J. Phys. Chem. 1987, 91, 2959-2962 A, type bands. Notably, an increase in the angle of incidence results in a larger value for the SP/SS ratio. Bands with a large SP/SS ratio should be assigned to Bg type, and they are seen with low relative intensity. Also in agreement with the molecular orientation parallel to the surface is the fact that the relative intensity of the PP spectra increases when the angle of incidence decreases. When the angle of incidence is 45O (and the direction of observation also forms a 45O angle with the film’s normal) a new band a t 463 cm-I is clearly observed. After a number of measurements that probe the angle dependence for this band, it was concluded that the 463-cm-I band must be due to an outof-plane vibration. Conclusions Infrared and Raman spectra of PTCDA films were obtained
2959
and an empirical assignment of vibrational modes is proposed. Infrared spectra indicate that PTCDA films have a well-defined molecular organization, where the molecular plane and the substrate surface are parallel. SERS and SERRS spectra differ from their unenhanced counterparts in relative intensities and some new broader features were observed. This has prompted further investigation of polarization properties and distance dependence that are presently in progress. Acknowledgment. Financial assistance from the National Sciences and Engineering Research Council of Canada is gratefully acknowledged. Registry No. PTCDA, 128-69-8; KBr, 7758-02-3; Ag, 7440-22-4; In, 7440-74-6; quartz, 14808-60-7.
Linear Solvation Energy Relationshlps for the Hydrogen-Bonded Complexes of m -Cresol J. N. Spencer,* John A. Andrefsky, Jina Naghdi, Lisa Patti, and John F. Trader Department of Chemistry, Franklin and Marshall College, Lancaster, Pennsylvania 17604 (Received: September 15, 1986; In Final Form: January 23, 1987)
Free energies, enthalpies, and entropies for the hydrogen-bonded complexes of m-cresol with various bases in CC14 solvent have been determined from calorimetric and spectroscopic data. These data have been analyzed by linear solvation energy relationships using solvatochromicparameters. Dipolar interactions of the free base with solvent are shown to be significant for all thermodynamic parameters. Conclusions drawn from the use of free energy data alone can be misleading.
Introduction Solvatochromic parameters have been used to correlate and predict a variety of solvent effects.’ The linear dependence of solvent effects on these parameters allows an analysis based on molecular structure and theoretical concepts. Despite the large number and variety of solvent effects that have been treated with these parameters, no work is known to the authors for which all the thermodynamic parameters for hydrogen-bond formation are available for a selected system. Consequently, conclusions concerning solvent effects have often been based only on free energy considerations. Rather imprecise entropies have been used only in one instance to test correlations with solvatochromic parameThe only reported hydrogen-bond enthalpy relationships with these parameters have been with enthalpies3 determined by pure base calorimetric methods which do not allow the calculation of the other thermodynamic parameters. In this work ten bases, four carbonyl, one sulfoxide, and five ether compounds, were studied with the proton donor m-cresol. Calorimetric and near-IR spectroscopic methods were used to determine entropy, enthalpy, and free energy data in C C 4 solvent. Experimental Section Both the calorimetric and spectroscopic methods of data collection have been previously des~ribed.~ A least-squares technique . which gives the best data fit by minimizing the equilibrium constant and enthalpy is used to analyze the calorimetric data. Equilibrium constants were also determined by near-IR spectroscopy by application of Beer’s law. A combination of calor(1) Taft, R. W.; Abboud, Jose-Luis M.; Kamlet, M. J.; Abraham, M. H. J . Solution Chem. 1985, 14, 153. ( 2 ) Kamlet, M.J.; Gal, Jean-Francois; Maria, Pierre-Charles; Taft, R. W. J . Chem. Soc., Perkin Trans. 2 1985, 1583. (3) Taft, R. W.; Gramstad, Thor; Kamlet, M. J. J. Org. Chem. 1982, 47, 4551. (4) Spencer, J. N.; Campanella, C. L.; Harris, E.M.;Wolbach, W. S.J. Phys. Chem. 1985,89, 1888.
0022-3654/87/2091-2959%01SO10 , ,
I
imetric and spectroscopic data could then be used to determine the thermodynamic parameters for hydrogen-bond formation. The heat of interaction, Q,is determined calorimetrically by injection of m-cresol into a dilute solution of the base in CCl,; Q is related to the enthalpy of hydrogen-bond formation, AH, by Q = AHC,V where V is the volume of the reaction mixture and C, is the equilibrium concentration of the adduct. C, is found from the equilibrium constant determined by near-IR spectroscopy, and AH is then calculated from C,, Q, and V. All correlations to be made with these data will use the equilibrium constants obtained by least-squares methods and AH as determined by the calorimetric method alone. For the spectroscopic studies the m-cresol concentration was about 0.005 M and the base concentrations ranged from 0.005 to 0.2 M. m-Cresol concentrations were chosen for the calorimetric analysis so as to avoid any self-association of m-cresol. Self-association is spectroscopically observable at concentrations of m-cresol of about 0.01 M. The base concentrations for the calorimetric work ranged from 0.05 to 0.5 M. All reagents were dried over suitable drying agents and distilled under N2. The enthalpy of solution of m-cresol in CC14 at 298 K was determined to be 3.74 f 0.07 kcal mol-]. In this work correlations with log K , AH, and A S will be attempted according to the general equation5 XYZ = XYZ,
+ bp + SA* + e,$ + CI.L
where XYZ is either log K , AH, or AS,XYZ, is the value of XYZ in a reference state, (3 measures the proton accepting ability of the base, A* is a measure of dipolar/polarizability interactions, p is the dipole moment, and ,$ is a parameter which relates family-dependent properties to family-independent properties, Le.; carbonyl bases and ether bases may have different types of hydrogen-bond acceptor sites and thus may belong to different families. Good correlations are observed only when bases having ( 5 ) Kamlet, M. J.; Abboud, Jose-Luis M.; Abraham, M. H.; Taft, R. W. J . Org. Chem. 1983, 48, 2811.
0 1987 American Chemical Society
2960 The Journal of Physical Chemistry, Vol. 91, No. 11, I987
Spencer et al.
TABLE I: ThermodynamicParameters for H-BondFormation by m-Crewl in CCl, at 298 K
Ks-"
-r--
Me2S0 DMA THF THP DMF butyl ether cyclohexanone dioxane ethyl acetate anisole
131 f 30 8 9 f 17 10.0 f 0.2 10.5 f 0.5 55 f 11 4.1 f 1.0 11.2 f 0.2 6.4 f 0.4 7.4 f 0.1 1.1 f 0.4
K,lb _. 110 f 21 76 f 8 6.8 f 1.0 8.7 i 0.1 58 f 20 2.9 f 0.4 12f 1 7.1 f 0.4 8.9 f 2.0 0.98 f 0.50
-AH,e 6.2 f 0.3 6.1 f 0.2 4.8 f 0.5 5.6 f 0.1 5.5 f 0.1 4.6 f 0.5 4.9 f 0.1 4.1 f 0.1 3.6 f 0.3 2.4 f 0.2 I
-AH-? -.
A v . ~cm-' 346 318 ... 283 280 283 277 240 233 169 153
-Asd
6.3 f 0.1 6.2 f 0.1 5.7 f 0.5 5.9 f 0.1 5.5 f 0.3 5.5 f 0.3 4.7 f 0.1 4.0 f 0.1 3.2 f 0.2 2.5 f 0.7
11.8 f 0.5 12.2 f 0.4 15.3 f 1.7 15.5 f 0.3 10.4 f 1.2 16.3 f 1.0 10.8 f 0.4 9.5 f 0.4 6.4 f 0.8 8.4 f 2.6
" Determined by near-IR spectroscopy. Calculated from least-squares analysis of calorimetric data. A H in kcal mol-'. Calculated from combined spectroscopic-calorimetric data (kcal mol-I). dCalculated from AH,, and KaI (cal K-I mol-I). CThefrequency shift is the difference between the unbonded m-cresol peak 3614 cm-l and the bonded peak. The error is f 5 cm-I. similar types of hydrogen-bond acceptor sites are considered. Because of the close correlation between 1.1 and r*,multiple dependence correlations involving both p and r* are meaningless. Only those multiple dependency correlations having confidence levels greater than 90% will be considered. The criterion of Ehrensod to distinguish when single-parameter regressions may be discarded in favor of multiple regressions was used. Kamlet et a].' have shown good correlations are obtained when the logarithm of the equilibrium constant is plotted vs. the dipole moment, p, of the base, or vs. T * , or vs. j3. Even better correlations have been obtained by allowing for multiple dependencies of log K on j3 and r* or on j3 and p. These workers have found that formation constants of 4-FC6H40H with various bases in six solvents could be described by an equation of the form log K = log KO+ bj3 + ST*.' In all six solvents the sign of b is positive, in three of these solvents the sign of S is positive, and in three the sign is negative. The interpretation given was that a positive sign for b means that as 8 increases the stability of the complex increases and this is reflected by an increase in log K . A positive sign for S implies an increasing stability of the complex with increasing value of the r* parameter. This was interpreted to mean that dipolar interactions in the complex between acid and base increase with increasing a*. A negative sign for S was interpreted as meaning that dipolar interactions between the free base and solvent destabilize the hydrogen-bonded complex, shifting the equilibrium to lower log K values. The interpretation which was drawn from the signs of these parameters was derived from the following considerations: (a) Dipolar interactions between acid and base shifts the equilibrium to the right. (b) Dipolar interactions between the complex and the solvent shifts the equilibrium to the right. (c) Dipolar interactions between free acid and free base with the solvent shifts the equilibrium to the left. (d) Increased electron donating ability of the base to the acid as measured by increased j3 value (Le., increased ability to donate an electron pair) shifts the equilibrium to the right. The same considerations are applicable to entropy and enthalpy correlations, and analysis of solvent effects on these thermodynamic parameters will be interpreted in terms of dipolar interactions of base and complex with solvent and of dipole-dipole interactions i n t h e complex.
Results Thermodynamic parameters and frequency shifts are given in Table I for the hydrogen-bonded complexes of m-cresol. The frequency shifts are differences between the fundamental hydroxyl stretch of unbonded m-cresol in CCl, (3614 cm-') and the bonded hydroxyl stretch. Entropy changes were calculated from the calorimetric equilibrium constants by using the enthalpy changes calculated from calorimetric data. Solvatochromic parameters for the bases of this study are given in Table 11. ( 6 ) Ehrenson, S . J . Org. Cbem. 1979, 44, 1793. (7) Kamlet, M.J.; Dickinson, C.; Gramstad, Thor; Taft, R. W. J . Org. Chem. 1982, 47, 4971.
TABLE 11: Solratwhromic Parameters" MezSO DMA DMF cyclohexanone dioxane
THF n-butyl ether ethyl acetate anisole THP
Irb
**a
B
4.1 3.8 3.8 2.7 1.8 1.8 1.2 2.7 1.2c 1.8
1.00 0.88 0.88 0.76 0.55 0.58 0.24 0.55 0.73 0.51
0.76 0.76 0.69 0.53 0.37 0.55 0.46 0.45 0.22 0.54
€" 0.0 0.0 0.0 0.0 0.20 0.20 0.20 0.0 0.20 0.20
"Reference 5. bReference 6. cRiddick, J. A.; Bunger, W. B. Techniques of Chemistry; Wiley-Interscience: New York, 1970; Vol 11.
Correlations of A H with AS for hydrogen-bonded systems are well-known.* For a given acid with a series of bases belonging to the same family, generally AH and AS are linearly related. For the ethers in Table I the correlation is -AH = -0.055
- 0.367AS
r = 0.947, SD = 0.54 where r is the coefficient of correlation and SD is the standard deviation. For the carbonyl and sulfoxide bases -AH = -0.21 - 0.52AS r = 0.942, SD = 0.50 The two equations show clearly that AH-AS plots depend on the base family. Another family-dependent relation is that of A H and Av: -AH = 0.24 + 0.018211~ (carbonyl and sulfoxide) r = 0.991,
-AH = -1.59
SD = 0.20
+ 0.0257Av
(ether)
r = 0.984, SD = 0.30 Because the j3 parameter is a measure of the proton accepting ability of the base, a correlation between p and Av would be expected: Av = -34.1 + 479p (carbonyl a n d sulfoxide) r = 0.970, Av = 77.5
SD = 20
+ 3928
(ether)
r = 0.968, SD = 16
The solvatochromic parameter l allows the correlation of family-dependent properties by a single equation: Av = -7.2 4368 + 328i (all bases)
+
r = 0.966,
SD = 18
(8) Jotsten, M. D.; Schaad, L. J. Hydrogen Bonding Marcel Dekker: New York, 1974.
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 2961
Hydrogen-Bonded Complexes of m-Cresol
TABLE III: Correlations between Thermodynamic Parameters and the Solvatochromic Parameters XYZ = XYZo bfl Su* e[ CM
+ +
XYZ"
XYZ0
b
-AHc -AHc -AHc -AHc -AHe -AHc -AHCS
-0.453 -0.64 -0.756 0.272 1.60 7.43 -0.937 -0.84 2.14 1.01 -0.352 0.129 -0.797 1.06 1.59
8.83
- m , c
-AHc,e -AH,, -AH,, -AHc -AHc -AHc -AHe
S
+ + e
c
1.70 7.29 10.4 2.00 -5.19 9.59 8.26 12.6 9.83 14.0 4.73 11.5 9.33
7.71 14.1
1.76
-2.38 -1.12 -0.91 1
6.69 -1.14
3.64 -0.823 -1.65
3.54 0.560 2.91 1.33
4,
11.7
14.1
-1.58 1.61
0.521
-1 1.3
r
SD
0.973 0.889 0.971 0.982 0.454 0.638 0.976 0.691 0.916 0.983 0.982 0.986 0.988 0.993 0.997
0.34 0.68 0.36 0.32 1.49 1.29 0.33 1.08 0.60 0.27 0.30 0.29 0.28 0.23 0.14
0.940 0.954 0.960 1.ooo
0.23 0.21 0.20 0.1 1
0.716
2.57
"The subscript c refers to carbonyls and sulfoxide considered alone, e refers to ethers alone, and c,e refers to combined carbonyl, sulfoxide, and ether data. The enthalpy of hydrogen-bond formation correlates well with
8 for carbonyls and sulfoxide taken as one family and for ethers. -AH = 0.453
+ 8.838
(carbonyl and sulfoxide)
r = 0.973, SD = 0.34 -AH = 0.272
+ 10.408
(ether)
r = 0.982, SD = 0.32
The 8,f multiple dependence does not give as good a correlation for the ethers, carbonyls, and sulfoxide together as does 0,p: -AH = -0.937 9.598 + 7.77f (all bases)
+
r = 0.967, SD = 0.33
-AH = 1.01 + 12.68 - 1 . 1 2 ~ (all bases) r = 0.983,
SD = 0.27
Poor correlations are found for AH of the ethers, carbonyls, and sulfoxide together as a function of 8 (r = 0.851) or I.( ( r = 0.466) independently. The best correlation for the entropy for all bases taken together is
-AS = 6.41
+ 34.48 - 5 . 2 6 ~ (all bases)
r = 0.980,
SD = 0.72
For the logarithm of the equilibrium constant the fl,p correlation is again better than the B,[ correlation which is at a confidence level below 90% when compared to the correlation with 8 alone. log K = -0.313
+ 2.918 - 1.586
(all bases)
r = 0.960, SD = 0.20 log K = -0.668
+ 0 . 3 2 9 ~+ 1.748
r = 0.984,
(all bases)
SD = 0.13
The usual interpretation given to the log K vs. f l , correlation ~ is that a larger 8 shifts the equilibrium to the right due to increased proton accepting ability of the base and that the stability of the complex is further enhanced by the dipole-dipole interaction in the complex. This interpretation follows logically given only free energy data. However, when entropy and enthalpy data are examined, a different interpretation is called for. Most correlations with the solvatochromic parameters have relied on free energy data alone; the present work is one of the few in which all the
thermodynamic parameters for a given system are known. The correlation of AH for all bases together shows that AH becomes more negative as 8 increases but becomes more positive as p increases. Thus, increasing the dipole moment of the base does not result in increased complex enthalpy; rather, the complex is destabilized as the dipole of the base increases. That the monomers in a hydrogen-bonded equilibrium are more solvated than the complex is well-known. All gas-phase properties are correspondingly larger than those in solvating medium. Thus, as the dipole of the base increases, the free base-solvent interactions increase, and they do so in a way which is not compensated by dipole-dipole interactions in the complex or by increased complex-solvent dipole interactions. Similarly, the entropy correlates with 8 , in ~ such a way that as (3 increases AS becomes more negative; Le., as the bond in the complex becomes stronger, a correspondingly larger loss of entropy occurs. This is the basis for AH-AS correlations. As the dipole of the base increases, the base-solvent interaction increases and the entropy change is correspondingly less negative. This is the ~ meaning of the negative sign of the dipole term in the 8 , correlation for -AS. The positive sign for the dipole term in the 8,p correlation with log K arises not because of an enthalpy effect but rather because of an entropy effect. As the base-solvent interactions increase with increasing base dipole moment, the entropy change for complex formation becomes more favorable; that is, there is less entropy loss in the formation of the complex because the entropy of the free base is lowered by dipolar base-solvent interactions. This may be seen more clearly by using the usual relation AG = AH- TA!3 = - R T l n K with the enthalpy and entropy correlations
+ 12.68 - 1 . 1 2 ~ (kcal mol-') = 6.41 + 34.48 - 5 . 2 6 ~ (cal K-' mol-')
-AH = 1.01
-AS
to obtain the free energy relations AG = 0.90 - 2.358 - 0 . 4 5 ~ log K = -0.66
+ 1.720 + 0 . 3 3 ~
Because the entropy enters as a negative in the free energy equation, the entropy dipole term appears as a contributor to the formation constant of the complex. Thus, the dipole term for AG and for log K depends on how AH and A S are influenced by dipolar interactions.
2962
J. Phys. Chem. 1987, 91, 2962-2969
Table I11 lists some of the many correlations possible with this system. The reported correlations in the text are the best found within statistical limits. Correlations of AH and log K with p and together are good ( r = 0.976 and 0.960, respectively), but they are not as good as with /3 and p together ( r = 0.983 and 0.984, respectively). The t parameter seems to be useful in some cases, but it appears, as previously noted, not to give highly precise relationships. Correlations of carbonyl and ether enthalpies separately with P,T* are good, but the correlation with @,a* for carbonyls, sulfoxides, and ethers combined is 0.916. The threeparameter correlation of AH for carbonyls and ethers together with P,p,t is statistically no better than with ( 3 , ~alone; the same correlation with P,T*,[ is better than for P,x* but not better than P,P.
Conclusion Enthalpy, free energy, and entropy changes for the formation of the hydrogen-bonded complexes of m-cresol with ten bases are correlated best with terms which are related to the electron pair donating ability of the base and dipole moment of the base. The significance of the dipole term in the free energy correlation is not that dipoledipole interactions in the hydrogen-bonded complex add to the stability of the complex but rather that free base dipolesolvent interactions make the entropy change for complex formation more favorable. Conclusions drawn from free energy data alone which suggest that hydrogen-bonded complexes may be considered to be hydrogen-bonded dipolar complexes must be
rethought. The incorporation of enthalpy and entropy data is necessary to reach conclusions concerning the factors which are important for complex stability. There is an increasing body of evidence to suggest that solvation of the monomers in hydrogen-bonded equilibria is significant for thermodynamic parameter~.~>’J~ We had previously suggested that these interactions may be predominantly specific donoracceptor interactions.’ The present work and other submitted work’’ now suggest that both dipolar and donor-acceptor interactions may be present and that in some cases the dipolar interaction predominates. For example, the well-known pyridineCCl, interaction can now be shown to consist of about 75% dipolar interactions with the remainder being due to specific interactions probably of a donor-acceptor type.” For cyclohexanone, one of the bases of the present work, the dipolar interactions with CCl, are also about 75% of the total solute-solvent interactions.” Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and to Franklin and Marshall College for support of this research. (9) Spencer, J. N.; Modarress, K. J.; Nachlis, W. L.; Hovick, J. W. J. Phys. Chem., in press. (10) Spencer, J. N.; Holmboe, E. S.;Firth, D. W.; Kirshenbaum, M. R. J. Solution Chem. 1981, I O , 745. (1 1) Spencer, J. N.; Andrefsky, J. C.; Grushow, A,; Naghdi, J.; Patti, L. M.; Trader, J. F. J. Phys. Chem. 1987, 91, 1673.
Effective Diffusion Coefficient of a Two-Phase Material S. Sridharan and R. I. Cukier* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824- 1322 (Received: September 22, 1986; In Final Form: December 24, 1986)
A multiple scattering theory is presented for the effective diffusion coefficient De of a two-phase material. A local field analysis is used to obtain a multiple scattering expression for the Clausius-Mossotti function, (De- D,)/(D, 20,), in
+
terms of a reference medium diffusion coefficient, D,, characterizing propagation in the reference medium. Its lowest order result is analyzed for both aggregate and separated grain structures. For separated grain structures (discrete objects, taken to be spheres for our calculations, embedded in a matrix) the second virial coefficient is expressed in terms of the one-sphere scattering operator and the propagator in the matrix material and evaluated by a multipole expansion method. The choice D, = De leads to an effective medium theory expression which must be solved by a self-consistent method. A pair-level effective medium theory is formulated and solved approximately. This effective medium theory is compared with its predecessors.
1. Introduction A large variety of materials can be characterized as being heterogeneous on a coarse scale. That is, a material property takes on different values in different parts of the material, with the scale of the heterogeneity sufficiently large that at each spatial “point” the material properties obey macroscopic constitutive equations. For example, in the steady-state diffusion of some permeant species in a composite material the mass flux j is related to the concentration gradient V n via j ( r ) = -D(r)Vn(r); V.j = 0 where D ( r ) is a spatially dependent diffusion coefficient. Other examples involve the dielectric, elastic, magnetic, electric, thermal, and viscous properties of composite materials.’-4 For the sake (1) Landauer, R. Proceedings of the First Conference on the Electrical and Optical Properties of Inhomogeneous Media, Ohio State University, 1977, Garland, J. C.; Tames, D. B., Ed.; American Institute of Physics: New York, 1978; No. 40, p 2 . (2) Batchelor, G.K. Annu. Reu. Fluid Mech. 1974, 6,227.
0022-3654/87/2091-2962$01.50/0
of definiteness we shall use the language of a diffusion process, though it is also useful to have the dielectric problem in mind. A macroscopic sample of material (one large compared with the scale of the heterogeneity) is characterized by a relation between the averaged flux J = (j) and the averaged concentration gradient V N = ( V n ) of the form J(r) = -D,VN(r). This relation defines the effective diffusion coefficient De and is the objective of the calculation. There are two main problems to be addressed in a calculation of D,. First, the composite material’s structure must be characterized. This structure is usually prescribed statistically. S e n d , the averaging procedure must be carried out over the statistical distribution. There are two, disparate, principal composite structures:’ an aggregate grain structure and a separated grain structure. The ( 3 ) Herczynski, R.; Pienkowska, I. Annu. Rev. Fluid Mech. 1980,12,237. ( 4 ) Kroner, E.; Anthony, K.-H., Eds. Proceedings of the Third International Symposium on Continuum Models of Discrete Systems, Freudenstadt, June 1979; University of Waterloo Press: Waterloo, Canada; 1980.
0 1987 American Chemical Society
