S. W. TUCKER AND 5. WALKER
1270
Dielectric Studies. XXVII.
Relaxation Processes of
Pyrrole-Pyridine and Chloroform-Pyridine Systems
by S. W. Tucker University of Aston, Birmingham, England
and S. Walker Chemistry Department, Lakehead Univeraity, Port Arthur, Ontarw, Canada
(Received October i? 1969) ,
Dielectric absorption measurements have been made on ternary solutions of pyrrole, pyridine, and cyclohexane and the relaxation time of the hydrogen-bonded complex deduced. A similar study has been made of a pyridine, chloroform, and cyclohexane system. By comparison of the relaxation time of the complex with that of a molecule of similar size and shape, it is shown that the pyrrole-pyridine and chloroform-pyridine systems each form 1: 1 complexeswhere the hydrogen bonding is of the type NH. . . H and CH. . .N, respectively. This dielectric approach yields information as to both size and shape of small complexed species in solution.
Introduction The formation of hydrogen bonds between two polar solute molecules in a nonpolar solvent has been studied by a number of techniques.‘ Perhaps the most fruitful measurements have been made using nmr and ir approaches. These methods detect hydrogen bond formation and, in some cases, yield the association constant. They do not, however, yield direct information as to the size and ahape of the complex. It was our aim to examine the feasibility of determining the relaxation time of a polar complex in equilibrium with its two polar components in a nonpolar solvent and from that to deduce information as to the size and shape of the complex by comparison of its value with that of a rigid molecule of similar size and shape. Two approaches will be taken to determine the relaxation time of the complex: (i) that for the pyrrolepyridine system where a literature association constant for 1:1 complex formation will be assumed and (ii) that for the pyridine-chloroform system where the relaxation time will be deduced solely from dielectric data. Thus procedure (ii) is an independent evaluation of the complex size and shape, whereas that of (i) is dependent on that of another method in that the type of complex formed (e.g., a 1:l) is assumed. However, method (i) (and also ii) not only yields a check on the type of complex formed but may give specific information regarding its shape. For example, the relaxation time of a 1:l complex of pyridine and pyrrole would be very dependent as to whether the hydrogen of the NH group of the pyrrole hydrogen bonded to the ?r-electrons of the pyridine along the six-fold axis or whether it formed a linear hydrogen bond of the type NH . iS. Thus the relaxation time approach differs from that of nmr and ir techniques in that it can sometimes yield direct information on both size and shape of small complexed species. The Journal of Physical Chemistry
Experimental Section The apparatus and procedure for determining the dielectric constant and loss have been previously described.2 Materials. Pyridine was purified by drying initially with potassium hydroxide and then phosphorus pentoxide. The pyridine was then distilled from a spinning band column of about thirty theoretical plates and then stored over phosphor\uspentoxide. Chloroform was purified by washing with sulfuric acid and distilled water. This was followed by washing with sodium hydroxide solution. It was then shaken six times with distilled water and dried over calcium chloride before being distilled from phosphorus pentoxide. Pyrrole was dried over potassium hydroxide pellets before distillation. Samples of each were analyzed by infrared and gas chromatography techniques to check purity and dryness. Results The dielectric absorption of dilute solutions of pyrrole and pyridine in cyclohexane at 15, 25, 35, and 50” were measured at 9.313, 16.20, 23.98, 34.86, and 70.0 GH5. In addition, the static dielectric constant at 2 MHz for each solution was determined. The data for these solutions were treated in the usual mannera and the results are given in Tables I and 11. Ternary solutions of pyrrole and pyridine in different mole fraction ratios in cyclohexane at 25’ and in a 1:1 mole fraction ratio at 15,35, and 50’ were also measured. (1) G. C. Pimentel and A . L. McClellan, “The Hydrogen Bond,” W. H. Freeman and Co., San Francisco, Calif., 1960. (2) W. F.Hassell, M. D. Magee, 8.W. Tucker, and S. Walker, Tetrahedron, 20, 2137 (1964). (3) M.D. Magee and S. Walker, Trans. Faraday Soc., 6 2 , 3093 (1966).
DIELECTRIC STUDIES
1271
c1 + cz + c3 =
Table I: Dielectric Constant and Loss Data for Solutions of Pyrrole and Pyridine in Cyclohexane a t Specified Weight Fractions we
i
Then
- -EO Ef
, Frequency, GHe 9.313 16 -20 23.98 34.86 70.0
€'
Pyrrole at 16" (wa
=
€It
0,06738)
2.216 2.204 2,175 2.161 2.118
I
I
Pyrrole at 35O (w2
9.313 16.20 23.98 34.86 70.0
Pyrrole at 50° (wn
9.313 16 -20 23.98 34.86 70.0
2.170 2,160 2.145 2,133 2.095
(w2
5
(WI
2.139 2.106 2,055
-
0 0255 0.0358 0.0476 0.0547 0 0682 I
0,03356)
0.0365 0 0554 0.0738 0.0815 0.0853 I
0.03355)
0.0263 0.0435 0.0597 0.0675 0.0748 0.03366)
w2712
w
+
1
+
2 2 = v f 0 73
czwrz
+
1
+
+ 1+
Caw73
w2722
w
2
2 73
= VIf
-
Previous polarization studies of the system by Gomel and Lumbrosoe have determined the dipole moment of the pyrrole-pyridine complex to be 4.05 D, which is slightly larger than the sum of the parent molecules, 3.93 D. Happe7 has calculated the association constant of the system in cyclohexane a t different temperatures from nmr measurements, and his results have been used to interpolate the association constants a t the temperatures used in the present work. If a and b are the initial mole fractions of pyrrole and pyridine, respectively, in the ternary solutions, and the mole fraction of this 1:1 complex7formed is m,the association constant K will be given by
I
-
+
c 3
Discussion
0.08083)
2.173 2,163 2.148 2.125 2.071 Pyridine at 50°
9.313 34.86 70.0
N
0,0309 0.0413 0.0584 0 0651 0.0678
2.221 2,209 2.194 2.170 2.092 Pyridine at 35O
9.313 16.20 23.98 34.86 70.0
0.06387)
I
Pyridine at 15O (wz
9.313 16.20 23.98 34.86 70.0
I
-
1
+ 1 +c2w
where the symbols have their usual meaning. Providing that 71, 72, and T8 are of similar magnitude, a plot of q f against 7" will approximate to a semicircle, but when the ratio of any two reiaxation times is large, and their weight factors significant, the beginning of the separation into two distinct dispersion regions becomes apparent. In the pyrrole-pyridine system at 25", rZ 73 2.5 X 1O-lZ sec for the noncomplexed molecules in cyclohexane solution.
0 0471 0.0668 0.0771 0 0805 0.0905
2.179 2,168 2.154 2.143 2.096
Em
+
I
-
-
E', _ - C1ur.1 1 w2712 Eo - Em
I
2.251 2.229 2,197 2,179 2 130
Em
and
0.0443 0.0563 0.0663 0 0693 0.0651
Pyrrole at 25O (we = 0.06958)
9 313 16.20 23.98 34.86 70.0
1
K=
?
0.0226 0.0587 0.0750
m
(a - m)(b - m)
Thus, by using Happe's association constant, m may be calculated for each solution. By using the literature value for the dipole moment of the complex ( p c ) , the dispersion of the complex (Do) may be deduced from the Debye equation p2
-
= SiCTM(E0 -1 - ,E
4rNd
The experimental data did not give a Cole-Cole4 semicircle, but a flattened plot for which e,, the highfrequency dielectric constant, could not be determined by the usual procedure. Bud65 has considered the complex dielectric constant to be the sum of Debye terms arising from discrete relaxation processes. For the pyrrole-pyridine system, three relaxation processes would be expected corresponding to the free pyrrole (74, free pyridine (r3), and the pyrrole-pyridine complex (rl), each process having the weight factors C1,C2, Cs,respectively, where
€0
~
+2
em
- I)
+2
to be
Do =
+ 2)2mdl
pO24rN(e1
27kTM1
where MI, €1, and cl1 are the molecular weight, static dielectric constant, and density of the solvent, respec(4) K.S.Cole and R.H. Cole, J. Chem. Phys., 9, 341 (1941). (5) A.Bud6, Phys. Z., 39,706 (1948). (6) M.Gomel and H. Lumbroso, Compt. Rend., 252, 3039 (1961). (7) J. Happe, J . Phys. Chem., 65,72 (1961).
Volume 74, Number 6 March 19,1970
1272
S. W. TUCKER AND S. WALKER
Table I1 : Dipole Moments ( p ) , Dielectric Constant a t Infinite Frequency (e-), Static Dielectric Constant (SO), Distribution Parameter (a),and Mean Relaxation Time (TO)for Specified Weight Fractions (wz) of Pyrrole and Pyridine in Cyclohexane Solute
w2
T,‘C
Pyrrole
0.05738 0.06959 ’0.05387 0,06083 0.03355 0.03355 0.03355
15 25 35 50 15 35 50
Pyridine
ro
x
101’
2.6 2.5 2.4 1.9 3.0 2.5 2.2
P
a
EO
€a
1.70 1.70 1.70 1.70 2,23 2.23 2.23
0.25 0.22 0.18 0.16 0.06 0.05 0.03
2,239 2.269 2.195 2.178 2.231 2.180 2.141
2.007 2.012 1.999 1.984 2.032 2 * 001 1.973
Table 111: Interpolated Equilibrium Constant ( K ) ,Calculated Dispersions, and Relaxation Time ( T ~of) Complex for the Pyrrole-Pyridine System in Cyclohexane
Solution
A B C D
E F G
Initial mole fraction pyrrole 4
Initial mole fraction pyridine b
OC
0.02352 0.01764 0.01532 0.03468 0 02320 0.02329 0.02308
0.02333 0.02582 0.03119 0.01711 0.02297 0 02375 0.02315
25 25 25 25 15 25 50
I
I
T,
27.5 27.5 27.5 27.5 35.3 21.7 15.9
-
DT = Do 4- DP 4- DPY and em for the solution may be calculated from €0
- DT
where eo is the measured static dielectric constant for the solution. The dispersions of the pyrrole-pyridine system are given in Table 111. The e” us. c’ plot is given in Figure 1 for one of the pyrrole-pyridine systems; the outer envelope embodies the experimental curve. The dispersions for the pyrrole, pyridine, and the complex are PQ, QR, and RS, respectively, and the distribution coefficients of the pyridine and pyrrole are taken into account in the corresponding Cole-Cole semicircles. The complex is assumed to have a zero distribution coefficient which would normally be the case for a species of such a size. The data for these ternary solutions are given in Table IV and those for the pyridine-chloroform-cyclohexane systems in Table V. For dilute solutions of polar molecules, dielectric loss at each wavelength is proportional to the mole fraction. Thus, from measurements at one or more The Journal of Physical Chemistry
Dispersion com p 1ex
m
0.00724 0.00609 0 00635 0.00735 0.00800 0 00647 0.00613
K
tively, since for dilute solutions EO N e, €1 and eo - e, is the dispersion of the complex. The dispersion of the free pyrrole D p and free pyridine DPYmay be calculated using the same equation with the appropriate values for the dipole moments and mole fractions. The total dispersion DT will then be given by
em =
Mole fraction complex
I
I
t 04 I
;’’! 0.05
Dispersion pyridine
DC
Dispersion pyrrole D,
0.120 0.101 0,106 0.122 0.140 0.102 0.075
0.048 0.034 0 026 0.080 0.047 0.048 0.046
0 081 0.099 0.125 0 049 0.080 0.080 0.079
DUY I
I
I
TI
x
lola
-25 -2 1 -J22 ~ 2 3 -35 -20 ~ 1 4
m 2’1
Figure 1. The
E’
e’-
R 2.2
2.3 S
vs. s‘ plot for a pyrrole ( m = 0.03468)-pyridine
(m = 0.01711)mixture in the solvent cyclohexane a t 25’ where m is the initial mole fraction of the polar component. The dispersions for the pyrrole, pyridine, and the complex are PQ, QR, and RS, respectively.
concentrations, the loss at each waveband of the free pyrrole e p t t and free pyridine epy” may be estimated. The loss of the complex eO” is given by Ec’l
= Emesa”
- (6P”
+
EPY”)
These calculated eo” values have been inserted on the absorption curve for the complex in Figure 1 taking into account that the higher the frequency the closer the point will lie to the e, value. The relaxation time (q)of the complex has then been deduced from this curve by employing the equation
v/u =
UT1
where v is the chord on this curve between the estimated loss point and eo, and u is the distance from the calcu-
DIELECTRIC STUDIES
1273
Table IV: Measured Dielectric Constant and Loss Data, and emeae” and the Calculated Loss of the Free Pyrrole and Pyridine ep” E ~ ~ ’and ’ Complex eo’’ for the Pyrrole-Pyridine System in Cyclohexane”
emeBg’
+
Table V: Dielectric Constant and Loss Data for Ternary Solutions of Pyridine and Chloroform a t 26’ a t Specified Mole Fractions a and b, Respectively, in Cyclohexane Frequency, GHz
Soh- Frequency, tion
GHs
mew’
A
9.313 16.20 23.98 34.86 70.0 (2KHz) 9.313 16.20 23.98 34.86 70.0 (2KHz) 9.313 16.20 23.98 34.86 70.01 (2KHz) 9.313 16.20 23 98 34.86 70.0 (2KHz) 9.313 16.20 23.98 34.86 70.0 (2KHz) 9.313 16.20 23.98 34.86 70.0 (2KHz) 9.313 16.20 23 98 34.86 70.0 (2KHz)
2.179 2.161 2.147 2,129 2.081 2.3132 2.179 2.162 2.139 2.128 2 095 2.2891 2.202 2.180 2.153 2.134 2.095 2.2994 2.179 2.160 2.141 2.124 2.100 2.3114 2,179 2.161 2.147 2.129 2.081 2.3509 2.170 2.152 2.123 2.116 2.064 2,2749 2.149 2.123 2.109 2.082 2.054 2.2187
B
C
D
I
E
E’
G
I
I
erneas”
ep”
4- €py’l
0.0782 0.0749 0.0708 0.0686 0.0618
0.020 0.034 0.041 0.049 0.052
0.058 0.041 0.030 0.020 0.010
0.0698 0.0691 0.0674 0 0672 0.0620
0.021 0.034 0.042 0.052 0.054
0.050 0.035 0.025 0.015 0.008
0 0772 0.0769 0.0755 0.0682 0 065
0 023 0.039 0.049 0.060 0.063
0 054 0.038 0.027 0,010 0 * 002
0.0779 0.0750 0.0685 0.0657 0.060
0.020 0.041 0.044 0.046 0.050
0.058 0 034 0.025 0.020 0,010
0.079 0.0759 0.070 0.065 0.0566
0.024 0.034 0.043 0.047 0.049
0.055 0.042 0 027 0,018 0.008
0 0746 0 0737 0.0689 0.0679 0.0586
0.021 0.034 0.043 0.050 0.054
0.053 0.040 0.026 0.018 0.005
0.0641 0.0673 0 0644 0.0605 0.0627
0.026 0.032 0.035 0.043 0 052
0.038 0.035 0.029 0.017 0.011
.mesar
9.313 16.20 23.98 34.86 70.0
2.141 2.134 2.118 2.105 2.062
a
I
I
I
I
I
I
I
coaled'
h0%Sft
rcalcd”
a = 0.01751, b = 0.02779
eot’
9.313 16.20 23.98 34.86 70.0
=
0.0352 0.0438 0.0476 0.0535 0.0519
9.313 16.20 23.98 34 86 70.0
0.035 0.041 0.048 0.055 0.055
0.02687, b = 0.01203
2.167 2.161 2.147 2.130 2.072
0.0360 0.0469 0.0548 0.0634 0.0655
u = 0.01294, b
I
2.13 2.12 2.11 2.10 2.06
2.107 2.101 2.092 2.081 2.061
=
2.16 2.15 2.14 2.12 2.07
0.036 0.046 0.056 0.066 0.070
0.01740
0.0238 0.0287 0 0322 0,0360 0.0384 I
2.10 2.09 2.09 2.08 2.05
0.022 0.028 0.034 0.039 0.040
2.12 2.11 2.10 2.09 2.06
0 030 0.036 0.042 0.049 0.050
a = 0.01268, b = 0.03365
I
9.313 16 20 23.98 34.86 70.0 I
2.125 2.120 2.110 2.100 2.072
0.0288 0.0375 0.0421 0.0471 0 0490 I
I
I
‘The lettering characterizing the solution is that employed in Table 111. lated high-frequency dielectric constant for the complex and the same loss point. The 71 values for the complex for the four solutions a t 25’ (see Table 111) are in good agreement and the trend of decreasing relaxation time with increase in temperature can be seen. The relaxation time of the complex of -23 X 10-l2 sec rt 20% (Table 111) may be compared with that of the molecular relaxation time of p-phenylphenol in Nec a t 25’ benzene8 which has a value of 23 X
which is a molecule fairly similar in size to a 1: 1 complex of pyrrole and pyridine where the NH. * . N is linear. Thus these relaxation time values establish both the size and shape of the complexed species and are in agreement with the 1:1 type of complex favored by Gomel and Lumbrosoa and also by H a ~ p e . ~ Four solutions each having a different mole fraction ratio of pyridine to chloroform were studied in cyclohexane at 25”. The Cole-Cole plots approximated to semicircles, and so the high-frequency dielectric constant em could be determined by computer analysis. Pyridine in various solvents has been previously examined by Hassell.9 For Debye behavior the plot of e’ vs. e ” d 0 is a straight line of slope - T , but for two relaxation times, sufficiently distinct in magnitude, a curve results. The extremes of slope then give an estimate of 71 and r2, but the steeper slope gives a value less than the true 71 and the lesser slope is greater than 72. The present results showed two slopes, yielding relaxation times (8) F . K. Fong and C. P . Smyth, J . Amer. Chem. Soc., 85, 1565 (1963). (9) W.F.Hassell, Ph.D. Thesis, University of Aston in Birmingham, 1966. (10) W.P.Purcell, K. Fish, and C. P. Smyth, J. Amer. Chem. SOC., 82,6299 (1960).
Volume 7.4, Number 6 March 19, 1970
8, W. TUCKER AND S. WALKER
1274
Table VI : Static Dielectric Constant, High-Frequency Dielectric Constant, Relaxation Times,a Distribution Coefficient, and Weight Factor Data for Various Mole Fractions of the Pyridine-Chloroform System in Cyclohexane at 25"
Solution
A
B C D a
Initial mole fraction pyridine
Initial mole fraction ahloroform
0.01761 0.02687 0.01294 0.01268
0.02779 0.01203 0.01740 0.03365
70
3.8 3.2 3.3 3.6
Tinit
T8eo
71
72
a 1
a
to
em
12 10 8.5 9.5
3.4 3.4 2.6 3.3
29 30 27 30
2.9 2.8 2.9 2.9
0.27 0.19 0.20 0.25
0.18 0.17 0.18 0.19
2.1650 2.1890 2.1176 2.1487
2.018 2.018 2.018 2.020
The relaxation time values have been multiplied by 1019.
which are referred to as Tinit and T~~~ and the results are given in Table VI, where Tinit provides a lower limit for the relaxation time of the complex (TI). Pyridine has a T~ (mean relaxation time) of 2.7 X 10-l2 sec in cyclohexane at 25O, and for chloroform in cyclohexane the sec (literature values ranging value is -3.5 X from 3.2 to 4.1 X 10-l2 sec) and the distribution coefficient, zero. Thus, it was thought feasible to analyze the results in Table V into two relaxation timesj3the shorter one (r2)being taken as a composite relaxation time of uncomplexed chloroform and pyridine. The rseovalue would thus be an upper limit for the r2 value. The r2 value obtained from the analysis of 2,9 X 10-l2 sec may be compared with rseo-3.3 X 10-l2 sec and lies between that for the molecular relaxation of chloroform and pyridine. The mean relaxation time ( T O ) values are not appreciably longer
The
JOUTW~
of Physical Chemistry
than the r2 values, indicating that the weight factor for the T~ process is much larger than that for the complex itself. These relaxation time values are given in Table VI. The relaxation time of benzotrichloride in cyclohexane at 25" is 23.5 X 10-l2 sec." A 1:1 complex of chloroform-pyridine complex with the N . . .H-C linear would be slightly longer and would be expected to have a longer relaxation time. The T I value of -30 X sec obtained from the analysis would seem reasonable for reorientation of such a complex and may be compared with the molecular relaxation times of 33 X 10-l2 sec for phenyltrimethysilane in cyclohexane at 25O." Thus, this approach indicates the formation of a 1: 1 complex and also identifies its shape. (11)
J. Crossley and 8. Walker, Can. J . Chem,, 46,841 (1968).
