method are not as consistent as those obtained by high-frequency (Table 111). Moreover, it should be noted that none of the potentiometric titration graphs for these oils had sharp breaks at the end point (see Figure 1). On the other hand, the high-frequency titration graphs all had sharp breaks (see Figure 5). The latter method can thus be said to give a more meaningful end point. A back-titration method was also tested. Excess standard alcoholic hydrochloric acid was added to the oil sample, and the excess was back-titrated with standard alcoholic potassium hydroxide. The end point could not be obtained any more accurately, so this method only increased the total error. An alternative potentiometric titration method, similar to the ASTM D664 method, uses glacial acetic acid as the oil solvent, and glacial acetic acid/perchloric acid as titrant (8.5 ml of 72 perchloric acid 300 ml of glacial acetic acid 20
+
+
ml of acetic anhydride, diluted to 1 1. with glacial acetic acid; about 0.1N in perchloric acid). This solvent/reagent system gives better results than the one using alcoholic hydrochloric acid, as far as the potentiometric titration method is concerned, but was found to be unsuitable for high-frequency analysis, since no sharp break could be obtained in the graph. ACKNOWLEDGMENT
The authors express their thanks to the Council of Wellington Polytechnic, and British Petroleum (N. Z.) Limited, for generously allowing the time to investigate high-frequency oil analysis, and for the use of their facilities. RECEIVED for review December 7, 1967. Resubmitted March 3, 1969. Accepted April 18, 1969.
Dielectrometric Titrations: Quantitative Acid-Base Titrations Robert Megargle,' George L. Jones, Jr., and Donald Rosenthal Department of Chemistry, Clarkson College of Technology, Potsdam, N . Y . 13676
When an acid reacts with a base in a low dielectric constant solvent, the formation of an ion-pair can be detected by the increase in the dielectric constant of the solution. Measurement of the dielectric constant provides a good method for detecting the endpoint of acid-base titrations in benzene when the reaction proceeds quantitatively. Comparison is made with spectrophotometric titrations, and theoretical titration equations are derived to explain the absorbance and the dielectric constant data. Titrations between picric acid and triethylamine or N,N-dimethylbenzylamine in benzene were performed asexamplesof the technique.
MEASUREMENT of the dielectric constant (e) during the course of a titration which proceeds to completion in low 6 solvents should be a satisfactory method for determining the end point in any case where there is a large difference in the dipole moments of the reactants and products. For example, in the reaction of an acid HA, with a base B, an ion-pair salt BH+A-, which usually has a large dipole moment b),may be formed. HA
+ B e BH+A-
During the course of a titration in which such a salt is formed, E of the solution will increase rapidly until the constituent being titrated has been converted quantitatively to the salt, and less rapidly thereafter. Successful dielectrometric determinations have been performed in the titration of trichloroacetic acid in benzene or dioxane with triethylamine (I); of amines in dioxane with picric acid, p-toluenesulfonic acid, and trichloroacetic acid ( 2 ) ; of trialkylaluminum compounds in benzene or cyclohexane with such electron donors as triethylamine, tetrahydro1 Present address, Department of Chemistry, University of Missouri, Columbia, Mo. 65201
(1) P. J. R. Bryant and A. W. H. Wardrop, J. Clrem. Soc., 1957, 895. ( 2 ) M. Ishidate, H. Nishizawa, H. Sano, and I. Horikoshi, Yakugaku Zasshi, 81, 1303 (1961). 1214
ANALYTICAL CHEMISTRY
furan, butyl ether, and isoquinoline ( 3 ) ; and of benzoic acid in benzene with triethylamine and tripentylamine (4). The reactions between picric acid (PiOH) in benzene and the bases triethylamine (Et3N) and N,N-dimethylbenzylamine (Me2BzN) were chosen for this study because of their simplicity (5-ZZ). In the absence of complicating reactions the titration curves can be calculated in terms of the dielectric properties and concentrations of the reactants and products. In this study the experimental results of dielectrometric and spectrophotometric measurements obtained during these titrations were compared with results calculated from theoretical titration equations. THEORETICAL TITRATION EQUATIONS
If a measurable property, P, of a solution depends linearly upon the equilibrium concentration of each solute, [i], then P
=
Po
+2
ut
[i]
(2)
i=l
where POis the constant contribution of the solvent, n is the number of solutes, and ut is the proportionality constant for the ith solute. For an acid-base reaction which proceeds quantitatively to the right in Equation 1, Equation 2 takes the forms (3) E. Hoffmann and W. Tormau, 2.Anal. Chem., 186, 231 (1962). (4) E. N. Gur'yanova and I. G. Beskina, J . Gen. Chem. USSR, 33, 914(1963). ( 5 ) M. M. Davis and E. A. McDonald, J. Res. N.B.S.,42, 595 (1949). (6) M. Davies and G. Williams, Trans. Faraday SOC.,56, 1619 (1 960). (7) M. Davies and G. Johansson, Acra Chem. Scand., 18, 1171 (1964). 41, l(1948). (8) A. A. Maryott, J. Res. N.B.S., (9) C . Kraus and C. P. Witschonke, J. Amer. Cliem. Soc., 69, 2472 (1947). (10) E. K. Ralph and W. R. Gilkerson, ibid., 86, 4783 (1964). 38, 527 (1947). (11) A. A. Maryott, J. Res. N.B.S.,
+ UXCX+ (us - ax) CT P = PO+ (a8 - UT) CX +
Before end point: P After end point:
=
PO
uTCT
(3)
(4)
where C is the analytical concentration, X refers to the constituent being titrated, T to the titrant, and S to the salt. In spectrophotometric titrations, Equations 3 and 4 become Beer’s law expressions when P = A / b (absorbance/cell path length), PO = 0, and uf = molar absorptivity (ai). Linear relationships in dielectrometric measurements can be derived from either the Debye equation or the Onsager equation ( 1 2 ) . [For a thorough discussion of the merits and demerits of the Debye and Onsager equations, see ( 1 2 ) . ] The Debye equation was derived for spherical gas molecules. If it is assumed that an isolated dipolar solute molecule in a sea of nonpolar solvent molecules is an approximation of a dipolar gas, then at a given temperature the Debye equation for dilute solutions whose densities conform to Equation 2 can be shown ( 1 3 ) to assume the form of Equation 2
The proportionality constant derived for this equation is Pi =
4
T NA 3000
__
[(YO
(1000~;- Mi)
+ai+--
3kT
where
1
NA is Avogadro’s number, a the polarizability, pi the magnitude of the dipole moment, M the molecular weight, and the proportionality constant ui from the density-concentration form of Equation 2. The reasonable assumption of a linear relationship between density and concentration for dilute benzene solutions of triethylammonium picrate (Et3NHOPi) and N,N-dimethylbenzylammonium picrate (MezBzNHOPi) was experimentally verified with deviations less than 0.1 parts per thousand (13). From the Onsager equation (14), it can be shown (15) that a single dilute polar solute of concentration N I molecules per cm3 and dipole moment p i in a nonpolar solvent is well approximated by
where the subscript m refers to measurements at high frequencies extrapolated to low frequencies so that the orientation polarization is negligible but the atomic and electronic polarizations are not. E - and (€,)I are for the solution and solute, respectively, and are obtained by extrapolation of visible range refractive index (n) measurements to infinite wavelength and use of the relation E , = (nm)z. For dilute benzene solutions of Et3NHOPi and MezBzHNOPi the variation of e , with concentration is small compared to the variation of the last term of Equation 7 so that E , is approximately eo. When Equation 7 is extended to include n solutes it assumes the form of Equation 2.
(12) C. J. F. Bottcher, “Theory of Electric Polarisation,” Elsevier, 1952.,
(13) R. Megargle, Ph.D. Thesis, Clarkson College of Technology, New York, 1968. (14) L. Onsager, J. Amer. Chern. SOC.,58, 1486 (1936). (15) C. P. Srnyth, “Dielectric Behavior and Structure,” McGrawHill, 1955, p 28.
Yi =
4 R p i z NA [eo 3000 k T 2 eo
+ 211’
+ (e,){
(9)
Values of Pi and yi can be obtained as the slopes of linear - l)/(e 2) us. C or e us. C plots, respectively, for dilute solutions of each solute. Equation 5 assumes the exact forms of Equations 3 and 4 when P = ( e - l ) / ( ~ 2), Pa = ( f o - 1)/ (eo 2), and u = P ; Equation 8 assumes similar exact forms when P = E , PO= eo, and u = 7.
+
(e
+
+
EXPERIMENTAL
Materials. CHROMATOGRAPHY. The purity of benzene and each organic base was determined by gas chromatography using a column of Apiezon L-KOH on Chromosorb W. Solvent. C & + was washed 3 times with conc H2SOa, once with H 2 0 , 2 times with 2M KOH, 4 times with HzO and dried in a silica-gel column. The middle fraction, obtained by distilling from P206through a 700-mm Vigreaux column, showed no significant impurities. Acid. Picric acid (PiOH) was purified by successive recrystallizations from H 2 0 and a C6H6-EtOH mixture. The latter solvent mixture was evaporated to pure EtOH prior to filtration. The PiOH was then dried in a vacuum oven at 60 “C and stored in a desiccator. Bases. Et3N was refluxed with acetic anhydride for several hours and triply distilled from dried KOH. The constant boiling fraction from the final distillation showed impurities totalling less than 0.5 ppt. MezBzN was distilled from dried KOH; it contained impurities totalling less than 0.9 ppt. Salts. 0.15 moles of PiOH, recrystallized once from HzO, was mixed with 0.16 moles of pure Et3N in C6H6-EtOH solvent, distilled to pure EtOH solvent, and filtered. The triethylammonium picrate (Et3NHOPi) was recrystallized two more times. 0.026 moles of PiOH, recrystallized once from H 2 0 , was mixed with 0.068 moles of MezBzN in C6H6, boiled, and recrystallized twice from C6H6. Et3NHOPi and MezBzNHOPi were each dried in a vacuum oven and stored in a desiccator prior to use. Solutions. Stock solutions of acid and base in benzene were prepared gravimetrically for each titration. Acid solutions were checked by potentiometric titrations of aliquots, diluted 1 :4 with EtOH to obtain complete miscibility, with aqueous NaOH. Base concentrations were checked by adding excess HC1, EtOH, and back titrating potentiometrically with aqueous NaOH. The deviations were less than 0.5 in most cases. Acid-base and base-acid titrations were simulated by series of solutions which were prepared by adding a constant amount of one constituent and varying amounts of the other to 100 ml flasks and diluting to the mark with C6H6. Dielectric Constant Apparatus. Dielectric constants were measured by the heterodyne beat method (16). The instrument employed three separate crystal-controlled oscillators, three variable capacity-controlled oscillators, and three mixers connected as shown in Figure 1. The cell and precision capacitor (General Radio 722-D on low scale) were in parallel with connections kept as short as possible to reduce nonlinearities introduced by stray inductance. This pair of capacitors was switched into the tuning circuit of one of the three variable oscillators. At the same time, a second, but carefully shielded section of the switch selected the output from the proper mixer. Tests showed that stray capacity was accurately reproduced at each position when the switch was turned. The fixed frequency oscillators were of Colpitts design and are described by Gruen (17). The 2.5-MHz (16) H. B. Thompson, J . Chem. Educ., 43,66 (1966). (17) H. Gruen, Electronics, 30, No. 1, 146; No. 8, 177 (1957).
VOL. 41, NO. 10, AUGUST 1969
0
1215
-
'
II-
VAR. OSC.
500kc
I
I
I - VVAR. A R . OSC. 1.5 mc
Spectrophotometry. The absorption spectra of the solutions in the visible range were obtained with a Cary 14 recording spectrophotometer equipped with a thermostated cell compartment. Matched silica cells with 0.1-cm pathlengths and ground glass stoppers were used.
I
o *
2.5 mc
R
PR EClS I ON CAPACITOR
RESULTS AND DISCUSSION
-
-
Figure 1. Block diagram of dielectric constant apparatus
and 1.5-MHz variable oscillators were similar except that the crystals were replaced with LC circuits and the feedback networks were modified to insure dependable performance. The 500-kHz oscillator was a cathode coupled oscillator. The entire oscillator-mixer section of the instrument was placed in a thermostated compartment controlled to 1 0 . 1 "C. A General Radio 1311 audio oscillator was used to produce audio beats with the difference signal from the appropriate mixer. Earphones and an oscilloscope were used to determine when the difference signal and the audio signal were the same frequency. Three separate sets of oscillators have the advantage over one set with different tuned networks because more efficient shielding is possible, less switching is necessary, and each oscillator can be peaked at the frequency for which it is designed to operate. Assuming dielectric dispersion in benzene below 5 MHz is negligible, the instrumental arrangement allowed three almost independent estimates of e to be made with one cell filling. The circuits common to the three oscillator systems were the regulated power supply, the detection devices, and the cell-precision capacitor combination. Deviations in solution composition, moisture content, or irregularities in filling the cell were reflected in the measurements at all frequencies. The cell (Figure 2) consisted of two concentric brass cylinders. The inner cylinder was 2.661 in. long and 1.870 in. in diameter and was connected to the tuned circuit by a rod, coaxial connectors, and coaxial wire in such a way that the entire inner circuit was completely shielded. The outer cylinder, with an inside diameter of 1.960 in. and an inside length of 2.861 in., was maintained at ground potential. Brass tubes, terminating in brass standard taper 10/30 joints, allowed the attachment of a glass system to fill, empty, clean, and dry the cell without disturbing its physical location in a constant temperature (10.02 "C) oil bath. Dry samples could be introduced without exposing them to the wet atmosphere. The dielectric constant of an unknown solution, ei, can be determined by measuring ACi, the difference in electrical
Table I. Determination of the Cell Constant, l/Co, by Least Squares Re1 error 1ICo SD of 1/Co in 1/Co Frequency (pf-l) X IO4 (pf-1) X 106 (95% level) 500 kHz 9.9182 2.93 0.706% 1 . 5 MHz 9.8504 2.96 0.705% 2 . 5 MHz 9.7159 3.50 0.853z
1216
ANALYTICAL CHEMISTRY
capacity of the cell when it is filled with the unknown compared to when it is filled with a solution with a known dielectric constant, ee. Co is the capacity of the cell with vacuum between the plates.
Cell'Constant. The cell constant, l/Co, in Equation 10 was found by measuring A c t , compared to C6H6 ( E = 2.2740), at 25 "C for a series of pure liquids of known E at 25 "C. l/COwas obtained as the least squares slope for ACt os. e t . The liquids employed and the values (averages of values reported in References 18 through 33) were: CC14, 2.227,; o-xylene, 2.5670; cyclohexane, 2.0174; toluene, 2.3740; ethylbenzene, 2.39Z4; tetralin, 2.749s; n-pentane, 1.836. The cell constants and the random error at each frequency are presented in Table I. Assumptions, Proportionality Constant. Titration curve equations were derived assuming (a) either Beer's law or the Debye equation or the approximate Onsager equation is applicable to dilute solutions, and (b) the titration reaction is adequately represented by Equation 1 and proceeds quantitatively. Measurements of A or E for various concentrations of PiOH, base, and picrate salt resulted in linear concentrationA / b , €, or (e - 1 ) / ( ~ 2) relationships for each species. Table I1 indicates that assumption (a) is valid for the individual constituents and that the picrate salts, as expected, had coefficients larger than the acids or bases. The discrepancy between the experimental points and a linear least squares fit is less than the experimental uncertainty in every case. The validity of assumption (b) is also clearly indicated by the picrate salts conforming to Beer's law and Equations 5 and 8, and the absence of rounding near the equivalence point in the titrations involving Et3N,Me2BzN, and PiOH. Titrations. Figures 3, 4, and 5 are typical of the agreement between the twelve experimental titrations and their corresponding theoretical equations. Estimates of the deviation of experimental points from the theoretical curves for each
+
(18) A. Petro and C. Srnyth, J. Amer. Chem. SOC.,80, 73 (1958). (19) A. Brown and D. Ives, J. Chem. SOC.,1962, 1608. (20) C. Meredith and G. Wright, Can. J. Chem., 38, 1177 (1960). (21) R. Mecke and R. Joeckle, 2.Electrochem., 66, 255 (1962). (22) J. Timmermans, A. Piette, and R. Philliupe, .. . BUN. SOC.Chim. Belges, 64,5 (1955). (23) E. Trieber. J. Schurz. and H. Koren. Monatsh.. 82. 32 (1951). t24j R. Mecke and K . Rosswag, 2.Elek;rochern., 60, 47 (1956). (25) J. Miller, J. Amer. Chem. SOC.,64, 117 (1942). (26) P. Narasimhan and S. Soundararajan,J. Madras Uniu., 23B, 22 (1953). (27) A. Altshuller, J. Phys. Chem., 58, 392 (1954). (28) S. Rau and D. Rao. Pro. Indian Acad. Sei., 2A, 232 (1935). (29) A. Gundyrey, N. Namethkin, and A. Topchiev, Doklady Akad. Nauk. SSR,121, 1031 (1958). (30) L. Hartshorn, J. Parry, and L. Essen, Proc. Phys. SOC.(London), 68B, 422 (1955). (31) R. LeFevre, Trans. Faraday Soc., 34, 1127 (1938). (32) "Table of Dielectric Constants of Pure Liquids," National Bureau of Standards Circular 514, U. S. Government Printing Office, Washington, D. C., 1951. (33) L. Heil, Phys. Reo., 39,666 (1932). '
1-O
-H
Figure 3. Spectrophotometric titrations of 2.0132 X 1 0 - 3 M PiOH with Et3N (0) and 1.0085 X 10-sM E3tN with PiOH (A). Solid lines = theoretical curves
of the titrations are presented in Table I11 as standard errors from the theoretical curve, SETC.
=
Figure 2. Cross section of dielectric cell
Li='
1
n
where n = the number of experimental points and y t = experimental A/b, e, or (e - l)/(e 2) value corresponding to a similar y t theoretical value. Relative average SETC values were obtained by dividing average SETC values by average ( E - l)/(e 2) = 0.3 or average E = 2.28,
+
A-amphenol connector ; C-banana plug; E-adapter ; D-standard taper 10/30 brass joints; F, H-vent and filling tubes; G-center conductor; B, K, Glock nuts; K-nylon bushing; M-cell top; Winner cylinder; P-cell body; Q-nylon centering pin
+
Table II. Least Squares Proportionality Constants for Theoretical Titration Curves
P
aat40mA Value SD
Material
90
PiOH EtaN MezBzN Et3NHOPi Me2BzNHOPi
5.5
0 0
... ...
7489 7208
18.9 37.6
Y
Value
SD
Value
SD
0.0812 0.0065 0.0231 2.6531 2.4947
0.0160 0.0117 0.0752 0.0081 0.0117
0.495
0.102 0 . C71 0.481 0.040 0.059
0.040
0.173 16.480 15.452
Table In. Standard Error from Theoretical Titration Equations (SETC) for Twelve Titrations
SETC Equations after E. P.
Equations before E. P. Titration No.
Solution being Titrated ( M X 108)
1 2
1.000 PiOH
2.0132 PiOH 1.001 EtsN 1,0085 Et3N 1.9872 EtsN 2.0006 EtaN 2.9735 EtaN 0.9987 PiOH 2.9974 PiOH 1.0038 MezBzN 1.9964 Me2BzN 2.9880 Me2BzN
3 4 5 6
7 8 9 10
11 12
Average SETC Relative Average SETC
Titrant
A/b
EtsN EtBN PiOH PiOH PiOH PiOH PiOH Me2BzN MezBzN PiOH PiOH PiOH
0.24 0.28 0.08 0.02 0.82 0.19
... *..
0.17 0.12 0.60
...
0.28
(5)
e X lo4
Alb
6.22 14.1 18.5 3.67 8.25 5.08 5.44 5.49 7.56 16.0 22.9 19.5
2.48 5.48 1.96 2.38 7.37 6.80 6.64 3.03 3.62 8.65 11.7 9.09
0.18 0.42 0.46 0.08 1.77 0.34
11.1 37
5.77 2.5
lo5
(5) lo'
e X lo4
8.44 16.9 15.2 14.6 6.67 14.1 14.9 7.74
2.61 6.57 7.48 6.72 2.00 5.88 5.24 4.96
0.09 0.89
13.6 29.1 21.4
6.48 14.9 10.1
0.49
14.8 49
6.63 2.9
... ...
0.14
*..
...
...
~~
VOL. 41, NO. 10,AUGUST 1969
1217
2.32 2.31
E 2.30 2.29
2.28 I
I
0 CONC OF TITRANT
[Mx IO3]
Figure 4. Dielectrometric titrations of 2.9774 (0) and 9.9868 X 10- 4MPiOH(A) with MezBzN
x
10-3M
I CONC
Solid lines = theoretical curves
These deviations can arise from errors in E , A , stock solution concentrations, or the predetermined ut, Pi,and vr values. An error of j~0.0005in E , resulting in an uncertainty of 8.2 x in ( E - 1 ) / ( ~ 2) was estimated for the instrument. Errors in A / b were difficult to estimate because of a problem in positioning the cell in the holder discovered only after all but titrations 2 and 6 had been performed. None of the data were discarded because all sets yielded satisfactory end points. This error may be responsible for the occasional less-thansatisfactory fit of the theoretical spectrophotometric curves. The reported molar absorptivities were taken after solution of this problem. The concentrations of the constituent being titrated and the titrant should be accurate to & O S % except in the case of titration 3, the first to be performed. Standard deviations in Table I1 indicate the accuracy of u, @, and y values. These latter sources of error may be responsible for systematic deviations. For example, discrepancies in Figure 3 may indicate that either too high a value of a E t 3 N H O P i or too low an initial PiOH concentration was employed. Because the SETC values are comparable to the possible experimental errors, it was concluded that the theoretical equations accurately describe the titrations. The Debye and Onsager equations are equally satisfactory in the concentration range studied. The point of intersection of two fitted linear regression equations was taken as the experimental end point and compared with the theoretical end point calculated from the known titers. The average error and standard deviation of the average error for twelve titrations, where E , ( E - l ) / ( ~ 2), and A/b are plotted us. volume of titrant, were -3.54, k6.87; -4.44, k6.88; -13.1, and ~ t 1 5 . 5ppt., respectively. The average titration error was not significantly different from zero. Effects of Water. Anhydrous benzene is extremely hygroscopic and picks up water from glassware and the atmosphere. When benzene solutions were prepared using dry glassware in air, the amount of water in the resulting solutions was greater than the amount of total acid and base in most of the solutions. To determine whether water affected the acid-base reactions, the reagents and solutions for titration 6 were prepared in a dry nitrogen atmosphere inside a glove box and transferred to the dielectric cell without direct exposure to wet air. Coulometric Karl Fischer titrations (34) of the solutions after the measurements indicated the solutions
+
+
(34) R. Swensen and D. Keyworth, ANAL.CHEM., 35,863 (1963). ANALYTICAL CHEMISTRY
I
4
Figure 5. Dielectrometric titrations of 2.9735 x 10-SM (01,1.9872 X 10-aM (a), and 1.0085 X 10-aM (A) Et3N with PiOH
Solid Lines = theoretical curves
1218
OF
I
2 3 TITRANT [MxIO3]
were (2 to 5) X 10-4M in water. This was considerably less than the concentration of Et3N titrated (2 X lO-3M). The results of this titration did not differ significantly from the other Et3N-PiOH titrations (see Table 111). Therefore, small amounts of water do not appear to participate in the overall acid-base reaction. Water analyses of the solutions indicated that where the solutions had a certain water content, the benzene solvent used in that experiment had a similar water content. Because the dielectric constant of each solution was determined by comparison with solvent (to determine Act), the estimate of E of the solution does not change much with small water contamination. Dissociation Constants. Because no measurable rounding near the end point was detected, it was concluded that the formation of Et3NHOPi and MezBzNHOPi proceeded quantitatively. A measure of the rounding is AE‘ = Emessured - Eesleulated at the end point, where the Eoaloulsted value is obtained from linear equations fitted to the experimental data. The uncertainty in AE’ was 0.001, and from the data it was concluded that AE’ < 0.001. A AE‘of 0,001 corresponds to a picrate concentration of about 6 X 10-5M. Therefore, the formation constant Kmust be greater than 8 X lo5:
K’
(3 X 10-3) - (6 X 10-5) (6 X 10-5)2
(12)
Comparative Utility. Rapid and accurate dielectrometric titrations in which E is reproducible to approximately k0.0002 can be performed for reactions involving the formation or disappearance of a species with a large p in a low E solvent when the cell is designed for direct titrant addition. Under suitable conditions simple dielectric constant measurements can be used rather than titrations. Higher concentrations can be titrated than those employed in the usual spectrophotometric titrations. In general, the highest concentration that can be titrated is limited only by the solubility and chemistry of the system. In principle, smaller changes in dielectric constant could be measured and more dilute solutions employed in a cell with a larger electrical capacitance. For acids, bases, and salts with /3 and y values about equal to those of Et3N (or Me2BzN), PiOH, and the corresponding salt, it seems impractical to attempt titrations at concentrations below about 10-4M because of possible variations in moisture content or impurities. The precision obtained appears to be comparable to that of spectrophotometric titrations. Solutes or solvents can be used which have un-
desirable spectral properties. On the other hand, spectrophotometric measurements can frequently be used at lower concentrations and for the determination of a particular species in a mixture. High frequency titration methods (35, 36) employ comparable radio frequencies and have the advantages that the electrodes are not in contact with the solution and that conducting solutions can be measured. However, the equivalent circuit of the necessary cell is more complicated and e or conductance of the solution is not related in any simple way to the measurement. The measurements are usually strictly empirical, titration curves vary in shape with frequency, and (35) W. J. Blaedel in “Physical Methods in Chemical Analysis,” W. G. Bed, Ed., Academic Press Inc., New York, 1956, p 108. (36) C. Reilley in “New Instrumental Methods in Electrochemistry,” by P. Delahay, Ed., Interscience, New York, 1954, Chap. 15.
observed variations are usually due mainly to conductance changes in solution (36) rather than changes in e. Other techniques applicable to low dielectric constant solvents have both advantages and disadvantages. Thermometric titrations are limited to fast reactions with large heats of reaction. Cryoscopic and ebullioscopic methods can only provide information about chemical behavior at the freezing and boiling points. Vapor pressure techniques are restricted to non-volatile solutes dissolved in volatile solvents. Conductance methods are limited because the principal reactions in low E solvents do not produce ions. RECEIVED for review December 12, 1968. Accepted May 22, 1969. The authors acknowledge NDEA fellowship support for R. Megargle. A portion of this work, taken in part from his Ph.D. thesis, was presented to the American Chemical Society in Chicago in September 1967.
Thermal Field-Flow Fractionation of Polystyrene Samples Gary H. Thompson, Marcus N. Myers, and J. Calvin Giddings Department of Chemistry, University of Utah, Salt Lake City, Utah Field-flow fractionation, a recently developed separations concept, is used in conjunction with a thermal field to separate high molecular weight polystyrene fractions. A rectilinear channel device is described which is more successful than the earlier capillary column which yielded only partial resolution. At high field strength (temperature gradient) lower molecular weights were separated by high molecular weight fractions were retained to the extent that they were lost. Reverse temperature programming was thus indicated; this consists of applying large temperature gradients at first, and then slowly decreasing the gradient to permit higher molecular weights to be eluted. The method separated molecular weights ranging from 3600 to 860,000. FIELD-FLOW FRACTIONATION (FFF) is a separation method in which a lateral field of some kind is coupled with nonuniform axial flow to induce differential migration ( I , 2). The lateral field can, in theory, be electrical, magnetic, centrifugal, thermal, etc., or some combination of these. The fields can also be varied or programmed in such a way that larger molecules are gradually released from the more slowly flowing wall regions. The method resembles that of chromatography in that the separation of distinct zones is achieved by differential migration along a narrow tube through which liquid is flowing; it is unlike chromatography in that the separation occurs in a single-phase system and requires an external field. An imposed lateral temperature gradient--i.e., a thermal field-was employed in this study. Thermal diffusion is the phenomcnon in this case producing the necessary lateral concentration gradients. Separations based on thermal diffusion have been accomplished mainly in countercurrent columns. Such columns have employed either forced or natural convection to cascade the separation. The thermogravitational column, introduced (1) J. C. Giddings, Sep. Sci., 1, 123 (1966). (2) G. H. Thompson, M. N. Myers, and J. C. Giddings, ibid., 2, 797 (1967).
by Clusius and Dickel in 1938 (3), is the most successful of these. A horizontal temperature gradient is used to induce both concentration and density gradients, the latter causing an upward flow at the hot wall and a countercurrent or downward flow at the cold wall. While generally efficient for binary separations, the method suffers from parasitic remixing which occurs at the boundary of the downward and upward flow, and does not readily lend itself to the isolation of multicomponent mixtures. GralCn and Svedberg ( 4 ) first suggested the possibility of employing thermal diffusion to fractionate macromolecular systems. They attempted to fractionate proteins but obtained instead an evaporative effect which concentrated the proteins without fractionating them. Debye and Bueche (5) were the first to successfully fractionate polymers. They used a thermogravitational column and polystyrene in toluene. Other workers have alio utilized the thermogravitational column to study the polystyrene-toluene system (6, 7). A review of much of the polymer work has been recently published (8). The present paper describes separations achieved by thermal diffusion in a FFF mode which utilizes unidirectional-Le,, not countercurrent-flow. In this case the fluid is made to flow between two long horizontal plates with a vertical rather than horizontal temperature gradient. In this respect the apparatus is like the flow cells described by Jones (9),Thomaes (IO), Turner ( I I ) , and Turner and Butler (12). However, (3) K. Clusius and G. Dickel, Naturwissenschaften, 26, 546 (1938). (4) N. GralCn and T. Svedberg, ibid., 29, 270 (1941). ( 5 ) P. Debye and A. M. Bueche, “High Polymer Physics,” Chemical Publishing Company, New York, N. Y., 1948, p 497. (6) G . Langhammer, H. Pfennig, and K. Quitzsch, 2. Electrochem., 62, 458 (1958). (7) D. L. Taylor, J . Polym. Sci., Part A, 2,611 (1964). (8) A. H. Emery, Jr., in “Polymer Fractionation,” M. J . R. Cantow, Ed., Academic Press, New York, N. Y., 1967, p 181. (9) A. L. Jones, U. S. Patent 2,723,034 (1955). (IO) G. Thomaes, J. Chim. Phys., 53, 407 (1956). (11) J. C. R. Turner, Chem. Eng. Sci., 17, 95 (1962). (12) B. D. Butler and J. C. R. Turner, Trans. Faraday SOC.,62, 3114 (1966). VOL. 41, NO. 10,AUGUST 1969
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