method to the mathematical model he deems appropriate. Numerical results are given and compared with the results of the least squares method.
where fi(tc) = the Gaussian function for the jth peak at time
Aj to,j
wj
INAN EARLIER PAPER the author and his coworkers described the practical application of the least squares method to chromatograms ( I ) . As part of an effort to accelerate the curve fitting process, this paper describes a “short cut” computation method of resolving fused peaks of chromatograms. If the underlying curves are Gaussian, the method has a sound theoretical basis and can produce in practice fits comparable to least squares approximations (2-4). The principal advantages of the method are its speed of computation, its requirements for only two data points per peak, its simplicity, its ease of programming, and its satisfactory fits. Its prime disadvantage is the validity of the assumption of the Gaussian curves as the mathematical model. The technique is sufficiently general, however, that other models may be employed at the user’s option. THEORY
We assume that the trace of each peak of the chromatogram is described by a Gaussian curve (1) S. M. Roberts, D. H. Wilkinson, and L. R. Walker, ANAL. CHEM.,42, 886-893 (1970). (2) N. R. Draper and H. Smith, “Applied Regression Analysis,” Wiley, New York, N.Y., 1966, Chapter 10. (3) F. B. Hildebrand, “Introduction to Numerical Analysis,” McGraw-Hill, New York, N.Y., 1956, Chapter 10. (4) E. L. Stiefel, “An Introduction to Numerical Mathematics,” Academic Press, New Yoxk, N.Y., 1963,Chapter 4. 502
0
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
ti
maximum amplitude of the jth Gaussian peak = time at which the amplitude of the jth peak occurs = “width” of the jth peak = one standard deviation =
We assume that the measured data can be represented as a sum of Gaussian curves S
Y(ti) =
A j exp j=l
(ti
2
to,j)’
wj2
1
, i = 1 , 2 , . . , 2 s (2)
where Y(ti) = measured data point (corrected for base-line drift) at the time ti = total number of Gaussian curves s
If we assume that the t o , jpoints are fixed and known as observed in the trace, then each peak is characterized by two parameters A , and wj. This means that with two measurements (corrected for base-line drift) per peak that A , and wj can be determined. Once the parameters are known, it is a simple matter to integrate the Gaussian curves and obtain the relative areas under each peak. Some investigators feel that t o , jshould not be considered fixed but should be considered as variables. In this case t o , j is handled in the same manner as the parameters A , and wj. The solution method consists first of linearizing the transcendental Equations 2, and then solving iteratively for the parameters A, and wj, j = 1,2,, , ,s. Each Gaussian function in Equation 2 is approximated by a Taylor series up to and including first order terms.
