503
DIELECTRIC PROPERTIES OF ALKYLAMIDES
5. Perhaps the best agreement between the various methods for calculation of the potential barrier is in predicting the position of greatest reactivity in a molecule both toward electrophilic and nucleophilic substitution. Acknowledgments. This research was supported by the Ordnance Materials Research Office. J. J. K. wishes to thank the Soroptimist Federation of the Americas for a study grant. The authors wish to thank Dr. A. Kende for several helpful discussions on the chemistry of nonalternant hydrocarbons.
perfo!med assuming all C-C bond distances equal to 1.40 A. As a verification that the localization energy results are quite insensitive to the experimental irregularities in the geometries of these molecules, the localization energy calculations were repeated for azulene using the latest experimental datal3 for its structure. These results are presented in Table I1 and it may be seen that the order of reactivities remains the same and quantitatively the values differ by only 0.01 to 0.03 e.v. (this set using the experimental azulene structure is consistently higher).
Appendix The calculations in the main part of this paper were
(13) J. M. Robertson, H. M. M . Shearer, G. A. Sim, and D. G. Watson, Acta Cryst., 15, 1 (1962).
Dielectric Properties of Alkyl Amides.
I.
Vapor Phase Dipole
Moments and Polarization in Benzene Solution1
by Richard M. Meighan2 and Robert H. Cole Department of Chemistry, Brown University, Providence, Rhode Island
(Received September 13, 1963)
The dipole moments of six amides have been determined from vapor phase dielectric constant measurements a t 110' a t pressures from 1 to 20 mm. with the following results (in debyes) : N-methylformamide, 3.82; N,N-dimethylformamide, 3.80; acetamide, 3.75; N-methylacetamide, 3.71 ; N,N-dimethylacetamide, 3.80; N-methylpropionamide, 3.59. The dielectric constants of solutions of N-methylacetamide and its isomer, N,N-dimethylformamide, in benzene were determined a t 25' and concentrations from 0.0001 to 0.03 N . The existence of a dimer equilibrium for the former solute can be inferred as well as a dimer moment 1.6 times that of the monomer. Descriptions are given of the differential cell transformer bridge techniques used and procedures found to give reliable results.
Introduction The dielectric properties of liquid amides are remarkable for the wide ranges of dielectric constant values observed and their large temperature coeficients. Data for several amides which illustrate the diversity of behavior have been reported in the literature and have been supplemented by further measurements in this laboratory which will be reported in a companion paper to this one. The very large ai-
electric constant values for N-methylpropionamide (for example, E = 340 a t -40') strongly indicate chainwise association as does other evidence; rather smaller values for formamide and acetamide suggest appreciable but more random correlations; at the other extreme, N,N-dimethyl amides have much smaller (1) Taken in part from the Ph.D. thesis of R. M. Meighan. (2) Rohrn and Haas Company, Philadelphia, Pa.
Volume 68,Number 3 March, 196h
504
dielectric constants, of magnitudes expected for normal polar liquids. Unfortunately, it has not been possible to put these lnterpretations on a quantitative basis or to test possible models of association by hydrogen bonding, the difficulty in most cases being either that no molecular dipole moments have been measured or that several reported solution values are in poor agreement. The first objective of the work reported here accordingly was to determine reliable dipole moments for several amides with interesting dielectric behavior as liquids. It was felt that vapor phase dielectric constant measurements would be far more satisfactory for the purpose than solution values if they could be made with sufficient accuracy a t the low temperatures and vapor pressures necessary to prevent decomposition. Vapor phase measurements have been made with satisfactory precision for reasonably polar molecules a t pressures in the range 1 to 20 mm. Dielectric data were first obtained on water and chlorobenzene to test the method, which was then applied to six amides of interest. Dielectric constant measurements were also made on dilute solutions of two amides in benzene: K-methylacetamide, for which dimer formation by hydrogen bonding is expected and for which Davies and Thomas3 have determined an equilibrium constant from osmotic pressure data, and N,N-dimethylformamide, which is isomeric to N-methylacetamide but for which hydrogen bonding to nitrogen is blocked by the two methyl groups. The purpose thus was to compare the two sets of results in order to obtain information about the polarity of the N-methylacetamide dimer. To do this satisfactorily, quite precise data a t low concentrations were needed; differential methods developed for the purpose are described below.
Experimental
RICHARD M. MEIGHAN AND ROBERT H. COLE
Water was removed by distillation; the residue was vacuum distilled, dried over calcium oxide, and further purified by three vacuum distillations, n Z 51.4346, ~ lit.6 1.4345. Water used was taken from the laboratory still and recrystallized once or twice; chlorobenzene from Eastman was dried over calcium chloride and phosphorus pentoxide. The benzene used in the solution measurement, certified reagent grade from Fisher Scientific Co., was refluxed for 48 hr. over calcium hydride, distilled, and thereafter handled in closed systems. The density a t 25” was 0.8738 g./ml., the interpolated value from data cited by Timmermans* is 0.8738 g./ml.; the measured dielectric constant was 2.275 a t 25O, in good agreement with the value 2.274 recommended by Maryott and Smith.g A transformer bridge method was used to determine the direct capacitance difference between two closely matched cells, one containing the unknown (vapor or solution) and the other the reference (vacuum or pure solvent). The pair for vapor measurements was constructed from the aluminum plate assemblies of two General Radio Type 1403 fixed standard air capacitors; these were mounted in heavy brass cases using strain relief Kovar seals for support and electrical leads to the bridge circuit. The direct vacuum capacitances were 440 pf., matched to 0.25 pf. or better depending on temperature. The cells for solution measurements were also of three terminal parallel plate construction with smaller, heavier stainless steel plates; their vacuum capacitances of 10.93 pf. were matched to 0.06 pf. The capacitance balancing and other bridge circuits used were similar to those described by Johnston, Oudemans, and Cole’O with some modifications to improve sensitivity and precision to 0.0001 pf. for the vapor phase work; addition of a current preamplifier to minimize detector circuit loading further improved this figure by a factor ten for the solution measure-
The amides used were, with the exception of Kmethylpropionamide, obtained from Eastman Distillation Products Industries. The following were used without further treatment : K-methylformamide, n 2 3 ~ (3) M. Davies and D. K. Thomas, J . Phys. Chem., 60, 767 (1956). 1.4310, lit.4 1.4310; ?J,n’-dimethylformamide, n 2 2 * 4 ~(4) G. R. Leader and J. F. Gormley, J . A m . Chem. Soc., 73, 5731 (1951). 1.4290, lit.5 1.4294; acetamide, m.p. 79-80’. N( 5 ) I. Heibron, et al., Ed., “Dictionary of Organic Compounds,” Methylacetamide was vacuum distilled over calcium Oxford University Press, Sew York, N. Y., 1953. oxide and fractionally recrystallized a t room tempera(6) G. F. D’Alelio and E. E. Reid, J . A m . Chem. Soc., 5 9 , 109 (1937). ~ 1.4268. N,N-Dimethylacetamide ture, n 3 2 1.4282,lit.e (7)J. R. Ruhoff and E. E. Reid, ibid., 59, 401 (1937). was allowed to stand over potassium hydroxide and (8) J. Timmermans, “Physico-Chemical Constants of Pure Organic calcium oxide and fractionally distilled a t 31 mm., Compounds,” Elsevier Publishing Co., New York, N. Y., 1950. 66-68’ ; n 2 5 ~1.4359, lit.’ 1.4351. K-Methylpropion(9) A. A. Maryott and E. R. Smith, Table of Dielectric Constants of Pure Liquids, NBS Circular 514, U. S. Government Printing Office, amide was prepared by Mr. W. I. Yathan from proWashington, D. C., 1951. pionic acid (Olin-Mathieson) and a 40% aqueous solu(10) D. R. Johnston, G. J. Oudemans, and R. H. Cole, J . Chem. Phys., 33, 1310 (1960). tion of methylamine (Eastman Distillation Products). The Journal of Physical Chemistry
DIELECTRIC PROPERTIES OF ALKYL AMIDES
ments. These small differences are meaningful and usable because of the three terminal differential measurements used, which eliminate lead capacitance errors and largely compensate thermal drifts and other minor instabilities of the cells. The auxiliary apparatus for introducing vapor into one cell and determining its pressure included a means for connecting a liquid sample bulb which could be degassed, a metering value, and a diaphragm separator by which the vapor pressure could be matched t o nitrogen pressure read by an external oil manometer. All parts of the system containing vapor were immersed in an oil bath or heated electrically to prevent condensation. Most of the measurements were made at l l O o , with a few a t lower temperatures, and the maximum usable vapor pressures (see below) were usually less than 15 mm. The principal source of experimental difficulty was ridding the system of water vapor, which could be removed sufficiently to prevent contamination and erratic results for the amides only by prolonged evacuation a t 150'. Two effects attributable to vapor adsorption were noticed in the course of determining the variation of capacitance with vapor pressure. The first was that the extrapolated intercepts of these curves for zero pressure were often slightly larger than the measured vacuum capacitance (sometimes by as much as 0.004 pf.); the second was that the curves showed marked abrupt changes in slope a t about one-thirdathe saturation vapor pressure and were sometimes thereafter a little erratic. It was found, however, that the initial slope of capacitance us. pressure was very reproducible under otherwise good conditions, and we are confident that it results from true vapor polarization. Of some interest is the fact that Zahn" many years ago noticed a very similar change of slope for water vapor, which he attributed to condensations on metal surfaces of the measuring cell. For the solution measurements, solute was added from a Koch buret to a mixing flask containing about 90 ml. of benzene. This was in turn connected in a closed system with the capacitance cell, provision being made for circulation of solution by benzene-saturated nitrogen. Measured densities of 0.1 M amide solutions agreed to 0.02% with values calculated assuming additivity of molar volumes; this assumption was therefore made in calculating all other stoichiometric concentrations.
Results and Discussion The measured capacitance differences AC as a function of pressure P were linear in all cases below a maxi-
505
P(mm Hg) .20
I
I
I
8
4
0
12
Figure 1. Variation of capacitance difference (pf.) with pressure P (mm.) for N-methylformamide vapor a t 110'.
mum pressure as already described, and a representative curve for N-methylformamide a t 110' is shown in Fig. 1. These and the other data were fitted by least squares to determine the slope ACIAP in mpf./ farad). I n Table I, mean values mm. (1 mpf. = of these slopes for the indicated numbers n of runs are listed, together with standard deviations u of this mean slope : us calculated from deviations of individual slopes from the mean, and up calculated from standard deviation for the individual runs. Evaluation of dipole moments was made by the standard Debye expression
AC/C,
= e
+
- 1 = ( ~ T N / V ) ( L Yp 2 / 3 k T )
where e is the dielectric constant, C, the vacuum capacitance of the cell, N / V the number density, and kT has the usual meaning. Using the ideal gas law for N / V and introducing the slope ACIAP gives kT AC '/a (1) p = [3kT 4nC, AP - a)]
(-
in which the molecular polarizability a is the only unknown. For water and chlorobenzene, we have used values of a corresponding to the values A = ~~
(11) C. T.Zahn, Phus. Rev., 35, 1047 (1930).
Volume 68,Number 3 March, IS64
RICHARD M. MEIGHAN AND
506
~
ROBERTH. COLE
~~~
Table I : Vapor Capacitance Variation with Pressure and Derived Dipole Momenta
Subatance
Water Chlorobenzene N-Methylformamide
N, N-Dimethylformamide Acetamide N-Methylacetamide N,N-Dimethylacetamide N-Methylpropionamide 0
Value of
p
f,
oc.
Number of runs
AC/AP, mpf./mm.
3 1 9 2 3 8 3 6 2 3
3.588 4.712 13.73 15.11 13.92 13.16 13.26 14.04 17.51 12.78
90 90 110 90 110 110 110 110 70 110
obtained using literature value for a.
UP
0.014
0.020 ,024 ,033 ,033 ,011 ,033 ,024 ,016 ,033 ,012
... ,029 .108* .012 .031 ,052 ,019 . 014b .016
AUR),
p ( 1.1 aR);
D.
D.
1.86-= 1.72. 3.83 3.82 3.82 3.76 3.73 3.81 3.83 3.61
... 3.82 3.81 3.80 3.75 3.71 3.79 3.81 3.59
These are average rather than standard deviations.
41Noa/3 = 3.8 and 31.5 cm.a, respectively, from literature data cited by Maryott and Buckley.'2 (The quantity A so defined is the induced molar polarization related to molar refraction, N O being Avogadro's number.) For the amides, a choice of a or A is more difficult, and we have used two. One is the value calculated from the liquid refractive index and denoted by LYR in Table I. This is doubtless too small as it includes no atomic polarization from nuclear displacements. An upper limit in the case of N-methylpropionamide can be inferred from unpublished microwave measurements on the liquid which F. I. Mopsik has made in this laboratory; these extrapolate to a high frequency dielectric constant E, corresponding to a = 1 . 8 a ~ . As a plausible compromise and one often assumed, we have calculated values of p using a = 1.1a~ which are listed in the last column of Table I. As the results in Table I with the two choices of a show, the differences in calculated dipole moments are about 0.3%. The dipole moment values 1.86 D. for water and 1.72 D. for chlorobenzene agree to within 0.5% with averages of recent literature values in ref. 12; we believe. these results are good evidence of the accuracy as well as precision of the present method for measurements a t pressures below 20 mm. The only literature values with which our dipole moment results for amides may be compared directly are from solution measurements. For S,K-dimethylformamide, Lee and Kumler13 reported 3.92 D. in benzene, 3.95 D. in dioxane, and 3.90 D. in heptane as compared to our 3.80 D. For acetamide, these authors gave 3.07 D. in benzene and 3.70 D. in dioxane, while Bates and Hobbs14 reported 3.44 D. in benzene and 3.90 D. in dioxane, Kumler and Porter'j reported 3.72 D. in benzene, and our value from Table I1 is 3.75 D. For N,N-dimethylacetamide these last authors The Journal of Phyeical Chemistry
or.
found 3.79 D. in dioxane, Thompson and La Planche16 found 3.72 D. in benzene and 3.70 D. incyclohexane, and our value is 3.80 D. About all that can be inferred from the comparison is the presence of considerable difficulties in the solution measurements. A related but not directly comparable result is the value 3.714 D. obtained for formamide from the microwave Stark effect by Kurland and Wilson,17 which is not far from any of the values for six other amides in Table I, and in particular is quite close to our value 3.75 D. for acetamide. The solution measurements in benzene were undertaken as already mentioned to study differences in concentration dependence for N-methylacetamide and N,N-dimethylformamide. Measured capacitances were reduced to dielectric constants E and the differences E - el, where el is the measured dielectric constant of solvent, were fitted to a quadratic function of stoichiometric molarity C (moles/liter) by a least squares machine program. The data for two runs with each solute, each run consisting of 16 points for the range 0.0001 < C < 0.03 M , gave the following results and standard deviations. N-Methylacetamide (A)
(12) A. A. Maryott and F. Buckley, Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State, NBS Circular 537, U. S. Government Printing Office, Washington, D. C., 1963. (13) C. M. Lee and W. D. Kumler, J . A m . Chem. Soc., 84, 571 (1962). (14) W. W. Bates and M. E. Hobbs, ibid., 73, 2151 (1951). (15) W. D. Kumler and C. W. Porter, ibid., 56, 2549 (1934). (16) H. B. Thompson and L. A. La Planche, to be published. (17) R. J. Kurland and E. B. Wilson, Jr., J . Chem. Phys., 2 7 , 585 (1957).
DIELECTRIC PROPERTIES OF ALKYLAMIDES
EA
EA
-
-
€1
(il
=
=
507
+
(1.66 f 0.95) X lo-’ (1.8110 f 0.0018) X 10-aC (7.18 f 0.059)C2 -(0.32
f
+
+
0.99) X lo-‘ (1.8177 f 0.0018)C (7.03
f
+
(2)
0.058)C2
N,N-Dimethylformamide (F) EF
-
el =
-(2.16
f
+
1.47) X. (1.8563
f
(0.306 EF
-
=
O.OOl9)C f
0.061)C2
+
-(1.93 i 1.10) X (1.8548 f 0.0023)C (0.379
f
+
+
I
1
I
(3)
I
DIMETHYLFORMAMIDE
0.087)Cz
The constant terms are comparable with the least and with count from the measuring scale (1 X the standard deviations of a single measurement (1.7 to 2.4 X they thus give no indication of significant systematic error, This point is mentioned because solution data frequently fail to satisfy the condition that they should extrapolate smoothly to data for the pure solvent (see, for example, the discussion by Smith’*). This satisfactory extrapolation is shown graphically in the plots of (EA - EJ/C and ( E F - el)/C against C in Fig. 2, which also show the consistency of data from the two pairs of runs in relatios to the differences between the two solutions. We have chosen to analyze the solution data in terms of the Debye expression, which can be written
where M 2is the mean square dipole moment of solute for number density N 2 / V , and E, is the dielectric constant of induced polarization in the solution. In the limit NZ/V + 0, the quantity e, - el should approach zero linearly with N2/V, and we may therefore write
where No Is Avogadro’s number and C the solute concentration. The coefficient E representing differences in induced moments of solute and solvent cannot be evaluated exactly because of uncertainty about for atomic polarization. With the choice a = l . l a ~
C (MOLEWL) I
I
001
I
0.02
003
I
Figure 2. Values of dielectric constant increments divided by concentration C plotted against C for solutions of N-methylacetamide and N,N-dimethylformamide in benzene a t 25”.
the solutes, this coefficient E very nearly vanishes with benzene as solvent, and with a = a8 calculated values of M are changed by about 0.2%. With the choice E = 0, comparison of linear terms in eq. 2, 3, and 5 gives the dipole moment values 3.82 D. for N-methylacetamide and 3.86 D. for K,Ndimethylformamide. These are significantly larger than the values 3.71 and 3.80 D. from the vapor measurements. The differences are in the opposite direction to the usual solution effect, but are not anomalous because both molecules are roughly prolate spheroids in shape with the dipole moment vector lying nearly along a short figure axis. For this geometry, various theories of “solvent effects” agree in predicting that apparent solution dipole moments from the Debye formula will be larger than the vapor value, as is observed (for discussion of these theories, see Smith’* and Smythlg). We next consider the differences between the two amides as expressed by combining eq. 2 and 3 to give the difference in dielectric constant EA - EF of the two solutions (18) J. W. Smith, “Electric Dipole Moments,” Butterworths Scientific Publications, London, 1955. (19) C. P. Smyth, “Dielectric Behavior and Structure,” McGrawHill Book Co., New York, N. Y., 1955.
Volume 68,Number 9 March, 1961
RICHARD M. MEIGHAN A N D ROBERT H. COLE
508
EA
-
EF
=
-(0.0413
f
0.0019)C
(6.76
EA
f
0.07)C2 (6)
The linear term has the sign expected from the difference in dipole moments of the two solutes; its magnitude is only about half that expected on this basis, but this could easily arise from a small difference in solvent effects. The quadratic term is considerable and significant and will now be used in conjunction with equilibrium data of Davies and Thomas3 to estimate a mean square dipole moment of a postulated 5methylacetamide dimer in benzene. We assume that the quantity e, in eq. 4 is the same for the two solutions at the same stoichiometric concentration C . Denoting monomer concentration and mean square dipole moment of N-methylacetamide by CA and / J A ~ , the corresponding dimer quantities by Cd and Kd2, and mean square moment of S,N-dimethylformamide by p~~ then gives
where
(7) I n this expression, we have assumed that differences in solvent induct,ion effects can be neglected. The necessary relations between CA,cd, and C are obtained 2cd = C from the stoichiometric condition CA and the equilibrium constant Kd = C A / C ~ which ~, from the work of Davies and Thomas has in our units the value 6.15 l./mole. A t the concentrations involved CA/Cd is small enough that the approximate solutions (CA/C) = 1 - 2KdC, cd/c = KdC may be used. With these values, eq. 7 becomes
+
Jouriial of Physical Chemistry
-
EF
=
F ( ~ A-’ P F 2 ) c
+ F(pd2 -
2p~~)KdC (8)~
The calculated coefficient of C is -0.086 as compared with the experimental -0.041 in eq. 6; this discrepancy has already been discussed. By equating the coefficients of C2 and using known values of F and Kd, one obtains p d 2 = 2 . 6 4 p ~corresponding ~, to an r.m.s. dimer moment of 6.03 D. This is of course much larger than the value zero for opposed monomers and it *is appreciably larger than the value p d 2 = 2 p one ~ ~ would have for random relative orientations of the two molecules in the dimer. The accuracy of this figure is difficult to assess, but it is probably limited more by the approximations of the theory than by experimental errors in the equilibrium constant and quadratic dielectric coefficient. It thus seems unwarranted to go much beyond the qualitative conclusion that the results indicate a significant degree of correlation acting to make the dipole moments of the two monomer molecules more nearly parallel than for random correlation. Other implications of these results and the vapor dipole moment data will be discussed in a companion paper on dielectric properties of liquid amides to follow. Finally, it seems appropriate to point out that the results obtained in this work show that small differences in dielectric properties for vapor or solutes at low concentrations can be measured with considerable precision, and the principal limiting factors appear to be such things as adsorption and traces of impurity rather than electrical instrumentation, Acknowledgments. This work was supported in part by grants from the U. S. Air Force Office of Scientific Research and the Yational Science 120iindation, and some of the equipment development was made possible by a research grant to R. H. C. from the California Research Corporation.
