J. Phys. Chem. 1981, 85,3211-3215
Figure 7 shows the two correction functions plotted isothermally against reduced density. At low temperatures, the large maximum in AaTP probably has no physical significance because it occurs in a physically unattainable region. At low temperatures, the correction AaSVis negative. Finally, Figure 8 shows a logarithmic scaling plot of Ips - p(T,)I vs. T,- T for temperatures below T,; here pE is the saturated density. This plot was prepared to determine the scaling parameter 0 in the equation lP8 - P(T,)I
-
(Tc -
(4.1)
When the corrected equation of state is used, p = 0.38 in the range T,- T = 2-12 K. This calculated result agrees well with the experimental value ( p = 0.36) but is larger than the theoretical (Ising) result (p = 0.325). Very close to the critical point, our equation of state necessarily gives the mean-field result p = 0.5.
3211
5. Conclusion The calculations reported here suggest that two wellknown weaknesses in the van der Waals model for fluids can be corrected by adding to the calculated Helmholtz energy analytical correction functions with only a few empirical coefficients. These correction functions improve agreement with experiment for the second and third virial coefficients and for the two-phase region at temperatures near the critical. These empirical corrections may suggest to theorists how a more fundamental correction to the van der Waals model may be constructed without resorting to the currently popular but inconvenient method where the hard-sphere diameter (cutoff parameter) is a function of both temperature and density. Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US.Department of Energy under Contract No. W-7405-ENG-48.
Direction of the Dipole Moment in the Ester Group E. Salz,+J.
P. Hummet,$ P. J. Flory,
IBM Research Laboratory, San Jose, California 95 193
and M. PlavriE Department of Chemistry, Stanford University, Stanford, California 94305 (Received: March 24, 198 1)
The directions of the dipole moments in esters RCOOR’ in which R and R’ are alkyl or aryl groups have been deduced by analysis of experimental values of dipole moments of six compounds containing two polar groups, one or both of which are esters. New determinations of molecular dipole moments are reported for dimethyl truns-1,4-cyclohexanedicarboxylate and for truns-l,4-cyclohexanedioldiacetate. The moment of the ester group is directed (in the positive sense) at an angle 73 = 123 f 3” from the R-CO axis in both aromatic and aliphatic esters, formates excepted.
Introduction The magnitudes of the dipole moments, p , of esters RCOOR’ are quite insensitive to the character of the groups R and R’ provided that they are nonpolar. For methyl formate (R = H, R’ = CH3), p = 1.77 D.l For methyl esters of aliphatic acids, and those with larger alkyl groups R’ as well, p = 1.80 f 0.05 D according to the most reliable determinations from dielectric measurements on dilute solutions in nonpolar s o l ~ e n t s . ~Dipole ? ~ moments of alkyl benzoates are somewhat greater, being in the range p = 1.90 f 0.06 D.3 For phenyl acetate, values of p ranging from 1.65 to 1.78 have been The direction of the dipole moment in the plane of the ester group has been determined unambiguously only for methyl formate (R = H) and for the methyl esters of fluoro (R = F) and cyano (R = CN) substituted formic acids. From analysis of the microwave Stark spectrum of methyl formate, Curl1 found f i = 1.77 D, with the dipole moment making an angle of 39” with the C=O bond. According to the valence geometry established by his analysis, the corresponding angle between the positive direction of /I and the H-C bond is T = 86” (see Figure 1). Williams, Owen, On leave from Departamento de Quimica Fisica, Facultad de Ciencias, Universidad de Extremadura, Badajoz, Spain. *Present address: IBM, East Fishkill, NY 12533. 0022-3654/81/2085-3211$01.25/0
and Sheridan7 similarly found p = 2.83 D with T = 47” for the total dipole moment of methyl fluoroformate, and p = 4.23 D with T = 26” for methyl cyanoformate. These methods are not readily applicable to more complicated esters. Exner et ala8have estimated 7 = 115 f 4” by vector addition of bond dipole moments in substituted benzoic acid esters. The reliability of this method is questionable for adjoining bonds subject to mesomeric effects. Accurate assessment of the direction of the dipole moment of the ester group is essential for the interpretation of properties of molecules such as triglyceridesg and polymeric esters containing a plurality of ester groups. Besides its relevancy to the dipole moments of such more (1)R. F. Curl, Jr., J. Chem. Phys., 30, 1529 (1959). (2) R.J. W. Le FBvre and A. Sundaram, J . Chem. Soc., 3904 (1962). (3)A.L.McClellan, “Tables of Experimental Dipole Moments”, Vol. 11, Rahara Entrp., El Cerrito, CA, 1974. (4)M.honey, R.J. W. Le FBvre, and 5.5. Chang, J.Chem. SOC., 3173 (1960). (5) 0. Exner, 2. Fidlerovl, and V. JehliEka, Collect. Czech. Chem. Commun., 33,2019 (1968). (6)B. Krishna, S.K. Bhargava,and B. Prakash, J . Mol. Struct., 8,195 (1971). (7)G . Williams, N.L. Owen, and J. Sheridan, Trans. Faraday Soc., 67,922 (1971). (8)0.Ewer, V.JehliEka, and J. Firl, Collect. Czech. Chem. Commun., 36, 2936 (1971). See also 0. Exner, “Dipole Moments in Organic Chemistry”, Georg Thieme Verlag, Stuttgart, 1975. (9)W. L. Mattice and E. Saiz, J.Am. Chem. SOC.,100,6308 (1978).
0 1981 American Chemical Society
3212
The Journal of Physical Chemistry, Vol. 85, No. 22, 1981
Y
TABLE I: Dipole Moments of Simple Esters
4 I
I I
PE
1
Saiz et al.
0-R'
\' 0
Figure 1. Reference frame affixed to the ester group. The positive direction of the dipole moment pEof the ester group is indicated by the arrow.
complex molecules and their configurational averages, the direction of the group dipole moment is required also for analysis of the Kerr constant obtained from electric birefringence measurement^.^ In the present investigation,we have evaluated the angle 73 of the dipole moment of the ester group (see Figure 1) by analysis of the dipole moments of difunctional molecules containing two polar groups, one or both being esters. On the supposition that inductive effects may perturb the direction of the molecular dipole moment, we have separately analyzed results from the literature on aromatic esters in which either R or R' is aryl. The analysis of the aliphatic ester group rests on determinations of the dipole moments of dimethyl trans-1,4-cyclohexanedicarboxylate (CDC) and trans-1,4-cyclohexanedioldiacetate (CDA) reported in this paper. The direction of the dipole moment of the ester group in molecules in which R and R' are hydrocarbon groups is established within narrow limits. Experimental Section Synthesis of Dimethyl trans-1,I-Cyclohexanedicarboxylate (CDC). trans- 1,4-Cyclohexanedicarboxylic acid (Aldrich) was refluxed with an excess of thionyl chloride in a dry, three-neck, round-bottom flask fitted with a condenser and a drying tube. The mixture was heated until the acid dissolved. Remaining thionyl chloride was removed under reduced pressure. The residue was suspended in dry chloroform, and freshly distilled methanol was slowly added. The excess methanol and solvent were removed by distillation under reduced pressure. The residue was recrystallized twice from pentane, mp 68-69.5 "C (lit.Io 68-69 "C). Synthesis of trans-1,4-CyclohexanediolDiacetate (CDA). A mixture of cis- and trans-cyclohexanediol (Aldrich) was refluxed in a 3-fold excess of acetic anhydride. The excess anhydride was removed by distillation under reduced pressure. The partially crystalline residue was recrystallized 4 times from heptane, mp 102-103.5 "C (litall 102-103 "C). Dipole-Moment Determinations. Dielectric constants of carbon tetrachloride solutions of the esters were measured at 25 "C with a WTW Dipolemeter Model DM-01 a t a fixed frequency of 2.0 MHz. Measurements were performed on solutions of three monoesters, methyl isobutyrate, isopropyl acetate, and methyl benzoate, in addition to the diesters CDC and CDA. Mole fractions of solute were varied from ca. 0.005 to 0.05 in each instance. Refractive indexes of solutions and pure solvents were measured at the same temperature with an Abbe refractometer. Dipole moments were deduced by analysis of the (10)M.Baron, E.L. De Zenobi, and M. Davidson, J. Mol. Struck, 24, 432 (1975). (11)L.N. Owen and P. A. Robins, J. Chem. SOC.,320 (1949).
compd ethyl acetate methyl isobutyrate isopropyl acetate methyl benzoate phenyl acetate
&E, D
(lit, values)
1.84'9 '' 1.80,' 1.7628
this investigationa
1.78 1.79 1.88
1.84,' 1.89,b1.9414 1.65,41.72,' 1.7V Average from sources Estimated errors are tO.02 D. quoted in ref 3. TABLE 11: Summary of Results
MCB
1.89 113 1.89 117 DMT 1.89 121 DAB 1.654 121 1.714-6 125 CDC 2.12 t 0.02 1.7@ 122 CDA 1.55 f. 0.02 1.79' 125 For the diesters these are root mean squares (p2)1'2 with averages taken over all conformations. Taken from the measured value for the analogous monoester, methyl isobutyrate; see Table I. From the value for the analogous monoester, isopropyl acetate; see Table I. MBB
1.95 t 0.0214 1.82'' 2.2519-" 2.104
data according to the procedure devised by Smith12 and Guggenheim.13 The contribution of the term dependent on the refractive indexes amounted to -9% of the calculated dipole moment. Dipole moments obtained for the monoesters are presented in Table I together with results taken from literature sources. Close agreement with published values is apparent. Values obtained for the diesters are ( p c ~ c ~=) ~ ' ~ 2.12 f 0.02 D (lit.'' 2.09 f 0.08 D) and ( P C D A ~ ) ~ / = ' 1.55 f 0.02 D, configurational averages being denoted by angle brackets. These results are included in Table I1 with values taken from the literature for other difunctional esters. Analysis of Experimental Results Methyl p-Chlorobenzoate ( M C B ) and Methyl p Bromobenzoate (MBB). The dipole moments reported for these two compounds are given in the second column of Table 11. Both were determined from dielectric measurements in benzene; those on MCB were carried out by Jones et al.14 at 25 "C and on MBB by Bergmann16 at 14 "C. Taking the dipole moment of each of these compounds to be the vector sum of the moment px-c attributable to the halogen-phenyl bond and the moment pE of the ester group, one obtains
cos 73 =
h M X B 2 - pX-X2 - pE2)/(2wX-CpE)
(1)
We identify pE with the mean of the values reported for the dipole moment for methyl benzoate? 1.89 D as given in Table I, with which our determination given in the last column of Table I is in close agreement. Dipole moments pX4 are provided by results for chloro- and bromobenzene. For the f ~ r m e r , lCl4 ~~J= ~ 1.60 f 0.03 D, and, for the latter,17 pBrC = 1.58 f 0.03 D. Both values are averages (12)J. W.Smith, Trans. Faraday SOC.,46,394 (1960). (13)E.A. Guggenheim, Trans. Faraday SOC.,45,714(1949);47,673 (1951). (14)R.A.Y.Jonee, A. R. Katritzky, and A. V. Ochkin, J.Chem. SOC. B, 1795 (1971). (15)E.Bergmann, J. Chem. Soc., 402 (1936). (16)See ref 3, pp 171-2. (17)See ref 3, pp 170-1.
The Journal of Physical Chemktty, Vol. 85, No. 22, 1987 3213
Direction of the Dipole Moment in the Ester Group
;
Y'
4 o----,
X'
t Flgure 2. Trans conformation of the DMT molecule. See legend for Figure 1.
of determinations in benzene. Substitution of these moments into eq l yields the results given in the last column of Table 11. Dimethyl Terephthalate (DMT). The geometrical representation of the DMT molecule is shown in Figure 2. Conformational analysis supplemented by X-ray crystallographic data on this compound and its analogues indicated the stable conformations to be those in which the ester groups are copolanar with phenylene.ls The ester groups of DMT may, therefore, be either trans (as shown in Figure 2) or cis with respect to one another. The dipole moments for the respective forms are zero and 2& sin 73. Coulombic interactions between the two dipoles favor trans over cis; energies of these two forms otherwise should be sensibly equal. If w is the statistical weight of cis relative to unity for trans then (pDMT2)
= w(1
+
sin
TE)~
(2)
Weissbergerlgand william^'^^^^ found pDMT = 2.2 D in benzene at 25 "C. Gur'yanovael and KlagesZ2arrived at the slightly larger values of 2.30 and 2.31 D. The mean of these results has been selected for our purpose, as recorded in Table 11. Substitution of this mean value together with p E = 1.89 D (see above) into eq 2 yields TE = 122.7" if dipolar interactions are ignored and, hence, w = 1. Random torsional fluctuations about the perferred conformations increased the dipole moment of the trans form and decrease that of the cis to extents that are virtually of equal magnitude and, therefore, are of no consequence. The Coulombic energies of the two forms were estimated by representation of the electric asymmetry by point dipoles situated on the extension of the C-CO axis (X axis in Figures 1 and 2) at the point where it intersects the line connecting the two 0 atoms, i.e., at a distance of 0.61 A from the carbonyl carbon. An effective dielectric constant of 3.5 was employed. We thus find the energy of the cis from to exceed that of trans by ca. 50 cal/mol. Hence, w = exp(-50/RT) = 0.92 at 30 "C. Repetition of the calculation of TE according to eq 2 on this basis gives rE= 120.7" (see Table 11). Thus, Coulombic interactions do not affect the result significantly. p-Diacetoxybenzene (DAB). The stable conformations of phenyl acetate are those in which the plane of the ester is rotated 58 f 10" from the phenyl plane.ls Accordingly, four conformations representing combinations of rotations 41and $ J ~N f 58" about the phenylene axis (X?are accessible to the DAB molecule shown in Figure 3. The projections of the ester groups on a plane perpendicular (18) J. P.Hummel and P. J. Flory, Macromolecules, 13,479 (1980). (19)A.Weissberger and J. W. Williams, 2. Phys. Chem., Abt. B, 3,367 (1929). (20)J. W. Williams, Phys. Z., 29, 683 (1928). (21)E. N. Gur'yanova and N. I. Grishko, J. Struct. Chem. (Engl. Transl.),4, 339 (1963). (22)G. Klages and P. Knobloch, 2. Naturforsch. A , 20,580 (1965).
Flgure 3. Trans conformation of the DAB molecule. The reference frame XYaffixed to the ester group corresponds to the one adopted in Figures 1 and 2. Additionally, the symmetry axis X'of the molecule is indicated.
Flgure 4. Structure of the CDC molecule shown in Its most stable conformation 0,O. See legend for Figure 1.
to the axis are inclined at angles 9 = 0,64,180, and -116O in the respective conformations, 9 being measured from the trans form in which the ester dipole moments are antiparallel. The dipole moment pi of conformation i is given by pi = pE sin 73'[2(1 - COS 9i)11/' (3) where TE' is the angle between pE and the axis X'. The configurationally averaged square of the dipole moment is (PDAB')
= CwipLi2/Cui 1
I
= 2pE2 sin2 TE'[C@i(l- COS
+J/Cwi]
(4)
where wi is the statistical weight of conformation i. Estimation of dipole-dipole interactions for the various conformers in the manner described above yields relative energies of 0,8,41, and 24 cal/mol for the values of @ in the order quoted above. Corresponding statistical weights wi at 25 "C are 1.000,0.987, 0.933, and 0.960. Substitution in the bracketed expression in eq 4 yields 0.980 for this quantity, which equals unity if wi= 1 for all i. The difference is scarcely significant. The value 0.98 has been used in the following calculations. According to Aroney, Le FBvre, and Chang: the dipole moment of DAB determined in carbon tetrachloride at 25 "C is 2.10 D. For phenyl acetate under the same conditions, they found WE = 1.65 D. On this basis we obtain 73' = 114.6'. Other measurements on phenyl acetate indicate a larger dipole moment. Exner et aL5 report pE = 1.72 D for this ester in benzene and Krishna et al.6 found pE = 1.78 in CC14. Substitution of the mean of the three values, 1.71 D, into eq 4 yields 73' = 118.7'. Since in phenyl esters LCOC* exceeds LCC*O by ca. 6" (where C* denotes the carbonyl carbon), these values of rE'yield the results given in the last column of Table 11. Dimethyl trans-l,4-Cyclohexanedicarboxylate(CDC). The sterically favored conformations for this molecule are those in which the ester groups are coplanar with the axial C-H bonds. Shown in Figure 4 is the conformation in which each carbonyl bond, C*=O*, is cis to the neigh-
3214
Saiz et al.
The Journal of PhysicalChemistty, Vol. 85, No. 22, 1981 n
Flgure 5. Structure of the CDA molecule shown in its 0,O conformation. See legend for Figure l .
x
boring C-H bond. We desi nate this as the 0,O conformation. Withg lCI+* = 1.20 , IC= 1.35 A, ICC* = 1.50 A, LCC*O* = 126.3’, KC*O = 111.4’ and with carbon atoms in the ring tetrahedral, interatomic distances are dCHrp = 3.09. According to force-field calculations carried out with the energy functions specified previ0usly,2~the increased repulsion between H and 0 in the I)= a conformation compared with that between H and O* in the 1c/ = 0 form is largely compensated by the greater CH2.* SO* distance compared with CH2.* -0. The foregoing analysis is supported by evidence from microwave spectra of methyl a ~ e t a t e ~ indicating ~ p ~ ~ a 3-fold rotational pontential with an energy barrier of 300 cal/mol. The minima are located at the conformations with C* = O* eclipsing C-H, as in Figure 4. The replacement of two of the H atoms of the acetate group by CH2groups in CDC raises the energy for two of these conformations by 1.5 kcal/mol, thus eliminating two of the minima. Weaker repulsions between the CH2 groups and 0 in the $ = 0 conformation tend to diminish the preference for I)= 0 over I)= P , as pointed out in the paragraph above. Compared with uncertainties of estimates of the nonbonded interactions, dipole-dipole interactions between the two ester groups are negligible. We conclude that the difference between the energies of the I)= a and I)= 0 conformations is in the range 0-200 cal/mol. The corresponding statistical weight w of the 4 = P state relative to 4 = 0 may range from 1 to 0.7, therefore, at ordinary temperature. Dipole moments of the 0,O and a,a conformations are zero. The relative incidence of the O,?r and a,O states having nonzero moments in 2 w / ( l + w ) ~ . Analysis in terms of discrete states gains validity, the shallowness of the minima notwithstanding, from the fact that fluctuations from these minima increase the square of the dipole moments for the 0,O and a ,conformations ~ to about the same extent as they decrease p 2 for 0,a and a,O. Effects of ring distortions are subject to analogous compensations. It follows that
-
( I L C D ~ ~=)
[2w/(l
+
sin TE)’
(5)
From the results here reported (see Table 11)we obtain = 122.6’ for w = 1 and 73 = 121.2’ for w = 0.7. The value given in the last column of Table I1 is the rounded mean of these two results.
4, deg.
Figure 6. Conformational energies calculated for isopropyl acetate (model compound for CDA) as a functlon of rotation about the C-0 bond. V , = 1.0 kcal/mol (solid line); Vo = 0 (dashed line).
trans-1,4-Cyclohexane~~o~ Diacetate (CDA). In the conformation of reference shown in Figure 5, the ester groups are coplanar with the axial C-H bonds, the carbonyl distance oxygens being apposed to H. The small H.-.O* (2.04 A) and the preference for staggered conformations about the C-0 bond render the energy in this symmetric conformation a maximum relative to nearby conformations, Minima are to be expected at torsions in the range 30 < 141 < 60’ from this conformation. At large torsions, the repulsions between CO and the CH2groups pendant to CH raise the energy. Relief at 4 = a is partial only, since the CO group is impacted by both groups in this conformation. Force-field calculations, carried out by using the parameters given elsewhere%together with an inherent 3-fold torsional potential V&4) of 1.0 kcal/mol, are shown by the solid curve in Figure 6. The barrier for the ester group may be presumed to be substantially lower than that for the C-0 bond in ethers, namely, ca. 1.8 kcal/moLZ6 The effect of the torsional potential on the form of the curve in the vicinity of the minimum is minor, as the dashed curve in Figure 6 calculated for V&$) = 0 demonstrates. Dipole-dipole interaction energies are negligible compared to uncertainties in the force-field calculations leading to the curves shown in Figure 6. Hence, they are ignored. The mean square of the molecular dipole moment is given in this instance by (pCDA2)
= 2&3* sin2 T E ’ ( ~ - (COS
4)’)
(6)
where, as before, rE‘is the angle between the dipole moment of the ester group and the C-0 bond. According to the microwave spectrum of methyl acetate,’ LC*OC LCC*O 6’. X-ray crystallographic data on aliphatic estersg indicate a difference of ca. 5O, which value we have adopted. Averaging over the potential shown in Figure 6, one obtianed (cos 4) = 0.707 f 0.01. Substitution of this result into eq 6 together with (/LcDA’)’/’ = 1.55 D and PE = 1.79 D yields 73’ = 120’. Hence, 73 = TE’ + 5’ = 125’ (see Table 11).
TE
(23) D.Y. Yoon, U. W. Suter, P. R. Sundararajan, and P. J. Flory, Macromolecules, 8, 764 (1975). (24) J. E. Wollrab, “Rotational Spectra and Molecular Structure”, Academic Press, New York, 1967. (25) D. G. Lister, J. N. MacDonald, and N. L. Owen, “Internal Rotation and Inversion”, Academic Press, New York, 1978.
Conclusions The average of T E for the four diesters is 123’. All fall within f2’ of this mean. Angles calculated from the dipole (26) A. Abe and J. E. Mark, J. Am. Chem. SOC.,98, 6468 (1976). (27) C. W. N. Cumper and P. J. Langley, Trans. Faraday SOC., 67,35 (1971). (28) H. Powels and P. Hayskens, Bull. SOC.Chim. Belg., 83,407 (1974).
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
’
