an expanding role for gas chromatography:
The MEASUREMENT of PHYSICAL and CHEMICAL PARAMETERS J. CALVIN GlDDlNGS and KANA1 L. MALLIK
.
to extremes of pressure and temperature. One can study the dilute Henry's law region or investigate full isotherms. Second, various mass transport properties can be measured. The possibilities (not all presently reduced to practice) include gas, liquid, and surface diffusion coefficients, adsorption-desorption kinetics and interfacial transfer rates. Finally there is a miscellaneous group dealing mainly with the properties of complex materials. Here one measures surface areas and permeabilities, detects phase transitions, and characterizes complex chemical mixtures. We exclude here the conventional role of GC-separation for preparative or analytical purposes. This exclusion holds even when the analysis is used to characterize reaction mechanisms and constants.
THEORY AND SCOPE The theory of chromatography describes the dynamic processes involved in the migration of solute peaks through sorbent media (75). This theory tells us that for h e a r sorption, changes in the first moment of the concentration profile-Le., the rate of migration of the peak's center of gravity with respect to the fixed mediaare normally determined by the equilibrium properties of solutes in the sorbent-fluid system. Furthermore, theory shows that changes in the second moment with respect to the peak's center of gravity-i.e., a measure of the rate of spreading the peak-are determined by the rate of various diffusion and kinetic processes. VOL. 5 9
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I n principle, the main function of the basic theorydescribing the evolution of chromatographic peaks in terms of physical and chemical parameters-can be inverted to yield values of these parameters from the measured first and second moments of the concentration profiles. This is true for both gas and liquid chromatographic systems. Success of this approach depends on the integrity of theory and instrumentation; its ultimate value depends upon accuracy and convenience when compared to other methods for abstracting the same parameters. Although linear or nearly linear GC-described above-is central to both analytical and nonanalytical applications, nonlinear GC has been used on occasion. Much effort, beginning with the first theoretical work in chromatography (57), has gone into the theory of solute migration in the presence of nonlinear isotherms. Nonlinearity so complicates the theory that one must generally invoke the assumption of local equilibrium between gas and sorbent-thus precluding the characterization of rate and diffusion parameters from GC data and ignoring their effect on equilibrium curves. Nonetheless, with the help of equilibrium theory, the experimental profiles can be deconvoluted to yield approximate sorption isotherms (8). A more satisfactory approach to nonlinear isotherms will be discussed shortly in connection with equilibrium parameters. I n order better to visualize the GC approach a n d understand its relative merits, an idealized experiment is described. One starts with a long (1 to 10 meters), narrow tube containing a specified sorbent in granular form. A gas stream forced through the tube passes over, through, and between the granules. A narrow spike (or front) of solute is then injected into the gas streams at the tube entrance. The solute, if nonsorbing, is carried downstream with the velocity of the carrier gas (-10 cm./sec.). If the solute partially sorbs, its overall velocity is reduced to a value proportional to that fraction remaining in the gas phase at equilibrium. As the solute peak advances, it also widens at a rate governed by diffusion and other processes (75). Eventually the solute will appear as a concentration pulse at the column outlet. A detector and recorder system attached to the outlet will reveal the elution peak in the form shown in Figure 1. As suggested earlier, the peak’s position-particularly its holdup relative to the “air” peak-reveals the equilibrium distribution of solute between sorbent and gas phase. Its width is indicative of the rate of such items as diffusion and sorption-desorption, for example. Whether one measures equilibrium or transport properties, certain common advantages stem from the above approach. First, only trace amounts of solute are consumed. With today’s sensitive detectors (such as flame and argon ionization and electron capture), amounts as low as mole can often be revealed. Second, the experiment is completed with relative speed, usually in minutes with the theoretical possibility of completion in seconds. The high speed is fundamentally made possible by the highly dispersed state of the sorbent 20
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
and its intimate contact with the flowing gas. Thirdand strangely enough, a comparatively unexploited advantage-the GC system can separate and purify as it measures the requisite properties. With this and the above-mentioned advantages, we can visualize for the future the rapid and convenient measurement of the properties of complex and rare substances-e.g., biological-which may normally exist only at trace levels in mixtures. Of similar interest are the simultaneous separation and measurement of properties of certain molecules in various isotopic and isomeric-e.g., diastereoisomeric-forms. These species, ordinarily difficult to fractionate, can be studied conveniently with respect to isotopic and other incremental effects because the increments can be observed directly and errors are self-canceling. IVhile only trace levels of volatile solutes arc needed, more severe demands are made of the sorbents. The latter are needed in roughly gram quantities. They should be relatively nonvolatile at the temperature of interest to avoid being carried off in the gas stream. This condition has been particularly restrictive for liquid adsorbents or solvents (gas-liquid chromatography) ; to date these liquids have been restricted mainly to high molecular weights. It is possible to extend the volatility range considerably by presaturating the gas stream with vapor before it enters the column. However, one should avoid a substantial pressure drop in the column since the expanding gas increases its capacity for vapor as it moves through the column. By supporting the liquid on large glass beads and using slow flow rates to avoid expansion, we have found it possible to work successfully with a water liquid phase at 2” C. (27). The GC method should be particularly adaptable to extremes of temperature and pressure. One can effectively isolate the column from other parts of the system and subject it to these extremes. Some aspects of this possibility will be discussed later. As noted above, the GC experiment generally proceeds with relative ease and speed. Perhaps the most timeconsuming task is the data interpretation-particularly for transport properties where the width of the profile must be measured with great accuracy. This problem
Time or Gas Throughput Volume
Elution Time or Volume
Figure 1. Detector response (or concentration) as a f u n c t i o n of time or elution volume measured from the point of injection
can now be solved with various automatic data collection, storage, and interpretation devices. The measurement of the location (equilibrium property) and of the area of many simultaneous peaks is now a well deveIoped art and could, if desired, be applied to equilibrium measurements. The automatic measurement of peak width (transport properties) has recently been accomplished in this laboratory using a digital readout system in conjunction with a digital computer (48). Equilibrium Parameters
I n the linear case one can obtain the distribution coefficient K for either gas-liquid (partition) or gas;solid (adsorption) equilibrium from the rate of migration of discrete solute peaks in gas-liquid and gas-solid chromatography, respectively. I n practice, as noted above, migration rates reveal themelves in terms of the time or gas throughput volume needed to carry the peak’s center through the entire column (Figure 1). I n precise terms, the distribution coefficient for gas-liquid equilibrium is (5):
K
=
(V,o - V,)Vl
where V: is the corrected retention volume (gas volume needed for elution and corrected for compressibility), V, the column void volume (as occupied by gas and usually measured by the “air” peak), and V I is the volume of stationary liquid in the column. For the less popular gas-solid equilibrium, VI must be replaced by surface area, adsorbent mass, or some other appropriate measure of the extent of the adsorbent phase. Note that K , which is the liquid/gas concentration ratio, is logically measured as a ratio of volumes; gas to liquid. Once the fundamental equilibrium constant K becomes obtainable, a host of derivative parameters can be acquired. These include activity coefficients; free energy, enthalpy, and entropy of mixing and of vaporization; and vapor pressures and boiling points. They can include thermodynamic properties of the solutegas mixture-for instance, the second virial coefficient. Furthermore, they in some cases encompass “foreign” equilibrium constants-e.g., those for some kinds of chemical reactions and for adsorption at gas-liquid interfaces. Specific advances in measuring these parameters will be mentioned later. Isotherm linearity can, when desired, be approached by using exceedingly low concentrations-a condition made experimentally feasible by high sensitivity detectors. Characterization of sorption isotherms beyond the linear range is generally more difficult, as mentioned earlier. A peak rich in solute will have a wide range of concentrations, reaching a maximum at the peak apex and more or less rapidly approaching zero in either direction. No simple relationships, as in Equation 1, govern elution volume. While in principle, the isotherm for the peak’s concentration range can be obtained from the measured concentration profile, in practice, much sensitivity to detail is lost because deconvolution is based on equilibrium theory in which dynamic contributions to peak dispersion are ignored.
HelfFerich and Peterson have largely solved this problem by a tracer pulse technique (25). Here solute at a fixed concentration level enters the flow stream. A small isotope pulse of the same concentration is then injected. The rate of migration of this peak is governed essentially by equilibrium at the fixed background level. Equation 1 can be applied, with K being the distribution coefficient at that particular concentration. The small isotope effect is ignored. The experiment can be repeated at other background levels to map out the isotherm to any desired detail. (Multicomponent equilibria and equilibria without a carrier gas can be measured with equal directness.) If a detectable isotope is not available, these authors suggest using the concentration pulse method. Here a small superimposed pulse of solute, which travels at a rate governed by the isotherm slope, is injected. The full isotherm is then generated by slope construction. The tracer pulse method is relatively new, and adequate experience has not yet been gained to prove its general utility. However the method appears unusually promising for the elucidation of isotherms for a broad concentration range. Unfortunately the overall appraisal of the G C method and the accuracy and limitations of GC-acquired equilibrium data have not yet been thoroughly evaluated. Everett and Stoddart ( 9 ) and Martire (40) have both presented critical discussions ; the former authors indicate that accuracy can be accomplished to better than 1yo. The comparison of partition coefficients with classically obtained values, reported in a later section, shows agreement ranging from 1 to 5%. I t is not entirely clear where the blame for discrepancies should lie. While it is difficult to generalize regarding the magnitude of uncertainty connected with G C data, some limitations are clear. For instance, the data are no more precise than is the location of the center of eluted peaks (Figure 1). This uncertainty can be estimated as considerably less than 1% if the peak is modestly sharp (>lo0 theoretical plates) and the experimental elution curve relatively noiseless. Similarly one must be cognizant of errors due to the assumption of ideal gases in correcting for pressure drop (9,39,47) and of noncompensating errors stemming from detector and recorder time lag and from extra-column dead volume (44). With care such difficulties should not lead to errors larger than j=l%. These will tend to diminish with increasing column length and decreasing flow velocity; they are perhaps reducible to the 0.1% level. A more fundamental question related to accuracy is the validity of the assumption that equilibrium governs peak migration. This assumption seems rather paradoxical when it is considered that we intend to acquire both equilibrium and nonequilibrium parameterse.g., sorption-desorption rates-from the same elution
*
J . Calvin Giddings is Professor of Chemistry, University of Utah, and Kanai L. Mallik was a postdoctoral associate at the University of Utah and is now located at the Tufts University School of Medicine. AUTHORS
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peak. Theory resolves this apparent paradox by showing that equilibrium is closely approached only at the peak center (75). Even the attainment of this equilibrium hinges on the condition that the relaxation time, t,, for equilibration with the sorbent, must be small compared to elution time, t,. I n fact, the fractional error associated with the equilibrium assumption is roughly t,/t, (75). This ratio is approximately one divided by the number of theoretical plates, or the order of 1 p.p.t. for typical columns. The reason for the low t, values (1 to l o p 3 sec.) in gas-liquid chromatography resides in the greatly dispersed form of the liquid phase. The high surface-to-volume ratio of the liquid units permits rapid diffusional equilibration. I t also has other implications, discussed next. Perhaps the greatest of all uncertainties connected with equilibrium data stems from the very same element that makes the GC method fast-the high surface-tovolume ratio (this factor can also be present in classical methods). There is clearly some perturbation of bulk properties at each interface. Chromatographers meticulously avoided direct adsorption at the solid-liquid interface for years only to find later that an unsuspected element of “Gibbs” adsorption, at the gas-liquid interface, was sometimes present (38). These difficulties are closely related to the relative polarity of solute and solvent. If direct adsorption is minimized and fairly large amounts of liquids are applied to relatively inert solid supports, errors can in all likelihood be kept down to 1% for most systems. I t is hoped that further work will be done to settle the crucial question of data accuracy using the GC method. If the results are in fact valid to about =+=1%, the method should generally prove invaluable for the study of dilute solutions. M’hile our main function in this article is to evaluate experimental GC in a n unorthodox (nonanalytical) role, we would be remiss not to mention the extensive correlations betwccn molecular structure and solution thermodynamics made by chromatographers in an effort to predict migration rates from structure, and vice versa. This work no doubt constitutes the largest body of results anywhere on solution interactions.
*
Transport Properties
As indicated earlier, theory dictates that the second statistical moment of a GC peak be governed by various mass transport phenomena. The peak, injected as a narrow spike, generally approaches a gaussian or ‘(normal density” profile as it widens. The most obvious explanation for this (there are others) has a statistical basis (75) : Molecular displacements from the mean migration distance stem from independent random molecular excursions (caused by various diffusion, flow, and rate processes, below). It has long been known that with a large number of such random displacements a &function (infinitely narrow spike) will approach a gaussian, and a sharp boundary (if one should be employing frontal chromatography) will approach a n Sshaped error function. 22
INDUSTRIAL A N D ENGINEERING CHEMISTRY
For experimental purposes one must obtain some measure of the peak width at elution. The width naturally appears in time units (or units proportional to time-e.g., distance along a chart) since elution profiles are concentration-time records. Either standard deviation or width at half-height, w1/2 = 2.36 7, will do (Figure 2 ) . Subsequently, ‘T is converted to theoretical plate height, H , or less frequently, to a n effective diffusion coefficient for peak dispersion. Experimental plate heights are obtained as
H = LT2/t;
(2) where L is column length and t , is elution time. T h e plate height, H , rather than the second moment about the mean, ?, is generally the junction where theory and experiment meet. It is important to note that the use of plate height as a measure of peak dispersion depends in no way on the now obsolete theoretical plate model for describing column processes. The parameter, H, now well established in the jargon of GC, is a valid measure of peak dispersion and little else (75). The necessary bridge between experimental values of plate height and basic mass transport processes is formed by chromatographic theory-. One complication in extracting parameters stems from the fact that several processes are simultaneously spreading the peak and must be accounted for theoretically. These are essentially of three kinds ( 7 5 ) : (1) Most obvious is the straightforward diffusion up and down the tube. This makes its greatest contribution at low flow velocities where there is relatively more time for diffusion before the peak is eluted. (2) There is dispersion caused by flow nonuniformity, the latter being present in viscous flow in general (recall the parabolic profile of Poiseuille flow) and accentuated by the complexities of the granular media. This phenomenon is especially complex because velocity fluctuations among molecules carried in the various streamlines can be attenuated either by lateral diffusion, or, in porous media, by a flow process. (3) Finally there is dispersion due to sorption-desorption phenomena. The finite rate of sorption and desorption leads to fluctuations in residence times in fixed and moving phases and then to fluctuations from the mean migration velocity. T h e effect is greatest at high velocities since individual random displacements are proportional to velocity.
Figure 2. Gaussian elution proJle f r o m GC. T h e standard deviation 7 (or alternatively the w i d t h at half height wi12) is a function of the rates of various mass transport processes
The detailed theories associated with phenomena-mainly the nonequilibrium coupling (77) theories-are rather involved. they show (75) that the plate height, H , has corresponding to the above phenomena :
B H=-+ v
+ l/Cgu + CsV
the above ( 76) and I n general, three terms
1
1/A
(3)
(11 (2) (3) where u is mean flow velocity. The terms B, A, C,, and C, are parameters whose exact dependence or transport constants, in some cases, are theoretically predictable and in others are obscured by complex geometrical factors. T o make sense of peak spreading, all these parameters must be accounted for somehow. This can be done variously by exact theory, by rendering individual terms negligible, by holding them constant while others vary, or by evaluating them with a reference solute. Pressure, temperature, flow velocity, and the nature of the carrier gas and column packing all constitute tools with which to enforce the necessary variations in parameters, as shown now. The simplest imaginable G C column (of the generalized type mentioned earlier) is a tube of round cross section which has been emptied of all packing and sorbent. The plate height simplifies to the following exact equation, whose crucial second term (the C, of Equation 2 ) was first obtained by Sir Geoffrey Taylor (50): 2 0 HE-> +U
d,2v
96 D,
(4)
This expression can be inverted to yield the binary gas phase diffusion coefficient, D,,for solute in carrier, as a function of measured plate height and the parameters v (velocity) and d, (tube diameter). Such a n approachfirst developed in this laboratory-has proved rapid and accurate (27). An equally valid alternative used by Knox and McLaren involves the measurement of diffusion occurring in a period of flow interruption (32). These methods provide the only working, currently productive examples of GC-acquired transport parameters. The extensions below, still mainly in the speculative or explorative stage, indicate the full scope of the method. Some promising possibilities exist for columns more complicated than the above-i.e., those which sorb and/ or contain packing. T o start with, the first term on the right-hand side of Equation 3 can always be obtained by extrapolation to zero velocity, v . This term-recall that it stems from diffusion up and down the columnis generally related to the gaseous diffusion coefficient D, by B = 2 yD,. The constant y accounts for obstruction to diffusion caused by the packing in the column. I t can be evaluated for a given column using a solute carrier gas pair of known diffusivity (22, 32). Once evaluated, D,values for other pairs could be determined. The necessity to extrapolate to zero velocity rightly implies that such a n approach would be more timeconsuming than above. The offsetting advantages are
twofold. First, since we are now allowed a n actively sorbing system, separation and purification can accompany the measurement. Second, G C has recently proved its applicability to low volatility solutes, with molecules of a size and complexity much greater than those previously studied with regard to gaseous diffusion. The latter may prove of basic interest in understanding the effect of polar groups, long chains, and branching on effective collision cross sections. While extrapolation to zero velocity provides one way of isolating transport terms, another makes use of the fact that the sorption-desorption contribution to plate height is insensitive to changes in the pressure or composition of the carrier gas. This has made it possible to split off the C,u term of Equation 3, and thus in theory to study any process with a time constant down to about 10 - 3 second related to desorption from solids, transfer across interfaces and diffusion through liquids (79). Liquid diffusivity is one parameter forthcoming from such a n analysis. If the liquid units in gas-liquid chromatography have a well defined geometry, it is possible to obtain a n exact theoretical expression for C, (75, 76u) and thus form a link between observed peak dispersion and the underlying rate parameter-liquid diffusivity, D1. The most successful system for this consists of spherical glass beads with solvent added in small amounts (about 1% by weight). The solvent immediately seeks the narrow crevices near the bead contact points by virtue of capillary forces, and forms doughnut-shaped units for which (73) : C, = R(l - R)r2/12D1
(5)
where R is the retention ratio (solute-to-gas velocity) and r is the “doughnut” radius. While this expression has not yet been used in measuring unknown diffusion coefficients, work in our laboratory with known systems indicates that agreement can be made better than 10% (18). While the method is still relatively inaccurate, the speed and the simplicity of the apparatus (compared, for instance, with the Gouy diffusiometer) may prove of value for rough preliminary measurements. If liquid does not exist in a tractable form, one would again find it necessary to calibrate the column with a known solute-solvent pair. Theory shows that the form of C, shown in Equation 5 is quite generally correct, with only a numerical coefficient for the calibration. This untried approach might prove more accurate, and would certainly give more freedom in the choice of systems (including capillary columns) than the purely theoretical approach of Equation 5. Besides the proposed measurement of liquid diffusion, several other applications have been suggested. One involves rapid desorption rates from porous solids and surfaces (74). A second would yield the interfacial transfer rate of solute through a gas-solvent interface in the presence of surface active agents. The latter application has been tried; it appears to compete well with other techniques and to extend the scope to new kinds of systems (27). VOL. 5 9
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Another interesting application of GC is that suggested and implemented in preliminary experiments by Bassett and Habgood (2). These authors measured the rate constants for the catalytic isomerization of propane using catalyst instead of conventional packing in their column. By this means reaction takes place on the column, leading to a zone distortion which depends on rate constants and the level of adsorption of the reaction components in a theoretically calculable way. I t is difficult to generalize regarding the accuracy of experimental transport parameters obtained by G C methods. Involved are the problems of obtaining peaks free from outside disturbances and end effects; of measuring their width precisely; and of the degree of interference by competing peak-broadening processes. I n the simplest and best developed case-the measurement of binary gas phase diffusion coefficients in unpacked columns-we have developed apparatus and techniques which appear to yield correct values to within a very satisfactory 2%. The scope, advantages, and limitations of the GC method in transport measurements involve some of those same factors mentioned earlier in a general contextspeed, sensitivity, simultaneous separation and purification, data interpretation, solvent volatility and amount, and rapid equilibration, One potential study deserving special note pertains to high pressures. By using small bore tubing, only small total volumes-e.g., 1 cc.-need be subjected to pressure. The apparatus is relatively simple, for example, Dr. Marcus Myers and others have constructed two working units in our laboratory for high pressure GC studies which serve to pressures of 2000 atmospheres. When one considers the scarcity of transport coefficients at high pressures and the clues they provide for the theoretical understanding of molecular transport processes, this area of endeavor merits fuller development.
Miscellaneous Parameters
Some additional parameters can be determined from the apparatus typically used in GC. One can, for instance, conveniently obtain surface areas in terms of the size of nitrogen peaks desorbed under controlled conditions from columns filled with adsorbents (42). The BET equation is used in conjunction with these data. Permeability, viscosity, and related parameters connected with flow through porous media can also be acquired. A rather unique application of GC has been proposed by Davis, Petersen, Haines, and others (6). Here one characterizes complex and relatively nonvolatile materials-kg., asphalts-by noting the relative retention times of various solutes. I n essence the material is distinguished and identified by solute spectra, with the advantage that one can choose as many or as few spectral lines of selected types as are consistent with the information desired. One should be able to discern acid-base properties, unsaturation, and other gross chemical characteristics. 24
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Another application of GC-which could equally well be classified with equilibrium properties-is the determination of phase transition temperatures in solvents. Any transition involving molecular rearrangement will cause a discontinuous change in partition coefficient or retention time. Freezing points (45) and transitions between smectic and nematic phases in liquid crystah (28) are discernible in this way. Clearly in some casese.g., most freezing points-there are simpler ways tc detect changes in phase. I n some cases, however, when the transition is not readily apparent or when high pressures and/or temperatures are desired, the GC method may prove to have distinct advantages.
M A I N S T R E A M S OF PROGRESS We confine this section to those nonanalytical applications actively competitive with conventional measurement techniques. These applications have received considerable experimental attention and the methods are generally well defined. Unfortunately the most explored areas are not always the most interesting. We have, nonetheless, resisted the temptation to detail the exciting-but presently more scanty-progress on such topics as rate processes (2, 27), high pressure equilibrium studies (49), stability constants (23),adsorption at gas-liquid interfaces (38), second virial coefficients ( 7 ) , transition temperatures (45’), and complex material characterization (6). An overall appraisal of these topics, along with a few details, was given in the last section. Further information is available in the cited literature. Unfortunately there has been no recent exhaustive review of nonanalytical GC, although there is a partial review in (5). Even the limited subject areas chosen here will not be discussed fully; otherwise the first one by itself would merit a separate article. We confine this section to illustrations of the most significant areas explored, the general methodology, and the comparison of GC and classical results. Literature references are confined to a few principal citations. Gas-liquid Equilibrium
The co-inventor of gas-liquid chromatography, Nobel Laureate A. J. P. Martin (37), early recognized the potential of his exciting new analytical technique for the study of equilibrium. As early as 1955, he suggested that GC “provides perhaps the easiest of all means of studying the thermodynamics of the interactions of a volatile solute with a non-volatile solvent and its potential value for providing this type of data should be very great.” His forecast has since been extensively implemented. The investigation of gas-liquid equilibrium is at present foremost among the characterization studies covered in this paper. One begins with a column of the type used in gasliquid chromatography-Le., a narrow tube in which a specific liquid in a highly dispersed form is supported on the inert solid framework of a porous, granular material. As noted, solute peaks traversing the column
are held back or “retained” to a degree dependent upon their equiribrium affinity for the stationary liquid. Equilibrium properties are obtained through the measurement of retention parameters. In practice, experimental work has mainly dealt with extremely dilute sclutes in the linear or Henry’s law region. The work reported below is all confined to this range, Values of the fundamental equilibrium constant, the“ liquid-gas partition ratio K, stem directly from the application of Equation 1 to measured retention volumes. In the last few years many workers have obtained new results in this area. Porter, Deal, and Stross (44) (the first authors to explore gas-liquid equilibrium by GC) and Anderson and Napier (7) compared their GC data with those obtained from classical methods. The values were found to be in good agreement as shown in Table I. The first-named group showed that a six-fold change in column length or a tenfold change in carrier gas velocity had no appreciable effect on partition coefficient. This observation and the general agreement of Table I lend confidence to the validity of the GC approach. TABLE I. COMPARISON O F P A R T I T I O N COEFFICIENTS OBTAINED FROM G C AND CLASSICAL METHODS K from Temp,, K from Classical Solute-Solvent System a C. GC Data Methods
n-Heptane-diisodecyl phthalate 105 (DIP). 2-Propanol-DIP. 105 Benzene-polyethylene glycol cresyl ether (PGCE)h 80 80 Cyclohexane-PGCE* a
“
57.6
57.2 f. 1
26.1
25.8
71.6 18.9
73.0
=k
1
(47). While such data should be accurate to within about A¶%, as noted earlier, we doubt that this level is yet reached commonly. Unfortunately there is very little to judge it by. Some of the few experimental checks available are shown in Table 11. While discrepancies exist in some cases, this does not necessarily condemn the GC data since the classically obtained values are perhaps no more reliable. In most cases the agreement is fair and in some it is excellent.
TABLE II.
A C T I V I T Y COEFFICIENT A T I N F I N I T E D I LUTlON
Tern#.,
Solute-Solvent System
OK.
GC Value
Benzene-DNParb Benzene-DNPC Cyclohexene-DNPb Cyclohexene-DNPC Cyclohexane-DNPh Benzene-biphenyld Methanol-HDepf Methanol-HDf Acetone-HDf Acetone-HDf Methylethyl ketone-HDf Methylethyl ketone-HDf n-Pentane-DNPC n-Octane-DNPC
326 303 326 303 326 363 298 313 298 313 298 313 303 303
0.52 0.56 0.64 0.93 0.82 1.11 71 45 6.3 5.1 3.8 3.1 0.108 0.142
Classical Value 0.52
0.56 0.68 0.93 0.84 1.10 75 43 6.1 5.2 3.6 3.2 0.108 0.143
D N P = dinonyl phthalate. From Kenworthy, Miller, and Martire ( 2 9 ) . From Everett and Stoddart ( 9 ) . d From Clark and Schmidt ( 4 ) . * H D = hexadecane. f From Kwantes and Rijnders (33). a
19.9
Datafrom Porter, Deal, and Stross (44). Data from Anderson and Napier ( I ) .
Solute activity coefficients at infinite dilution, ym, express the same equilibrium phenomenon as above, but in a d,ifferent context (that is, by reference to pure solute and equilibrium with its vapor). Classical methods for determining y m are time consuming and require a good deal of experimental precision (30). This contrasts with the speed and simplicity inherent to the GC method. The activity coefficient y m can be obtained directly from the liquid-gas partition coefficient by the following relatibnship (5)
where V I denotes the molar volume of the solvent, bo is the vapor pressure of pure solute, T is the temperature of the column, and @ is the gas constant. The K value used must, of course, pertain to infinite dilution. The ideal gas law must hold else fugacity will replace bo. In practice y m is more conveniently obtained from an experimental parameter called the specific retention volume than it is from the partition ratio. A rough literature survey shows that over ’ 800 y m values have already been obtained in this way from GC data
The same methodology which provides the direct equilibrium parameters, K and y m ,has also been used to obtain numerous derivative quantities such as free energies, enthalpies (7, 4, 26, 36), and entropies of mixing and vaporization from solution, vapor pressures (3, 26), and boiling points. Enthalpies of vaporization are measured with particular frequency since one needs only the temperature dependence of elution volumes or times, and need not know the liquid-gas volume ratio. This simplicity no doubt accounts for the fact that these were the first accurate thermodynamic quantities obtained from the GC technique (36). Gas-Solid (Adsorptive) Equilibrium
While far less effort has been devoted to adsorption than to partition systems, enough has been done to show that GC is a convenient tool for adsorption studies. Of foremost interest has been the determination of adsorption isotherms. The classical method of deconvoluting peak or boundary shapes-which we saw earlier to suffer from an incomplete allowance for kinetic effectshas been used most often, and with apparent success. Gregg and Stock have directly compared isotherms obtained by GC and gravimetric methods; the agreement is very satisfactory (24). This result is encouraging, but there is little assurance that kinetic effects would be negligible in all systems. There are as yet no VOL. 5 9
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clear criteria to establish this validity. Meanwhile the intrinsically more satisfactory tracer pulse method is so recent that no body of evidence yet speaks for or against it. Only one application-reported by its inventorsrelates to the experimental problems of obtaining adsorption isotherms (43). Along with isotherm studies, there is an increasing interest in the thermodynamics of adsorption in the linear range. Adsorption heats, particularly, are obtained with ease from the temperature dependence of the elution time of small, dilute solute peaks. This method is a simple application of the van’t Hoff equation. Kiselev ( 3 7 ) has shown that a n advantage of GC compared with calorimetry stems from the improved sensitivity and higher operating temperatures which assure linearity. H e discusses examples where adsorption heats vary with the technique (actually with the coverage) due to adsorbate-adsorbent interactions, Bebee and coworkers (72) have studied critically the use of discrete validity of two G C approaches-the measuring peaks and the use of a frontal method-in heats of absorption (and isotherms). The two methods yielded values in good accord with one another and with calorimetric determinations. Incremental Parameters
The superb separating power of GC makes possible the measurement of small differences in properties between closely related solutes. O n a column of N theoretical plates, two solute peaks can be disengaged if their free energies of sorption, AGO, differ as follows (75) :
(7) where &T is the gas constant-temperature product and R, as before is the retention ratio. At room temperature and with a retention ratio of 0.2, a column of ten thousand theoretical plates will disengage solutes differing by only 30 calories per mole free energy. Since more plates than this can be generated if necessary and a partial overlap of peaks can be tolerated, we can envision measurements of incremental free energies down to a few calories. These values can be further broken down into incremental enthalpies and entropies. The convenience of this approach and the outstanding accuracy to be gained from the direct measurement of small differences have prompted several recent papers. A prime object has been the field of isotope effects. Falconer and CvetanoviC showed the utility of the G C method with respect to isotopically substituted hydrocarbons (70). By use of a 300-ft. capillary column (130,000 theoretical plates) coated with squalane solvent, the various solution thermodynamic increments were obtained for a large group of compounds. Incremental free energies varied from 20 to 76 calories, thus conforming with the requirements of adequate separation. These authors showed that isotopic boiling points could be estimated with a reliability better than 0.3” C. (relative to the light isotope), all with less than a millionth 26
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
of a mole of solute. Similar advances have been made by Liberti, Cartoni, and Bruner (35). The thermodynamic increments of diastereoisomers and the chemical basis of these increments have been studied recently by Rose, Stern, and Karger (46). With a precision of *2 calories per mole, these authors were able to consider experimentally the effect of bulk dissymmetry at the alcoholic asymmetric carbon and the distance between the optical centers of diastereoisomeric esters. The study of differences in geometric isomers, while generally not so intricate because the thermodynamic increments are larger, is nonetheless advanced by the special advantages of the G C approach. An illustration is provided in the work of Bauman, Straus, and Johnson where boiling points were estimated for positional straight chain isomers of C ~ to O C15alkylbenzenes ( 3 ) . The various isomers are difficult to prepare in pure form, but isomeric mixtures can be simultaneously separated and characterized by GC. Isomeric effects have also been studied by Langer and Purnell (34). Transport Properties:
Gas Phase Diffusion Coefficients
Rather extensive measurements of binary gas phase diffusion coefficients have been made using GC equipment having an unpacked nonsorbing tube (27). As mentioned earlier, the dispersion of a solute peak can be related by exact theory to the diffusivity of solute in carrier gas. The first experiments based on this concept were performed with a commercial apparatus needing “end” corrections for injection and detection processes. The speed of the method was indicated by 200 separate determinations of the diffusion coefficient in 36 hours (20). Later equipment has eliminated the need to correct for “end” effects ( 7 7 ) . Accuracy has been estimated as within about 2Yc,but it is difficult to judge since other methods incur comparable errors. A comparison of several experimental diffusion coefficients obtained by GC and other methods is shown in Table 111. A significant variation in the GC technique has been developed by Knox and McLaren (32). These authors begin the experiment in the usual way, but then arrest
TABLE 1 1 1 . COMPARISON O F BINARY GAS PHASE D I F F U S I O N COEFFICIENTS A T ONE ATMOSPHERE PRESSURE
System
He-A5 COZ-H~“ He-Np N2-COp NyC2H4b Nz-CdHlo*
T,
O
C.
23 25 25 25 29.5 29.3
GC Value, Sq. Cm./ Sec .
Sq Cm ./Sec.
0.729 0.665 0.687 0.163 0.170 0.100
0.725, 0.733 0.638, 0 . 6 4 6 0.688 0.167 0.174, 0.174, 0 . 1 6 7 0.0985, 0.1006
Lit. Values,
.
a From Table I I in Giddinps and Seager (20). GC values by earlier technique with “end” correction. * From Table II in Fuller and Giddines ( 7 1 ) . G C ualues from newer technique and equipment.
the flow when the peak is part way along the tube. The diffusion occurring in the period of interruption is determined from the width of the final elution peak, That component of total peak dispersion occurring during flow is subtracted out by observing the variation in peak width with interruption time. Diffusion coefficients determined by this method also compare well with literature values. Surface Area
Nelsen and Eggertsen first demonstrated that GC instrumentation could be used to measure surface areas (42). I n accord with the conventional method, the amount of Nz adsorbed at various pressures is measured, then interpreted through the BET equation (the method is obviously adaptable to isotherm determinations). The measurement, however, is greatly simplified. The Nz adsorbed at liquid nitrogen temperature is eluted by warming. Its amount is determined quickly and accurately by recording the area of the elution peak. Helium is used as a carrier gas and one avoids working with a complex vacuum system. Special commercial instrumentation has now grown up around the GC approach to surface area measurement. The original authors compared the GC and conventional pressure-volume method using five adsorbents with widely varying surface areas. The comparison is shown in Table IV. TABLE IV. COMPARISON OF G C A N D CONVENTIONAL M E T H O D I N T H E MEASUREMENT OF SURFACE AREAS
Area, Sq. Meters/Gram GC Conventional
Adsorbent Firebrick F u r n a c e black Silica-alumina Cracking catalyst, used Alumina Silica-alumina Cracking catalyst, fresh
3.4 25.7
3.1 24
101
103
231
237
455
43s
‘ T h e agreement between methods is quite satisfactory.
CONCLUSION rt
Although long overshadowed by a superb separating capability, the nonanalytical use of GC is rapidly emerging as a major discipline in its own right. An increasing number of equilibrium and transport properties can be made to influence elution profiles and can be characterized quantitatively by the extent of that influence. The value of this approach stems in part from the same experimental characteristics that chromatographers have cultivated with care for more than a decade; detectors that respond with sensitivity and integrity, rapid equilibration and elution, versatility, automation, and separating power as needed. The GC system is almost unique in the information it can provide on only a few pmoles of solute. It is entirely unique in its speed and ability to separate these minute quantities from contaminants as it assesses their properties.
More fundamental work is clearly needed to define the scope and limitations of the GC method. This kind of work should hasten the development of the new discipline to maturity. I t would involve the usual hazard to attempt to envision what maturity will bring, but it is not difficult to image that speed, accuracy, and areas of application might be so improved and extended that huge blocks of compounds could be characterized with respect to many properties in single fully automated runs. Then finally would basic intermolecular theories have the data necessary to assure rapid, continuous, and orderly growth. REF E R ENCES Anderson, J. R., Napier, R . H., Australian J . Chem. 10, 250 (1957). Bassett, D. W., Habgood, H. W., J . Phys. Chem. 64, 769 (1960). Bauman, F., Straw, A. E., Johnson, J. F., J . Chromatog. 20, 1 (1965). Clark, R . K., Schmidt, H. H., J . Phys. Chem. 69, 3682 (1965). (5) Dal Norgare, S., Juvet, R. S., Jr., “Gas-Liquid Chromatography,” Interscience, New York, 1962. (6) Davis, T. C., Petersen, J. C., Haines, W. E., Anal. Chem. 38, 241 (1966); Amy, J. W., Rogers, L. B., private communication, March 14, 1966. (7) Desty, D. H., Goldup, A., Luckhurst, G. R., Swanton, W. T., “Gas Chromatography, 1962,” M. van Swaay, Ed., Butterworths, Washington, 1962. (8) DeVault D J Am. Chem. Soc. 65 532 (1943). Glaueckauf, E., Nature 156,749 (1945); C;emkr,E., Monatsh. Chem.’92, 112 (19Ll). (9) Everett, D. H., Stoddart, C. T. H., Truns. Faraday Soc. 57, 746 (1961). (10) Falconer, W. E., Cvetanovik, R. J., Anal. Chem. 34, 1064 (1962). (11) Fuller, E. N., Giddings, J. C . , t o be published. (12) Gale, R . L., Beebe, R. A., J . Ph s. Chem. 68, 555 (1964); Beebe, R. A,, Evans, P. L., Kleinsteuber, T. C. W., Ricgards, L. W., J . Phys. Chem. 70, 1009 (1966). (13) Giddings, J. C., A n d . Chem. 33, 962 (1961). (14) Zbid., 36, 1170 (1964). (15) Giddings, J. C., “D namics of Chromatography, Part 1. Principles and Theory,” Dekker, New Jork, 1965. (16) Giddings, J. C., J . Chem. Phys. 31, 1462 (1959). (16a) Giddings, J. C., J . Phys. Chem. 68, 184 (1964). (17) Giddings, J. C., Nature 184, 357 (1959). (18) Giddings, J. C., Mnllik, K . L., Eikelburger, M., Anal. Chem. 34, 1026 (1962); Hawkes, S. J., Russell, C. P., Giddings, J. C., Jbid., 37, 1523 (1965); James, M. R., Giddings, J. C., Eyring, H., J . Phys. Chem. 69, 2351 (1965). (19) Giddings, J. C., Schettler, P. D., Ibid., 36, 1483 (1964). 1, 277 (1962). (20) Giddings, J. C., Seager, S. L., IND.ENC.CHEM.FUNDAMENTALS (21) Giddings, J. C., Seager, S. L., J. Chem. Phys. 33, 1579 (1960); Giddings, J. C., Seager S L IND ENO CHEM FUNDAMENTALS 1 277 (1962)’ Seager S. L GeertsAn ‘L & Giddings J. C ’ J . Chem. Eng. Datd 8, 168 (196i); BoheAen, J:: Purnell, . i. H.,3. Chem. Sol. 196i: p. 360. (22) Zbid., 35, 2242 (1961). (23) Gil-Av, E., Herling, J., J . Phys. Chem., 66, 1208 (1962). (24) Gregg S J Stock R “Gas Chromatography, 1958,” D. H. Desty, Ed., p. 90, Ackderni:Press, NeG’York, 1958. (25) Helfferich,F., Peterson, D. L., Science 142, 661 (1963). (26) Hoare, M. R., Purnell, J. H., Truns. Faraday Snc. 52, 222 (1956). (27) James, M. R., Giddings, J. C., Eyring, H., J. Phys. Chem. 69, 2351 (1965). (28) Kelker, H., Ber. Der Bunsen Gcrellschnft, 67, 698 (1963). (29) Kenworthy, S., Miller, J., Martire, n. E., J . Chem. Ed. 40, 541 (1963). (30) Keulemans, A. I. M., “Gas Chromatography,” Reinhold, p, 182, New York, 1957. (31) Kiselev A V in “Advances in Chromatography” Vol. IV, J. C. Giddings and R. A. Keiler,”Eds., Marcel Dekker, New York, in ’,res,. (32) Knox, J. H., McLaren, L., Anal. Chem. 36, 1477 (1964). (33) Kwantes A., Rijnders G. W. A. “Gas Chromatography, 1958,” D. H. Desty, Ed., 125, Academ\c Press, NedYork, 1958 (34) Langer, S. H., Purnell, J. H., J.Phys. Chem. 67,263 (1963). (35) Liberti, A., Cartoni, G. P., Bruner, F., J . Chrnmolog. 12, 8 (1963); also Anal. Chem. 38, 298 (1966). (36) Littlewood, A . B., Phillips, C. S. G., Price, D. T., J . Chem. Soc. 1955, p. 1480. (37) Martin, A. J. P., Symposium on Gas Chromatography, SOC.for Anal. Chem., Stevenston, Scotland, May 1955. (38) Martin, R. L., Anal. Chem. 33, 347 (1961). (39) Martire, D. E., Locke, D. C., Zbid., 37, 144 (1965). (40). Martire, D. E., Pollara, L. Z., in “Advances in Chromatogra h y ” J. C. Giddings and R. A. Keller, Eds., Vol. I, p. 335, Marcel Dekker, New !‘o,k, 1965. (41) Martire, D. E., Pollara, L. Z . , J . Chem. Eng. Data 10, 40 (1965). (42) Nelsen, F. M., Eggertsen, F. T., A n d . Chem. 30, 1387 (1958). (43) Peterson, D. L., Helfferich,F., Cam, R. J., A.Z.Ch.E. J., in press. (44) Porter, P. E.,Deal, C.H.,Stross, F. H., J . Am. Chem.Snc. 78,2999 (1956). (45) Rangrl, E. T., M.S. Thesis, Rice University, Houston, 1956. (46) Rose, H . C., Stern, R. L., Karger, B. L., Anal. Chsm. 38, 469 (1966). (47) Schettler, P. D., Jr., Giddings, J. C., Zbid. (submitted). (48) SFhettler, P. D., Thompson, G. H., Myers, M. N., Giddings, J. C., unpublished results. (49) Stalkup, F. I., Kobayaski, R., A.Z.Ch.E. J . 9, 121 (1963). (50) Taylor, G., Proe. Roy. Soc. (London) A219, 186 (1953). (51) Wilson, J. N., J . Am. Chem. Soc. 62, 1583 (1940). (1) (2) (3) (4)
.;
Work supported by Public Health Service Research Grant GM 10851-09 from The National Institutes of Health. VOL. 5 9
NO. 4
APRIL 1967
27
