J. Phys. Chem. 1981,85,3215-3221
moments of the para halogenated aromatic esters are somewhat lower. The difference, if real, may be due to mesomeric effectss peculiar to compounds of this class. In the cyclohexane derivatives with carboxyl groups in 1,4 positions, inductive effects should be minimal. The carboxyl groups are well separated, and the polarizability of the intervening aliphatic ring is low. The molecular dipole moments depend on the conformation and could conceivably be affected by distortion of the cyclohexylidene ring. Effects of distortions on the mean square dipole moment are readily shown to be very small, and the conformational analysis is sufficiently precise to render errors
3215
from this source inconsequential. It is especially noteworthly that TE is sensibly the same for aromatic and aliphatic esters according to results for the last four examples in Table 11. The C-C*=O* angle is -127’. Hence, the dipole moment of the ester group is nearly antiparallel to the C*=O* bond. Acknowledgment. This work was supported in part by the National Science Foundation, Polymers Program, Grant DMR-80-06624, to Stanford University. M.P. gratefully acknowledges financial support from the Scientific Fund of Serbia.
Optical Anisotropies of Aliphatic Esters Paul J. Flory,” Enrlque Salr,+ Burak Elman,$ Peter A. Irvlne, and John P. Hummel IBM Research Laboratory, San Jose, California 95 193, and Deparlment of Chemistry, Stanford Universiw, Stanford, California 94305 (Received: June 17, 198 1)
Mean-squared optical anisotropies (r2)of methyl acetate (MA),methyl isobutyrate (MIB), dimethyl trans1,4-cyclohexanedicarboxylate(CDC), isopropyl acetate (IPA), and trans-1,4-cyclohexanediol diacetate (CDA) have been determined from depolarized Rayleigh scattering by solutions of these esters in CC14. Molar Kerr constants, and from them the quantities ( p ) (pT&p) where p is the dipole moment and & is the anisotropic polarizability tensor, have been determined from measurements of electric birefringence on solutions of these esters, likewise in CCl+ Effective anisotropy tensors &E for ester groups of the types (-CH2)2CHCOOCH3(I) and CH3COOCH(CH2-)2(II),evaluated from (r2)and { p ) on MIB and CDC and on IPA and CDA, respectively, are similar but not identical. Agreement of calculations with experimental results validates formulation of the anisotropy tensors for the respective disesters as sums of tensors for the monoesters, MIB for type I and IPA for type 11, with appropriate contributions from bonds of the cyclohexylene group. Results for MA are incompatible with the tensors deduced for esters of types I and 11, apparently owing to inductive effects of substituents close to these ester groups.
Introduction The optical anisotropy of a compound having a plurality of functional groups that contribute to the molecular anisotropy is sensitively dependent on molecular geometry and conformation. It is therefore a potentially useful criterion of molecular structure and spatial configuration, as has been demonstrated in recent publi~ations.l-~ The optical anisotropy is embodied in the traceless part & of the polarizability tensor a. It may be characterized by its invariants that can be determined by experiment. One of these is the comprehensive measure of anisotropy defined by y2 = (3/2) trace
(a&)
(1)
or by its configurational average ( r2)for nonrigid molecules. This (squared) “optical anisotropy” may be evaluated from the depolarized Rayleigh scattering (DRS) by the molecule of interest. Appropriate measurements are conducted on dilute solutions in a solvent of low anisotropy. The contribution to the DRS by the solute in the limit of infinite dilution is proportional to (r2),after On leave from Departamento de Quimica Fisica, Facultad de Cienciaa, Universidad de Extremadura, Badajoz, Spain. *Onleave from School of Engineering, Bogazici University, Bebek, Istanbul, Turkey. 0022-3654/81/2085-3215$01.25/0
suitable corrections for extraneous collisional effects.6s6 A “probe” of the anisotropy tensor & is afforded by the electric birefringence, evaluated as the molar Kerr constant ,K. Specifically, if the molecule of interest possesses a permanent electric moment p the Kerr constant serves for the evaluation of the quantity II.~&CL, or its configurational average (pT&p),where pT is the transpose or row form of vector p. This quantity, which for simplicity we denote by 8, affords a measure of the excess polarizability in the direction of the dipole moment relative to the mean polarizability. Elucidation of the spatial form of the molecule under consideration from optical measurements of the kinds indicated depends on formulation of 6 as the (tensor) sum of contributions from constituents of the molecule. Each such contribution is considered to be locally invariant within the group it represents. The sum obviously depends on the mutual orientations of the constituent groups. These orientations depend, in turn, on the structure and (1) U. W. Suter and P. J. Flory, J.Chem. SOC.,Faraday Trans. 2,73, 1521 (1977). (2) E. Saiz, U. W. Suter, and P. J. Flory, J . Chem. Soc., Faraday Trans. 2, 73, 1538 (1977). (3) A. E. Tonelli, Macromolecules, 10, 153 (1977). (4) W. L. Mattice and E. Saiz, J.Am. Chem. SOC.,100,6308 (1978). (5) G. D. Patterson and P. J. Flory, J.Chem. SOC.,Faraday Trans. 2, 68. 1098 (1972). .~~ ~.. ~. ~ . .
~ , .
(6)C. W. Carlson and P. J. Flory, J . Chem. SOC.,Faraday Trans. 2,
73, 1505 (1977).
@ 1981 American Chemical Society
’
3216
Flory et al.
The Journal of Physical Chemistry, Vol. 85, No. 22, 1981
conformation of the molecule. analytical reagent grade (Aldrich Chemical Co.). A bond additivity scheme would, in principle, provide Depolarized Light Scattering. The light-scattering photometer designed by Pattersod for measurement of a set of constitutive contributions suitable for this purpose. Such schemes have been discredited because of inductive depolarized Rayleigh scattering at 90° was used with minor effects7p8that may be commensurate with the intrinsic refinements to be described in detail in a forthcoming polarizabilities of the bonds. Effects of this nature tend publication.1° A 15-mW He-Ne laser (A = 632.8 nm) with to invalidate constitutive schemes that seek to express the vertical polarization ratio better than 10001 was used as molecular polarizabilitytensor as the sum of contributions source. With a lens, the beam incident at the cell was partially focused. The lateral dimensions of the rectanof individual bonds. Such effects are of short range, gular cell are 1X 1cm, with faces of Schlieren quartz flats. however. Hence, if larger groups instead of individual bonds are chosen as the primary polarizable entitie~,'-~#~ Narrow band-pass filters of nominal widths 18 and 53 cm-l, one may reasonably expect to succeed in formulating a respectively, were inserted in the scattered beam preceding constitutive scheme that will account for the anisotropy its entrance into the photomultiplier tube as a means of of the polarizability of the molecule in its various conseparating collision-induced anisotropic scattering from formations. The molecular geometry in each conformation that due to the intrinsic molecular anisotropy,sp6which must, of course, be fully taken into account. latter is sought. Their transmission spectra were determined with a double monochromator using white light, the Implementation of the scheme briefly indicated requires that the anisotropy tensors for constituent groups be wavelength calibration being provided by the He-Ne line. known, together with their dipole moments. The ester The attenuation factors gl(wo)and g2(w0)required to express the fractions of the collision-induced depolarized group is prominent among groups occurring in molecules radiation transmitted by the respective filters were evalof biological importance and in various polyesters. The uated by numerical integration over the measured transdirection of its dipole moment has been evaluated in the mission spectra of the filters. The spectrum of the collipreceding papersg Here, we devote attention to the ansion-induced radiation was characterized by the mean isotropic part of the polarizability tensor for the ester frequency range wo, its form being represented as described group. Inasmuch as substituents in the immediate vicinity previously.6 For carbon tetrachloride wo = 12 cm-'. of the group may be inductively affected, it is important The measured intensities were analyzed according to the to distinguish ester groups according to the substituents following procedure devised by Carlson and Florya6The attached directly to them. molecular scattering intensity Imol was separated from the Of particular interest are ester groups having structures total scattering intensities Il and I2 observed by means of of the types I and 11. The former (I) occurs in polyfilters 1 (18 cm-l) and 2 (53 cm-l), respectively, by use of COOCHj OCOCH, the equation -C
H p-C
I H -CH2I
-C
H2-C
I H -CH2-
(acrylates); its simplest analogue is methyl isobutyrate (MIB). Structure I1 occurs in poly(viny1ester)s, and, with additional ester substitution, in glycerides and lipids. Isopropyl acetate (IPA) is the simplest example of an ester of type 11. One of the principal axes (2)of &E for the ester group is perpendicular to the plane of the group. Three quantities must therefore be determined for full evaluation of &E: the diagonal elements &x and i i y along X and Y axes located in the plane of the group and the off-diagonal element &xu.The tensor being traceless, &Z = --@x + &y). In this paper, we present results of DRS and electric birefringence measurements yielding (r2), ,K, and (0)for several aliphatic monoesters and for two diesters, dimethyl trans-1,4-cyclohexanedicarboxylate (CDC) and trans-1,4cyclohexanediol, diacetate (CDA). From these results, supplemented by the dipole moment vector PE, we evaluate the tensors &E for esters of types I and 11. Experimental Section Materials. The preparation of trans-1,4-cyclohexanedicarboxylic acid dimethyl ester (CDC) and trans-1,4cyclohexanediol diacetate (CDA) is described in the preceding paper.9 Other esters were of 99% purity or better according to the suppliers: Matheson Coleman and Bell for methyl acetate (MA), Aldrich Chemical Co. for methyl isobutyrate (MIB) and isopropyl acetate (IPA). Carbon tetrachloride used as solvent was spectrograde (Matheson Coleman and Bell); p-dioxane, also used as a solvent, was (7) R. L. Rowel1 and R. S. Stein, J. Chem. Phys., 47, 2985 (1967). (8)J. V.Champion, A. Dandridge, D. Downer, J. C. McGrath, and G. H. Meeten, Polymer, 17,511 (1976). (9) E. Saiz, J. P. Hummel, P. J. Flory, and M. Plavsic, J. Phys. Chem., preceding paper in this issue.
1mo1
I1
= [I1 - k ~ / g d ~ I / [-ff~kl/g2)1 ~
(2)
where gl and g2are the attenuation factors identified above for the collision-induced DRS; fl and f2are the attenuation factors for the much narrower (w < 2 cm-') central Lorentzian representing the molecular depolarization. For carbon tetrachloride and dilute solutions therein, gl/g2 = 0.54 and values of fl and f2 are effectively equal to unity. The intensity attributed to the solute is ent poiyte = poAytion - 4solventpol mol
(3)
where $Polvent is the volume fraction of solvent in the solution. Calibration according to procedures previously employed6i6permits conversion of intensities to absolute Rayleigh ratios RZ; from which apparent optical anisotropies are calculated according to Yap:
= (15/p)(A/2d4[3/(n2 + 2)I2R!3
(4)
where p is the number density of solute molecules in the solution, X is the wavelength in vacuo, and n is the refractive index. Extrapolation of raptto infinite dilution gives the intrinsic anisotropy y2 for the solute. Electric Birefringence. Measurements required for evaluation of molar Kerr constants ,K were carried out by using an improved version of apparatus described previously.2J1 The cell constructed according to a design by Suter12consists of brass electrodesseparated by ceramic spacers. The cell is 1.0 X 0.35 cm in cross section and 14.5 cm in length (1). Only 5 mL of solution is required to fill the cell. The quartz windows are secured by Teflon elastomer O-rings. This latter feature minimizes strains (10) P.Irvine and P. J. Flory, manuscript in preparation. (11) R. T. Ingwall, E. A. Czurylo, and P. J. Flory, Biopolymers, 12, 1137 (1973). (12) U.W.Suter, private communication.
-
The Journal of Physical Chemistry, Vol. 85, No. 22, 1981 3217
Optical Anisotropies of Aliphatic Esters 3.0
TABLE I: Summary of Experimental Results compd
(P),
(,y2), A 6
101",K, cm5 statvolt-, mol-'
D* A 6
1.6, 2.0 2.6 13.5 15.8
2.1 (2.25a) 1.6, (1.65=) 2.4, -2.1, -1.8,
1.3, 1.0, 1.5, -1.8, -1.7,
~~
MA
MIB IPA CDC CDA
a Calculated from measurements of LeFe'we and S ~ n d a r a m 'in~ benzene.
1.5
0
0.2
0.4 0.6 0.8 'Pz, Volume Fraction Solute
1.o
Figure 1. Apparent optical anisotropies y2 of methyl acetate (MA), methyl isobutyrate (MIB), and isopropyl acetate (IPA) measured in CCI, as functions of the volume fraction (p2 of solute.
17
16
*
(0
a N+%
15
0.8 1 0
0.10
0.20
0.30
q 2 , Volume Fraction Solute
Figure 3. Ratios of the difference AB = B - Bo between electric birefringences of solution and solvent (CCI,) to the molarity m (In mol ~ m - plotted ~ ) against volume fractions of monoesters.
14
13 0
0.10 0.20 p2
