Solvation of
Alcohols in Nondipolar Solvents
1203
riration of Dilute Associating Solutions. V. Solvation of Alcohols in
dkcki* and J. Jadtyn Laboratory of Moiecolar Interactions, Institute of Physics, Polish Academy of Sciences, 60-1 79 Poznan, Smoluchowskmgo 7 7 / 1 9 , Poland (Received November 12, 1973)
Results on dipole polarization of solutions of alcohols in saturated hydrocarbons in the low concentration range up to 5 mol % are presented. In the range of 0.1 to 2 mol % a constant value of the polarization is observed. In this range, also, thermodynamic and nmr anomalies, observed by others, corroborate a strong deviation from the ideal association model. For an explanation of the experimental facts, a model i s proposed which takes into account solvation of alcohol molecules by those of the nondipolar solvent (in addition to association). This model attempts to explain the dependence of the polarization on the concentration and temperature as well as the differences for the hydrocarbons investigated. The number of solvent molecules, solvating a molecule of alcohol, can be of the order of lo2 near the melting temperature of the solvent pointing to the presence of two coordination spheres. At room temperature solvation is very well apparent in cyclohexane and n-tridecane, but nearly imperceptible in n-hexane.
Introduction Research on association processes of alcohols and phenols in nondipolar solvents is proceeding in many plac88.2-21 Notwithstanding the various techinques employed, the problem still remains unsolved. Opinions diverge widely as to the structure of the multimers arising in these processes and as to the values of the equilibrium constants accounting for the successive steps of the association process. Good agreement with experiment is in some cases achieved by assuming a single kind of multimers, e.g., tetramers, although a process of this kind would hardly appear plausiblle. Parts I-IVl contain results concerning the dielectric polarization of dilute solutions of butanols in cyclohexane, n-hexane, and n-tridecane and of phenol in cyclohexane in the concentration range of f 2 5 5 mol % of the alcohol (fi = Ni/(N1 3- N z ) , I = 1,2, is the nominal concentration of the ith component in mole fraction) a t temperatures of 10, 20, 30, 40, and 50". The experimental procedure is described in detail e1st:where.l The earliest systematic investigation of the dielectric polarization of very dilute cyclohexane solutions of alcohols by Ibbitsori and Moorez3 has already revealed certain unexpected properties. At concentrations ranging from 0.1 to 2 mol %, the polarization of the alcohol remained practically const,mt, independent of concentration, and equal to that of thie monomers. These results, corroborated by ir absorption ~itudiies,~~ suggested the existence of a concentration range in which association is hindered. This conclusion, however, is a t variance with the generally accepted model of iderrl association. Independently, in the same range of concentrations, such unusual propert Les were detected in solutions of alcohols by Wbycicka, et u1.,z425in thermodynamical studies, and by Dixon22 in nmr measurements of chemical shift. The partial molar enthalpy as well as the chemical shift exhibit unexpectedly a point of inflection in the concentration range of (3.1-2 imol%. Aiming a t an explanation of this highly interesting behavior of the solutions, we propose here a model taking into account, besides equilibria between monomers, di-
mers, and trimers, solvation of the monomers of the alcohol by a nondipolar solvent. Experimental Results We shall express the dipolar polarization of the alcohol P @ i p in units of polarization on the monomer
Values of P2dlp are calculated from experimental data using Debye's formula which, for so highly dilute solutions, yields practically the same results as that of Onsager. The details of the calculations leading to and Rp are found in part 1.l Figure 1 shows the experimental concentration dependence of R, for solutions of 1-butanol in cyclohexane a t 10, 20, 30, 40, and 50". The curves for 2-butanol and 2methyl-2-propanol in cyclohexane1 are similar, Figure 2 shows Rp(f2), a t 20", for 1-butanol in n-hexane, cyclohexane, and n-tridecane, whereas Figure 3 shows R(f2), a t 20", for the 1-butanol, %butanol, 2-methyl-2-propano1, and phenol in cyclohexane. The full experimental data as well as the concentration dependence of the dielectric permittivity and density of the solutions are given in parts I-IV.1 In all the systems investigated similar curves were obtained, revealing two distinct regions, The first region, defined in Figures 3 and 7 as comprising the concentrations 0 5 f i 5 L, is characterized to within experimental error by a constant value of the polarization. The second region, covering higher concentrations f2 > L, is characterized by a decrease in polarization. The ensuing discussion will concern the width of the region L specific to the phenomenon under investigation and coincident with the inflection region of the concentration-dependent curves of partial molar e n t h a l p ~ ~ and ~ 7 ~chemical 5 shift.22 From the experimental results (Figures 1-4), the following conclusions can be drawn: (1) the width of the region L is strongly temperature dependent (Figures 1 and 4); (2) the width of the region L is strongly dependent on the solvent, notwithstanding the fact that all solvents used were saturated hydrocarbons (Figure 2); (3) the The Journalof Physical Chemistry, Vol. 78, No. 12, 1974
J~ Malecki and J , Jadzyn
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n - butanol I 1 I I I 3 4 5 f2fmole%l Figure 1. Dipola polarization R, of solutions of 1-butanol in cyclohexane vs concentration and temperature.
-
i i - L i _ i _ _ L - I
0
Rp
2
!
I
I 2 3 4 5 ,'i iro/e%I Figure 3. R, vs. f l , at 20°, for solutions of I-butanol ( 0 ) ,2butanol (A),2-methyl-2-propanol (O),and phenol ( X ) in cyclohexane.
0
I -
t i 1
L
finale XI
20 16
72
08 n -butanol
05 0
A
1
2
I
I
-
I
1 2 3 f,[moIe%l Figure 2. R, vs. I p s at :No,for solutions of I-butanol in n-hexane (01n-tridecane , (e)and cyclohexane ( X ) . I
width of the region 1, is, to within experimental error, independent of 1 he associating compound, notwithstanding the fact that the solutes used differed strongly in their ability to associate (1-butanol, 2-methyl-2-propano1, phenol, Figure 3). Theoretical Model The dipole polarization of an associating compound is usually considwed to represent the polarization of a mixture of multimers; in our notations
where the summation extends over all the complexes present in the solution, phi i s the dipole moment of a complex of h molecules of the solvent and i molecules of the associating substance, whereas
iNhiIN2 is the concentration of the h,i-fold complex, Nhl the number of such complexes in the solution, and N Z = Zh,LiNhl that of molecules of the associating substance. According to eq 1, the region L,, characterized by a constant value of the polarization, can exist in the case of association only if the contributions to polarization from the open and ring multimers mutually cancel out to ensure fulfillment of the condition b2) = pmonz throughout L. This, however, would appear to be an exception rather than the rule. Nor would such mutual compensation explain the thermodynamic anomalies24 and nmr results.22 A change in temperature ought to destroy the compensation, but no such effect is, in fact, observed. Finally, the Xhr
04
E
The Journalof Physical Chemistry, Vol. 78,No. 12, 1974
'-10 0 10 20 30 40 50 t 1°Cl Figure 4. The region L (in units of the concentration f 2 ) as a function of temperature for solutions of 1-butanol in n-tridecane ( A )and cyclohexane ( 0 ) . fact that the width of region L is independent of the nature of the associating substance is a strong argument against compensation. One is thus led to the conclusion that the association process of dilute solutions is subject to a perturbation by some additional factor and that, contrary to expectation, dilute solutions deviate considerably from the ideal association model. We propose, in order to explain the experimental facts, that the monomers of the alcohol are solvated by the nondipolar solvent. Since we are dealing with dilute solutions, we omit tetramers and higher multimers and restrict our considerations to the formation of dimers and trimers. We consequently write the following set of equilibrium equations between monomers, dimers, and trimers o i the alcohol and molecules of the solvent A, nS + S,AI K," A, A, A2 Kz (2)
+
A,
+ + Alz
Ft A3
K3
Since the number n of solvent molecules in a complex can be quite considerable, we shall henceforth be referring to it as a solvate. The equilibrium constants are expressed in the usual way in terms of true molar fractions
K, = y a 2 h K3 = TaJa:! K," = 8'an/al 2a2 f 3a3 a,,== I
+
(3)
a, + The quantities ab and the previously introduced concen-
Solvation of Alcohcils in Nondipolar Solvents
1205
1' I
, Lmx
=
=
1.64 mole %
10 09
08 07
06 05 Figure 5. Theoretical cui'ves of R, vs. f 2 and n (the number of solvating molecules of the solvent), at constant K2 = 20, K3 = 25, and K,, = 5 28 (Air, = -1 kcai/mol). The dashed curve shows R p ( f 2 )for ihe traditional association model (K, = 0, n = 0).
?10 lymox 5 123 =
trations mi are related as follows a,= xolli
a, -- xnl
i
=
1,2,3
(4)
w herie as
17
Y==fzal
fl
=\,
08
\
07 06
+- fJa1 + a2 + a,? + (1 - n)a,l
05 0
(5) The set of eq 3, the parameters of which are given by the equilibrium constants K1, Kp, and K, as well as the number n of solvent molecules in the solvate, is resolvable numerically. The solutions a, of eq 3 were used together with eq 1 and 4 for the calculation of theoretical Rp(f2) curves. To this aim, we assumed a dipole moment of the solvate p n l = ,umon and dimer and trimer moments amounting to poz = O.8CLmon and p o 3 = 0. The calculations were performed by an Odra 1013 computer. Figure 5 shows the theoretical curves RP(fz) a t the constant values Kz = 20, K3 = 25, and Ken = 5.28 (AF, = -1 kcal/mol), with n varying. The dashed curve is that of RP(f2) for K, = 0, n = 0, Le., for the traditional association model. Figure ti shows curves of Rp(f2) with K, as the variable parameter, the others being K2 = 20, K3 = 25, and n = 60. The meaning of the dashed curve is the same as in Figure 5 . Finally, Figure 7 shows curves of RP(f2) and their dependence on the association constants K2 and K3 a t constant rt = 60 and K, = 1.05. =
09
- nfzan
fl
Conclusions The preceding calculations, shown in the graphs of Figures 5-7, show that the model including solvation provides an explanation of the region L of constant polarization. In particular, these calculations permit the following statements: (1) the width of the region L depends strongly on n (Figure 51, and on K, (Figure 6); (2) the width of the region L is practically independent of the association constants Kz and K3 even if the latter vary widely (Figure 7). These conclusions are readily put in correlation with the previously stated conclusions from the experimental facts. The experimental strong dependence of the region L on the temperature and solvent is a result of the dependence of L on Ks and n. The experimental fact that L is independent of the nature. of the associating substance results
mole %
=
v
6=
v
Figure 6. Theoretical curves of R p ( f 2 ) at constant K2 = 20, K3 = 25, and n = 60. The variable parameter is K,. The dashed curve has the same meaning as in Figure 5.
\
-
2 3 4 S fz fmole mole % 1 Figure 7. Theoretical curves of R,(fp) at constant K, = 1.05 and n = 60. Variable parameters are the association constants K Z and K 3 . directly from our model, in which L is practically independent of the association constants K Z and K3. Hence, in order to explain the experimental results, only the two parameters K , and n have to be fitted. However, K Z and K3 were constant a t 20 and 25, respectively, in most of our calculations. This choice of association constants was based on attempts to determine these quantities from the study of nonlinear dielectric effects.8 With regard to the high error of that method, however, Kz = 20 and K3 = 25 are no more than rough assessments, though this is irrelevant to our conclusions because L is independent of Kz and K3. It results from eq 5 that nfza, < f ~Hence, . as a, tends to unity with K , m , the width of the region L has to satisfy the condition
-
L
< 1/(n + I)
(6) Figures 6 and 7 show the maximal width of L. Thus, with growing n, the anomalous region L shrinks and becomes more difficult to detect experimentally. On the other hand, with decreasing n, the region L expands. simultaneously becoming increasingly diffuse, so that for n 5 10 it is practically no longer distinguishable (Figure 5 ) . There exists but one interval of n values where a region L is markedly present and experimentally detectable. Our calculations show that this is the case for the interval 20 < n < 200. Such large values of n are astonishing and point to the presence of a t least two solvation spheres. We draw yet another conclusion from condition 6. Obviously, a decrease in temperature has to cause a rise in n, The Journal of Physical Chemistry, Vol. 78, No. 72, 1974
John M. Pochan and DarLyn D. Hinman
1206
-
and a t the melting point n m . Hence, the point of intersection of the L ( T ) curve and the temperature axis should define the melting temperature of the solvent. The curves of Figure 4 appear to confirm this. The lack of a well-defined 1, region in the case of n-hexane (Figure 2) is probably due to the fact that the measurements were carried out a t ttmperatures considerably above the melting point, which m the occurrence amounts to -94.3"; consequently, the values of n and Ks are small, and the L region unapparent. The model proposed here, by taking into account, in ion to msociation, solvation of the alcohol moleby those of the nondipolar solvent, succeeds in explaining the anomalous shape of the dipole polarization of alcohols in the range of low concentrations (0-2 mol %). The model permits a qualitative explanation of the experimental tempwature dependence of polarization as well as the differences observed for the alochols and hydrocarbons investigated. The number n of solvent molecules, solvating a dipolar molecule, can attain an unexpectedly high value of the rader of IO2? suggesting the presence of two coordination cqdieres. Such a situation exists near the melting t e n ~ p ~ E ~tm t u of r ~the solvent. At room temperature, solvatior i s very marked in the case of cyclohexane (tm 6.5') and n-tridecane itm = -6.2"), but practically unobservable in that of n-hexane (t, = -94.3'). (1) Parts I-IV 1 Jadzyn, J Marecki, K Prafat, P Kedztora, and J Hoffmanrt, Acta Phys Polon , submitted for publication
(2) P. Bamelis. P. Huyskens, and E. Meeussen. J. Chim. Phys., 62, 158 (1965). (3) H. Wolff and H. E. Hoppel. Eer, Eunsenges. Phys, Chem., 72, 710, 722 (1966). (4) G. E. Rajala and J. Crossley, Can. J. Chem., 49, 3617 (1971); 5Q 99 (1972). (5) J. Crossley, L. Glasser, and C. P. Smyth, J. Chem. Phys., 5 5 , 2197 (1971). (6) L. Glasser, J. Crossley, and C. P. Smyth, J. Chem. Phys., 57, 3977 (1972). (7) K. Sosnkowska-Kehiaian, W. Rebko, and W. Woycicki, Bull. Acad. Polon. Sci., Ser. Sci. Chim., 14,475 (1966), (8) J. Mafecki, J. Chem. fhys., 43, 1351 (1965); Acta Phys. Polon., 28, 891 (1965); 29,45 (1966). (9) J. Biais, B. Lemanceau, and C. Lussan, J. Chim. Phys., 64, 1019, 1030 (1967). (IO) W. Storek and H. Kriegsmann, Ber. Bunsenges. Phys. Chem., 72, 706 (1968). (11) J. J. Bellamy and R. J. Pace, Spectrochim. Acta, 22, 525 (1966); J. J. Bellamy, K. J. Morgan, and R. J. Pace, ibid., 22, 535 (1966). (12) P. Bordewijk. M. Kunst, and A. Rip, J. Phys. Chem., 77, 548 (1973). (13) T.S.S.R. Murty, Can. J. Chem., 48, 184 (1970). (14) A. N. Fletcher and C . A. Heller, J. Phys. Chem., 71, 3742 (1967). (15) A. N. Fletcher, J. Phys. Chem., 73, 2217 (1969); 74, 216 (1970). (16) C. Brot, J. Chim. Phys., 61, 139 (1964). (17) P. Huyskens and F. Cracco, Bull. Sac. Chim. Belg., 69, 422 (1960). (18) P. Huyskens, G. Gillerot, and Th. Huyskens, Bull. SOC.Chim. Belg., 72, 666 (1963). (19) P. Huyskens, R. Henry, and G. Giilerot, Bull. SOC. Chim. Fr., 720 (1962). (20) J. Malecki and 2. Dopierala, Acta Phys. Pobn., 36, 385, 401, 409 (1969). (21) A. Weisbecker, J. Chim. Phys., 64, 297 (1967). (22) W. B. Dixon, J. Phys. Chem., 74, 1396 (1970). (23) D. A. lbbitson and L. F. Moore, J. Chem. SOC.B, 76, 80 (1967). (24) K. M. Woycicka and W. M. Recko, Bull. Acad. Polon. Sci., Ser. Sci. Chim., 20, 783 (1972). (25) K. M. Woycicka and 6. Kalinowska, Bull. Acad. Polon. Sei., Ser. Sci. Chim,, in press.
A Theory of Mollecular Association in Cholesteric-Nematic Liquid Crystal Mixtures John M. Pochan" and DarLyn D. Hinman Xerographic Technology Department, Xerox Corporation, Webster, New York 14580 (Received January 7 7, 1974) Publmition costs assisted by Xerox Corporation
A theory based on molecular association is proposed to explain reflective pitch measurements in cholesteric-nematic mixtures. It is shown that pitch in a series of mixtures can be theoretically predicted using an inverse pitch relationship [ ~ / X T = Z,X,/AE]with two variables; the number of nematic molecules associated with a given cholesteric molecule, and the reflective pitch of the pure complex material. Some mixtures are totally characterized by keeping the reflective pitch of the pure complex constant and varying the complex number. The method appears to be totally applicable for optically active nonmesomorphic materials in riematics as well as chiral nematics in nematics.
Introduction Liquid crystals are a unique state of matter exhibiting optical properties of crystalline materials (birefringence) and rheological propeirties of liquids (relatively low viscosities). One liquid crystalline state, the cholesteric, also exhibits enhanced optical rotatory power over optically active monomeric units comprising the phase, i. e., the ability to rotate a plane of polarized light is much greater than the additive sum of the individual components comprising the aggregated helical structure of this mesophase. The Journal of Physii:al Chemistry, Vol. 78, No. 12, 1974
In addition, the optical activity manifests itself in the ability of the Grandjean texture of the mesophase to selectively reflect one component of circularly polarized 1ight.l Saeva and Wysocki have recently shown2 that the electronic transitions in these systems are affected by the asymmetric electronic field caused by the cholesteric helical aggregate which results in the observation of extrinsic circular dichroism (CU). It has also been s h o ~ n that ~,~ the electronic transitions of molecules dissolved in the
