t h a t pressure change and temperature effects exactly cancel each other: j X T/Q = 1
where j is the James and Martin correction factor. If pi and PO are inlet and outlet pressures, respectively, p i / p o = b, and =
2= dT
3 .__ (b2 - 1) 2 (b3 - 1) 3 ib
++12)1 2
2Q b(b
I n other words, the variable, b, must be controlled along a line whose slope is described b y the above equation. This line is not straight, but is almost so. KOattempts have been made to operate in this manner, although the control problem does not appear to be especially difficult. K h e n programmed runs can be made in this way, i t will be possible to achieve the simplification suggested by Equation 5 . It may he that the use of Equation 5 will provide a method of predicting emergence temperatures which is superior to that described here. Further work will ckcide this point. Method of Prediction of Emergence Temperature. A brief outline of t h e method was given previously. It will be described in more detail in t h e following paragraphs. The quantity a for a given peak can be found by Equation 4,(rearranged) : a = -aB 8 ZL
Here, everything is known except a. The problem is to find T,. the peak temperature, from a. This is done by means of a chart
of log us. ( $ I - & ) , a n example of which is shown in Figure 4. Values of a t suitable intervals of and 62)are shown in Table IV. These numbers were computed as previously explained. They have been rounded from values accurate in the sixth significant figure, so t h a t the maximum error in the numbers given is one part in 2000. This is considerably greater accuracy than can be made use of here. It will be observed (Figure 4) t h a t the linear distance between two given lines of constant $1 is the same for any value of ($1- $2). Also, the distance between lines of constant $1 changes very slightly as changes. This means that interpolation between these lines is practically linear. For example, if linear interpolation is used for a point halfway between two lines, the error is about one part in 200. -4step-ise procedure for this calculation is given below. It is assumed that 0 and B have already been determined from two or more isothermal runs. 1. Calculate 0
(+
3
= -
2. Find$ll+l = @ / A ) 3. Refer to the chart and find a. Move along horizontally to a point representing $1, bet-xeen two chart lines of constant (integral) $1. .4t this point, which satisfies both + and o1, read off ($1
- 93).
Example: $1 = 9.31 + = 1.67 X 10-6 Distance between ($1 = 9.0) and ($1 = 10.0) is67.5mm. 0.31 X 67.5 = 21.0mm. At a point 21 mm. down from $1 = 9.0, find a. This defines one and only one point on - $2) = the chart. This point lies on 0.88. 4.
From
($1
- +2), find $2.
$2, find T,(T, = &/e). 6. From T,, find t,, the time
5. From
[t, =
( T , - A ) / a ] ,if t, is desired rather than T,.
If it is desired t o use the internal standard technique, a value of which is computed from e, B, A , and T , only can be obtained by reversing the calculation procedure [Le., start with ($1-$2)]. This value of can then be used to compute a n effective a/u. Thus it is clear t h a t the method requires only the most elementary arithmetic operations, in connection with the chart. LITERATURE CITED
(1) Ambrose, D., Keulemans, A. I. SI., Purnell, J. R., , ~ N A L . CHEM.30, 1582 ( I 958). (2) “Chromatographic Data,” J . Chromatog., 2 , D33-L)45 (1959). (3) Dal Nogare, S., A s . 4 ~ . CHEW 32,
1F)R (1960). (4) Dal‘Nogare, S., Harden, J. D., l b i d . , 31,1829 (1959). ( 5 ) Dal Xogare, S., Langlois, W. E., Ibid., 32,767 (1960). (6) Giddings, J C., J . Chromatog. 4, 11 (1960). ( 7 ) Habgood, H. LY., Harris, W. E., A r a ~ CHEM. . 32, 450 (1960). (8) Hastings, C., Hayward, J. T., Wong, J. P., “Amroximations for Digital Comouters.”‘ Princeton Cniv. press.. 1955: (9) James. James, A. T.. T., Martin. Martin, -4.J. P.. P., Biochem. J :. 50, 679 (1982j. (1982). (10) Porter, P. E., Deal, C. H., Stross, F. H., J . Am. Chem. SOC.78, 2999 (1956). (11) “Sfpe, Cosine, and Exponential Functions, Federal Works Agency, W.P.A. Sponsor: Satl. Bur. Standards, recent edition, Government Printing Office, Washington, D. C. \
,
RECEIVEDfor review hugust 30, 1960. Accepted January 30, 1961. Division of Analytical Chemistry, 138th Meeting, ACS, S e w York, X. Y., September 1960.
A Vapor Detector Based on Changes in Dielectric Constant J. D. WINEFORDNER, D. STEINBRECHER, and W. E. LEAR University of Florida, Gainesville, Fla.
b A sensitive stable vapor detector based on response to changes in dielectric constant i s described. This detector consists of a variable capacitor mounted in a special cell which allows gas to flow between its plates. The capacitor i s part of the resonant circuit of a Clapp oscillator, the output of which i s beat against that of a reference oscillator. It i s shown theoretically and verified experimentally that if the difference frequency between oscillators i s adjusted to zero with a pure carrier
gas flowing through the cell, the presence of an impurity vapor in the cell produces a difference frequency which i s a linear function of the amount of an organic liquid introduced into the cell via the carrier gas. Experimental results show that the response of the detector i s extremely rapid and i s nearly insensitive to high carrier gas flow rates and variations in flow rate. It should be possible to use this detector for monitoring flow streams, particularly as applied to gas chromatogra phy.
T
describes a vapor detector which is sensitive to changes in dielectric constant. The detector consists of a special cell constructed to allow gas flow betn-een the plates of a capacitor m-hich is part of the tank circuit of a 70 mc. per second Clapp oscillator. The output of this oscillator is beat against that of a reference oscillator and the difference frequency is a direct-reading determined by frequency meter. When the difference frequency is adjusted t o zero with a pure carrier gas flowing through the HIS PAPER
VOL 33, NO. 4, APRIL 1961
e
515
cell, it is found that the introduction of a n impurity vapor results in a difference frequency which is directly proportional to the amount of an organic liquid introduced into the cell via a n injection port in the carrier gas flow stream. Oscillator circuits have recently been used by Chien (3) and by Gauss and Gillman (5) for the determination of dielectric constants of pure gases. The gas-tight brass cell used in the present work is similar to that described by the latter authors, and the oscillator and direct-reading frequency meter circuits are essentially the same as those used by Blaedel and hIalmstadt (1, 8) in their work on high frequency titrations. Griffiths (6) suggested that a dielectric detector is feasible for gas chromatographi-. The first operative detector using this principle was described briefly by Turner (IO). His equipment, while requiring fewer electronic components, is inherently less sensitive than that to be described here. Turner gives no theoretical treatment of the method, and the only experimental results shon n are threqhold sensitivities for acetone and diethyl ether. PRINCIPLES OF
METHOD
Mixer
4ail-, 01 ~
111
4mV0pZ Kz = 3kM
T
absolute temperature k Boltzmann constant N o = Avogadro's number p = density of gas d l = molecular weight of gas cy = polarizability of gas p = dipole moment of gas = =
Consider t v o oscillators 0 and 0, and a mixer circuit M as shown in Figure 1, u-here 0 is a reference os,illator of adjustable but known frequency fo, and 0. is the sample oscillator of frequency fo. n hich depends upon the dielectric constant of the gas flom-ing between the plates of capacitor C,. The difference frequency, F d , between oscillator 0 and 0, is then given by
where D is a constant dependent on the circuit components of the sample oscillator but independent of C,. If C, is the capacitance of C, when in a vacuum, then, for any other medium having dielectric constant E , the capacitance of C, is given by C, = Coe. When pure carrier gas of dielectric 516
ANALYTICAL CHEMISTRY
Frequency
-
Meter
Reference f
0
O s c *I I o t o r
constant e , is flowing betneen the plates of C,, then c*= c, = CoEg (3) d i e r e C, is the capacitance of C, nhen only pure carrier gas is passing betn een its plates. If Fd is always adjusted to zero \Then pure carrier gas is floning through the detector cell containing the capacitor C,, then
The well known Debye equation (9) for the dielectric constant, E , of a gas is
KI =
Fd
M
However, if a small volume of a liquid sample is injected into the carrier gas and if the injected sample is assumed to be instantaneously and completely vaporized, then the capacitance of C, is given by
c, = Coe.
(5)
where E* is the dielectric constant of the injected vapor samp!e and is given in terms of ps, as,p a l A f S , and T by Equation l (the subscript s referring to the particular sample injected into the carrier gas). It will be assumed that the injected sample is instantaneously vaporized and moves through the column as a plug of vapor. Experimentally i t has been shown that the vapor plug approximates a sinusoidal density distribution. It n-ill also be assumed that all readings of F d are taken a t the maximum density of pure organic vapor within the cell. Since each value of F d is measured n ith respect to the carrier gas (i.e., F d is adjusted to zero when only carrier gas flow through the detector cell), the value of F d resulting from the injection of the sample iq given by the equation TI hich results n-hen Equation 4 i- substituted into Equation 2. I t is D 1 1 F d = fo = D - -371
xs [z,
(6)
If C, is factored out of the denominator of each term in Equation 6, and if
Fi
Equation 3 for C, and Equation 5 for C, are substituted into Equation 6, the result is
The carrier gases used in the experimental part of thib work nere either helium or nitrogen. both of n hich have zero dipole moment and Iery small polarizability. Therefore. e o = 1.0000 is a valid approximation. By ubstituting for cs from Equation 1 Equation 7 then becomes 1
Fd
=
-
41
+ p s ( K 1+ y ] (8)
If the last tcrni of Equation 8 is expanded in a binominnl yeries, terms of order higher than the firqt may be neItill be used for obtaining quantitative results. Equation 9 predicts a linear relationship between Fd and density (or amount of component introduced) of a certain component a t given temperature, T , and at a given operating frequency, fo. This is verified by t h e plots given in 520
ANALYTICAL CHEMISTRY
Figures 6 and 7 for volumes smaller than 0.06 ml. Equation 9 also predicts a linear relationship between F d and 1/T for a given component a t a certain density and for a particular operating frequency j d . This has been verified by a plot of the data given for acetone in Table I. Injection volumes larger than 0.06 ml. produced a slight curvature in the calibration curves, Fd us. volume injected. According to Equation 9, this plot should be linear. However, Equation 9 is derived on the assumption that sample injection and vaporization are instantaneous, and, therefore, all vapor plugs must remain in the detector cell the same interval of time. Experimentally i t was found that volumes larger than 0.06 ml. required several inches of plunger movement with the particular hypodermic syringe used. This produced a noninstantaneous sample injection. Also vaporization 01 large samples was probably not instantaneous, which would also cause trailing out of vapor in the column. Both of these factors result in failure of instantaneous sample injection and experimentally cause somewhat wider base widths for larger samples &e., greater than 0.06 ml,). Although peak heights are used in plotting t h e calibration curves, areas under the response curyes (Figure 8) could also be used. Because of the sharpness of the response curves, peak heights could be determined more accurately than areas under the curves. Although not studied experimentally, the speed with which a vapor can be detected using a dielectric detector should be limited only by the read-out mechanism. For example, most recorders have a full-scale response time of 1 second, so a vapor plug which passes through the detector in less than 2' seconds will not be recorded accurately due to the inability of the recorder to respond this rapidly. For this reason no flow rates greater than 3 cubic feet per hour were used. Hovever, if very high speed detection were
ever necessary, oscillographic techniques could probably be used. The basic sensitivity of the vapor detector and associated circuitry described in this paper can be given in terms of the cell capacitance change which is needed to produce a full-scale deflection on the recorder, Le., a change of only 6 X 10-6 ppfd. produced a fullscale deflection for a frequency difference of 2000 C.P.S. The noise level for this response vcas less than 20y0 of the full-scale deflection. Even though the analytical sensitivity of the dielectric detector for acetone is somewhat poorer than the sensitivity quoted by Turner (IO), the basic instrumental sensitivity of this detector is much greater than t h a t of Turner. This discrepancy can be easily explained by the difference in detector cell size (the detector cell in this paper had a volume of 10 cc. whereas the volume of Turner's cell was only 0.3 cc.). Therefore, b y a reduction of detector cell size, the analytical sensitivity could be increased considerably. Except for the signal generator and the recording milliammeter, the detector cell and associated circuits were very inexpensive. All circuits involved in this paper rrere simple to construct. Sctually the commercial signal generator is not a necessary part of this instrument because it is possible t o replace it by another oscillator and detector cell identical to the one used for the sample. Through the one cell carrier gas plus sample would pass, and through the other cell only carrier gas would pass. This would then be a self-balancing reference oscillator. This would not only decrease the cost of the instrument considerably but would also increase its stability. I n the derivation of Equation 9 it is assumed that the resonant frequency of the Clapp oscillator rarirs inversely with +'E. This means that capacitors C1and Cs (Figure a),the resistance of the oscillator tank circuit, and the capacitance of the coaxial lead to the test cell have been neglected in determining
the rcsonaiit frequency. If the capacitors C1 and Cz are made large with respect to C, and if t h e tank circuit resistance is small, these effects can be neglected with little error. The lead capacitance may be important however, and in t h e experimentttl oscillator which was built, i t had a value of 4 ppf. compared t o a value of 6 ppf. for the test re11 capacitance. It can be shown that for t h e small changes in C, which occur with different gases as the dielectric, the effect of lead capacitance can be taken into account by writing Equation 9 in the approximate form,
(10)
where C L is t h e lead capacitance. The correction factor, cL + c,’ has no 8‘
effect on the linearity of F d with
p.
or
1
n-ith T,and it is only necessary to consider lead capacitance when ps or cys is being calculated from measurements of Fd us. pa a t two values of T. There is the apparent application of a dielectric detector for the monitoring of gases in flow streams, especially as applied to gas chromatography. Although the dielectric detector is not as sensitive as some vapor detectors (flame or ionization detectors), it is capable of responding much more rapidly than most other detectors and is much less scmitive t o changes in carrier gas flow rate. The detector is, therefore, particularly suited to quantity separations and purifications in which a high carrier gas flow rate is desirable, as well as to rapid separations of components. I n both of these applications most other
vapor detectors do not respond curately . LITERATURE CITED
(1) Blaedel, 11‘. O., Malmstadt, H. ANAL.CHEM.22, 734 (1952). (2) Ibzd., 24, 450 (1954). (3) Chien, Jen-Yuan, J . Chem. Educ. 494 (1947). (4) Clapp, J. N., Proc. I.R.E. 36, 356 (1948).
\ - -
--,
(9) Smyth, C. P., “Dielectric Behavior and Structure,” McGram-Hill, Kern
York, 1955.
(10) Turner, D. (1958).
IT., A-ature
181, 1265
RECEIVEDfor review -4ugust 5, 1960. Accepted January 18, 1961.
Gas Chromatographic Analysis of Some Volatile Phosphorus Compounds S. H. SHIPOTOFSKY’ and H. C. MOSER Departmenf of Chemistry, Kansas State University of Agriculture and Applied Science, Manhattan, Kan. A rapid gas chromatographic method of analysis for mixtures of phosphorus trichloride-thiophosphoryl chloride, phosphorus trichloride-phosphoryl chloride, and dimethyl phosphite-diethyl phosphite was developed. The area per cent of each peak of the chromatogram closely agreed with the weight per cent of the corresponding component of the mixture. The column and detector used with the reactive inorganic compounds were constructed from inert materials. Described i s a simple, yet dependable, thermal conductivity cell made from borosilicate glass with tantalum filaments.
K
and coworkers (9)analyzed mixtures containing phosphorus trichloride and phosphoryl chloride by first hydrolyzing them and then determining the amount of tri- and quinquevalent phosphorus. Because the method was quite lengthy and was not applicable to some of the compounds of interest to the authors, a more general and rapid gas chromatographic method n a s sought. Some of the volatile phosphorus comEELER
Present address, Procter and Gamble
Co., Ivorydale Technical Center, Cin-
cinnati 17, Ohio,
pounds such as the phosphorus halides react readily with the integral parts of commercial chromatographs. This necessitated construction of an instrument m-ith inert materials. Ellis and Iveson ( 1 ) successfully used gas chromatography to analyze mixtures of reactive halogen and interhalogen compounds. -1column packing similar to theirs was used in the present study. EXPERIMENTAL
Apparatus. Regular gas chroniatographic equipment was used except for t h e thermal conductivity cell used for t h e reactive compounds a n d t h e columns. T h e columns were constructed from coiled, borosilicate glass tubing, one 246 em. long x 7 mm. O.D. and t h e other 86 cm. long x 8 mni. O.D., used with t h e inorganic and organophosphorus compounds, respectively. Each end of the column was fitted with a 1z/6 socket joint. Provision was made for sample injection through a rubber serum cap placpd a t the entrance of the column. A GowMac Model 9286 thermal conductivity cell was used for the organophosphorus compounds. The cell constructed for use with the reactive compounds (Figure 1) was designed so that two resistors of the Wheatstone bridge circuit were directly in the path of the gas flow. The filaments in the gas stream n-ere made
from 2-mil unannealed tantalum wire and were coiled by winding the wire around a 26-gage hypodermic needle. The proper length of filament was then spot-melded to a support assembly. The remaining pair of filaments in the bridge circuit were made from coils of resistance wire. Kot shown in Figure 1 was a copper envelope surrounding the borosilicate tubing of the sensing resistors. The envelope, which served as a temperature stabilizer, \vas made of 28-gage copper wire. Helium carrier gas was passed through two 60-em. glass columns packed with Drierite before introduction into the chromatograph. Column Preparation. T h e liquid phases employed n-ere di-n-butyl phthalate and Apiezon K oil for separation of t h e organic compounds and Kel-F 90 grease for separation of t h e inorganic compounds. T h e y were deposited in the conventional manner (3) on 20180 mesh Fluoropak 80, a commercial brand of ground Teflon. One end of the column was sealed with a small plug of glass wool, and the column packing I\ as introduced in small quantities from the open end. Following each addition the columnxas rotated, thereby moving the packing to the plugged end. The packing was then gently tamped down with a copper wire, one end of which was curled to present a flat surface. About 11/2 inches of untamped packing TTas added each time and compressed to about 1 inch until VOL. 33, NO. 4, APRIL 1961
521
