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Polarity of Binary Liquid Mixtures.

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126) W. A. Herrmann, C. Kriiger, R. Goddard, I. Bernal, Angew. Chem. 89
(1977) 342; Angew. Chem. I n f . Ed. Engl. 16 (1977) 334: P. Hofmann, Angew. Chem. 91 (1979) 591; Angew. Chem. Int. Ed. Engl. 18 (1979) 554.
(271 There are some further details, not discussed here but treated elsewhere
[lo, I x , 3cI. In particular, the ML2 will have another relatively low-lying
orbital when L is a x acceptor.
[28] W. D. Jones, M. A. White, R. G. Bergman, J. Am. Chem. Soc. 100 (1978)
6770.
129) a) M. Green, J. A. K. Howard, R. N. Mills, G. N. Pain, F. G. A. Stone, P.
Woodward, J. Chem. Soc. Chem. Commun. 1981, 869: b) For some other
compounds containing a similar unit see L. M. Cirjat,
Huang, Z.-H.
Zhu, L. F. Dahl, J. Am. Chem. Sot. 102 (1980) 6623.
[30] N. M. Boag, M. Green, D. M. Grove, J. A. K. Howard, J. L. Spencer, F.
G. A. Stone, J. Chem. SOC.Dalton Trans. 1981. 2170.
[31] a) F. G. A. Stone, Acc. Chem. Res. 14 (1981) 318 and references therein:
L. Busetto, M. Green, J. A. K. Howard, B. Hessner, J. C. Jeffery, R. M.
Mills, F. G. A. Stone, P. Woodward, J. Chem. SOC.Chem. Commun.
1981. 1101; T. V. Ashworth, M. J. Chetcuti, L. J. Farrugia, J. A. K. Howard, J. C. Jeffery, R. Mills, G. N. Pain, F. G. A. Stone, P. Woodward
Reactiuity of Metal-metal Bonds. A C S Symposium Series 755 in M. H.
Chisholm: Washington 1982, p. 299. b) For futher molecules of type 71
and 72 see E. Sappa, A. m. Manotti Lanfredi, A. Tiripicchio, J. Organomet. Chem. 221 (1981) 93: J . R. Shapley, J. T. Park, M. R. Churchill, C.
Bueno, H. J. Wasserman, J. Am. Chem. Soc. 103 (1981) 7385: G. Jaouen,
A. Marinetti, 8. Mentzen, R. Mutin, JK.-Y. Saillard, B. G. Sayer, M. J.
McGlinchey, unpublished results.
[32] a) W.-D. Stohrer, R. Hoffmann, J. Am. Chem. SOC.90 (1972) 1661: b) R.
E. Williams, Inorg. Chem. 10 (1971) 210: Adu. Inorg. Chem. Radiochem.
18 (1976) 67; c) S. Masamune, M. Sakai, H. Ona, J. Am. Chem. SOC.94
(1972) 8955; S. Masamune, M. Sakai, H. Ona, A. L. Jones, ibid. 94
(1972) 8956; d ) H. Hart, M. Kuzuya, ibid. 94 (1972) 8958.
[33] See in this context: J. Chandrasekhar, P. v. R. Schleyer, H. B. Schlegel,
Tetrahedron Lett. 1978, 3393.
[34] Cf. [li]for the relevant literature citations.
[35] H. Hogeveen, P. W. Kwant, Acc. Chem. Res. 8 (1975) 413. For some related main group structures see: P. Jutzi, F. Kohl, P. Hofmann, C. Kriiger,
Y.-H. Tsay, Chem. Ber. 113 (1980) 757.
[361 But apparently not a stable structure after all: A. Sevin, A. Devaquet,
Now. J . Chim. 111977) 357; T. Clark, P. v. R. Schleyer, ibid. 2 (1978)
665.
[371 R. J. Al-Essa, R. J. Puddephatt, P. J. Thompson, C. F. H. Tipper, J. Am.
Chem. SOC.I02 (1980) 7546 and references therein.
[381 C. P. Casey, D. M. Scheck, A. J. Shusterman, J. Am. Chem. SOC.101
(1979) 4233.
[391 Cf. M. Saunders, H.-U. Siehl, J. Am. Chem. SOC.102 (1980) 6868 and references therein.
(401 The exceptions include Zr(BH,),, W(RCCR)>(CO), Cp,M a n d Cp,MR,
Cp,U, UO?Lh;among others. For the relevant references see S.-Y. Chu,
R. Hoffmann, J. Phys. Chem. 86 (1982) 1289 and [3a].
[411 D. M. Hoffman, R. Hoffmann, C. R. Fisel, J. Am. Chem. SOC.104 (1982)
3858: D. M. Hoffmann, R. Hoffmann, J. Chem. SOC.Dalton Trans., in
press.
[421 H. J. Langenbach, E. Keller, H. Vahrenkamp, J. Organomet. Chem. 191
(1980) 95.
Polarity of Binary Liquid Mixtures
By Heinz Langhals*
In contrast to the thoroughly studied polarity properties of pure liquids, only little is known
about the polarity of mixtures of liquids, although the majority of mechanistic and preparative work is not carried out in pure phases. Using a widely applicable two-parameter equation, polar behavior of binary liquid mixtures can be described quantitatively as a function
of their composition. Based on this equation, satisfactory explanations are found for deviations observed for binary solvent mixtures from the linear correlation of polarity scales, as
well as for the unusual activation parameters estimated by Winstein for solvolysis of tert-butyl chloride. Applications of the equation range from a rapid test for determining water contents of solvents, the study of reaction mechanisms, to polymer chemistry.
1. Introduction
2. Empirical Polarity Scales
Solvent polarity has been interesting to chemists for
some considerable
Macroscopic physical quantities, such as dielectric constant o r refractive index are of
only limited use for studying chemical reaction behavior
and the associated molecular p r o c e ~ s e s ~ ~the
~ ~ develop-*~:
ment of the empirical polarity scales, however, was a substantial advance. The oldest, the Y-scale of Winstein and
G r u n ~ a l d [ ~ - "shown
],
in equation (l), is based on the solvolysis of tert-butyl chloride and often correctly describes
the influence of solvents on the rate of chemical reactions.
Today, the Winstein Y-values are widely used as a primary polarity scale. Being derived from a solvolysis reaction, the Y-scale is, however, confined to polar media.
Therefore, a number of other polarity scales[" of wider applicability were developed, based on reaction kinetics o r
spectroscopic data. Scales derived from solvatochromism
of dyes are noted for their straightforward and precise
measurement112.13]. Most remarkable is the ET(30)-scale of
Dimroth and R e i ~ h a r d t " ~ . ' which
~],
has become the most
widely used scale: the solvatochromic dye pentaphenyl pyridiniumphenolate 1, which serves as reference substance,
k
lg-=
ko
Y
k = r a t e constant of the solvolysis of (CH,),CCI in the medium to
be studied
k,=rate constant of the solvolysis of (CH3)3CCl in 80% ethanolwater.
[*I
Priv.-Doz. Dr. H. Langhals
Chemisches Laboratorium der Universitat
Albertstrasse 21, D-7800 Freiburg (Germany)
724
0 Verlag Cliemie GmbH. 6940 Weinheim. 1982
0570-0833/82/1010-0724 $ 02.50/0
Angew. Chem. I n [ . Ed. Engl. 21 (1982) 724-733
exhibits a peak shift of its longest wavelength UV/VIS-absorption maximum-one of the largest known-when the
solvent polarity is changed; moreover, it is soluble in almost all known solvents. The ET(30)-values are the excitation energies [kcal.mol-'] of 1 and are calculated from
A,,,, of the solvatochromic peak of 1 according to formula
(2).
ET(30)=28590 [kcal~nm~mol-']/A,,,
ries expansion[241as well as by using several hyperbolic
function~[~~I.
It was shown recently[261that plotting ET(30)-values
against the logarithm of the molar concentration of the
more polar component (Inc,) produces curves with a linear
section. This is shown in Figure l a for the typical mixture
N-tert-butylformamide-benzene.
(2)
ET(30)-values show good linear correlation with the Y-values of various solvents1I1.It is remarkable that such linear
correlation of polarity scales is observed not only between
ET(30) and Y, but also applies to most empirical scales"].
The fact that a polarity concept applicable o n the molecular scale exists, even if it is only comprehensible on an
empirical basis, had important consequences for both mechanistic and preparative organic chemistry.
A few polarity scales d o not correlate with the ET(30)scale (see Section 3.2). One, for example, is the donor
number D N of Gutmann1161,
which describes Lewis basicity
rather than polarity of a solvent. The DN-scale has proved
useful for describing processes involving the nucleophilicity of the solvent. It was recently attempted to include
other such solvent properties together with polarity in a
multi-parameter
This evaluation corresponds to the principle of polylinearity (PPL) of Palm["],
and is similar to the multi-parameter evaluation of Cramer[20.2 I ]
3. Binary Mixtures
For practical applications empirical polarity scales characterize polar behavior of liquids reasonably well. Surprisingly, however, the linear correlation which applies to pure
solvents deteriorates when solvent mixtures are included", 15-221. However, such mixtures are rather useful for
studying solvent effects, since the properties of various solvents can be adjusted continuously by changing the mixture ratio.
3.1. Polarity as a Function of Composition
A widely applicable equation containing only a few parameters for the quantitative description of the polarity of
binary solvent mixtures as a function of their composition
was long a key problem.
Dimroth and Reichardt et ~ 1 . ~ ' used
~ . the ET(30)-scale,
for example, to study the polarity of the binary mixtures
ethanol-water, isopropanol-water, methanol-water, acetone-water, 1,4-dioxane-water, pyridine-water, 2,6-lutidine-water, and piperidine-water as a function of their composition. Plotting the ET(30)-values versus composition, expressed as v01.-% of one component, however, does not afford a linear relationship, as one might expect but strongly
curved lines which could not, as previously found in other
I . 20.231, be readily interpreted. Approximation of the
complex functional curve has been attempted by 'Taylor se[*] lf a relationship between two scales is not only monotonic, but also li-
near, it can be concluded that both scales conform to the same law.
Angew. Chem. h i . Ed. Engl. 21 (19821 724-733
Fig. 1. ET(30)-values for the mixture N-tert-butylformamide-benzene, a) as a
function of Inc,, b) as a function of In(c,/c*+ 1) from equation (3).
In the study of solvolysis reactions, Tommila1*'I also
found curves with linear sections by plotting Igc, of binary
mixtures against the free activation enthalpy of solvolysis.
The linear section was interpreted as arising from nucleophilic solvent participation in the reaction. Nucleophilic
solvent participation of this type, however, is not possible
in the case of the ET(30)-scale.
Using the ET(30)-scale with dye 1 as reference substance
the course of the curve can be examined even at low concentrations c,. In this region the curve deviates from linearity and as c,-O it tends to E+(30), the ET(30)-value of
the pure, less polar component (cf. Fig. la). Using the
dual-parameter equation (3) the entire course of the curve
can be described in closed form, including the curved sectionfZ61.
+ 1+
(:::
ET(30)=ED.1n -
1
E:(30)
(3)
ET(30) in equation (3) is the polarity of the binary mixture: E+(30) and cp were explained above, and E D and c*
are the parameters of the equation. They can be determined graphically[26.281
or using the POLAR computer program[261.The validity of equation (3) can be demonstrated
725
+
by plotting ET(30) against In (c,/c* I ) using, for example,
the mixture N-rut-butylformamide-benzene (Fig. Ib). This
produces a straight line which is shown covering a region
of three orders of magnitude of cp. Deviations from this
linear section are statistical in nature and correspond to
experimental error.
In terms of the criteria used in all the polarity scales
studied to date, equation (4) is a valid description of polar
behavior of binary liquid mixtures as a function of their
composition“”]. The linear relationship between Pti or
Pc;- @,, respectively, and In (cp/c* I), for some polarity
scales mentioned in Table I is illustrated in Figure 2.
+
3.1.1. The Parameters of Equation (3)
The parameter EDhas the dimension of energy and is a
measure of the sensitivity of the ET(30)-scale towards relative changes of c,. The parameter c*, with the dimension of
concentration, divides the curve in Figure l a into two
parts-this can be demonstrated by considering the limiting value of ~ 2 ’ If~ c,<c*,
~ . a linear relationship between
ET(30) and cp results, as can be shown by applying a series
expansion to equation (3). Thus, in this concentration
range, the contributions of both components to polarity
are cumulative[*).
If, however, c , > c* a linear relationship between ET(30)
and Inc, results. This case corresponds to the linear part of
the curve in Figure l a ; thus, c* divides this curve into a
linear and a logarithmic part, and specifies the threshold
value at which the two liquids start to interact according to
equation (3).
The experimentally accessible range of cp extends from
the pure, less polar component, c,=O, to the pure, more
polar component, cp=c;“’. As mentioned previously, the
polar contributions of both components are approximately
and the frecumulative over the entire range, if c* %c;“’,
quently postulated linear relationship between polarity
and composition of the mixture is satisfied (review: [ ’ ’I).
If, however, c* is very small, say <0.06 mol. L- I, the correlation between polarity and e,, is non-linear over the experimentally relevant concentration range.
3.1.2. Further Polarity Scales
The conformity to a natural law indicated by equation
(3) for the ET(30)-scale has also been found with other polarity scale^['"^'^, and can be expressed in general form by
equation (4).
(4)
I n equation (4) Pc is the polarity of the binary liquid mixture according to an empirical polarity scale and
is the
Pc; value of the pure, less polar component. The parameters c, c*, and E D are as described in equation (3). Essentially, both equations show similar behavior when considering limiting values (see Section 3.1.1).
Empirical polarity scales, a selection of which is shown
in Table I , are based on various effects, such as n+n* absorption (Nos. 1,4-7), charge-transfer absorption (No. 3),
fluorescence (Nos. 8,9), and solvolysis (No. 2). The &(I)scale (No. 5) responds not only to the polarity of the medium, but also shows sensitive response to its hydrogen
bonding/donor character.
[*J Plotting ET(30)values against lnc,, produces a curved line: the left branch
in Figure la.
126
Fig. 2. Linear relationship between P<, and In(r,/c*+ I ) for various polarity
scales (equation 4): A E,(30) ethanol-I-decanol, x = I ; 0 Y water-methanol,
Y = I:
Z methanol-acetone, x = 2 ; V n; ethanol-n-heptane, x = I, ordinate
f<,- C! + 5.8.
Table 2 gives an impression of the range of validity of
equation (4), and shows the results of applying it to the
nine polarity scales in Table 1. The number and variety of
the components used-polar protic, dipolar aprotic, and
non-polar solvents, including aromatic solvents, were combined-lead to the conclusion that equation (4) provides a
general description of the polarity of binary mixtures and
is not confined to certain types of solvent[3R1.Its validity
for scale 5 and the mixture e t h a n ~ l - w a t e r ~ ~which
” ] , has a
strong tendency to form H-bonds, is particularly notable.
Thus, polarity effects caused by hydrogen bonding are also
described by equation (4).
3.1.3. Special Cases
Special features are observed with the solvent mixture
water-1,4-dioxane: up to a water content of ca. 50%, normal behavior according to equation (3) is observed with
the ET(30)-scale. At a certain critical concentration ckr
however, the linear relationship abruptly gives way to a
second, steeper relationship with other ED- and c*-Values[’91
In the following discussion, the concentration ranges
and c,>c,
are designated region 1 and region 11.
For the mixture water-1,4-dioxane, the sudden change at
ck (discontinuity in the 1st derivative) can even be detected
if E,(30) is plotted against Inc,, i.e. without introducing
further parameters.
The existence of two regions of validity for equation (3)
with a critical change at c k could be interpreted by considering that largely isolated water molecules occur at low
water concentrations in region I, and that formation of hydrogen bonded structures of water occur in region 11. In
another context it was postulated that 1,Cdioxane acts as
a “solvent-structure-breaker”13y1.This model is consistent
with the results of the polarity measurements.
c,<ck
Angew. Chem. I n t . Ed. Engl. 21 (1982) 724-733
Table I . Empirical solvent polarity scales.
No.
Scala [a]
Reference
Substance
Solvent dependent process
Definition [b]
1
1
2
2
n-n*-absorption
Solvolysis relative to solvolysis in 80% ethanollwater (k,,)
E~(30)=28590/rl,m,[C]
k
Y=Ig-[d]
ko
Z = 28 590/d,.,, [Cl
nl; = 28 590/d,.,, Ic, el
ET( 1) = 28 950/L,,
[c]
MOED=28590/1,,, [c]
X R = 28 590/L, ,x [Cl
Sl = 28 590/d, ,x [c]
Sz=28590/Ar,,,, [c]
z
3
nt
4
MOED
XH
6
7
SI
S.
8, R = C H i
8, R = H
5
CT-absorption
n-n*-absorption
n-n*-absorption
n-n*-absorption
n-n*-absorption
fluorescence
fluorescencc
Ref.
[a] For other polarity scales, see [I].[b] At 25 "C. [c] Molar excitation or emission energies in kcal. mol- I : for conversion into Sl units, multiply by the factor 4.2. [d]
In Y units; for conversion into kcal.mol-', multiply by the factor 0.733. [el In [I71 molar excitation energies are stated in c m - ' . These were converted into
kcal. mol ' for direct comparison with other scales.
~
Table 2. The parameters E D and c * from equation (4) for bindry solvent mixtures
No.
I
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
Components [a]
I -Butanol-acetone
Ethanol-acetone
Methanol-acetone
Wasser-acetone
N-rert-Butylformamide-acetone
Butanediol- 1,4-acetonitrile
Ethanol-acetonitrile
I -Hexanol-acetonitrile
Methanol-acetonitrile
Water-acetonitrile
N-fen-Butylformamide-benzene
Water-/err-butyl alcohol
Water-/err-butyl hydroperoxide
Ethanol- I-decanol
I -ButanolLdimethylformamide
Ethanol-dimethylformamide
Methanol-dimethylformamide
Water-dimethylformamide
I-Butanol-dimethyl sulfoxide
Ethanol-dimethyl sulfoxide
Acetonitrile- I ,4-dioxane
I-Butanol- 1.4-dioxane
Ethanol- 1.4-dioxane
Methanol- 1.4-dioxane
Methanol- 1.4-dioxane
Nitromethane- I ,4-dioxane
Propiononitrile- 1 ,4-dioxane
Water- 1.4-dioxane
Water-ethanol
I -Butanol-nitromethane
Ethanol-nitromethane
Methanol-nitromethane
Water- I-propanol
Acetone-pyridine
I -1lodecanol-pyridine
Ethanol-pyridine
I -HexanolLpyridine
Methanol-pyridine
Nitromethan-pydridine
(err- Pentanol- pyridine
Water-pyridine
I-Butanol-CS.
I -Octanol-CSI
Pinacolone-CSl
I -Butanol-tetramethyl urea
Ethanol-tetramethyl urea
Water-ethanol
Water-methanol
Methanol-acetone
Ethanol-acetonitrile
Methanol- 1.4-dioxane
Water-ethanol
Ethanol-ti-heptane
Angew. Chem. In/.Ed. Engl. 21 (1982) 724-733
0.01- 10.9
0.02-17.1
0.03-24.7
0.06-55.4
0.01-9.0
0.01 -12.5
0.01-17. I
0.01-8.0
0.03-24.7
0.06-49.8
0.01-9.0
0.06 -33.2
0.4-7.4
0.02- 17.I
0 01.- 10.9
0.02-17. I
0.03-24.7
0.06-38.8
0.01- 10.9
0.02-17.1
0.02-19.1
0.01-10. I
0.02-17.1
0.03-3.0
3.0-24.7
0.02- 18.6
0.0 I 14.1
0.6-55.4
0.06-55.4
0.01- 10.9
0.02-17.1
0.03-22.2
0.06-55.4
0.03-12.2
0.004-4.5
0.02-17.1
0.01-8.0
0.03-24.7
0.02- 18.6
0.005-8.3
0.06-49.8
0.01-10.9
0.01-6.4
0.3-8.0
0.0 I 10.9
0.02-17.1
0.06-30
0.06-55.4
0.03-24.7
0.02-17.1
0.03-24.7
0.06-55.4
0.02-17. I
~
~
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
3
3
4
4
42.2
42.2
42.2
42.2
46.0
46.0
46.0
46.0
46.0
46.0
35.2
43.9
49.7
47.6
43.8
43.8
43.8
43.8
45.0
45.0
36.0
36.0
36.0
36.0
(32.) [ml
36.0
36.0
36.0
51.9
46.3
46.3
46.3
50.7
40.2
40.2
40.2
40.2
40.2
40.2
40.2
40.2
32.6
32.6
32.6
41.0
41.0
- 2.05
- 1.12
66.3
72.2
63.0
74.8
78.7
0. I4
0.14
0.10
0.31
0.27
0.01
0.10
0.08
0.06
0.15
0.017
1.01
0.312
4.09
I .64
0.607
0.696
11.43
4.29
2.69
0.77
0.90
0.72
0.98
0.089
1.01
1.41
0.58
6.83
0.06
0.03
0.0 I
4.34
32.06
0.89
12.75
1.1 1
5.84
13.62
0.95
5.48
0.03
0.06
7.89
0.9 I
0.81
7.48
24.0
0.65
0.80
2.66
3.08
2.93
I .99
2.27
2.53
2.83
1.87
1.53
1.83
1.08
I .83
2.07
2.42
2.82
1.40
2.35
3.20
2.78
3.55
9.24
4.93
3.95
3.23
5.39
4.99
7.67
4.09
3.49
3.33
4.34
1.64
I .43
1.41
1.66
I .70
4.0 I
2.90
9.64
2.90
6.92
6.46
1.02
7.09
2.42
2.83
9.30
3.56
3.5 1
0.64
3.91
4.66
2.76
8.52
- 1.71
-3.13
0.01
0.02
0.02
0.02
0.0 I
0.06
0.01
0.02
0.03
0.02
0.02
0.05
0.02
0.02
0.02
0.04
0.05
0. I 8
0. I
0.05
0.03
0.03
0.03
0.03
0.08
0.03
0.03
0.05
0.04
0.02
0.03
0.02
0.02
0.13
0.03
0.17
0.05
0.08
0. I4
0.03
0.12
0.03
0.06
0.26
0.03
0.03
0.01
0.03
0.0 I
0.04
0.18
0.02
0.04
0.99952
0.99939
0.99973
0.99963
0.99948
0.99749
0.99972
0.99876
0.99877
0.99877
0.99935
0.99666
0.99922
0.99915
0.99936
0.99792
0.99745
0.99527
0.99475
0.99794
0.99909
0.99973
0.99975
0.99980
0.99828
0.99929
0.99834
0.99922
0.99232
0.999 14
0.99704
0.99947
0.99768
0.987 10
0.99901
0.99554
0.99763
0.99802
0.99384
0.99341
0.99599
0.99906
0.99676
0.99459
0.99936
0.99925
0.99956
0.99972
0.99993
0.9978 I
0.99384
- 0.99846
-0.99681
31
28
29
29
31
31
30
29
31
27
30
26
12
30
30
30
31
27
30
30
29
30
30
20
10
31
30
22
27
31
30
29
30
28
30
31
30
31
30
29
29
30
30
16
31
31
12
II
31
47
31
31
33
-
-
16.5 [k]
-
-
12.0
-
-
8.7
13.7
-
7.7
13.7
-
~
3.0
(3.0)
-
_.
22.0
[q
-~
6.5
8.5
10.0
36
-
3.0
7.5
4.0
-
-
25
-
-
6.8
-
25
-
727
Table 2. Continuation
~~
~
No.
~~
Components [a]
CP
Ib, cl
54
55
56
57
58
59
60
Water-ethanol
Methanol-acetone
Water-ethanol
1 -Butanol-nitromethane
Methanol-acetone
Methanol-acetone
Wasser- I-propanol
0.06-55.4
0.03-24.7
0.06-55.4
0.01-10.9
0.03-4.0
4.0-25
0.06-55.4
Reference
substance
f2
C*
[d, el
[c, 4
5
35.2
49.7
49.3
0.3 1
55.9
5.47
44.4
2.86
61.2
0.50
(58.3) [m] 2.1 I
54.7
1.53
6
6
7
8
8
8
ED
[d, fl
6.67
2.25
2.04
- 1.15
-2.19
- 1.58
-0.47
a(Ed
[gl
0.10
0.01
0.06
0.15
0.02
0.01
0.01
r
[hi
0.99740
0.99952
0.99186
-0.98776
-0.99962
-0.99983
-0,99604
n
ti1
34
30
24
31
22
10
31
Ck
[c, 4
25
-
25
4.4
4.0
(4.0)
36
[a] The more polar solvent is mentioned first; both components in alphabetical order. [b] Concentration range studied. [c] In mo1.L-I. [d] I n kcal'mol-'. [el f G
value of the less polar component, see [2J.[fl See text. [g] Variance of ED.[h] Correlation coefficient of equation (4). [i] Number of points. [kJIf c m > c kE,=6.8
,
and
c*=6.1. [I] If cp<ck,ED=20.0 and c*=19.1. [mlExtrapolated value.
ter, as the more polar component, affects dioxane within
region I. Since the effective polarity of water is substantially lower at high dilution than in concentrated solutions,
one might venture to conclude that specific interaction of
water molecules in molecular associates is responsible for
the high polarity of pure water, rather than the characteristics of the isolated water molecule.
The occurrence of a second, steeper line according to
equation (3) is not confined to the mixture water- 1,4-dioxane, but can also be observed with other mixtures, especially with those including water, e. g. w a t e r - a c e t ~ n e [ ~ ~ ' .
The mixture water-ethanol has been studied extensively
using several polarity scales[291.All the scales studied produced double lines (three examples are shown in Figure
4).
6
5
il;
1
0
"G
50
-
LO-
Fig. 4. Double lines according to equation (4) for the mixture water-ethanol
E T ( 1 ) , x = l , y = 4 ; A n;,x=l,y=4,ordinate:
(No.29): 0 Y , x = 2 , y = I ;
.-
I
PG-E i 7 . 1 .
1
-2
0
2
hcp-
It
fig. 3. Double line for the mixture water-1,4-dioxane (No. 28).
In Figure 3, the linear part of region I can be extrapolated into region I1 (broken line; an even more exact result
is achieved by plotting against In(c,/c*+ 1) instead of
Inc,). Thus, for C,=C?,
a virtual polarity value is obtained for water, Pv = 56, which is smaller than the actual
polarity value of 63.1[*].Pv is the polarity with which wa-
728
It is remarkable that the various polarity scales produce
c,-values which coincide within the limits of experimental
error"]. Thus, the double-line phenomenon is not peculiar
to the ET(30)-scale, but must be taken as a characteristic of
the binary mixture water-ethanol. This problem will be discussed in more detail in Section 4.1.
Even more interesting than the examples mentioned
above are mixtures of I-butanol and acetonitrile or nitromethane, and of ethanol and nitromethane, which repre[*I In Figure 4 the break points appear at different abscissae since the c* values vary for each polarity scale.
Angew. Chem. Int. Ed. Engl. 21 (1982) 724-733
sent a further type of binary mixture[311.Here, also, two
straight lines are observed. The second line, however, has a
negative slope, contrary to the previous cases. This is
shown in Figure 5 for the mixture l-butanol-nitromethane.
J
I
/*‘
L 0
5
5
In Ic, / c*+ 1)
L
-
S
2
W
U
intc,/c*+l)-*
Fig. 5. Relationship between ET(30) and a) In(c,/c*+ I ) and b) In(c,/c*+ 1)
for the mixture I-butanol-nitromethane.
The polarity of the mixture increases as cp increases and
reaches its maximum at ck. As cp increases further, however, the polarity again decreases and attains the polarity
value of the pure, more polar component at
Within
region I , c,<ck, normal behavior according to equation (3)
is observed (see Fig. 5a). Within region 11, however, nitromethane, which as a pure substance is less polar, interacts with I-butanol like a more polar additive. Accordingly, in this region there is a linear relationship between
ET(30) and In(c,/c*
I), where c, is the molar concentration of the less polar component (Fig. 5b). By analogy t o
the previous examples, a virtual polarity can be defined for
the polar component I-butanol. Contrary to these previous
cases, however, it is greater than the actual polarity of the
alcohol.
Mixtures with cp=ck are substantially more polar than
their components. This phenomenon, known as “elevated
or the “synergetic polarity
can be
explained by a hydrogen-bond/donor-acceptor model : the
additive, which itself has low polarity, promotes the formation of a polar solvent structure. This behavior is remarkable insofar as it contradicts the usual view that the polarity
of a solvent mixture lies within the limits of the polarity of
its components ; furthermore, the polarity of solvents can
be enhanced by adding less polar components.
vents are concerned. A few scales form an exception, but
these also mutually correlate. This behavior typically occurs with weakly polar merocyanines with positive solvat o c h r o m i ~ m [ ~ .One
~ * ~ .of the first cases to be studied is
Br~oker’s[’~I
xR-scale (Table 1, No. 7), which is based on
the solvatochromism of dye 7. Polarity scales such as xR
will be discussed extensively here, particularly their application to binary solvent mixtures.
Studies of the solvatochromism of phthalimide derivatives 8 indicate that these exhibit strongly positive solvatochromism in fluorescence phenomena, and this was proposed as the basis for the S polarity scale by Zelinski et
u1.[35.361
(for the influence of oxygen, cf. l3’l). Absorption by
these dyes is also solvatochromic~301.
A linear relationship
with the ET(30)-scale exists for fluorescence, but for absorption a linear relationship with the XR-scale is observed.
Thus, dye 8 is especially suitable for clarifying the previously mentioned exceptions, since it supplies a common
basis for both groups of polarity scales.
It is known that the ground state (So) of 8 has only a
small dipole moment; however, the first electronically excited state ( S , ) , has a large dipole moment[’]. The different
behavior of 8 in absorption and emission can be explained
by assuming that states with large dipole moments are
strongly solvated by polar solvents, whereas states with
small dipole moments are solvated weakly: the FranckCondon principle for electronic transitions applies to the
solvating shell of a dye[431.The electronic transition takes
place in such a short period of time that solvation is unable
to follow by reorienting the solvent molecules. Consequently, orientation will only influence solvation in the initial state of an electronic transition, but not the final state.
The latter will still bear the solvating shell of the initial
state, and can only be stabilized by polarization effects.
Absorption and fluorescence of 8 proceed as given in the
scheme in Figure 6. The initial state, So, is little influenced
by polar solvents.
+
3.2. Slow and Fast Processes
The majority of polarity scales show mutual linear correlation and with the Y- and ET(30)-scales, as far as pure solAngew. Chem. l n t . Ed. Engl. 21 (1982) 724-733
4
I
M
Fig. 6. Schematic representation of absorption and emission processes o f dye
8 in polar solvents.
The excited state, S , , has a large dipole moment, but is
surrounded by the solvating shell of the So state. Thus, solvent polarization effects are crucial for absorption- by
analogy to the
scale.
Excitation is followed by relaxation of the solvating
shell; the lifetime of the excited state ( S , ) of cu. lo-‘ to
xR
729
lO-'s is long enough to permit a more favorable orientation of the solvent molecules surrounding the dye molecule. The transition from s, to s',corresponds to the modification (M) as described for reactions of the excited state
in which the excitation energy is
Finally, the
transition from S ; to S;,occurs by fluorescence, the energy
of which is fully influenced by solvent orientation phenomena (besides polarization effects) because the dipole
moment of the initial state of this electronic transition is
large. It is therefore reasonable that the fluorescence of 8
correlates with the ET(30)-scale. The absorption of dye 1 is
subject to an analogous situation. However, in most cases,
the behavior of other dyes is by no means as extreme as the
absorption of 7 or 8, and a combination of polarization
and orientation effects are observed. Frequently, however,
the orientation phenomena prevail, and this results in correlation with the ET(30)-scale. These considerations
allow the conclusion to be made that dye 7 (XR scale) is a
polarity indicator for short measuring times, whereas dye 1
(ET(30) scale) is suitable for long measuring times (cf. the
concept proposed by B a k h s h i e ~ ~ ~In~ 'organic
).
chemistry
the orientation of the solvent, a relatively slow process, is
o f crucial influence. Thus, it is reasonable that such processes are correctly described by the ET(30)-scale.
Equation (4) characterizes the polar behavior of binary
liquid mixtures according to the XR-scale or to an absorption scale using dye 8 as reference. Thus, it can be concluded, that equation (4) will also describe the polar behavior of binary solvent mixtures in fast processes. Equation (4) cannot, therefore, be solely attributed to the concentration of the polar solvent on the surface of the
Further information on solvent structure is provided by comparing the c* values of dye 8 in solvent mixtures for absorption and
Y
5
0
-5
Fig. 7. Thermodynamic data for the solvolysis orterr-butyl chloride in ethanol-water [ I I].
simple functional course, and that the apparently simpler
quantities AH' and AS', however, appear so complicated. Since the solvolysis of tert-butyl chloride is sensitive
to polarity changes in the medium, an analysis of Winstein's and Fainberg's measurements using equation (4) appears appropriate. As shown in Figure 8, the free energy of
activation AG$X of the solvolysis of tert-butyl chloride in
ethanol-water mixtures and the correspondingly proportional quantities Ink,,, or Y can be described quantitatively by equation (4) as a function of composition.
An interesting point is-as with other polarity scales
(see Section 3.1.3)-that two regions of validity of equation (4) with a critical transition point at ck Z= 25 mol . L- '
(double lines) are observed. Thus, the free entropy of activation shows nothing anomalous. The high precision o f
Winstein's kinetic measurements must be stressed; this is
clearly expressed by the lines in Figure 8 and Figure 2.
4. Applications of Equation (4)
Equation (4) characterizes, quantitatively, the polar behavior of binary liquid mixtures, and there are no shortage
of examples of its use as a "tool" in many areas o f chemistry. Applications to mechanistic problems are discussed
first.
4.1. Solvolysis of tert-Butyl Chloride in Ethanol-Water
The discovery of the Winstein relationship['], which is
based on the solvolysis of fert-butyl chloride, played a key
role in the development of the empirical polarity concept.
Subsequently, Winstein studied the influence of temperature on the solvolysis of tert-butyl chloride in ethanol-water mixtures['". The free energy of activation, AG', of this
reaction decreases as a monotonic function without strong
curves as the water content of the mixture is decreased: the
course of AH' and AS', however, is more complex and
maxima and minima occur (see Fig. 7).
This unusual and surprising behavior led to numerous
speculations'"'3Y-4X-541.
A satisfying explanation of the experimental data published 25 years ago has yet to be
found. It seems to contradict experience that the AC' value, which is composed of enthalpy and entropy terms has a
730
Fig. 8. Analysis of solvolysis data of ,err-butyl chloride in ethanol-water according to equation (4).
The activation enthalpy AH' and the activation entropy
AS' of the reaction were calculated from the rate constants at only two temperatures, respectively'' '], in the
range 0 to 45 vol. Yo water at 25 and 50 "C and in the range
of 50 to 100 vol.% water at 0" and 25 "C. It can be shown
that for the series of measurements at 0 "C and 50 "C equation (4)also holds (see Table 3); their E D and c* values are
only slightly different from the measurements at 25 "C.
Anyew. Chem. In,. Ed. Enyl. 21 (1982) 724-733
Table 3. Application of equation (4) to the Winstein scale.
T [a1
Range [b]
En [c]
c*
25
50
0
25
(AH')Ibl
I
2.9
2.4
2.6
2.1
-0.944 [i]
11.6
9.7
0.001
0.001
0.26
1
I1
I1
I
[d]
4.2. Nonlinear Winstein Relationships
M
Y" [el
r
1.97
- 0.52
(-26.9)
(-26.1)
(26.1) [h, i]
0.9991
0.9998
0.9845
0.9935
0.9996
-
n [gl
9
7
12
10
6
[a] Temperature in "C. [b] See text. [c] In Y units. [d] mol' L- I. [el Extrapolated Y value for ethanol. [fl Correlation coefficient. [g] Number of points. [h)
Activation energy. [i] In kcal. mol- I.
The change of temperature from 0" to 50 "(3 for the calculation of the activation data was conducted at a water
concentration of ca. 25 mol. L-' (the second temperature
was 25 "C in all cases). By chance, this value coincides approximately with the value of ck corresponding to the intersection point of the two lines in Figure 8. Based on this,
the course of the functional curve of AH' in Figure 7 can
be characterized.
For c,,<ck (region I, A H f -lnk29x-Ink,2,), A H f is a
monotonic function of the water content. The ED and c*
values of Ink are only slightly different at 2.5 and 50°C.
Thus, even the solvent dependence of A H + is approximately described by equation (4) (Table 3). In this correlation the expansion of the liquid must be taken into account, since at a given content in VOI.~/O the molar water
content is temperature dependent.
In the region c p = c k a number of factors cause AH' to
have a rather complex dependence on concentration. Going beyond ckr its temperature dependence and the temperature change have the effect that the individual measurements for determining AH' are made partly in region I
and in region 11. This results in the unusual functional
course of AH'.
Finally, in the region c p > ck(region 11) a monotonic dependence of the AH' values on the solvent composition is
observed, as in region I. The additional maximum at very
high water contents may be a result of mixing problems
and will not be discussed here (this is dealt with in [4x.ss1).
The concentration dependence of ASf (Figs. 7 and 8), can
be explained in an analogous manner to the difference between AH' and AG'.
The solvolysis of tert-butyl chloride in ethanol-water,
discussed here at length, is characteristic of other solvolysis reactions in solvent m i x t ~ r e s ~ " ~ ~,~which
~ ~ ' ~can
~ ' be
-~~]
treated in an analogous way, and is also generally typical
of mechanistic studies in them. Furthermore, the reference
point of the Y-scale, 80 vol.% ethanol/water, may present
problems if the temperature differs substantially from
25 "C.
Another result of the previous analysis is of general interest: for reactions influenced by the polarity of the medium, the free energy of activation, AG', should, at least
in solvent mixtures, be a more simple parameter than A H
and AS', since these always contain contributions from
the thermal expansion of the liquid, which are not reaction-specific. Special attention is, therefore, required when
a solvent mixture exhibits two regions of validity of equation (4) (cf. also Section 4.2).
'
Angeul. Chem. In!. Ed. Engl. 21 (19821 724-733
The results just mentioned lead to other applications of
equation (4) to mechanistic studies: Linear correlation of a
process with the Winstein relationship is often used as a
mechanistic criterion, by analogy to other linear free energy (LFE) relationships (e.g. see 132.'0-641 ). In the first
place, the value m , the slope of the straight line, is interpreted as a measure of the sensitivity of the reaction studied to solvent polarity effects, and is often related to increase or decrease of charge separation leading to the transition state. Furthermore, a linear correlation over a large
range of solvent polarity is used as an indication of a uniform reaction mechanism in different solvents. In order to
obtain a sufficient number of measurements, reactions are
usually studied using solvent mixtures, often ethanol-water.
As the polarity of these mixtures is governed by equation (4), it seems worthwhile to redefine the previously
mentioned mechanistic criteria on the basis of equation
(4).
From equation (4), the slope m of a relationship between
two polarity-dependent processes PGIand Pc;2is described
by equation (5).
(5)
A good linear relationship between Pc,, and PCizrequires
that the slope m in equation ( 5 ) is independent of c,, and
hence, one of the following three conditions must be fulfilled :
The c*-values of both processes are similar (c; ;=c;). The
logarithmic term in equation (4) has an approximately
equal numerical value in both cases for a given value of
c,. Consequently, PGIand PG2 are linearly dependent.
The c*-values are different in both cases, but considerably larger than C ~ " ~ ( C ; , C ~ % C ~Equation
" ~ ) .
(4) can be
expanded in both cases as a Taylor series, which as
usual is terminated. A linear relationship between Pc,
and c, results and, likewise, a linear relationship between PGIand PG2.
The c*-values are different, but both very small. In each
case PG and Inc, are linearly dependent and, therefore.
also PGland PG2.
Often, one of these three conditions is fulfilled. However, if a nonlinear relationship is found, e.g. with the Winstein scale, it does not necessarily follow that there is a
change in mechanism, or even that a continuous transition
from one mechanism to another occurs upon varying the
medium (cf. also Lc'51). This information is obtained only by
estimating the c*-values.
Even more complicated is the influence of the solvent
and its dependence on c,, when mixtures with critical transition points (double lines) are used. These are observed
particularly when solvolysis reactions are carried out in
frequently-used binary mixtures such as acetone-water,
1,4-dioxane-water and ethanol-water (see Table 2)[2'J.4"1.
An example for the mixture ethanol-water is described
here.
73 1
Brown er a/.1661
studied the solvolysis of isopropyl, cyclohexyl, and 2-adamantyl tosylates in ethanol-water. The
free energies of activation show good linear correlation
with the Y-scale u p to a water content of ca. 50%. At higher
water contents, substantial deviations are observed, which
represent a regular break in the LFE relationship (Fig. 1 in
l6']).Nucleophilic solvent participation with a change in
reaction mechanism was discussed. This appears to be
contradicted by the behavior of isopropyl tosylate, which,
although hardly shielded and easily accessible to nucleophilic attack, shows the smallest deviations. These were finally attributed to a specific solvation of the leaving anion,
since the corresponding mesylates show linear relationships with the Y-scale.
The solvolysis data can be analyzed on the basis of
equation (4). The break in the LFE relationship is observed
at a water content of ca. 50% and can be interpreted as a
critical transition point (see Section 3.1.3). Since similar c*
values are found for the solvolysis of tert-butyl chloride
and the various tosylates, a discussion of the E D values according to equation ( 5 ) is sufficient. For tert-butyl chloride
and cyclohexyl mesylate (Table 4, Nos. 1 and 2), the ratio
of the E D values is almost equal in regions I and 11. Thus,
an approximate LFE relationship is observed for the entire
water concentration range. The relatively low ED,,value of
No. 2 even explains the slight deviations at high water contents.
Table 4. Solvolyses [ I I , 661 in solvent mixture ethanol-water at 25°C
I
2
3
4
5
{err-Butyl chloride
Cyclohexyl mesylate
2-Adamantyl tosylate
2-Propyl tosylate
Cyclohexyl tosylate
6.7
4.7
4.7
3.2
8.3
11.6 - 16.1
10.8 - 17.3
8.3 -21.6
12.9 - 14.7
32.8 - 16.8
6.3
4.6
9.9
5.0
7.7
0.001
(0.001) [dl
0.001
(0,001) [d]
0.001
- 7.16
- 11.7
- 9.1
units. [b] In mo1.L-I. [c] Value for pure alcohol extrapolated
from equation (4). [dl Estimated, since too few points available for calcula-
[a] In
tion.
The tosylates, however, behave quite differently (Table
4, Nos. 1, 3, and 4). The much higher values of E D in region I1 result in LFE relationships, whose slopes are almost
twice as large as those in region I. Therefore, breaks in the
relationships must exist at ck (Fig. 1 in @'I). The c* value of
cyclohexyl tosylate (Fig. 4, Nos. 1 and 5 ) no longer coincides well with that of No. 1. Appropriately, the resulting
LFE relationship is considerably inferior. In this case, a
simple comparison of the E D values is not sufficient. Detailed analysis, however, shows that No. 5 behaves in the
same way as Nos. 3 and 4. The solvolysis reactions in acetone-water mixtures can be analyzed in an exactly analogous manner.
Sridharan and V i t ~ l / o [studied
~~]
the solvolysis of geminal dihalides in 1,4-dioxane-water. Here, also, the LFE relationship with the Y scale turned out to be nonlinear, with
two straight lines. This was attributed to a change of reaction mechanism and transition to nucleophilic solvent participation. It can be shown, however, that the critical transition point of the 1,4-dioxane-water mixture coincides
with the point of intersection of the two lines.
732
The last examples show that the existence of an LFE relationship is a limited mechanistic criterion for studying
solvent-dependent processes in solvent mixtures. Therefore, when examining such processes, binary mixtures
should be checked for critical transition points.
4.3. Further Applications
Using equation (4) conclusions about the composition of
binary liquid mixtures can be made by considering polarity-dependent p h e n ~ m e n a [ * ~. . M'
~ ixtures
~ - ~ ~ ] can be analyzed in this way. Suitable reference substances are solvatochromic dyes. The water content of organic solvents can
be estimated by this method, since water has a greater polarity than most organic liquids. The use of solvatochromic
dyes in practice was hitherto hampered by the nonlinearity
of the calibration curve, which necessitated a great number
of experimental points at low water concentrations1681. Using equation (4) it is now possible to linearize these calibration curves, so that only a few points are necessary.
Apart from this, the quasi-logarithmic relationship of
equation (4) furnishes the advantage of an almost constant
relative error in measurement over a wide concentration
rangeL4']. For a rough estimation of water concentration,
even visual comparison with a color scale is sufficient. Solvents such as dimethylformamide or dimethyl sulfoxide
present no problems, in contrast to what is experienced
with other methods. Colored solutions can be examined in
an analogous manner using solvatochromic fluorescent
dyes. A triple point method of measurement even dispenses with a fluorescence s p e ~ t r o m e t e r l ~ ~ ] .
Furthermore, the polarity of a solution can be adjusted
accurately by means of equation (4). This is of interest,
when a compound reacts by different mechanisms in polar
and nonpolar media. An example is the thermolysis of percarboxylic esters1691which in nonpolar media generally
proceeds homolytically with radical formation; in polar
media, however, heterolysis occurs according to the Criegee mechanism. If generation of radicals in a polar medium is desired, it is advantageous to adjust the polarity of
the medium to a point at which homolysis just prevails.
In other cases, where the addition of a small amount of
polar additive should enhance the solvent polarity as much
as possible[441,c* plays a key role. If c, <c*, the polarity is
strongly dependent on cp, but if c,>c*, only to a small extent (this relationship is roughly logarithmic). In order to
markedly enhance the polarity by addition of only a small
amount of polar additive, c p should be adjusted to approximately c*.
Furthermore, it can be concluded from equation (4) that
addition of a small amount of polar additive to a solvent of
low polarity can enhance the polarity substantially; on the
other hand, introducing a nonpolar additive to a polar medium produces hardly any reduction of polarity. This observation corresponds to a considerable amount of empirical data, for example, in chromatography, where polar additives have far greater influence on elution behavior than
nonpolar. Polymer chemistry is another field of application for equation (4), where it is not only valid for liquids,
but even holds for solidsi701:on the one hand, it characterAngew. Chem. Inl. Ed. Engl. 21 (1982) 724-733
izes the effect of polar components o n copolymerizations
and on the other, that of low-molecular weight additives
(plasticizers). This is useful in devising procedures for
manufacturing polymers with specific properties.
5. Outlook
Apart from the previously described areas of chemistry,
equation (4) can be utilized in many others which can only
be mentioned briefly here. In the study of reaction mechanisms, an opportunity is provided to characterize the influence of the medium on a chemical reaction, even when
the polarity varies as the reaction progresses. Since equation (4) even describes the polarity of pure alcohols as a
function of their chain length[”’, it can be expected that
the polarity of the pure substances can be composed of increments. The correlations are, however, nonlinear.
Polymer chemistry, offers yet another field of application. Not only can equation (4) be of use in adjusting the
polarity of the polymer to a particular value, in the methodical determination of polar additives which enhance polarity even at low concentrations, and in obtaining information on the effect of residual rnon~mer~’~I,
but it also offers the possibility of obtaining information on copolymerization parameters and on interactions between polymers.
Finally, preliminary studies o n ternary liquid mixtures
show that equation (4) can be extended to multi-component systems.
Gratitude is expressed to the Deutsche Forschungsgemeinschaft and the Bundesministerium fur Forschung und Technologie forJinancial support and to my mentor Prof. Dr. C.
Ruchardt f o r continuous encouragement. Calculations were
run at the Rechenzentrum of Freiburg University using the
computer program POLAR.
Received: August 12, 1980 [A 4281
German version: Angew. Chern. 94 (1982) 739
Translated by: Dr. Robert Winiker, Krefeld
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Chemie, Weinheim 1979.
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18 (1979) 98.
[3] C. Reichardt: Losungsmittele/fekte in der organischen Chemie. 2nd edit.,
Verlag Chemie, Weinheim 1973.
141 C. K. Ingold: Structure and Mechanism in Organic Chemistry. Cornell
University Press, Ithaca, NY 1953, p. 347-350.
[5] A. Streitwieser Jr., Chem. Rev. 56 (1956) 620.
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171 1. A. Koppel, V. A. Palm in N. B. Chapman, J. Shorter: Advances in Linear Free Energy Relationships. Plenum, London 1973, p. 203-280.
(81 S. Brownstein, Can. J. Chem. 38 (1960) 1590.
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2700.
[lo] A. H. Fainberg, S. Winstein, J . Am. Chem. SOC. 78 (1956) 2770.
[ I I J S. Winstein, A. H. Fainberg, J. Am. Chem. SOC.79 (1957) 5937.
[I21 E. M. Kosower, J. Am. Chem. Soc. 80 (1958) 3253.
[I31 L. G. S. Broker, G. H. Heyes, D. W. Heseltine, J . Am. Chem. Soc. 73
(1951) 5350.
1141 K. Dimroth, C. Reichardt, T. Siepmann, F. Bohlmann, Liebigs Ann.
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