RlKl KOBAYASHI PATSY S. CHAPPELEAR HARRY A. DEANS
APPLIED THERMODYNAMICS SYMPOSIUM
Physico-Chemical Measurements b y Gas Chromatography /
Gas chromatography is not just an
his paper reviews various aspects of the development T and application gas chromatography for the direct study of the following subjects: of
analytical tool: i t is a powerful and
I.
II.
accurate method for measuring many thermodynamic properties such as activity coefficients, heats of vaporization, solution and adsorption, and K-values. GC also affords a general technique for the study of the interactions of gases with solids or
liquids
III.
IV. V. VI. VII.
Gas-liquid chromatograehy without chemical reaction Gas-liquid interfacial ejects Relation of gas-liquid chromatography to extractive distillation and absorption Gas-solid chromatografihy without chemical reaction Chromatographic systems with chemical reactions Dzrect measurement of transkart coeficients Surface area and catalysis studies
The application of gas chromatography to enhance our understanding of these areas of interest has been overshadowed by our principal preoccupation with gas chromatography as a n analytical tool. Regardless of the primary objectives we hold, any profound developments in chromatography contribute to both phasesanalytical and nonanalytical. Table I gives the number of publications in various 5year periods devoted to the study of physicochemical phenomena by gas-liquid and gas-solid chromatography. A casual examination of Table I indicates a rapid proliferation of publications devoted primarily to the application of gas chromatography for the study of physicochemical effects in chromatographic columns. A further examination of the literature indicates that gas chromatography is at once versatile and complex as a means of studying gas-liquid and gas-solid interactions. VOL. 5 9
NO. 1 0 O C T O B E R 1 9 6 7
63
I rimah Number of Publications in
Gas-liquid -Gas-solid
1
I
I. GAS-LIQUID CHROMATOGRAPHY WITHOUT CHEMICAL REACTION Paper chromatography and liquid-liquid chromatography predate gas chromatography by many years and indeed must be credited with having provided the phenomenological and even theoretical impetus for the development of gas chromatography. Martin and Synge in their classical work on liquidliquid chromatography (728) made the speculation that gas-liquid chromatography might be used as a means of separating mixtures of volatile components. James and Martin (92) modified the liquid-liquid chromatographic theory of Martin and Synge to provide a gas chromatographic theory taking into account the mobile phase compressibility. Previous assumptions, such as the nonvolatility of the fixed liquid phase, the inertness of the carrier gas, and low solute concentrations, were retained. At an early date Martin (727) speculated that gasliquid partition chromatography might be useful for studying the behavior of solutes in solvent systems and in measuring the physical properties of solutes characterizing this ixhavior, and regarded gas-liquid partition chromatography (GLPC) “as a means, perhaps the easiest, for studying the thermodynamics of interaction of a volatile solute with a non-volatile solvent.” This prophesy was verified by the work of Pierotti, Deal, Derr, and Porter (747) who obtained partition coefficients and activity coefficients for several homologous series at essentially infinite dilutions. They showed that the results were in essential agreement with the extrapolated thermodynamic properties determined by classical methods. Further investigations were carried out by Porter, Deal, and Stross (749). Rangel (756)obtained the R-values of methane and propane at pressures from atmospheric to 54 7 p.s.i.a. at essentially infinite dilutions in the helium-n-decane system and showed that the K-values (ratio of mol fraction in the vapor phase to that in the liquid) were in essential agreement with those predicted from DePriester’s correlation. Rangel also demonstrated that the freezing point of the liquid phase could be determined by observing the discontinuity in the retention times versus temperature curve. Anderson (3) and later Anderson and Napier (4) showed that reliable heats and entropies of solution at essentially infinite dilution could be obtained from the temperature dependence of the partition coefficient. 64
INDUSTRIAL A N D ENGINEERING CHEMISTRY
I
Pn-1952
(783) Tswett (1906) described the first published account of column chromatography in which he had effected the separation of the colored pigments from plant materials by eluting the plant materials with a liquid phase through a column packed with a solid adsorbent. Color bands emerged from the column and gave rise to the term chromatography, which literally means “color writing.” (773) Kuhn, Winterstein, and Lederer (1941) refined the technique of Tswett. (780) Tiselius (1940 and 1943) further refined the technique of Tswett but as yet no theoretical model appeared. (728) Martin and Synge (1941) developed a new application of chromatographic principles in which an immobile liquid, lixed on a solid support material within the column, served as the stationary phase, while a mobile liquid carrying the components to be separated was percolated through the packed bed. The solutes were partitioned between the two liquid phases and became separated as they eluted through the column. Assuming the column to be composed of a number of equilibrium stages, the authors developed a theory for this process, the most important result of which was VR =
vg + V L / H
(1)
where H = equilibrium partition coefficient between the two phases, concentration in the mobile phase/concentration in the stationary phase V , = volume of eluent passing through the column before the peak maximum in solute concentration appears in the column effluent V , = total volume of eluent in the column VL = total volume of fixed liquid phase in the column Period 1952-56
(92) James a n d Martin (1952) further developed the chromatographic separation process by using a gas as the mobile phase and a liquid as the stationary phase. They modified the theory of Martin and Synge to account for the expansion of the gas phase during the course of its travel through the column. A difficult separation and microestimation of the volatile fatty acids from formic to dodecanoic acid were undertaken.
(727) Littlewood, Phillips, and Price (1955) introduced the notion of the corrected retention volume as a main parameter characterizing the GLPC process and from a variation of V , with temperature calculated heats of solution. (727) Martin (1956) speculated that gas-liquid partition chromatography might be useful for the study of the thermodynamics of interaction of a volatile solute with a nonvolatile solvent. (747) Pierotti, Deal, Derr, and Porter (1956) theoretically considered solvent effects in GLPC, in particular the relationship for the activity coefficient of the solute in the solvent in terms of the partition coefficient and the solute vapor pressure. (749) Porter, Deal, and Stross (1956) showed that GLPC elution data gave partition coefficients consistent with static measurements for n-heptane and 2-propanol in diisodecyl phthalate. The partial excess heats of solution were also calculated from the retention data for a large number of normal paraffins, cyclic compounds, and alcohols in squalene and diisodecyl phthalate. (756) Range1 (1956) used the development of Porter et al. for partition coefficients to calculate R-values for methane and propane in n-decane at moderate pressures (15 to 60 p.s.i.a.) which were found to be in substantial agreement with values predicted from the DePriester correlation (34). (3) Anderson (1956) described a method for the evaluation of heats and entropies of solution from gasliquid partition chromatography. Period 1957-6 1
As Table I indicates, the earlier successes in the studies of thermodynamics by GLPC stimulated a substantial volume of such work during the next 5-year period. Generalizations regarding the allowance for the solubility of the elution gas or gases in the liquid phase at high pressures, the use of binary mixtures as fixed liquid phases, and the pitfalls of using polar solutes when the liquid is placed on a substrate, which is not entirely inert to long range interaction forces between the solute and the solid phase, were made and observed. During this period it was also discovered that adsorption of the solute on the surface of a highly polar liquid phase gave results for GLPC partition coefficients that disagreed with static measurements The degree of discrepancy was found to be a function of the magnitude of the solute activity coefficient.
The investigations during this period are briefly discussed in the following approximately chronological order. ( 4 ) Anderson and Napier (1957) obtained GLPC partition coefficients for benzene and cyclohexane in polyethylene glycol. Heats and entropies of solution were also calculated from the elution data. (748) Pollard and Hardy (1957) obtained retention data on various solutes on typical liquids used for GLPC. (794) Wilzbach and Riez (1957) showed that extensive substitution of deuterium or tritium for hydrogen in organic compounds causes significant changes in the retention volumes of these compounds The significance of this observation is that one must work with moderately substituted species if one is to equate the physical properties of the untraced and traced analogs. Otherwise the equation of a particular physicochemical species to that of its substituted analog-e.g., a radioactive analog-will require a correction. (774) Kwantes and Rijnders (1958) calculated activity coefficients from GLPC partition coefficients for a number of nonpolar solutes in polar and nonpolar solvents and for polar solutes in polar solvents. Good agreement between chromatographic and static measurements was observed for each case except when polar solutes in nonpolar solvents were studied using crushed firebrick, a weak adsorbent, as the substrate. However, good agreement was obtained in the latter case when metal helices were used as the supporting material for the solvent phase. (792) White and Cowan (1958) used two different substrate materials : an organo-clay derivative (B.34, F. W. Berk and Co.) and paraffin coated Celite 545 (Johns-Manville Co.). When liquid paraffin was used as the stationary phase, the latent heats of vaporization for benzene, toluene, oxylene, n-hexane, cyclohexane, and n-heptane were in agreement with literature values ; for the B.34 chromatographic behavior of the paraffins was similar to that on liquid paraffin, but the behavior of the aromatic compounds on B.34 suggested a difference in the type of intermolecular interactions. (98) Jentzsch and Bergmann (1959) measured the retention times of various aromatic compounds with silicone oil on Celite and found that the corresponding vapor pressure ratios were consistent with those found in the literature. (753) Pyke and Swinbourne (1959) measured retention data of benzene, cyclohexene, cyclohexane, and VOL. 5 9
NO. 1 0
OCTOBER 1 9 6 7
65
cyclopentene vapors on polyethylene-glycol-octyl-crysel ether placed on alumina free refractory brick and calculated their respective heats of solution. (72) Bayer (1959) defined the “selectivity coefficient” which is equal to the ratio of the corrected retention volume or the ratio of the retention times. H e also defined the relative volatility ratio and calculated the ratios for several pairs of compounds. (796) Wolf and Ternow (1959) showed that silica gels of different characteristics yielded different partition coefficients for the same solute and stationary liquid phase. Stationary liquids such as dimethylformamide, diethylphthalate, and paraffin oil were used. The study indicated that silica gel was excessively polar for the study of thermodynamic properties even though the polar effects decreased with fixed liquid phase coverage. (777) Takamiya, Kojima, and Murai (1959) used GLPC and their theory for the evaluation of the solubility parameter of Hildebrand and Scott for the fixed liquid phase without knowledge of the heat of vaporization or molar volume of the solvent, provided the values are known for the solute gas. (80) Hardy (1959) obtained GLPC partition coefficients for various halogenated hydrocarbons in glycerol, dibutyl phthalate, dinonyl phthalate, and silicone oil 702. H e also used retention data obtained by Pollard and Hardy (748) to calculate partition coefficients and activity coefficients. (52) Franc (1959) measured the retention times of the isomeric phenols and discussed them in relation to the dipole moments of the stationary phases. ( 7 5 7 ) Preston (1959) computed K-values for light hydrocarbons in heavier paraffinic material from partition coefficients and found the former to be in substantial agreement with K-values obtained from generalized correlations. (723) Lopez (1959-thesis); (724) Lopez and Kobayashi (1960) reported K-values for n-butane in n-dodecane, and the heats of solutions and activity coefficients for the C4 hydrocarbons in furfural and found them to be in substantial agreement with published results. ( 7 ) Adlard, Khan, and Whitman (1960) calculated activity coefficients over a wide range of temperatures for GLPC elution data obtained for benzene and cyclohexane in dinonyl phthalate. (725) Mackle, Mayrick, and Rooney (1960) used the chromatographic peak height as a measure of the vapor pressure for 2-thiabutane, 3-thiapentane when equilibrium is established under controlled conditions. The heats of vaporization were calculated from the chromatographic data. (45)Evered and Pollard (1960) measured GLPC elution behavior for several normal alkanes, nitroalkanes, alkyl nitrates, and alcohols on the stationary phases squalene, dinonyl phthalate, and diglycerol. Activity coefficient and heats of solution were calculated from the data. (36) Desty and Goldup (1960) introduced the use of capillary columns for the study of thermodynamic 66
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
properties by GLPC. One problem that arose was the evaluation of the small amount of liquid phase in the capillary column. Agreement of GLPC data with static data was obtained. (47) Everett and Stoddart (1961) obtained activity coefficients of five paraffins and three aromatic hydrocarbons in dinonyl phthalate. Systematic comparison of the GLPC and static data compiled by Ashworth and Everett was carried out to confirm the applicability (7) of the method to such systems. (774) Stalkup and Kobayashi (1960) reported that the principles of GLPC previously applied to study vapor-liquid equilibrium ratios were extended both experimentally and theoretically to high pressures where the solubility of the elution gas (mcthane) in n-decane became appreciable. K-values for n-butane at infinite dilutions in the methane-n-decane were obtained for pressures as high as 1985 p.s.i a. over a range of temperatures. The GLPC data were shown to check the Kvalues of Sage and Lacey extrapolated to infinite dilutions. The basic equation for the K-value of component i is:
where K, Z,
= =
R T W
= = =
P = Vat* =
K-value of component i compressibility factor for elution gas mixture gas constant absolute temperature total moles of fixed liquid in the GLPC column total pressure retention volume of a solute peak measured at column conditions and must be a radioactk-e pulse if component i exists in the elution gas
Extension of the technique to study multicomponent vapor-liquid equilibria by using mixture elution gases was discussed. (49) Fanica (1961) measured partition coefficients at infinite dilutions by GLPC and calculated limiting values of the molar enthalpies. (53) Freegard and Stock (1961) carried out the static measurements on gas-liquid chromatographic systems to confirm the chromatographic method of obtaining thermodynamic properties. Static sorption data were obtained for various substances on squalene and dinonyl phthalate, frequently used as fixed liquids in chromatographic columns. The isotherms measured showed considerable curvature, emphasizing the need to restrict
AUTHORS Riki Kobayashi and Harry A . Deans are Professors of Chemical Engineering at Rice Uniuersity, Houston, Tex. Patsy S. Chappelear is Research Associate with the same department. The authors gratefully acknowledge the sukport of the h’ational Science Foundation for their chromatography studies.
The thermodynamic study of inorganic systems by meuns ot GLPC was introduced and developed during the period from 1962-66
oneself to small sample sizes to obtain symmetrical peaks. Tailing was attributed to adsorption on the solid support or at the gas-liquid interface. (20) Cbovin a n d Ducros (1961) carried out theoretical and experimental studies on the activity coefficients at infinite dilutions for homologous series of solutes and stationary phases. (90) Hofstee, Kwantes, and Rijnders (1961) measured activity coefficients of the solute when the solvent is more volatile than the solute by presaturating the carrier gas with the solvent. Nonpolar solid supports, namely, iron filings or siliceous supports coated with silver, were used to study vapor-liquid equilibria by GLPC when conducting studies involving polar solutes. Period 1%-
The period 1962-66 showed a continued proliferation
of thermodynamic studies by GLPC. The extensive measurements of partition coefficients and K-values at infinite dilutions were continued. Derived quantities such as heats, entropies of solutions, and free energies were examined for homologous series. Partition coefficients and K-value measurements were begun for the case of binary elution gases. Theories were developed to handle the generalized elution gas case and were applied to the binary elution gas case at high pressures. The bmary and multicomponent fixed liquid phase cases were derived and substantiated. It was recognized that the elution gas component and the perturbation components must be distinct by virtue of occurrence at infinite dilutions or by resorting to radicactive tracer perturbations and equating the physicochemical properties of the component in question and its radioactive analog. On the other hand, the successful separation of isotopes by GLPC indicates that the physicochemical properties of natural chemical compounds and their substituted analogs cannot always be equated, particularly when the substitution is heavy. The thermodynamic study of inorganic systems by means of GLPC was introduced and developed. The solubility of gases in electrolyte solutions was carried out and shown to be comparable to those obtained by manometric methods. The simultaneous determination of interaction second virial coefficients and activity coefficients was developed. By the systematic selection of the stationary phase the liquid phase activity coefficients were related to liquid phase structure and associations. The effect of chain length on solubilities was investigated.
The effect of pressure on the partition coefficients was confirmed to cause behavior similar to the effect of pressure on the K-values, (Vlx). Further studies were carried out to study gas-liquid interface and solid support effects of polar solute-nonpolar solvent systems in gas chromatography. Methods of minimizing these effects to obtain results which agree with static methods were discussed. Further work was carried out to determine activity coefficientsin volatile solvent systems. The more significant investigations during the period are discussed briefly in approximate chronological order. (77) Bruce et al. (1962) determined adsorption wefficients and partial pressures of gases in solution. (707) Khan (1962) gave a comprehensive review and discussion of the nonanalytical use of gas chromatography. (55) Fryer a n d Habgood (1962) presented a correlation of chromatographic retention volumes in terms of the heat and entropy of solution. (2) Adlard, Khan, and Whitman (1962) made further improvements and discussed some of the limitations of using capillary columns to measure thermodynamic properties. (48) Falconer and Cvetanovic (1962) successfully separated isotopically substituted hydrocarbons from their unsubstituted analogs by making use of subtle differences in physicochemical properties. (775) Stalkup and Kobayashi (1963) demonstrated that a mixture elution gas when perturbed with the same gases led to retention times not covered by the simple theory. The use of radioactive tracers was recommended. The studies were carried out to high pressures, and the theory of Stalkup and Deans (see below) was confirmed. The results were stated in terms of Kvalues (V/x). The use of GLPC to study high pressure freezing phenomena in the methane-n-decane system was also investigated. (172) Stalkup and Deans (1963) derived an analytical relationship observed by Stalkup and Kobayashi (above). It was shown that for a general N-component flowing phase, N 1 characteristic velocities arise. Numerical calculations were carried out for perturbations by small “radioactively” tagged and untagged samples of one of the components present in the elution gas mixture to confirm the difference in the elution times of the two perturbations (1961) (777). This theory further suggested the necessity of using tagged perturbation when the mixture elution gases and finite concentration K-values were sought.
-
VOL 5 9
NO. I O
OCTOBER 1 9 6 7
67
(58) Genkin et al. (1963) studied the influence of various polar solvents on the relative volatilities and activity coefficient ratios of the Cg hydrocarbons in mixtures. Both mixed and pure component stationary phases were studied. (7 75)Langer and Purnell.(1963) studied the elution characteristics of a number of halogenated aromatic and isomeric aromatic hydrocarbon compounds. Thermodynamic values were obtained to study the interactions involved. The effects of difference in molecular size were correlated with the calculated entropy values. (88) Henly, Rose, and Sweeny (1963 and 1964) derived theoretical relations for the determination of the solute-gas-liquid partition coefficient when multicomponent stationary liquid phases are used. The shape of the partition coefficient curves which is related to the degree and type of nonideality was discussed. T h e effect of high solute concentration on activity coefficients was investigated and found to have possible significance in preparative chromatography and equilibrium studies. ( 9 ) Barker and Lloyd (1963) determined partition coefficients for cyclohexane, methylcyclohexane, and benzene on typical stationary phase liquids. (54)Freegard and Stock (1963) obtained data on the absorption of CC14, CHC13, and CHzClz by squalene and dinonyl phthalate by static methods at different temperatures and concentrations to estimate activity coefficients a t infinite dilutions for comparison with values determined by GLPC. (735)Martire, Pollara, and Funke (1963) presented a method for the prediction of the activity coefficient at infinite dilution for nonpolar and polar compounds in various gas-liquid chromatographic solvents. (33)Degeorges and Vergnaud (1963) solved the problem of handling and analyzing corrosive gases such as chlorine and hydrochloric acid. Stationary phases were toluene, metaxylene, and silicone elastomer E-301. The heats of solution of the corrosive gases were determined from the retention volumes. (773)Stalkup and Kobayashi (1963) reported Kvalues at infinite dilutions for ethane, propane, and nbutane at 70, 40, and 0' F. for pressures up to 2000 p.s.i.a. The relationship derived for taking into account the solubility of the methane elution gas into the ndecane stationary phase was used to calculate the K68
INDUSTRIAL A N D ENGINEERING C H E M I S T R Y
values for these solutions under these conditions. (777)Stalkup (1961) measured K-values for ethane, propane, and n-butane in n-decane over a range of temperatures up to a pressure of 2000 p.s.i.a. H e experimentally determined retention times for perturbations of untagged methane as a function of the concentration of methane-helium mixtures in the heliummethane-n-decane system and found the retention times to be quite concentration dependent. Similar experiments were conducted using methane-propane elution gases with n-decane as the stationary phase. A physical argument for the extreme concentration dependence was proposed by Kobayashi shortly thereafter. I t recognized the need for the use of perturbations of radioactive analogs of the elution gas components to apply Equation 2. Stalkup and Deans (772)developed the analytical solution to the equations of continuity governing the chromatographic process to obtain the K-values of the components of a mixture being eluted through the chromatographic column. The K-values obtained theoretically were in good agreement with those predicted by correlations. Stalkup and Deans also carried out numerical calculations to demonstrate that the use of radioactive analogs of the elution gas components would yield a reasonable K-LTalue. They also studied the effect of mass transfer rates on the assumption of local equilibrium and found that local equilibrium could be assumed over a rather broad range of operating conditions. These solutions covered the case of the solute sample being one of the components of the elution gas, in which the K-values would be for the solute present at some finite concentration in the system, as well as the case of the solutes not being initially present in the elution gas-i.e., when the solute exists at infinite dilution in the vapor-liquid equilibrium system. (775) Stalkup and Kobayashi (1963) verified the equation developed by Stalkup and Deans for the case of a binary elution gas being perturbed by components common to those appearing in the elution gas. The relations of Stalkup and Deans are significant but of limited value because the general solution is not obtainable and only N - 1 retention times can be obtained for an N-component elution gas. The application of GLPC to study high pressure K-values at infinite dilutions and also to determine univariant freezing points of
The use of radioactively tagged sample molecules to determine high pressure vapor-liquid equilibria in multicomponent systems was a significant development in the study of N-component elution gases
liquids with dissolved gas were demonstrated and discussed. (709) Kenworthy, Miller, and Martire (1963) discussed the application of GLPC to determine activity coefficients and relative volatilities at infinite dilutions. Typical GLPC results were compared with static values. (770) Koonce (1963) developed general relations for the determination of K-values of an N-component system with all components present in finite concentrations in the liquid. Extensive experimental data were obtained for several mixtures of methane and propane in fixed liquid phases of n-heptane and n-decane. The experiments were conducted to pressures as high as 1000 p.s.i.a. The relationship developed assumes the previous assumptions of Equation 2 plus the additional assumption that the retention volumes were obtainable for elution gas components having the same physical property as the elution gas component but distinguishable from them. The fulfillment of this assumption was made available by recourse to radioactively traced analogs of the elution gas components,, The generalized equation for the IC-value of component
i is:
Vu* = corrected retention volume measured by ionization produced by radioactive solute sample for molecule All other terms were defined with the presentation of Equation 2 The rate theory developed by Stalkup and Deans for the case of sample molecules indistinguishable from the elution gas molecules was reverified for a binary elution gas by direct check with the results of Equation 3. (87) Helfferich and Peterson (1963) discussed theory for the determination of sorption isotherms and phase equilibria by a tracer method. No experimental verification of the theory was reported. The conclusions, however, were identical to those verified by Gilmer (64) and by Koonce (770). (39) Drake and Wilson (1963) obtained partition coefficients at infinite dilutions for methanol, ethanol, 1-propanol, and 2-propanol with stationary phases made up of solutions or MgCIn and PEG 400. Thus,
the fixed liquid phase was an associated mixture of ions and alcohols. (787) Ti& (1964) studied the thermodynamics of some volatile, water sensitive transition metal chlorides on molten salt stationary phases and calculated their heats of solutions. (720) Liberti, Cartoni, and Bruner (1964) showed that isotopic effectsof benzene and cyclohexane and their fully deuterated isotopes could be separated by GLPC and the differences in their thermodynamic properties dilineated. (772) Koonce and Kohayashi (1964) developed the use of radioactively tagged sample molecules to determine high pressure vapor-liquid equilibria in multicomponent systems. General equations for the determination of K-values in an N-component elution gas with a stationary liquid phase was derived and applied to the methane-propane-n-decaneand methane-propanen-heptane systems. Methane R-values were determined successfully, but inaccurate evaluation of the free gas volume led to moderate and serious errors at lower pressures. Agreement between the tagged and untagged K-values determined in the methane-n-decane system at infinite dilutions was found to be identical. (86) Helfferich (1964) discussed in a general way the phenomena observed by Stakup and Kobayashi (775) and analytically solved for the binary elution gas case by Stakup and Deans (772) that the rate of travel of a sample molecule distinguishable from the elution gas molecules-e.g., a radioactively tagged molecule, is, in general, different from the rate of travel of a pulse caused by a perturbation resulting from the injection of a sample made up of indistinguishable molecules. ( 7 9 0 ) Waksmundzki and Suprynowicz (1965) made a theoretical and experimental study of the use of binary stationary phases. The solutes used were furan, nhexane, cyclopentane, cyclohexane, cyclohexene, and benzene on a stationary phase of mixtures involving triacetin, pelargonic acid, n-tetradecane, and quinoline. (777) Koonce, Deans, a n d Kobayashi (1965) modified a previous mathematical description of the elution process (Equation 2) to include the case of an N-component elution gas, all components of which are soluble in the fixed liquid phase. A general solution was derived for the multicomponent elution gas from which VOL 59
NO. 1 0 O C T O B E R 1 9 6 7
69
Determination of activity coefficients, second virial coefficien ts, and other related thermodynamic functions can be obtained from GLPC. The conclusions that may be drawn from
the data are that under properly controlled experimental conditions data accurate to I to 2% can be obtained
70
INDUSTRIAL A N D E N G I N E E R I N G CHEMlSTR,Y
K-values for each component may be calculated if retention volumes are taken for each, provided molecules of the solute samples used are distinguishable from others of the same species present in the elution gas. Extensive experimental verification of the theory was provided in this paper and elsewhere (7 72). For the case of indistinguishable sample molecules, the rate theory development of Stalkup and Deans was verified experimentally for binary elution. (745) Peterson and Helfferich (1965) confirmed the theoretical and experimental developments of Koonce (770) and Gilmer (64)and later reported by Koonce, Deans, and Kobayashi (777) and Gilmer and Kobayashi (66). (734) Martire and Pollara (1965) measured the activity coefficients of 39 solutes in each of I solvents and each combination at three different temperatures. The data were taken systematically to aid in the development of a theory of solution for an infinitely dilute solute. (37) Cruickshank, Everett, and Westaway (1965) made a critical survey of GLPC activity coefficient work through 1964 and compared data closely. The conclusions drawn were that under properly controlled experimental conditions activity coefficient data accurate to 1 to 2% can be obtained by GLPC. (76)Gubbins, Carden, and Walker (1965) determined the solubility of OZand H, in aqueous solutions of KOH, HISO,, and HaPo,. The results obtained were comparable to those determined by manometric methods. (46) Everett (1965) determined interaction second virial coefficients and activity coefficients hy GLPC taking into account the effects of moderate gas imperfection. (22) Clark and Schmidt (1965) measured activity coefficientsand heats of solution at infinite dilutions for benzene in biphenyl, rn-terphenyl, and o-terphenyl, respectively. The resulting thermodynamic data could be correlated by the application of statistical thermodynamics of short polymers but not by regular solution models. (776) Langer and Purnell (1965) made a GLPC study of the thermodynamics of solution of aromatic compounds in a tetrahalophthalate liquid phase. The data were interpreted in terms of activity coefficients and related thermodynamic functions. (743) Peesar a n d Martin (1966) determined the thermodynamic properties at infinite dilutions from
GLPC data and used these in turn to predict the thermodynamic properties for various nonideal binary solutions. (757) Ratkovics (1966) measured the total pressure of a single mixture of methanol and chloroform and showed that the binary vapor-liquid equilibria at that temperature could be evolved by thermodynamic calculations. The general applicability of such a method would be open to question. (57) Geiseler and Jannasch (1966) derived enthalpies of vaporization from the relationship between integrated detector signal area and temperature for constant saturated vapor sizes. The results were used to explain the mechanism of separation of diastereoisomeric esters. (767) Rose, Stern, and Karger (1966) studied the mechanism of separation of diastereoisomeric esters by GLPC, in particular the effects of bulk dissymmetry and distance between optical centers. (758) Ratkovics (1966) evaluated the activity COefficients of ethanol, n-hexane, n-heptane, cyclohexane, and benzene with 0.1 to 0.8 weight Yo squalene on 0.1 mm. glass beads. I t was found that the value of the activity coefficient varied with the squalene loading on the column. The investigators felt that the optimum loading was in the neighborhood of 0.8 weight Yo. Various other thermodynamic properties were calculated. (767) Sie, van Beersum, and Rijnders (1966) measured partition coefficients of several hydrocarbons, ethanol, methanol, acetone, 1,l-dichloroethane, and npropyl chloride on squalene and glycerol using COZ as a carrier gas. Theoretical explanations of the drop in the partition coefficient with increasing pressure were analyzed in the light of the theory of corresponding states. Interaction second virial coefficients were determined by chromatography. They compared with data from other sources. (744) Pecsok and Gump (1966) made parallel GLPC and static vapor-liquid equilibrium studies to compare the results for polar solute nonpolar substrate systems. The polar solutes were methanol, ethanol, acetone, and diethylamine while squalene was the stationary liquid. Chromosorb supports were used. The conclusion : Gas-liquid interface adsorption was significant for the systems studied. Solid support adsorption of the polar solutes was believed to account for some of the discrepancies at low solute concentrations. (738) Moshier and Gere (1966) measured the gasliquid partition coefficient of some metal chelates in
Apiezon L and QF-1 liquid phases. The activity coefficient at infinite dilutions were derived from the data. (732) Martire (1966) reported that solute activity coefficients at infinite dilutions were obtained for paraffinic, olefinic, and saturated cyclic hydrocarbons dinonyl phthalate. Also 39 polar and nonpolar solutes in n-eicosane and squalene were determined at a single temperature. Calculations showed that the experimental data could be predicted by the Miller-Guggenheim and Flory-Huggins theories of solutions. (8) Barker and Hilmi (1967) discussed the apparatus and procedure for the determination of activity coefficients at infinite dilutions in volatile solvents by GLPC. Vapor-phase nonidealities were taken into account. The response range of the flame ionization detector was increased by diluting the column effluent. A katharometer was used when the solvent was a chlorinated hydrocarbon. (709) Kogansen, Kurkchi, and Levina (1966) evaluated the hydrogen bond energies between solute and solvents by GLPC. The method developed was based on the heat of solution of the solute-e.g., acetylene, and the heat of solution in two appropriately chosen stationary phases, one an inert solvent, and the other a subtance which formed H-bonds with the solute. (787) Van Horn and Kobayashi (1967) determined K-values for the lighter paraffin hydrocarbons in the methane-ethane-n-heptane, methane-propane-n-heptane, and methane-propane-toluene systems a t pressures as high as 1600 p.s.i.a. and temperatures down to -100' F. by GLPC. Binary elution gases were used with pulsing by radioactively traced analogs of the components in the elution gas. The K-values were consistent with the binary limits of the ternary systems determined by static experiments. (736) Masukawa, Alyea, and Kobayashi (1967) determined the free gas volume as a function of pressure at a fixed temperature by using a series of perturbing gases, namely, He, Ne, and Ar, a series of retention volumes through a column packed with n-octane on firebrick using methane as the elution gas. The free gas volume was obtained by extrapolating the series of retention volumes to that of a hypothetical perfect gas. Thus, it was possible to determine the methane K-value in the methane-n-octane system as a function of pressure and the volume change of n-octane as a result of the dissolution of methane in it, VOL. 5 9
NO. 1 0
OCTOBER 1967
71
The unusual phase behavior in ternary systems as affected
by temperature
is evident in the complexity of the phase diagram. The conditions and degree to which the gas-liquid interfacial effects might be relevant to the particular separation or
.. .. . ,
measurement being conducted have been recognized and studied
by
several investigators
..
.
..
. '
.
I' '
II. GAS-LIQUID INTERFACIAL EFFECTS Under certain conditions two types of adsorptive effects may be operative during the measurement of physicochemical measurements by GLPC in a quantitative way. The conditions and degree to which the effects might be relevant to the particular separation or measurement being conducted have been recognized and studied by several investigators. Thus, polar solutes eluted through a moderately or highly adsorptive solid phase impregnated with a nonpolar stationary phase may give erroneous partition functions (or K-values) due to long range interaction forces between the solute and the solid phase. This effect might be classed an adsorptive effect because it results from the direct interaction between the solute and the solid phase. Even though a weakly adsorptive solid is used, if the liquid coverage on the solid is insufficient, adsorptive effects between the solute and the solid can come into play and cause discrepancies between chromatographic and bulk partition coefficients (or K-values). Finally, it has been observed that when highly polar solvents are used (on the solid substrate) excem surface concentrations at the interface can occur when the solute is likewise highly polar. Considerable advance-
72
INDUSTRIA1 AND ENGINEERING C H E M I S T R Y
\ L
ments in defining when one is likely to encounter adsorption at the gas-liquid interface have been made. In fact, chromatography offers a promising tool for the investigation of properties at interfaces. (774) Kwantes a n d Rijnders (1958) found that activity coefficients at infinite dilutions obtained by GLPC did not check static equilibrium values. The explanation offered was that the long range interaction forces between the polar solute and the solid support through the nonpolar fixed phase took place. This effect can be minimized by using an essentially inert solid phase and/or thickening the nonpolar liquid layer. Liquid phase diffusional effects, however, may become significant if the liquid layer is excessively thick. (80)Hardy (1959) confirmed the observations made by Kwantes and Rijnders above. (76‘) Bohemen, Langer, Perrett, and Purnell(1960) studied the adsorptive properties of firebrick in relation to its use as a chromatographic support. (729) Martin (1961) introduced the notion that partition coefficients for highly polar solutes and highly polar liquid phases on the solid disagreed with static results because of significant solute orientation on the liquid surface. Martin termed the phenomena “adsorption at the gas-liquid interface.”
(730) Martin (1963) studied the adsorptive effects at the gas-liquid interface measured by GLPC in the light of Gibbs equation. The Gibbs equation allows the calculation of the concentration excess of solute at the surface. (733) Martire, Peciok, and Purnell (1964) substantiated the hypothesis that excess surface concentrations at the surface did m u r for molecular pain like those discussed by Martin by static measurements and concluded that surface adsorption could lead to discrepancies between the activity coefficients obtained by GLPC and static means. A semiempirical equation for the quantitative magnitude of the effect was presented. (26) Cremer (1965) utilized GLPC as a method of investigating interfacial phenomena. The Gibbs free energies for the interfacial phenomena as reflected by the retention volumes were evaluated. (737)Martire (1966) defined the conditions for which adsorption at the gas-liquid interface becomes significant. The relation between the effect of interfacial adsorption on various chromatographic p a r a m e t a was given. 111. RELATION OF GAS-LIQUID CHROMATOGRAPHY TO EXTRACTIVE DISTILLATION AND ABSORPTION The present state of development of GLPC permits one directly to relate vapor-liquid equilibrium data obtained by GLPC to extractive distillation and absorption processes in which the extractive or absorptive agents possess a low or uegliible volatility under process conditions. Further generalization of GLPC will allow us to relate GLPC measurements to essentially all processes which make use of vapor-liquid equilibrium information. It is not necessary that the ‘‘fixed” liquid component or components be completely nonvolatile but that the extent of the “fixed” component or components be measurable or estimable during the interval of time that the elution takes place. In the recovery of hydrocarbons, economic considerations usually require that the absorption take phce at the highest feasible pressure. High pressure GLPC has permitted considerable accumulation of data at pressures sufficiently high enough to obtain valuable vaporliquid equilibrium data under comparable conditions. The requirement that useful data need be at low temperatures has not been excessively difficult to overcome. (760) Rock (1956) discussed the theoretical and experimental requirements for the application of GLPC as a tool to study extractive distillation. The experimental VOL 5 9
NO. 10 O C T O B E R 1 9 6 7
73
(774) Stalkup and Koba- ' Generalized GLPC theoyashi (1960) (775) Stalkup and Koba- retically and experimentally to enable the study of yashi (1963) (772) Stalkup and Deans high pressure multicomponent vapor-liquid equi(1963)
yashi (1963) ( 7 72) Koonce and Kobayashi (1964)
measurements were made on binary and ternary systems representing simplified low
which were separated by clear bands of solvent. Tiselius (780)was among the early workers in the development of liquid-solid Chromatography. The earliest theoretical work on the subject was carried out by Wilson (793) who considered the displacement process for both pure and multicomponent mixtures. Wilson used a continuous rate theory to analyze the chromatographic process assuming instantaneous equilibrium at each point in the column and neglecting diffusive effects. DeVault (37) extended the theory of Wilson by including diffusive effects and the absence of point equilibrium. The partition chromatography introduced by Martin and Synge (728) was actually liquid-liquid chromatography since the solid phase served only to hold one of the liquid phases stationary. Nonetheless, the authors impact on the development of gas-solid chromatography (GSC) must have been significant since soon thereafter Turner (784) was investigating the use of a mobile gas eluent rather than a liquid phase to transport adsorbates in contact with the solid adsorbent phase. Claessen (27) also made investigations similar to those of Turner using a rudimentary form of gas-elution chromatography. One of the first individuals to demonstrate theoretically and experimentally that adsorption isotherms for a binary mixture could be measured by chromatography was Glueckauf (67, 68). Cremer and Prior (30) were among the earliest investigators successfully to apply the gas-solid elution technique to the separation of gases. They also determined heats of adsorption from their elution data. Period 1952-56
IV. GAS-SOLID CHROMATOGRAPHY WITHOUT CHEMICAL REACTION Although we are generally concerned with gas-solid elution chromatography, we will discuss other forms of gas-solid chromatography either for historical reasons or for useful techniques in the study of physicochemical phenomena. The so-called Chromatographic adsorption method of analysis was originated by the Russian botanist M. Tswett (783). I n his technique a solution containing a mixture of colored solutes was allowed to run through a vertical glass tube filled with an appropriate powdered adsorbent. The solutes adsorbed along the column, appearing as a series of colored bands which was known as a chromatogram. When a suitable solvent was poured through the column, he found that the colored bands were washed down the tube at different rates, the lowest-lying band emerging first. By recourse to a sufficiently long tube and a sufficiently large volume of solvent, it was found that the original components of the mixture could be separated into discrete bands 74
INDUSTRIAL A N D ENGINEERING CHEMISTRY
The period from 1952-56 witnessed the rapid increase in the application of elution gas-solid chromatography to the analysis of gases, particularly to those with low boiling points. Significant theoretical work was carried out during this period but little work was conducted to determine physicochemical properties by GSC. The references are cited during this period primarily for their indirect contributions to the development of chromatography and the development of GSC to measure physicochemical properties. (777) Lapidus and Amundson (1952) presented the most general solution to the elution GSC problem for linear adsorption isotherms. The assumption of uniform velocities was made, but longitudinal diffusion effects were considered. Solutions were presented for both point equilibrium in the column and for a finite rate of mass transfer. (99) Kasten, Lapidus, and Amundson (1952) solved the mathematical model of Lapidus and Amundson with the added condition of nonlinear adsorption isotherms. (89) Hiester and Vermuelen (1952) similarly treated the nonlinear adsorption isotherm case. (69) Goldstein (1953) considered the finite rate of mass transfer case with nonlinear adsorption isotherms as in reference 709. (95) Janak (1953) heavily contributed to the estab-
lishment of GSC as a means of analyzing low boiling gases and vapors. (759) Ray (1954) contributed to the early development of GSC as an analytical tool. (764) Schay a n d Szekely (1954) described the determination of COzadsorption on activated carbon by a frontal analysis. The free gas volume in the column was properly accounted for. Differential heats of adsorption were determined from the basic data. (96) Janak (1954) contributed to the analysis of low boiling vapors. (93) James a n d Phillips (1954) were among the first to describe the applications of frontal, elution, and displacement chromatography to the determination of adsorption isotherms. They determined the adsorption isothersm of cyclohexane and benzene on carbon by the frontal analysis. The breakthrough time was corrected for the dead volume of the apparatus but unfortunately not for the free gas volume of the column. (97) Janak (1955) made further contributions to the analysis of low boiling vapors and the behavior of GSC columns with various gases. (786) Van Deemter, Zuiderweg, a n d Klinkenberg (1956) simplified the nonequilibrium solution of Lapidus and Amundson and developed the solution in terms of vapor-liquid rather than vapor-solid mass transfer. I t is interesting to note that the final equation for the GSC and GLPC bear a great deal of resemblance.
Period 1 9 5 7 6 1
T h e application of frontal and elution GSC to the measurement of thermodynamic properties flourished widely during the next 5-year period, particularly if one considers the widespread application of GSC to the study of catalyst properties such as adsorption and surface areas. Both frontal and elution methods were applied to determine adsorption isotherms; however, the latter was restricted in use by the requirement of linear isotherms. This restriction has been lifted, particularly for those substances for which a tracere.g., a radioactive analog exists. The discussion of GSC with chemical reaction constitutes such a significant activity that it will be treated in Section V. (765) Schay, Szikeley, a n d Szigetvary (1957) extended frontal chromatography to the determination of mixed gas adsorption. The change in the volumetric flow rate of the carrier gas due to adsorption of the solute was taken into account. Adsorption isotherms of COz, CzH2, and their mixtures were determined by frontal chromatography. (763) Schay, Fejes, Halasz, a n d Kiraly (1957 a n d 1958) determined adsorption isotherms of carbon dioxide on carbon by frontal chromatography. The comparison of the isotherms determined by volumetric and chromatographic methods was found to be in good agreement. (70) Greene a n d Pust (1958) extended the method of Littlewood (727) (GLPC) to GSC to determine the heat of adsorption of some low boiling gases on charcoal and
light hydrocarbons on alumina and silica gel. The values so determined were in good agreement with those found calorimetrically. (77) Gregg a n d Stock (1958) were among the first to attempt determination of the complete adsorption isotherm from elution data, although they used the detailed form of the elution chromatogram rather than the retention volume. (78) Hanlan a n d Freeman (1959) showed that the first-order gas-solid interaction coefficient could be obtained by gas chromatography retention volumes, and that the potential energies of interaction can therefore be obtained from the temperature dependence of the retention volumes; also that the retention volume in GSC could be related to the concept of “apparent volume” in the equation of state for high temperature physical adsorption. Thus, a theoretical connection between static measurements and gas adsorption chromatography was established. (77) Habgood a n d Hanlan (1959) made an elution GSC study of the adsorptive properties of nitrogen and the simpler hydrocarbons on a series of steam activated charcoals. For all of the gases studied it was found that the initial slope of the isotherm and the intial heat of adsorption decreased with increasing degree of activation. This suggested that the elimination of the smaller pores due to the activation process more than counterbalanced the increased surface area of the more highly activated material. (737) Mortensen a n d Eyring (1960) used the retention times for 0- and p-H2 and for 0- and p-D2 to pass through an alumina column at 77.4’ K. using an He carrier gas to calculate the potential energy barrier hindering rotation and the sticking coefficient of the incident molecules. The height of the barrier and the sticking coefficients were reported. (782) T 6 t h a n d Graf (1960) used experimental retention volumes taken as a function of temperature to determine the heat of adsorption of carbon dioxide on an activated charcoal. The heat of adsorption at infinite dilution was taken as the slope of the log of the retention volume us. 1/ T curve (linear). (755) Raginskii et al. (1960) measured adsorption isotherms by a frontal desorption technique and also by the integration of the differential material balance equation under the assumptions of instantaneous establishment of equilibrium and negligible longitudinal diffusion using observed parameters from the desorption curve. Approximate agreement of the data with those established using a quartz spring balance was found. (73) Beebe a n d Emmett (1961) measured the heat of adsorption of nitrogen by calorimetric methods and by a GSC elution technique. Reasonable agreement of the heats of adsorption from the two sources was obtained. (40)Eberly (1961) studied adsorption at high temperatures of benzene or n-hexane on a 13X molecular sieve, silica gel, calcined alumina, and platinized alumina. The experiment consisted of eluting a pulse of adsorbate with argon or helium through the column and calculating the heat of adsorption from the retention VOL. 5 9
NO. 1 0 OCTOBER 1 9 6 7
75
volumes. A method of detecting irreversible adsorption was discussed. (27) Cremer (1961) made tests to compare the adsorption values of COz on activated charcoal by elution GSC and by static means. H e recognized that the corrected retention time applies to a local region of the isotherm. (42) Eberly and Spencer (1961) used elution chromatography to study high temperature adsorption of hydrocarbons on molecular sieves and other porous solids. Heats of adsorption were determined from the retention data. (78) Carberry (1961) examined mathematically the behavior of a concentration pulse passing through a tube packed with solid particles capable of reversibly adsorbing the pulsed component. He examined the linear, Fruendlich, and Langmuir equilibrium isotherm cases and concluded that only under the circumstance where a simple linear equilibrium prevails will a meaningful value of the equilibrium constant for adsorption be determinable by transient response (perturbation) studies. (40)Eberly (1961) measured the adsorption isotherms and surface area of catalysts by a continuous pulse flow method. Good agreement was obtained with static experiments. The method required the absence of diffusional effects and rapid establishment of equilibrium. (29) Cremer and Huber (1961) evaluated adsorption isotherms from the desorption fronts of single peaks in elution GSC. A series of retention volumes was obtained and their values were plotted against the corresponding concentration. The function obtained is the first derivative of the adsorption isotherm. A graphical integration leads to the isotherm. The method was applied to measure the isotherms of benzene on silica gel, alumina, and a silica-alumina cracking catalyst and to study the adsorption of hexane and benzene on alumina at high temperatures (300O to 500’ C.) by a displacement analysis. (75) Grubner (1961) critically evaluated the methods of obtaining adsorption isotherms developed by Glueckauf (67),by Schay and Szekeley (764,and by Kelsen and Eggertsen (740) and concluded that the heat of desorption method of Nelsen and Eggertsen gave the most accurate and reproducible results. 76
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Period 1961-66
The application of GSC both in the elution and frontal forms to measure adsorption isotherms, heats of adsorption, and other thermodynamic properties continued at a vigorous pace. I n addition to studies using conventional adsorbents and catalysts (presented in Section V), alkali metal salts and amorphous boron were used. The parameters to the 6-9 interaction potential have been determined from a theoretical treatment and the retention volume at low pressure. Simultaneous solution of the retention volume expression gave rise to an expression for the determination of both component and total adsorption for a mixture of any number of components. I n addition to the usual assumption for the retention volume equation it was assumed that the retention volumes of the sample molecules were distinguishable from the corresponding elution gas molecules. By recourse to tracer chromatography, the equations have been verified for pure and multicomponent systems from low to pressures as high as 1000 p.s.i.a. Finally, the concept of the hypothetical perfect gas perturbation has been introduced to allow the determination of the free gas volume, V,, a t any combination of pressure and temperature. The change in V , with the extent of adsorption permits the calculation of a quantity which is called the “volume of the adsorbed species.” Improved adsorption values and a knowledge of the adsorbed volumes allow the adsorption isotherms to be presented as Gibbs adsorption-Gibbs adsorption allowing for the finite size of the molecules-and as absolute adsorption. The calculation of the activity coefficient for the adsorbed species of a binary mixture adsorbed on solids is now possible. (50)Fejes, Czaran, and Schay (1962) presented a frontal GSC method taking into consideration the change in the flow rate due to the adsorption process in the column, The method was based on previously developed theories relating the shapes of the adsorption fronts in the diffusion area. (766)Scott (1962) found symmetrical peaks for the elution of h>-drocarbons at temperatures below their boiling points from an activated alumina column modified with sodium hydroxide, while the unmodified alumina column did not. Under the modified condi-
tions the heat of adsorption was of the same magnitude as the heat of vaporization of the liquid hydrocarbon. The GLPC partition isotherm behavior became similar to the adsorption isotherm behavior. (79) Hansen, Murphy, and McGee (1964) determined the dependence of the retention volumes on temperature for argon, nitrogen, carbon monoxide, methane, ethane, ethylene, propane, and propylene on Columbia activated carbon from 300' to 700' K. T h e interaction parameters for a 3-9 gas-solid interaction potential was determined using the chromatographic data and the asymptotic expansion of the equation of state based on the principle. (82) Harper (1964) used gas adsorption chromatography to study the interaction of a series of gases with a Columbia L activated charcoal surface. The data were treated in terms of a virial coefficient-type treatment of gas-solid interactions. The evaluation of meaningful parameters for the interaction potential placed stringent requirements on the accuracy of the data. (706) Kiselev and Yashin (1964) determined the heats of adsorption of the hydrocarbons methane through n-decane on silica gel. Absolute retention volumes were obtained. The differences of the heats of adsorption of hydrocarbon isomers did not depend on the geometry while the heats of adsorption increased with a decrease of the mean diameter of the pores and an increase in the carbon number of the compound. (75) Belyakova, Kiselev, and Kovaleva (1964) determined the heats of normal paraffin hydrocarbons and the corresponding normal alcohols on graphitized carbon black by elution GSC. The data served as a basis for the indirect determination of the energy of the interaction attributed to the presence of the hydrogen bonds. (65) Gilmer and Kobayashi (1964) using methane as a n elution gas, determined the K-values (equal to y / x or the initial slope in the presence of adsorbed methane) for ethane, propane, and n-butane at essentially infinite dilutions on silica gel to pressures as high as 2000 p.s.i.a over a range of temperatures. The K-values bore significant resemblances and differences to those typical of nonpolar vapor-liquid equilibrium systems. The Kvalues did not show a relative minimum in the K-value us. pressure curve, but did show a rapid rise as the elution gas pressure was increased.
(703) Kiselev (1964) discussed the various kinds of intermolecular interactions involved in gas chromatography. Improved quantum mechanical formulations of the interaction potentials between the adsorbate and the solute are needed. The need to control the relative contributions of nonspecific and specific interactions through the appropriate choice of temperatures and varieties of surfaces was discussed. (108) Knozinger and Spannheimer (1964) applied the method of Cremer and Huber (29) to determine the adsorption isotherms of benzene on silica gel at low partial pressures of benzene between 453' and 606O K. (64) Gilmer (1963) determined the adsorption isotherms for methane on silica gel from -40' ta 40' C. gravimetrically at pressures from 100 to 2000 p.s.i.a. By use of pure methane as the elution gas, retention volumes and K-values b/x) a t infinite dilutions were determined for ethane, propane, and n-butane over the same pressure and temperature range. A general relation for the determination of mixture adsorption from tracer retention volumes for each of the components being eluted through the adsorption bed was presented. The relation permitted the calculation of the component and total adsorption-Le., the adsorbed phase composition when the elution gas composition is known. The applicability of the relationship was verified for the methane-propane-silica gel system up to 1000 p.s,i.a. (66)Gilmer and Kobayashi (1965) developed general relationships for the determination of the total and component adsorption applicable to the case in which the perturbing gas components are distinguishable from the elution gas components. The relationship was verified over an extensive range of conditions for the methane-propane-silica gel system. The distinguishability conditions were achieved through the use of radioactively tagged analogs of the elution gas components. (722) Locke (1965) made predictions relative to the effect of pressure on the retention volume in GSC. The retention volume decreases slightly with gas imperfection of the carrier gas. GSC seems to be a more powerful technique for isotope separation than GLPC. (702) Kipping and Winter (1965) discussed the use of peak maxima as compared to the single injection technique for calculating adsorption isotherms. The VOL. 5 9
NO. 1 0
OCTOBER 1967
77
adsorption isotherms obtained by the single injection, frontal, and peak maxima techniques were discussed. (704)Kiselev, Chernenkova, and Yashin (1965) determined differential heats of adsorption determined for 02,N2, and various light hydrocarbons on zeolites of the molecular sieve type. The r-electrons, characteristic of the unsaturated hydrocarbons, led to considerably larger heats of adsorption than for the saturated hydrocarbons. (6) Arita, Kuge, and Yoshikawa (1965) estimated heats of adsorption of some low boiling hydrocarbons and inorganic gases on activated charcoal, alumina, silica gel, and synthetic zeolites. The results were compared with those obtained by static experiments. (788) Vespalec and Grubner (1965) used the method described by Glueckauf (68)for the determination of adsorption isotherms of organic vapors using short columns. The adsorbent was graphatized carbon black. Static isotherms of benzene and hexane on carbon black were measured for comparison purposes. (57) Feltl, Grubner, and Srnolkova (1965) obtained additional adsorption isotherms for benzene, n-hexane, and cyclohexane on alumina oxide from 20’ to 120’ C. using the frontal technique of Glueckauf mentioned above. Isothermal differential heats of adsorption were determined from the data. (56) Gavrilova and Kiselev (1965) applied the GSC thermal desorption method of Kelsen and Eggertsen (140)and 0. Grubner (75)to determine the adsorption isotherms of nonporous and coarsely porous adsorbents. The specific surface area was determined by a rapid relative method in which it was necessary only to determine the extent of desorption using a gaseous mixture of nitrogen and hydrogen containing about 5y0of nitrogen. (72)Grob and Weinert (1966) calculated heats of adsorption for various types of polar and nonpolar organic molecules over a range of temperatures The packing matcrial used was the chloride salts of alkali metals. For alcohol-paraffin hydrocarbon homomorphs, the retention volumes of the alcohol increased with the increase in molecular weight of the alkali metal salts while the corresponding hydrocarbon showed a decrease in retention volume. Heats of adsorption were calculated from the retention volumes. (170) Spannheimer and Knozinger (1966) demonstrated that the use of the temperature dependence of the retention volume to determine heats of adsorption requires an isosteric surface condition. ( 189) Waksmundzki, Rudzinski, and Suprynowicz (1966) applied the method of Cremer (25) to determine the “adsorption potential” of CS2 on silica gel. (74) Beebe, Evans, Kleinstenber, and Richards (1966) measured the adsorption isotherms of Nz, Ar, 0 2 , C C ,and C2F6 at low coverage on carbon black and on bone mineral. The frontal GSC method was used to check previously obtained data by elution chromatography and calorimetry. The agreement in the data from the three sources led to the conclusion that neither nonequilibrium conditions nor nonlinearity of the isotherms was a significant source of error. 78
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(746) Peterson, Helfferich, and Carr (1966) reported an apparatus to conduct tracer pulse chromatography and its application to measure adsorption equilibrium isotherms. The method has tremendous implications in the measurement of adsorption isotherms as it requires no integration of observed data. The method was similar to the one previously proposed and carried out by Gilmer (64, Koonce (710),and by Gilmer and Kobayashi (66) and proposed by Peterson and Helfferich (745). (185)Urone, Parcher, Greinetz, and Baylor (1966) used known constant amounts of solute in the carrier gas to measure retention times which could be extrapolated to zero sample size. Plots of the retention volume or amounts adsorbed versus the concentration of solute in the carrier gas showed that the variation of the partition coefficient with sample size followed a Fruendlich-type isotherm. Derived heats of solution were shown to increase with decreased sample size. (142)Parcher and Urone (1966) determined nonlinear isotherms for a polar solute at low concentrations on an active support which was coated in one case and uncoated in the other by a modification of the Glueckauf (68) method. The modification averted the necessity to measure the total area of the tailing portion of the chromatogram. ( 6 3 ) Gillespie, Hobson, and Gager (1966) measured heats of adsorption of Ivater, methanol, acetone, ammonia, and trimethylamine by GSC elution data using amorphous boron as the adsorbent. The high heats of adsorption pointed to the occurrence of chemisorption and surface reaction. (8485)Haydel and Kobayashi (1966,1967) presented component and total adsorption data for the system methane-propane-silica gel over a range of concentrations, temperatures, and pressures (up to 1000 p.s.i.a.). The experiments were based on the method developed by Gilmer and Kobayashi (66) using radioactively tagged methane and propane as the samples to satisfy the distinguishability condition between the latter and the elution gas components as required by the theory. Assuming that He was negligibly adsorbed at the conditions of the experiments, preliminary measurements were made to obtain the change in the free gas volume, V,, with extent of adsorption and hence the “adsorbed volumes.” Later studies by Masukawa, ,4lyea, and Kobayashi have shown that the He is adsorbed to some extent. (136) Masukawa, Alyea, and Kobayashi (1967) determined precisely the free gas volume, V g , using a series of perturbing gases, namely He, Ne, and Ar, during the elution of methane-ethane mixtures through silica gel and extrapolating the retention volumes of the series, in regard to energy, to a hypothetical gas of zero interaction energy at any pressure-temperature condition. Radioactively traced methane and ethane were used for the perturbations, which, together with the determination of V,, allowed the calculation of total and cornponent adsorption. The difference between the V , at low and some elevated pressure, together with the amount
adsorbed, permitted the calculation of the “adsorbed volumes per molecule” which are functions of pressure, temperature, and composition.
V.
CHROMATOGRAPHIC SYSTEMS WITH CHEMICAL REACTIONS
expression, a result equivalent to that observed by Taylor (779), Giddings (60, 67), and others. By suitable choice of experimental variables, it is presumably possible to maximize the contribution due to the rate process of interest. The perturbation method is thus a potential source of near-equilibrium reaction rate data. As yet, the authors are unaware of any such experiments.
General
The effect of reaction between species in a carrier or reaction with the stationary phase has been considered by a number of authors. I n particular, Giddings (60, 67) has given expressions for the change in H T U attributable to reactions with a number of different kinetic schemes. Klinkenberg (707) obtained an asyrnptotic solution for the peak resulting from an isomerization reaction occurring in a column assuming equilibrium adsorption of both isomers. The use of chromatographic effects to derive a reaction “beyond equilibrium” by separating products has been reported by several authors (726, 754, 778). local Equilibrium
The theory of local equilibrium chromatography was extended to include chemical reactions by Collins (23, 24) for a gas-solid system and Barrere (70, 7 7 ) for a gasliquid system. The number of peaks generated by a concentration perturbation was calculated for systems with multicomponent carrier fluid. The retention times of the various peaks were related to the stoichiometry of the reactions, the physical equilibrium relations for the components, and the chemical equilibrium equations obeyed. Most recently, the work of Deans, Horn, and Klauser (32) has extended the equilibrium theory to general two-phase systems. The use of retention times to obtain equilibrium data was discussed in all of these papers. A generalized retention theory applied to the study of complexing reactions has been reported by Purnell (752). Reaction Rate Studies in Reactive Systems
The works of Giddings (60, 67) and Klinkenberg (707) mentioned above gave specific cases in which peak spreading can be related to chemical reaction rate in a column. The merging of two peaks into a single dispersed peak as the reaction rate increases was noted in the latter work and also by Musser (739) who studied carbon-14 exchange between carbon monoxide and carbon dioxide on a water gas shift catalyst. The general theory of peak broadening by noninfinite reaction rates is discussed by Deans et ai. (32). An arbitrary equilibrium state in a multicomponent, multireaction system is perturbed to produce a set of peaks. Each peak has a distinct center velocity, an associated composition deviation, and a characteristic dispersion rate. The latter variable is related to the stoichiometry and equilibrium properties of the system, and to the nearequilibrium rates of all mass transfer processes and chemical reactions. Each rate process produces an additive term in the effective longitudinal dispersion
VI.
DIRECT MEASUREMENTS O F TRANSPORT COEFFICIENTS The realization that diffusion and transfer processes effect chromatographic peak shapes is quite old and is well documented in the literature. The basic paper of Taylor (779) gave the first quantitative explanation of effective longitudinal dispersion in terms of coupling between convection and lateral diffusion. The dispersion of a tracer pulse in a uniform capillary is governed by the composite relation
D,=Df-
R2U 2 48
D
(4)
which combines molecular and Taylor effects. This relation has been used by Giddings and Seager (62), Chang (79), and Hargrove and Sawyer (87) to measure binary diffusion coefficients for a number of dilute gas pairs. The additive nature of the contributions of various phenomena, seen in Equation 4, is apparently quite general. Giddings (59) extended this principle to include local mass transfer and adsorption rate effects in the usual chromatographic configurations. James, Giddings, and Eyring (94) have reported the measurement of accommodation coefficients for gas-liquid interfaces containing surfactant using an extension of this theory. The dispersion of a tracer pulse in a very general column flow has been discussed by Horn (97). Using a n extension of the moment method introduced by Aris (5)) Horn accounted for diffusion, mass transfer, and secondary flows in an arbitrarily complex column cross section. Here, as in the earlier work, each separate dispersing phenomenon produces a distinct term in an asymptotic dispersion coefficient such as given in Equation 4. Utilizing this feature to obtain a given transport coefficient from one of the terms is then a matter of experimental design. This procedure has evidently been confirmed only for molecular diffusion coefficients as noted above.
VII. SURFACE AREA AND CATALYST STUDIES A convenient and accurate method for the determination of surface areas of solids by a continuous flow technique was introduced by Nelsen and Eggertsen. Rapid extension of the method was carried out to improve the accuracy and range of applicability to solids with surface areas as low as 0.005 sq. m./gram. The surface areas of various chromatographic supports were measured and VOL. 5 9
NO. 1 0
OCTOBER 1 9 6 7
79
related to their differences in effectiveness of separation. Heats of adsorption for catalytic substances were measured u p to temperatures as high as 450° C. The chromatographic method averted the decomposition of the subject gas which would occur during slower static studies. A slug flow C O chemisorption method was developed for the determination of metal dispersion or specific metal surface area of multicomponent catalysts. (740)Nelsen and Eggertsen (1958) developed a rapid and accurate flow method for the determination of surface areas. The principle is based on adsorption of nitrogen by the solid from a fixed composition He,”% stream at liquid nitrogen temperature, followed by desorption upon removal of the liquid nitrogen coolant. The amount of nitrogen adsorbed at the corresponding relative pressure was determined from the peak eluted as a result of the desorption process The amount of nitrogen adsorbed for a monolayer coverage was determined from three such determinations at different Nz partial pressures and a BET plot. The surface area was calculated from the volume of nitrogen adsorbed for monolayer coverage, the sample weight, and the factor for the area covered by nitrogen per unit volume. Good agreement was obtained between conventional pressurevolume and chromatographic methods. Ways of improving the technique were suggested. The possibility of using the method to study adsorption rates was mentioned. (795) Wolf and Beyer (1959) extended the theory of Cremer and Prior (30) to derive a relation between the retention volume, the heat of adsorption, the surface of the adsorbent, and the carbon number in the case of paraffin hydrocarbons. ( 7 78) Lee and Stross (1959) introduced a method for the determination of surface area similar to the method of Nelsen and Eggertsen ( 140). (28) Cremer (1959) described the application of gas chromatography to determine the surface areas of adsorbents and catalysts. An equation relating the retention time to the “effective” surface area was derived. Chromatography was offered as a means of detecting the effect of decreased surface area on catalytic activity (25) Cremer (1959) described practical applications of GSC to the study of adsorbents and catalysts, namely the determination of: (1) the surface area of MgO prepared in different ways, and (2) the differences in the effective surface areas and the catalytic activities of fresh 80
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
and coked zinc-ammonium metavanadate catalyst from GSC measurements. (762) Roth and Ellwood (1959) made a number of modifications to the surface area measuring technique of Nelsen and Eggertsen (740) to improve the convenience and accuracy of the method. They prepared mixtures of helium and nitrogen for use as elution gases, used an improved scheme for ensuring constant flow, and made a calibration with each desorption step. (43) Ellis, Forrest, and Howe (1960) modified the surface area measurement technique of n’elsen and Eggertsen (740) to measure surface areas of materials as low as 0.005 sq. m./gram. Surface areas were measured on sands and oxides of uranium, mainly UOz, under varying degrees of fragmentation. (44) Ettre (1960) discussed a commercial apparatus for the determination of surface area based on the principle introduced by Nelsen and Eggertsen (140), further developed by Lee and Stross (778) and by the Perkin-Elmer Corp. Specific surface area measurements of both noncatalytic and catalytic adsorbents were reported. Column efficiency data and component resolution obtained with various columns were correlated with the surface area data for the solid support and the polarity of the compounds to be analyzed. (35) Derby and LaMont (1960) described refinements to the Nelsen and Eggertsen technique which make the procedure more feasible for determining the surface areas of uranium dioxide powders. Various methods of analyzing the data were discussed. (40)Eberly (1961) made high temperature adsorption studies of benzene on 13X molecular sieve, silica gel, alumina, calcined alumina, and 0.67, Pt on alumina. Conclusions were that the flow method was particularly useful for studying adsorption at high temperature conditions where static methods cannot be used because of long contact times leading to decomposition of the adsorbates. The benzene showed an irreversible adsorption on the platinum-alumina catalyst at high temperatures. (779) Leuteritz (1961) obtained the heats of adsorption of propane and butane from the retention voIumes of four ferric oxide catalysts with varying KzC03 contents. Surface areas were determined both by GSC and the BET methods and were found to agree. Small amounts of KzC03 (0.8 wt. yo) increased the surface area of the oxide, but larger amounts of KzC03 caused a
decrease in the surface area of the catalyst. (776) Stock (1964) discussed a method of determining surface areas of adsorbents similar to Nelsen and Eggertsen, but which through modification permits the determination of the surface area from a single elution experiment. The method had not yet been verified experimentally at the time of the publication. (47) Eberly and Kimberlin (1961) measured the adsorption of benzene and n-heptane on silica-alumina and molybdena-alumina catalyst at high temperatures by a “continuous flow injection technique.” All of the catalysts studied to temperatures as high as 427’ C. showed a reversible adsorption of benzene. (29) Cremer and Huber (1961) used high temperature GSC to measure adsorption isotherms of benzene and hexane on silica gel, alumina gel, and a SiOz-AlZ03 cracking catalyst in the temperature range from 300’ to 500’ C. Heats of adsorption data were calculated from the GSC data. The upper temperature limitations of the study appeared to be the stability of the solute and the adsorbent. (73)Gruber (1962) applied a perturbation method to determine the metal dispersion or specific metal surface area of multicomponent catalysts whose metal area corresponded to about 0.1 to 1% of the total surface area. The disappearance of the CO from the helium stream was picked up by a thermal conductivity detector and was equated to the irreversible adsorption of CO. The method was applied to platinum-on-alumina reforming catalyst to study the decrease in platinum dispersion due to sintering at high temperatures. ( 7 4 7 ) Oldenkamp and Houghton (1963) restudied by elution GSC isobutylene-activated alumina, a system for which the authors had previously studied the static adsorption characteristics. The shapes of the elution peaks were found to agree qualitatively with the nonlinear shape of the adsorption isotherm. (768) Skornik, Steinberg, and Stone (1963) determined the heat of adsorption of carbon monoxide on doped nickel oxide by perturbation GSC. The values of the heats of adsorption in general were found to be lower than those determined by conventional calorimetric method. The reason for the lower values was attributed to the irreversible adsorption of part of the carbon monoxide on the nickel oxide. (769) Smolkova, Grubner, and Feltl (1965) described a GSC method for the determination of specific surface areas of low surface area (0.01 to 0.05 sq. m./gram) substances using organic vapors. Measurements were conducted using benzene, n-hexane, and n-heptane on powdered alumina, magnesium oxide, titanium dioxide, and zinc oxide. Measurements were carried out into the “catalytic regions.” The GSC method can be used where very low surface areas are involved. (705) Kiselev, Nikitin, Petrova, and Txan’ (1965) determined adsorption and surface area characteristics of magnesium oxide using GSC. The dependence of the Surface area on the curing rate and time was studied. Derived heats of adsorption of several hydrocarbons were found to agree with static calorimetric values.
M g O with a small surface area was found to be poisoned by the adsorption of water.
REFERENCES (1) Adlard E. R K a h n M . A Whitman B. T., “Gas Chromatography,” R . P . Scott, ed:, p. 2nge, R. L. M., Htorhiirrn. J . 35, 1358 (1941). (129) Martin, R . L., Anal. Chem. 33, 347 (1961). (130) Ibzd., 35, 116 (1963).
82
INDUSTRIAL AND ENGINEERING C H E M I S T R Y
(131) Martire, D. E., Ibid., 38, 244 (1966). (132) Martire, D. E., paper presented at the 6th Intl. Symposium on Gas Chromatography and Associated Techniques, Inat. Perrol., Rome, Sepr. 20-23, 1966. (133) Marrire, D . E., Pecsok, R. L., Purnell, J. H., N d u w 203, 1279 (1964). (134) Martire, D. E., Pollara, L. Z . , J . Chem. Eng. D n l a 10, 40 (1965). (135) Martire, D. E., Pollara, L. Z., Funke, P. T . , paper presented a t Div. Anal. Chem., 152nd ACS hleeting, New York, Sept. 9-13, 1963. (136) Masukawa, S., Alyea, J., Kobayashi R . “ T h e Determination of the Free Gas Volume V in Gas Chrornatogra;hic’ Columns and Some Consequent Thermodyna;nicg~easurements,”paper presented at 153rd ACS hleeting, Miami Beach, April 9-14, 1967. (137) Mortensen, E. M., Eyring, H . , J . Phys. Chem. 64, 433 (1960). (138) Moshier R . W. Gere, D. R., Div. Anal. Chem., 152nd ACS Meeting, Piew York, Sept. i2-15, i966. (139) Musser, G . S., Ph.D. thesis, Rice University, Houston, 1965. (140) Pielsen, F. M., Eggertsen, F. T., .4nnl. Chem. 30, 1387 (1958). (141) Oldenkamp, R . D., Houghton, G., J . Phys. Chem. 67, 597 (1963). (142) Parcher, J. F., Urone, P., Nature 211 (5049), 628 (Aug. 6, 1966). (143) Pecsar, R. E., Martin, J. J., Anal. Chem. 38, 1661 (1966). (144) Pecsok, R. L Gump, B. H., paper presented a t Div. Anal. Chem., 152nd ACS Meeting, PiLC York, Sept. 12-15, 1966. (145) Peterson, D . L., Helfferich, F., J . Phqs. Chem. 69, 1283 (1965). (146) Peterson, D. L., Helfferich, F., Carr, R . J., A.I.Ch.E. J . 12, 903 (1966). (147) Pierotti, G. J., Deal, C. H., Derr, E. L., Porter, P. E., J . Am. Chem. Soc. 7 8 , 2989 (1956). (148) Pollard, F. H., Hardy, C . J., Anal. C h m Acta 16, 135 (1957). (149) Porter, P. E., Deal, C. H., Srross, F. H., J . A m . Chem. Sot. 78, 2999 (1956). (150) Porter, R. S., Johnson, J. F., IND.ENG.CHEM.52, 691 (1960). (151) Preston, S. T., Katural Gas Assn. Proc., 38th Annual Convention, Dallas, p . 33 (1959). (152) Purnrll, J. H., 6th Intl. Symp. on Gas Chromatography, Rome, Sepr. 20-23, 1966. (153) Pyke, B. H., Swinbourne.. E . S . .. durlralian J . Chem. 12. 104 11959). (154) Raginskii, S. Z . , Yanovski, >I I., . Gaziev, G . A , , Proc. Acad. Sci. U S S R , Phys. Chem. Sec. 140, 771-3 (1961). (155) Raginskii, S . Z. et ai.! Acad. of S a . (C’SSR) Proc. Phys. Chem. Sect. 131, 717 (1960). . , (156) Rangel, Enrique T., “Analysis of Low Temperature Chromatographic Separation of Methane-Propane .Mixtures with n-Decane on Celite,” Sf.S.thesis, Rice University, Houstdn, 1956. (157) Ratkovics, F., Acta Chim. 49, 71 (1966). (158) Ratkorics, F., M u g y . Kem. Folyoirnt 72, 279 (1966). (159) Ray, N. H., J . Appl. Chem. (London) 4, 21, 82 (1954). (160) Rock, H., Chem. Zng. Tech. 28, 489 (1956). (161 j Rose, H . C., Stern, R. L., Karger, B. L., Anal. Chem. 38,469 (1966). (162) Roth, J. F., Ellwood, R. J., Anal. Chem. 31, 1738 (1959). (163) Schay, G., Fejes, I . , Halasz, I., Kiraly, J., Acta Chim. Acad. Sci. Hung. 11, 381 (1957); Ibid., 14, 439 (1958). (164) Schay, G., SzPkeiey, G., Ibid., 5 , 167 (1954). (165) Schay, G., SzCkeley, G., Szigetvary, G., Ibid., 12, 309 (1957). (166) Scott, C. G., N o l u r e 193, 159 (Jan. 13, 1962). A,, Separafion 30. 1, 459 (167) Sie, S. T . , van Beersum, W., Rijnders, G . i?J, (1 966). (168) Skornik, S., Steinberg, M., Stone, P. S., Israel J . Chem. 1 (3a), 320 pp. (1963). (169) Smolkova, E., Grubner, O., Feltl, L., “Gas Chromatographie 1965,” pp. 509-516, East Germany Acad. of Sci., Berlin, 1965. (170) Spannheimer, H., Knozinger, H., Z..valurforsch. 21A, 256 (1966). I
.
.
(172) Stalkup, F. I.,Deans, H . A , , A.I.Ch.E.J. 9, 106 (1963). (173) Stalkup, F. I., Kobayashi, R., J . Chem. E n g . Data 8, 564 (1963). (174) Stalkup, F. I., Kobayashi, R., paper presented at A.1.Ch.E. Meeting, Washington, D.C., December 1960. (175) Stalkup, F. I.: Kobayashi, R., A.I.Ch.E. J . 9, 121 (1963). (176) Stock, R., Anal. Chem. 33, 966 (1961). (177) Takamiya, N.,Kojima, J., Murai, S., Kogjo K a g a k u Zarshr 6 2 , 1371 (1959). (178) Tarnaru, K., ‘Vatu72 183 (4657), 319 (Jan. 31, 1959). (179) Taylor, G . I., Proc. Roy. Soc. (London) A219, 186 (1953); Ibid., A223, 446; A225, 473 (1954). (180) Tiselius, A , , Arkiu. Kemi ,tlzneral. Geol. 14B (22) (1940); Ibid., 16A (18) (1943). (181) Tivinl,F “Thermodynamics of a n Inorganic System via Gas-Liquid Chroma1964. toeraohv. ,, $h.D. thesis, University of Illinois, Urbana,. August (182) T6th, J., Graf, L., Acta Chim. Acad. Sei. Hung. 22, 331 (1960); M o g y . K e m . Foljoirat 66, 123 (1960). (183) Tswett,M., Ber. Deut. Botan. Gel. 24, 316, 384 (1906). (184) Turner, Pi. C., N a t l . Petrol. News 35, R-234 (1943). (185) Urone, P., Parcher, J. F., Greinetz, R., Baylor, E. N., paper presented a t 19th Annual ACS Summer Symp. on Anal. Tech., Separation Techniques, Univ. of Alberta (Abstr. of papers, p. 5 ) , June 22-24, 1966. (186) Van Deemter, J. J., Zuiderweg, F . J., Klinkenberg, A., Chem. Etig. Sci. 5 , 271 (1956). (187) Van Horn, L. D., Kobayashi, R., “Vapor-Liquid Equilibria of Light Hydrocarbons a i Low Temperatures and Elevated Pressures in Hydrocarbon Solvents: T h e Methane-Propane-n-Heptane, the Methane-Ethane-n-Heptane, and the Methane-Propane-Toluene Systems,” J . Chem. En
