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 .ialues 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
1207
Molecular Association in Cholesteric-Nematic Liquid Crystal cholesteric mesophase become circularly dichroic (liquid crystal induced circular dichroism (LCICD)). In addition, the reflective pitch band of the cholesteric system is altered by the alddition of' B nonactive component. The most obvious case of this latter phenomena is the of fp-methoxybenzy1idene)-p-n-butylaniline additioq (MBBA), a room temperat,ure nematic material, to a variety of cholesterol derivatives. One example of this is the ~ B B ~ - c h o l e ~chloride t e ~ ~ ~system,2 which exhibits a c o m p e ~ ~ s a tpoint ~ o ~ at intermediate compositions. This type of' behavior indicates that the added nematic can not be considered as an inert diluent in these mixtures, but rather as a ~ ~ a ~ whose ~ e roptical ~ a ~activity is dependent on the second component in the mixture. Adams and aas have shown* thilt the characteristic reflective pitch band of mixed cholesteries and nematic-cholesteric mixtures can be described by
30
.m
o
.a .m
.40
la0
MOLE FRACTION
Figure 1 . Reflective pitch band vs. mole fraction MBBA in MBBA-DB (0)and MBBA-ACC (A) mixtures.
where XT is tho reflective pitch of the mixture, az the weight fraction of each component, and h, the reflective nt it was felt that eq pitch of the pure ~ o m ~ ~ o ni.e Initially, 1 with f(al, a2 .I = 0 could be used to describe all mixed systems; however, deviations from the expected linearity of such an equation led to the addition of f(a1, a2 . . .). The total equation adequately describes the functional dependence of the pitch band of mixtures. The use of weight fraction in such an equation remains puzzling. One would expect the helical aggregates of the cholesteric mesophase and, thus, the reflective pitch to be dependent upon the relative numbers of individual components. This type of interaction wi~uidrequire a mole fraction rather than weight fravhion dependence. The following molecular model is proposed to explain the pitch phenomena for the mixed choleqteric-nem wtie mesophase. ~
c e
I
Experimental Section Reflective pitches d liquid crystalline mixtures were measured on thin films of the Grandjean texture of the cholesteric mesophase in the Cary 14 uv-visible spectrophotometer. Examplefs of typical reflective pitch us. mole fraction of cholesteryl moiety in cholesteric-nematic MBlBA with cholesteryl chloride mixtures of (CCL), A8J4 xholestenyl benzoate (DB), and allyl cholesteryl carbonate (ACC:I"~are shown in Figures 1 and 2. With the exception of the MBBA-CCL, the data for the mixtures show increasing pitch with increasing nematic concentration. The reflective pitch tends toward infinity a t high MRRA conceni rations.
160
'0
e
IL
0
1
i 1
i
I
0
e
0.2
0.4 0.6 MOLE FRACTION I
08
IO
Figure 2. Reflective pitch band vs. mole fraction M B B A in an MBBA-CCL mixture.
The cholesteric and molecular complexes are assumed to have reflective pitches XC and XCN, respectively, while any unperturbed nematic molecules retain their infinite pitch. Equation 1is now written
Theory and D i ~ c ~ ~ ~ ~ ~ ~ ~ Saeva and Wysocki have suggested that electronic inwhere X , is the mole fraction of individual components, teractions within the cholesteric helix as well as the heliand the A, the wavelengths. X C and XCN are functions of coidal ordering of the solute will produce induced optical the complex number n, and, thus, some method of attainactivity in molteules dissolved in a cholesteric s o l ~ e n t . ~ , ~ ing n from experimental data was sought. We felt that a direct interaction between solute and solSection A. DB, a-Cholesteryl Hexyl Carbonate (avent ~ s o ~ e w hanalogous a~ to a charge transfer complex) H X C ) , ACC, and Cholesteryl 2-Propyn-1-yl Carbonate takes place which produces the shift in X O that occurs (CPC) with MBBA. An initial value fox X ~ Nwas chosen. when chiral solutei; are added to the nematic mesophase. Plots of AT (as obtained from eq 3) us. initial mole per Thus an equilibrium between cholesteric molecules (C) cent of MBBA were generated for a constant value of n. and nematic molecultes (N) is attained and a complex The value of n was then changed and the process repeatformed. ed. In this way a series of theoretical reflective pitches as C: 4- nN CN, (2) a function of n are generated. The results of such a calculation are seen in Figure 3 for an MBBA-CPC mixture. The equilibriumLof eq '2 is assumed to be far to the right.
*
The Journalof Physical Chemistry, Vol. 78, No. 12, 1974
John M. Pochan and Qarbyn Q . Hinman
0
.2
.4
.6
.8
1.0
LOG
1.2
1.4
1.6
1.8
2.0
X
Figure 4. Log n vs. log Xcpc, Data interpolated from Figure 6. X is the initial CPC concentration.
t-"
1
0ll-L(I
0.2
04 0.6 MOLE FRACTION
0.8
1.0
Figure 3. Theoretically produced pitch band as a function of composition for an MBBA-CPC mixture. Complex number n is varied. Experimental points (filled circles) are included: X(CPC) 1538 A, X(complex)30,000
A.
The experimental data are also included. It is readily seen that none of the theoretical curves fit the experimental data. Theoretical values of n can, however, be extracted where the experimental curve crosses the theoretical curves. Values of n as a function of initial mole per cent active material can thus be obtained. Figure 4 is a plot of ~ ~the ~ chosen t ~ ~ lcomplex ) . refleclog n us. log X ~ p ~ ( ~For tive pitch, n is an approximate inverse logarithmic function of the initial mole fraction of active material in the mixtures. By using this correlation in the theoretical calculation of AT, an excellent fit of the experimental data is obtained (see Figure 5 ) . A plot of concentration of the various components as a function of composition is shown in Figure 6. The experimental data can also be fit with other values of XCN . The other values yield slightly different linear fits of log n with log X c . Table I contains the theoretical fits of n with X c for various complex reflective pitches and optically active materials. In all cases the fit is as good as that shown in Figure 5 . It is interesting to note that in all cases the data can be described by keeping a constant reflective pitch ;and only varying the complex number with composition. A t this time, there is no experimental method of determining ACN or n independently, and rather than speculate furthl?r, or produce empirical relationships between the variables, our data are presented as XCN constant with n as function oi mixture composition. We would naturally assume that n and XCN are functionally dependent on X c . This is even more obvious when the equation relating n and X C is considered. A t high MBBA concentrations (>go%), the fitted data relating n and Xc indicate that the complex number becomes very large, i.e., for MBBA-DB, XCN = 57000 A at X c = 0.06, IZ == 12.4. The sphere of influence of the cholesteric molecule's asymmetric electron clouds fall off as The Journal of Physical Chemistry, Val. 78, No. 12, 1974
t
1
0
0 0
0.2
0.4
0.6
0.8
I.0
MOLE FRACTION
Figure 5. Theoretical and experimental reflective pitch vs. composition for MBBA-CPC mixtures: i c 30,000 ~ A, Xcpc 1538 A; logn = -1.0710gX - 0.177.
R-s and it would not be expected that the molecule's sphere of influence would extend beyond its nearest neighbors. In a close packing model this might lead to interactions with six other molecules. Complex numbers larger than this are, thus, unreasonable at high MBBA concentrations, and indicate the functional dependence of XCN as well as n on X C. The data in Table I may provide additional insight into interactions of the two systems. If our model is correct, it appears that the interaction between MBBA and the various test compounds differ. The log n relationship is approximately dependent on X for the DB derivatives, while the cholesterol derivatives vary, with two exhibiting inverse pitch relationships. This difference could be due to structural differences in the optically active molecules. It is interesting to note that our reflective pitch bands for the above compounds follow the general form of the
Molecular Association in1 Cholesteric-Nematic Liquid Crystal
1209
TABLE I: Fit Parameters for Log n us. Log X c for Mixtures of MBBA with Cholesteryl and A8~WholestenylDerivativesa Artive compoundb
h complex chosen
A
B
Gholesteryl 2. propy%-l-yl carbonate h 6260 A A8, I4-C holeoienyl benzoate X 2300 A
15,000 30,000 125,000 57,000 100,000 100,000 30,000 70,000 100,000
-1.13 f 0.03 -1.04 i 0.04 -0.596 f 0.070 -0.586 f 0.060 -0.520 i: 0.023 -0.996 0.047 -1.104 i: 0.053 -1.115 f 0.060 -0.727 f 0.081
- 0 . 3 2 4 i 0.030 -0.177 i 0.040 0.422 f 0.027 0.423 f 0.024 0.467 3z 0.012 -0.11 f 0.02 -0.17 3z 0 02 -0.16 3z 0.02 0.744 3z0.025
50,000 30,000
-0.691 f 0.107 -0.785 :?c 0.040
0,782 rjl 0,233 0.591 fO.083
Allyl chole rteryl carbonate X 4215 a-Hexyl cholesteryl carbonat e X 1600 L'Log n = A log X c
+ 13.
Reflective wavelength given for pure material.
'
I XCL
Figure 7. 0
.10
.m
, M .40
.eo
.70 INITIAL MOLE FRACTION CHOLESTERIC .!XI
.00
.90 1.00
Complex reflective wavelength vs. l / X m far MBBA-
CCL mixtures.
Figure 6. FinaE mole fraction of pure nematic, pure cholesteric, and cholesteric-nematic complex for CPC-MBBA as a function of initial1 cholesteric coniposition Data based on parameters in Figure 5
theoretical equations of Goossens7 for a symmetric internal field interaci ion in the mixtures. B. CCL--MBBA The data for CCL-MBBA presented a different problem from the other mixtures shown, in that an actual pseudonenratic (compensated) texture is obtained. This behavior is indicative of the fact that an optically active species other than CCL in the mixture has a sign opposite the negative -4880 8, pitch of CCL. A complete fit of the reflective data for this mixture was impossible using the techiniques outlined above. Various attempts using Xcw being both positive and negative failed. A method of overcoming this would be to have n and XCN vary with composition. Since we cannot anticipate the functional dependence of XCN the following was done. Inspecting the data in Table I indicates that for two of the cholesteryl derivatives the dependence of n on XC was inverse. The preexponential factor varied between -0.11 and -0.33, with most near -0.2. We, therefore, have assumed that log II = - log Xc - 0.2 in the CCL-MBBA mixture and have calculated (from eq 3) the XCN required to fit the experimental data. An attempt was then made to correlate XcN with Xc,in a variety of ways, the best of which is shown in Figure 7, a plot of XCN us. 1/Xc. It would appear from this plot that the effective pitch of the cholesteric-nematic complex must be positive throughout the entire composition range of this mixture and that the fimctional dependence of 1/XC reverses a t compensation. A possible better choice of the parameters
*I,O
.-' 0 0
0
e 0
60.03
0
IO
20
30
40
50 60 % MBBA
70
80
90
100
Reflective wavelength vs. mole per cent MBBA for a mixed (CCL, CN) cholesteric system with MBBA. Figure 8.
in the previous equation might produce more linear results. It appears that the effective pitch of the complex ('1) decreases with increasing CCL concentration, (2) minimizes at compensation, and then (3) begins increasing near 100% CCL. This indicates that the more cholesteric in the mixture, the lower the effective pitch of the complex. In the mixtures investigated, except for CCL-MBBA, plots of AT us. composition increase with increasing MBBA concentration. In some mixtures of MBBA with cholesteric materials, the reflective pitch band minimizes with composition as seen in Figure 8. It is obvious in these cases that the theory could be used to fit the data by The Journalof Physical Chemistry, Vol. 78, No. 12, 1974
Andre P. Persoons
I21
varying n and XCN with composition as has been done with MBBA-CCL. In conclusioin, a simple model of molecular interactions in cholesteric-nematic mixtures has been proposed to characterize the reflective pitch of the mixtures. It is based on complexes of optically active cholesteric molecules with nematic molecules. Parameters involved in the theoretical model, namely, the degree of complexation and the helical structure of the complex materials, have been deduced from experimental data. It has been shown that some cholesteric-nematic mixtures can be totally characterized by keeping XGN constant and varying the complex number n. in the case of CCL-MBBA mixtures, it has been shown ithat both n and XCN can vary with composition. However, X C N , varies in a discontinuous fashion. We believe this method to be totally general for optically active nonrnesomorphic materials in. nematics as well as chiral nematics in nematics. Tfiis method, although more complicated, i s also applicable to ternary or higher order mixtures of active materials in nematic mesophases.
This method of molecular complexing is not quantitative in that two variables which cannot be determined independently are presented. The method does present, however, cholesteric-nematic interactions in a easily pictured molecular framework.
Acknowledgment. The authors wish to thank J. 9. Wysocki and F. Saeva for the reflective pitch measurements used in this work. References and Notes ( l ) J. L. Fergason, "Liquid Crystals," in the "Proceedings of the International Conference on Liquid Crystals," Gordon & Breach, N. Y . , 1967. (2) F. D. Saeva and J. J. Wysocki, J. Amer. Chem. Sac., 93, 5928 (1971). (3) F. D. Saeva, Mol. Cryst. Liquidcrysf., 18, 375 (1972). (4) J. Adams and W. Haas, presented at the 166th National Meeting of the American Chemical Society, Chicago, Ill., Aug 26-31, 1973, Abstract. (5) This data (MBBA-ACC, MBBA-DB, and MBBA-CPB) has been provided by J. Wysocki. (6) MBBA-CCL reproduced by permission of the authors in ref 2. ( 9 ) W. J. A. Goossens, Mol. Cryst, Liquidcryst., 12, 239 (1971).
Field Dissociation Effect and Chemical Relaxation in Electrolyte Solutions of Low Polarity Andri! P. Persoons' Laboratory of Chemical and Biological Dynamics, University of Leuven, Leuyen, Belgium (Received October 29, 1973) Publication costs assisted by Katholieke Universiteit te Leuven and F.K. F.O. Belgium
A stationary chemical method for the investigation of ionic equilibria in media of low permittivity 3s presented. The technique is based on the application of pulsed electric fields of high amplitude and high frequency to modulate the conductivity of the sample solution, representing a nonlinear resistance as a consequence of the field dissociation effect. The modulation depth or efficiency of the conductivity modulation is measured with superposed fields of low frequency and low intensity whereby the advantages of frequency-conversion methods are fully exploited. The efficiency of conductivity modulation at low modulation frequency is a measure of the field dissociation effect. The relation between modulation depth and field dissociation is derived. Measurements were carried out on solutions of tetrabutylammonium picrate in diphenyl ether a t 50". The value obtained for the field dissociation effect is in close agreement with the theoretical value given by Onsager and confirms the experimental data of Mead and Fuoss. At increasing modulation frequency the finite rate of ionic dissociation equilibria introduces a decrease in rnoduhation efficiency. The relation between modulation depth, modulation frequency, field dissociation, and relaxation time of the ionic equilibrium is derived. Measurements on solutions of different electrolytes in weak polar media confirm these relation. From the dispersion of the field dissociation effect the relaxation time(s) of the ionic dissociation process(es) are calculated. Evidence was obtained for a dependence of the field dissociation effect on the frequency of the external electric fields used to modulate the conductivity of the electrolyte solutions. This effect may be related to the dynamics of the physical processes involved in the field dissociation effect. An extra advantage of the presented technique is the possibility of conductivity measurements in low conducting media without apparent interference of polarization effects.
Introduction Kinetic invesltigations of association-dissociation equilibria of ions were made feasible by the advent of relaxation spectrometry.2 These studies are mostly restricted to The Journal of Phys6;ai Chemistry, Vol. 78, No. 12, 1974
aqueous or aqueous-like media where ionic species are present in fairly high concentration. The study of chemical relaxation phenomena resulting from electrolyte equilibria in low-polar media is of interest. Such studies
