In the earlier stages of this work, we used uncoated capillary traps with good results. Because of theoretical considerations-we supposed that the coating would give a safer retention and that it would diminish the risk of decomposition of the sample-we changed to coated traps, and all the reported work was done with coated traps. It appears, however, that uncoated traps might be preferable in many instances. (At the time of printing, we had made experiments with a three-coiled uncoated trap which showed that a t least 320 pg of a mixture of different tetrachloroethanes can be trapped quantitatively. No experiments have yet been made to evaluate the peak broadening.) The precolumn was expected to become contaminated and spoiled very soon. I t was therefore designed to be simple and easily exchangeable. However, after three months' use, clean chromatograms were still obtained, and no serious interferences from contaminations were stated, except that the DDT peaks from standard test solutions became somewhat smaller and the DDE peaks somewhat larger. This indicated decomposition of DDT in the injection port. Large deposits from extracts were found there when the column was taken out, but the column filling was still in good condition. The precolumn was therefore redesigned to incorporate an exchangeable glass liner as shown in Figure 3, so that deposits easily can be removed without removal of the column. The described precolumn-capillary column system can obviously be modified in many ways. Right now we are assembling an arrangement in which the precolumn is not connected to detector D1 but via a T-tube and an an-off
topcock to detector D2. Since this line is used only to blow off the solvent and low boiling compounds and to determine the retention times of the analytes in the precolumn, losses of analyte can be tolerated there. The arrangement makes it possible to use an ordinary one-channel gas chromatograph and also to use other types of detectors. The handling of the equipment can undoubtedly be simplified considerably by the use of a multichannel stopcock instead of several two-way and three-way stopcocks, or by the use of automatic control equipment as described by Schomburg and Weeke (2).
ACKNOWLEDGMENT The authors are indebted to Nils Larsson for valuable glass blowing designs. LITERATURE CITED W. J. Kirsten and P. E. Mattsson, Anal. Lett., 4, 235 (1971). G. Schomburg and F. Weeke, "Gas Chromatography 1972", Applied Science Ltd., Barking, Essex, England, 1973, p 285. (3) K. Grob and J. J. Jaeggi, Chromtographia, 5, 382 (1972). (4) A. L. German and E. C. Horning, Anal. Lett., 5, 619 (1972). (5) D. R. Deans, Chromatographia, 1-2, 18 (1968). (6)E. C. Hornlng, C. D. Pfaffenberger, and A. C. Moffat, Anal. Chem., 44, 2
.- .
11973\ I _,.
(7) D. C. Fenimore, R . R . Freeman, and P. R. Loy, Anal. Chem., 45, 2331 (1973). ( 8 ) D. L. Buchanan and A. Nakao. J. Am. Chem. Soc., 74, 2389 (1952).
RECEIVEDfor review March 17, 1975. Accepted June 30, 1975. The work was sponsored by the Research Committee of the National Swedish Environment Protection Board.
Kinetic Measurements by Reactions during the Overlap of Elution Zones with Different Elution Speed in GasChromatographic Columns Paul Schulz Centrul de Chimie Timisoara, Romania
According to a classical method of kinetic measurement on liquid phase reactions by gas-chromatographic procedures, the lower volatility reaction partner Is previously dissolved in an adequate liquid phase. The volatile reaction partner is then Injected into a gas-chromatographic column containing this liquid phase. Using a somewhat different method, which may be called a "double-pulse technique", both reagents, which must have different elution characteristics and must react irreversibly, are injected consecutively into a gaschromatographic column containing an adequate liquid phase. The contact occurs by overlap of the elution zones in the column. An attempt is made to interpret the resulting conversion in the special case of second-order reactions. Kinetic data obtained with the esterification of mxyienoi with acetic anhydride are in fair agreement with values obtained by a classical method. Perspectives and limitations of this procedure are discussed.
Several techniques were described for catalytic and noncatalytic reactions in gas-chromatographic columns. Some procedures allow the investigation of liquid phase reactions
between a nonvolatile component dissolved in the liquid phase of the column and a volatile one injected and eluted through it. A number of irreversible reactions, e.g., the Diels-Alder reaction ( I , Z ) , the oxidation of trialkylphosphites (31, esterifications ( 4 ) , etc. were investigated using this technique. Because of the special requirements on the elution properties of the reagents involved (e.g., the magnitude of their reaction rate), this procedure is not widely applicable and is restricted to several special cases. It would be applicable for relatively fast reactions except for the limited relaxation time of mass transfer between phases in the gas-chromatographic column. These times are usually from to 1 second ( 5 ) .Under satisfactory conditions, reactions with half-times of about 10 seconds could be investigated without mass transfer perturbations ( I ) . A different technique to use for the reacting components to make contact in the chromatographic column is to inject the slowly eluting components first, and then after an adequate time, the components that elute faster. Contact and reaction occurs by the overlap of the eluting zones. Reaction should be fast enough to give measurable conversion, but should not approach diffusion control.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
1979
I
A + B-C+
--dQA dt
...
(10)
which may be written:
Flgure 1. Two-phase reaction system
dx
X
Figure 2. Peak overlap in the gas-chromatographic column
In our consideration of possible anomalies, the effects of liquid phase surface adsorption, the effect of the support, partition anomalies in the contact area, etc. were neglected, since the effects are small in special, well selected conditions. These conditions are carefully inactivated support material with high liquid phase content (6, 71, nonpolar liquid phases (6-8), and small sample amounts.
TWO-PHASE REACTOR In the reactor shown in Figure 1, an irreversible secondorder reaction takes place, the reaction partners being partitioned between phases M and N. The reaction follows second-order kinetics in both of the phases: A + B -C + ... (1) The reaction must be sufficiently slow for a permanent partition equilibrium of A and B between the phases M and N. QAM + QAN = QA
(2)
QBM-t QBN = QB
(3)
(5)
Using Equations 3 and 4,Equation 6 may be written:
Q dt Equation 11 describes simultaneously both second-order reactions in the phases M and N by a single, formal secondorder relation:
where V* is the virtual reaction volume: V* =
I(% +
VM)(2
+
VI>
(13)
In Equations 2 through 13, QA, QAM,and QAN are the total amounts (in moles) of component A, A in phase M, and A in phase N; QB, QBM, and QBN are the total amounts of component B, B in phase M, and B in phase N; K A and K B are the partition constants of A and B between the phases M and N; VM and VN are the volumes (in liters) of phase M and N; k M and k~ are the second-order rate constants (in liters per mole per second) for the reactions in phases M and N; CA* and CB* are the virtual concentrations of A and B (in moles per liter); V* is the virtual reaction volume; and k * is the virtual universal second-order rate constant.
REACTION DURING PEAK OVERLAP I N A GAS-CHROMATOGRAPHIC COLUMN Consider Figure 2. The more volatile reaction partner B is injected after the less volatile A into the column. Peak A is considered to be immobile, and peak B is moving with the relative elution speed. If an infinitesimal element of the partition zone of B, dx, crosses peak A and the relative elution speed and the peak shapes are constant during the contact, then according to Equations 12 and 14 dx (14) d t = hv,
-lcA 3
=
k*
cB*z*dx
(15)
AD
By addition of Equations 6 and 8, we obtain:
where 1* is the virtual reaction volume per column length unit.
(16) Using Equations 2, 3, 4, and 5 , we obtain by substitution in Equation 9:
Considering further:
we obtain Equation 18: 1080
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
A
and after integration:
-% eAvel
AQ
(19) where, according to Equation 13: l* =
I(& K.4
+
l)(&
+
1)
Figure 3. Graph of Equation 21
(20)
In Equations 14 through 20, Au, is the relative elution speed of the peaks of A and B; CA,* and CB,* are the initial local values of the concentrations of A and B in their repartition zones; 1* is the virtual reaction volume per column length unit; L is the column length; g is the gaseous phase volume per column unit length; 1 is the liquid phase volume per column length unit; QA, and QB, are the total injected amounts of A and B; and AQ is the amount converted by the reaction. Equation 19 describes the conversion of A and B by the reaction given in Equation 1. The partial reactions in the liquid and in the gas phase are both second-order reactions. The conversion depends on the relative elution speed during contact, the virtual reaction volume, the virtual secondorder rate constant k*, and the amounts of A and B involved. According to Equation 19, the conversion must not depend on the position of the samples relative to each other inside the column. Experimentally, we could confirm that, in the cases studied, no significant changes in the values obtained took place when the reaction was performed in different column zones and with varying peak shapes. This is so since broadening of the sample zones near the column exit reduces the concentrations of the reaction partners, but simultaneously increases the time that they are in contact. Because the supposed reaction is irreversible, no influence of the reaction product should be expected. If Equation 19 is rewritten as Equation 21 (21) where the parameter x' denotes the rate constant k, and the residual terms of the exponents are represented by U , V, and W. Suppose that U II' 1 W and W = 0, the curve does not intersect the abscissa (curve A in Figure 3). The magnitude of W reflects the amount converted ( W = AQ/Au,l*). If W = 0, then AQ = 0 , and no reaction occurs. If V > W > 0, the curve (B in Figure 3) intersects the abscissa a t a finite value of x . Conversion is partial. If V = W > 0, the intersection point of the curve (C in Figure 3) approaches an infinite value of x . Therefore, the reaction rate is virtually infinite and the conversion is total.
RELATIVE ELUTION SPEED I N THE MOMENT OF PEAK MAXIMA OVERLAP Considering an ideal carrier gas, the linear gas flow speed in the gas-chromatographic column will be:
A v , = v R F , - vRF, = v A R F
(24)
and thus, using Equations 22 and 23, after integration: At?, = vdoARF (25) JPo2 - X (P,2 - P f 2 ) The elution time of a sample with a given RF value from the column head to a given elution distance x will be: L dx - 2 = - 5 V.&,RF(P,~- pf2) pO3-
{
[P,i -;(Po2
-
p?)]
'I2}
and the elution distance: x =
Po2
-
Pf
2{Po2-
3 "do(Po2 - P f 2 ) R Ft ] 2 ' 3 } (27) L Overlap of the peak shaped maxima of the elution zones occurs when:
[ p O 3- 3
x~(t= ) xA(t
+
At)
Po2
-
Pf
and from Equations 25 and 27, the elution speed difference:
2L Po2 ARF Substituting RE = 1, x = L, and t = t , into Equation 27, where t , is the elution time of the air peak, we obtain
(31) Thus, Equation 30 becomes: 2
L 1 -
- ARF3 tA 1
-
(Pf/P0Y (Pf/PO)?
A V ~ ( A= ~)
Using the RF values of the involved reaction partners, the relative elution speed may be written as
(28)
Inserting RFA and RFB into Equation 27 and combining with Equations 26 and 28, we obtain the elution distance a t the moment of overlap as a function of the injection time interval: L x(At) = 2{P0 -
(22) (23)
(26)
3 1 - - At R F A R F 9 1 - ( p f / p o ) 3 ] t, ARF
(32)
Equation 32 gives the elution speed difference a t the moment of overlap of the peak maxima in the column as a
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
1981
function of the injection time difference of the two reaction partners. If x = L is inserted into Equation 29, it will be shown that overlap will occur at the column exit, and At will have the maximum possible value. No contact will be possible.
Therefore, compound B must be injected at At < At,,,. Because of the simplicity in determining At,,,, it is best to use an injection time interval of At,,,/2. Then, Equation 32 becomes:
-t
-
-1
Flgure 4. Experimental results obtained by the gas-chromatographic
(0-0)and by a classical (0- -0) procedure
In Equations 22-34: u is the linear speed of the carrier gas in the column; u, is the linear speed of the carrier gas at the column entrance; R F a and R F B are the RF values of the reaction partners; ARF is the difference of the RF values of the reaction partners; p is the pressure at a given column distance x ; p , and pf are the pressures a t the column entrance and exit; t is the elution time of a component from the column entrance to a given distance x ; At is the injection time difference of the reactants; and t , is the elution time of the air peak.
DISCUSSION Under the proper gas-chromatographic conditions such as a carefully inactivated support; a nonpolar, low-viscosity liquid phase; high liquid-phase content; sufficiently broadened elution zones of the reaction partners in the contact area; and adequate elution properties of the reaction partners, anomalies caused by the support, liquid-phase surface adsorption, and wall-catalyzed gas-phase reactions can be generally minimized. Working with small samples, local concentrations of the reaction partners in their elution zones that are too high must be avoided in order to prevent partition anomalies in the contact area. The exponential term containing the second-order rate constant k* in Equation 19 may be written, using Equation 11, as
Substituting the RF values:
In Equation 37, the gas-phase reaction was neglected for the reasons stated above. However, this relation assumes that only part of the reaction partners is dissolved in the liquid phase. If one of the compounds is very volatile, the correction may become significant. When one of the reaction partners is in excess, e.g., QA, >> QB,, the reaction becomes pseudo-first-order. Because of the small values of the exponents, Equation 19 may be written: * QAo eavel + 1 +- k*
where QBf = QB, reaction. Thus:
- AQ and is the final value of QB after (39)
Under the same conditions that make Equation 37 valid, Equation 39 becomes:
An equation similar to 40 was used by other authors in the classical procedure of kinetic measurements of liquid phase reactions in gas-chromatographic columns, e.g. ( I ) . where kl is the second-order rate constant for the liquidphase reaction and k, is the second-order rate constant for the gas-phase reaction. Since the purpose of these investigations is the determination of reaction rates in the liquid phase, particular conditions must be found in which the gas-phase reaction does not significantly contribute to the total conversion. Because of the often complicated kinetics in the gas phase, an accurate treatment of the gas-phase reaction would be difficult. If the gas-phase reaction is neglected, the conversion will reflect the liquid-phase reaction. Usually, the value of at least one of the two partition constants in Equation 35 is high. If the gas-phase reaction is not too fast compared to the liquid-phase reaction and the liquid-phase volume per column length unit is high, the term containing k , may become negligible compared to the term kl. Therefore
1982
EXPERIMENTAL VERIFICATION As an example, the reaction of acetic anhydride with m xylenol (l-hydroxy-3,5-dimethylbenzene) will be described. A 1-meter glass column, with 5-millimeter inner diameter, filled with 15% Squalane on Chromosorb W silanized (60-80 mesh) was used. Chemicals were purchased from Carlo Erba, Italy. The carrier gas was hydrogen. Catharometric detection was used. The gas chromatograph was a “Fractovap 2400 V” from Carlo Erba. Acetic anhydride and m-xylenol were pro analyst. Determinations were performed a t 120, 130, and 140 OC, and a t three different carrier gas flow rates (15, 30, and 60 cm3/ minute) at each temperature. In each case, the RF values of the reaction partners and the retention time of the air peak were determined precisely. At,,, was computed according to Equation 33, and the acetic anhydride was injected a t At,,,/2 after the m-xylenol was injected. Sample amounts between 1 X 10-5 and 5 X 10-5 mol were injected. Esterifications with acetic anhydride in nonpolar media are generally second-order reactions (9). Because of the
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
slow gas-phase reaction (9) and the reasons stated above, the decrease of the m-xylenol peak was attributed exclusively to the liquid phase reaction. Ave was computed according to Equation 34. By an iterative computer program, kl was determined according to Equations 19 and 37. Figure 4 shows the experimental results obtained. The agreement with measurements performed using a classical method, a stirred micro-reactor where the reaction took place in Squalane a t 80, 90, and 100 OC, is fair. The observed difference could be explained tentatively by the contribution of the gas-phase reaction to the overall conversion.
baday of the Centre of Chemistry, Timisoara, are acknowledged. LITERATURE CITED
ACKNOWLEDGMENT
(1) E. Gil-Av and Y. Herzberg-Minzly, Proc. Chem. SOC.,London, 316 (1961). (2)E. Gii-Av. J. Chromatogr., 13, l(1964). (3) C. E. Doring, W. Pehle, and G. Schmid, Gaschromatographie 1968,Vortrage des VI. Symposiums uber Gaschromatographie in Berlin, May 1968. Preprints, p 143. (4)V. G. Berezkin, V. S. Kruglikova, and V. E. Shiryaeva, Teor. Eksp. Khlm., 3, 553 (1967). (5)J. C. Giddings and K. L. Maiiik, lnd. Eng. Chem., 59, 19 (1967). (6)R. L. Martin, Anal. Chem., 33, 347 (1961). (7)R. L. Martin, Anal. Chem., 35, 116 (1963). (8) R. L. Pecsok, A. de Yliana, and A. Abdul-Karim, Anal. Chem., 36, 452 (1964). (9)E. A. Moelwyn-Hughes, "Physical Chemistry," 2nd ed., Pergamon Press, Oxford, New York, London, Paris, 1961,p 1249.
Helpful discussions with Helmut Ludescher of the Section of Mathematics of the Academy and with Zoltan Sza-
RECEIVEDfor review February 3, 1975. Accepted May 20, 1975.
Dielectric Constant Detector for Liquid Chromatography William F. Erbelding lndiana University-Purdue University at Fort Wayne, 2 10 1 Coliseum Blvd. East,
A device which senses changes In dielectric constant of the effluent from a liquid chromatographlc column has been used successfully to record chromatograms. The detector cell is a capacitor whose capacltance depends on the dielectric constant of the liquid between Its electrodes. A simple electronic circuit uslng five operational amplifiers converts the dlelectric constant changes to direct current signals for recordlng the chromatogram. Although not appropriate for use In hlgh performance liquld chromatography because of the large holdup volume of the cell and Its lack of provision for temperature stabilization, it is able to detect solutes in the range of 1 mglml. It Is demonstrated uslng several different chromatographic systems and Its behavior is compared with the expected behavior of the refractlve index and the UV absorption detectors.
Little information is available in chemical literature about the use of dielectric properties of eluates as a detection system for liquid chromatography. Laskowski and Putscher ( I ) have shown that the dielectric constants of certain petroleum fractions increase with oxygenation and such changes can be monitored with a device which is essentially a capacitor in a tuned amplifier circuit. Their instrument did not record a chromatogram. In 1958, Grant ( 2 ) , using a cell as a capacitor through which column effluent passed, electronically followed and recorded the change in dielectric constant as amino acids were eluted with n-propanol-water eluent from a column of powdered cellulose. Vespalec and Hana ( 3 ) ,using a specially designed capacitor cell in an electronic circuit which contained two oscillators and frequency meter, established that the sensitivity of this detection system can exceed the sensitivity of the refractive index detector if operating conditions are carefully controlled. These authors did not use their detector in conjunction with a chromatographic column. Many books and authors briefly mention dielectric constant as a basis for a feasible detection system (4, 5 ) , without citing references to published information. A conclusion drawn by some authors (6) is that a dielectric constant
Fort Wayne, Ind. 46805
detector would not be expected to have any advantages over the refractometric detector currently in wide use. A good dielectric constant detector is fundamentally related to a refractive index detector. For a substance without a permanent dipole moment, the dielectric constant t is related to n, the refractive index, through the Maxwell relationship, = n2, where n is measured in long wavelength (for example, infrared) light. For molecules with permanent dipoles, the dielectric constant is significantly greater than the square of the refractive index. It follows that if a change in 6 can be measured with the same precision that a change in n can be, then a dielectric constant detector can be more sensitive than a refractive index detector. Commercially available differential refractive index detectors are capable of sensing changes in refractive index down to 10-7 unit corresponding to a detection limit for many substances of 1 pg/ml (7). If the relative error in determining dielectric constant can be as low as as has been reported ( B ) , a reasonable estimate of sensitivity of a dielectric constant detector would also be in the range of 1 pg/ml. To realize these detection limits, however, careful thermostating is required for both systems. Because dielectric constant is an electrical property, changes in this property can be detected by appropriate electronic circuitry. Such circuits have been described ( I , 2). Almost always, a t least part of the circuit is an electronic oscillator. The capacitor cell, in which the eluate from the column is the medium separating the plates, may or may not be part of this oscillator circuit.
EXPERIMENTAL Reagents. Benzene and a commercial mixture of hexanes were used as single component eluents. Prior to use, these were passed through activated silica gel. Dichloromethane when used with commercial hexane as part of a binary eluent was not pretreated in any way. Chromatographic adsorbents were Davison Code 12 silica gel, 28-200 mesh, activated, and J. T. Baker aluminum oxide, neutral (for chromatography). The aluminum oxide was heated a t 400 'C for 16 hours and deactivated by adding appropriate amounts of water. Columns were packed under solvent in a buret of about 25-ml capacity. No attempt was made to equilibrate the water content of the eluent with the water content of the adsorbent.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
1983
