J . Phys. Chem. 1990, 94, 2537-2540 (Figure 6a). When ZrP particles orient completely, p is uniaxially fixed at a certain angle with respect to the electric field direction. Under these conditions, p is given bylo p = (3/4)(1 3 COS 24)@(E) (1)
+
where 4 is the angle between p and the surface of a ZrP particle and @ ( E ) is an orientation function taking the value of 0 at E = 0 and 1 at E = For E = 3-10 kV/cm, @ ( E ) is taken to be 1 since p stays constant with the increase of the field strength. Then p varies from -0.75 to 1.5 when 4 changes from 90' to 0'. If the p in a bound dye molecules makes a constant angle with respect to the surface of a ZrP particle but its two-dimensional distribution is random (Figure 6b), then p is given bylo p = (-3/8)(1 - 3 COS 24)@(E) (2) in which 4 is an angle between p and the surface of a particle. Assuming @ ( E ) = 1 at the present electric field strength, p takes on values from -1.5 to 0.75 for 4 = 0-90'. The values of p for n = 0-2 (1 .O-1.3) exceed the upper limit (0.75) predicted by (2). Therefore, we conclude that these adsorbed dye molecules orient their p's or the molecular planes of acridine groups in the same direction on the surface of a ZrP particle. The angle, 4, is calculated according to (1) as shown in Figure 7. The values of p for n = 3-9 (-0.3 to -0.4) lie within the range predicted by both (1) and (2). Thus it cannot be concluded whether these dye molecules are adsorbed as in Figure 6a,b. We compare the two orientation angles, 4, calculated according to (1) and (2), respectively. The results are shown in Figure 7. It is noted that 4 varies smoothly with the increase of n when the angle is calculated according to (2). On the contrary, 4 jumps from 42' to 58' when it is calculated according to (1). The continuous change of 4 calculated form (2) for n > 3 seems to support the view that the aggregation state of the bound molecules changes from a uniformly oriented state (Figure 6a) to a random orientation (Figure 6b), as the length of the alkyl group increases from n = 2 to n = 3. Most probably the long alkyl chain interferes with the stacking interaction of the acridine moieties. The present results are compared with those previously observed in the montmorillonite systems. In the latter case, the p was 0.9-1.1 for n = 0-9. Thus the dye molecules are adsorbed as in Figure 6a with an angle of 4 = 40-50'. There was no specificity observed for the length of the alkyl chain. In the oxide layer of a montmorillonite, the negative charges lie about 5 A below the
2537
v
e-?
60-
aJ
I
2
I I I
cn aJ 9
,
I
w 50-
I
I I
I I
7
30 I 0
2
4
6
8 1 0 (AO-Cn) Figure 7. Dependence of an angle, 6,on the length of the alkyl chain. For n = 0-2, the angle was calculated according to (1). For n = 3-9, the angle was calculated according to either (1) (upper curve) or (2) (lower curve).
n-
surface. The silicate sheet on the surface is not expected to interact with AO-C,. Therefore, a cation is attracted mainly by electrostatic forces. In this respect, the orientation of a dye molecule is determined mainly by the stacking interaction between the adsorbed molecules. By contrast, the negative charge of ZrP is localized on a phosphate group exposed on a surface of a particle. Though the structure of y-type ZrP has not been determined by X-ray diffraction, it is known that the structure consists of layers, which contain quadrivalent and divalent phosphate groups.I3 Accordingly, a bound molecule may experience steric interference from the neighboring phosphate groups. Under these conditions, the orientation of a bound molecule may not be determined solely by the stacking interaction with other bound species, but may reflect the regularity of the surface structure of microcrystalline ZrP. The effects of the alkyl groups are then expected to be enhanced. In this respect, a ZrP colloid recognizes the shape of a bound molecule more selectively than montmorillonite. (13) Clayden, N. J. J . Chem. Soc., Dalton Trans. 1987, 1877.
Application of Scaled-Particle Theory to the Problem of Micellizatlon Nilashis Nandi and Indra N. Basumallick* Department of Chemistry, Visva- Bharati University, Santiniketan 731 235, West Bengal, India (Received: February 14, 1989; In Final Form: August 21, 1989)
The cavity-forming free energies of micellization (AG',,) for a series of sodium alkyl (Cs-Ci4) sulfates have been computed according to scaled-particle theory (SPT). Other conventional components of free energies (AGOi) of micellization for these detergents have also been calculated by use of previously developed models. Analysis of AGO,, indicates that cavity-forming free energies play an important role in the process of micellization.
Introduction Recently interest in scaled-particle theory (SPT) has largely been stimulated'-' by its recognition as an acceptable theory for real fluids. The theory was devised' originally for calculating the reversible work required to create a cavity of suitable diameter in a hypothetical hard-sphere fluid. Since then, it has been ap*Towhom correspondence should be addressed. 0022-3654/90/2094-2537$02.50/0
plieds-14 to a wide variety of systems. Results of such exhaustive SPT applications emphasize the CavitY-forming energy as a vital (1) Reiss, H. Adu. Chem. Phys. 1965,9, 1; In Statistical Mechanics and Statistical Methods in Theory and Applications: A Tribute lo Elliott W. Montrolk Landman, u.; Ed.; Plenum: New York 1977. (2) Ben-Naim, A,; Tenne, R. J . Chem. Phys. 1977, 67, 627. (3) Pierotti, R. A. J . Phys. Chem. 1965, 69, 281. (4) Abraham, M. H.; Nasehzadeh, A. Can. J . Chem. 1979, 57, 71.
0 1990 American Chemical Society
2538
Nandi and Basumallick
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990
TABLE I: Values of Solute (Amphiphilic Tail and Head Group) Parameters at 25 'C
no. of carbon a t o m 9
H2O 8 10 12 14
molecular weight* zone A zone B 18.02 I14 28.26 I42 26.90 170 25.94 198 25.17
densities! zone A 0.9970 0.6985 0.7301 0.7511 0.7645
g cm-3 zone B 1.2670 1.2375 1.2159 1.1978
hard-corec diam, k surfactant head group 2.76 6.63 7.07 4.58 7.47 7.84
K 79.3 650 850 1050 1250
i024a,cm3 molecule-I 1.47 15.42 19 22.5 26.5
10-2'p:
molecules cm-3 33.3 3.69 3.1 2.66 2.33
"Number of carbon atoms in the hydrocarbon tail of the surfactant. *Zone A, micellar core equivalent to liquid hydrocarbon; zone B, ionic zone surrounding micellar core (see Figure 1). CObtained from ref 15 by Farrell's treatment.*l dFor surfactants. C N u m b e rdensity of solvent.
TABLE 11: Values of Different Components of Free Energies of Micellization in kJ mol-' at 25 'C no. of carbon atomsg
8 10 12 14
tail -23.99 -29.12 -34.30 -39.61
AGO," head group
-1.07 -0.95 -0.83 -0.77
AG',,, 4.85 6.36 7.89 9.03
AGotrans-rot AGoinlcrlacc AGodisp 5.02 7.46 10.02 12.62
8.83 10.82 12.65 14.48
7.89 9.14 11.66 14.61
AGoind
AGOh
4.7 5.04 5.3 5.63
-21.36 -27.46 -33.56 -39.66
AG',,: -15.13 -18.71 -21.17 -23.67
AGocrp16*27 -15.32 -18.68 -22.04 -25.41
"Number of carbon atoms in the amphiphilic tail of the surfactants. bAGo,lc = ZAG,.
present investigation. Ruckenstein considered free energy of micellization as the energy change associated with the process of transfer of 1 mol of surfactant from aqueous phase to "liq~idlike"'~ micellar core. The present study dissects the transfer process into the following: (1) rupture of the hydrophobic hydration sheath around the hydrophobic tail of the surfactant in the aqueous phase followed by its removal from its cavity; (2) collapse of the cavity in the aqueous phase; (3) creation of a suitable cavity inside the micellar core; (4) introduction of the surfactant into micellar core and development of favorable and unfavorable interactions with the aim to incorporate cavity-forming free energies (vide steps 2 and 3) and estimate its contribution to the free energy of micellization. This paper deals with calculation of cavity-forming free energies of micellization for a series of sodium alkyl (C8-Cl4) sulfates.
Calculation Cavity-Forming Work by SPT. Cavity-forming free energies have been calculated through3v7the usual SPT equation (1). Figure 1 . Schematic diagram of micelle formation for sodium alkyl sulfate. Zone A, zone B, and zone C represent micellar core, ionic zone, and bulk aqueous media, respectively; rg stands for radius of the core and d r stands for thickness of ionic zone.
component of solute-solvent interactions. SPT has been successfully applied to the problems of gas solubilitie~,~*~ solvation of electrolytes and nonelectrolytes,I0 salt effect," hydrophobic interaction^,^^^^^ and distribution of solutes in different phases,I4 but its possible application to the problem of micellization has not yet been examined. Studies on micellar systems are a subject of current intensive research. Among the recent thermodynamic studies Ruckenstein's a p p r ~ a c h ' ~used ,'~ to estimate the free energy of micellization from different reasonably assumed component free energies is much related to the (5) Desrosiers, N . M.; Morel, J. P. Can. J . Chem. 1981, 59, I . (6) Treiner, C. Can. J . Chem. 1977, 55, 682. (7) Desrosiers, N.; Desnoyers, J. E. Can. J . Chem. 1976, 54, 3800. (8) Pierotti, R . Chem. Reu. 1976, 76, 717. (9) Abraham. M. H.; Nasehzadeh, A. J . Chem. Soc., Faraday Trans. I 1981, 77, 321. ( I O ) Sen, U. J . Am. Chem. SOC.1979, 101, 2531. ( I I ) Masterton, W. L.; Lee, T . P. J . Phys. Chem. 1970, 74, 1976. (12) Rudra, S. P.; Chakravarty, B. P.; Kundu, K. K.; Basumallick, I . N. 2. Phys. Chem. 1986, 150, 21 1. ( I 3) Bhattacharya, P.; Basumallick, I. N. Indian J . Chem. 1987, 26A. 25. (14) Waterl, H.; Tanaka, M.; Suzuki, N. Anal. Chem. 1982, 54, 702. ( I 5 ) Nagarajan, R.; Ruckenstein, E. J . Colloid Interface Sci. 1979, 71, 580. (16) Nagarajan, R.; Ruckenstein, E. J . Colloid Interface Sei. 1977, 60, 22 1
where
Here m is the number of species of mixed solvent, p i is the number density of the ith species of diameter ai,k has the value 1, 2, or 3, N is Avogadro's number, P is the pressure, and R is the gas constant. Hard-sphere diametersIs ( b ) of the micellar core have been obtained from molar volume datal9 using Farrell's treatment20*2'and assuming the core to be equivalent to liquid hydrocarbon.I7 These hard-core diameters along with density datalg for these systems and water13 are tabulated in Table I. The cavity component of the free energy of micellization is obtained by use of (2). The values of hCo,,, for the tail part (17) Tanford, C. In The Hydrophobic Effect; Wiley: New York, 1973; J . Phys. Chem. 1974, 78, 2469. (18) Speedy, R. J. J . Chem. Soc., Faraday Trans. 2 1977, 73, 714. (19) Dictionary of Organic Compounds, 4th ed.; Eyre & Spottiswoode Publishers: London; Vol. 2-5. (20) Datta, J.; Kundu, K. K. J . Phys. Chem. 1982, 86, 4055. (21) Farrell, P. G.;Edward, J. T. Can. J . Chem. 1975, 53, 2965.
Scaled-Particle Theory in Micellization
The Journal of Physical Chemistry, Vol. 94, No. 6,I990 2539 AG'interface = g[(Aog/g) - a01
of the amphiphiles are shown in Table 11. During micellization the amphiphile tail and the head group are transferred to the micellar core and aqueous ionic environment, respectively, as shown in Figure 1. Since the cavity-forming free energies do alterZofor the transfer of simple solute from water to dilute aqueous salt solution, these parameters for the transfer of head group from bulk aqueous phase to ionic solution adjacent to micellar core have been calculated. For such a computation the density and molecular weight of the ionic zone (zone B in Figure 1) have been calculated tentatively from the respective volumes of zone B, single head group,15 and water molecules.13 The radius of core and thickness of zone B have been obtained from literature;I5 AGOca, for head groups along with related parameters are shown in Table 11. Free Energy Change Due to Dispersion and Inductive Interactions. Dispersive- and inductive-type solute-solvent interactions are generally calculated by the Lennard-Jones22method. Following the expression of Pierotti,* these interactions have been calculated for the surfactants both in aqueous and in micellar core. The basic parameters required for such calculations have been obtained from Abraham's work,z3after linear extrapolation of similar parameters for lower hydrocarbons. The energy expression for dispersive and inductive terms is given by (3).
The symbols have been explained earlier.22 The values of AGOdi, and AGOindare presented in Table 11. Free Energy Change Due to Hydrophobic Effect. Hydrophobic effect is a well-accepted driving force of micellization. This interaction is supposed to play a key rolez4 in the process of micellization and has been calculated by using (4). Since the AGOh = ( n - 1)(-3.051) kJ mol-]
(4) a-carbon atom adjacent to the head group does not penetrate into the micellar core, the inclusion of ( n - 1) in (4) is justified. the value of ACHlper -CH2- group (3.051 kJ mol-') has been estimated by using the relation12 (5) with standard free energyZ3 AGoh = AGOexp - AG",,, - AGOLJ (5) data of n-alkanes in water and 1-octanol. The values of AGOh for these surfactants for the transfer from aqueous to micellar phase are presented in Table 11. Free Energy Change Due to the Reduction of Translational and Rotational Degrees of Freedom of the Amphiphile after Micellization. When an amphiphile is transferred from the aqueous phase to the micellar core with rigid structure, it loses some of its translational and rotational degree of freedom which contribute to the total free energy of micellization. The free energy change due to the loss of transational and rotational degrees of freedom has been calculated through expression 6. I
r
I
AGotranS-rOt = RT (0.3nz
+ 0.3n - 0.4) -
L
( g - 1) In ( u / u , )
+ (g-
1) In
The symbols have been explained earlier.I5 The values of AG,,, are shown in Table 11. Free Energy Change Due to Interfacial Tension. When amphiphiles aggregate, a new interface is created. The free energy change due to the change of the nature of interface after micellization is given by (7). (22) London, F. Trans. Faraday Soc. 1936, 32, 8 . (23) Abraham, M. H.J. Am. Chem. SOC.1979, 101, 5411. (24) Mukherjee, P. In Micellization Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977.
(7)
The values of AGOinlcrfaceare shown in Table 11. Free Energy Change Due to Head-Group Repulsion. Headgroup repulsion is another important force that opposes micellization. Free energy change due to the head-group repulsion in ionic micelles has been calculated via the simple expression.16 This interaction is electrostatic in nature. Quantitatively it may be depicted by (8).
The symbols have been explained earlier.I6 The AGOel, values for these surfactants are tabulated in Table 11.
Discussion The noteworthy feature of the data presented in Table 11, is ' that the cavity component of free energy (AGO,,) contributes significantly to the process of micellization. Physically this means less work is required to create a cavity for accommodation of a surfactant molecule in micellar core than in water. This is not unlikely in the light of the well-knownz0liquid hydrocarbon model of micellar core, because cavity-forming energies of solutes in different organic solvents are in generalZ3less than those in aqueous medium. It is interesting to noteI4 that the favorable cavity effect of halobenzenes in 1-octanol makes it more soluble in this solvent than in water. The interaction energies of water-halobenzene and 1-0ctanol-halobenzene are comparable. Further, Table I1 indicates that free energy of cavity effect increases with the chain length of the surfactant and this is largely reflected in the free energies of micellization. It has been shown earlierI3that it is more difficult to create a cavity in aqueous phase containing nonpenetrating additives, which in effect provides a stronger drive toward micellization and thus lowers the cmc values of these detergents. Again, the hydrophobic solutes which penetrate the micellar core have been reportedZSto strengthen the free energy component of hydrophobic effect (AGO,,), but quantitatively this effect alone cannot accountZ5for the observed large favorable free energy change of micellization in the presence of such additives. After computation26of cavity-forming energies of such nonpolar additives in micellar core and water, it has been found that inclusion of the cavity term along with the hydrophobic effect improves the result. Thus, both in terms of concept and prediction, cavity energies have a promising feature in understanding the complex micellization process provided the uncertainties in SPT calculation for the cavity terms are properly assessed. Major uncertainties for cavity free energies are incorporated5,' via solute and solvent diameters. However, in the present calculation these molecular parameters have been taken from standard literature data or have been derived from literature data using well-established relations. For the sake of satisfaction we have calculated cavity terms of these surfactants varying cavity diameter to f0.2 8, and solvent diameter to f0.05 8,unit and noted that even after such variation a favorable cavity effect is observed in all the cases. Again the question of misuse of SPT2 to the larger molecular systems may be rejected considering the overwhelming success of SPT applied to system^^^^^^^^ consisting of long-chain linear hydrocarbonsg and multisubstituted aromatic compounds' and ionic solute^^.^ in aqueous, aqueous-organic, and organic media. Other Components of Free Energies of Micellization. It will be worthwhile to examine the contributions of other component free energies of micellization (vide Table 11). It is seen that major repulsive forces that oppose micellization operate through headgroup repulsion, repulsion due to restruction of translational and rotational motion of the surfactant within micellar core, and oil-water-type interfacial repulsion. Free energy contribution (25) Abu-Hamdiyyah, M.; Rahman, I. A. J. Phys. Chem. 1987,91, 1530. ( 2 6 ) Nandi, N.; Basumallick, I . Unpublished data. (27) Hepler, L. G.; Burchfield, T.; Rosenhelm, J. J . Colloid Interface Sei. 1980, 78, 191.
2540
J . Phys. Chem. 1990, 94, 2540-2545
through these repulsive component increases with increasing chain length of the surfactant. The dispersive-inductive-type interaction obtained through LJ calculation also follows a regular sequence with the chain length of the surfactants. Hydrophobic effect has been calculated according to the conventional method, and it is found (vide Table 11) to play an important role in dictating micellization. It is interesting to note that Ruckenstein1s-16 without considering LJ and cavity terms formulated a model for computing free energies of micellization, and computation based on his model is in excellent agreement with the experimental data. However,
careful scrutiny of the present approach and Ruckenstein’s analysis indicates that the major part of the cavity and LJ terms as used here have been incorporated through the solvent structure effect of Ruckenstein’s model. In conclusion it may be stated that though the results obtained in the present approach do not excellently agree with the experimental data, they adequately justify the inclusion of the cavity term in understanding the complex process of micellization.
Acknowledgment. N.N. is thankful to UGC for providing a Junior Research fellowship.
Surface-Enhanced Resonance Raman Scattering Excitation Profiles of Anthracyclines Adsorbed onto Silver Particles Giulietta Smulevich,* Anna Rita Mantini, and Mario P. Marzocchi Dipartimento di Chimica, Universitri di Firenze, via Gino Capponi 9, 501 21 Firenze, Italy (Received: February 15, 1989: I n Final Form: October 4, 1989)
The surface-enhanced resonance Raman scattering (SERRS) spectra and excitation profiles of epirubicin and idarubucin have been obtained. The depolarization ratios and their frequency dispersion were also measured for some bands of epirubicin. Some bands of BI species under the C, symmetry or pseudosymmetry are active and become increasingly more prominent as the excitation frequency is moved to the red. The results indicate that the chromophore portion of the drug interacts edge-on with the Ag surface. Moreover, different peaks of Raman excitation profiles for the A, and B, modes have been found. Both peaks shift to the red by increasing the adsorbate concentration. The results have been discussed in terms of both the “electromagnetic”and the “charge-transfer-complex”approaches. It is shown that both models can furnish convenient and consistent interpretation of the experimental data.
Introduction The Raman enhancement effect by molecules adsorbed on metal (Ag or Au) surfaces has been the subject of considerable interest in recent y e a r ~ . l - ~ Numerous theoretical models have been proposed. Most of the theories have been classified in two different categories: the “electromagnetic” theory, which predicts a large increase of the electromagnetic field at the metal surface, and the “chemical” or “charge-transfer“ enhancement mechanism, which predicts a large increase of the polarizability of the adsorbate. In order to adequately understand the Raman scattering by adsorbates, it would be necessary to measure the excitation profiles, Le., the dependence of the band intensity on the exciting frequency, of the various vibrational modes of the molecule. For visible-transparent molecules such as citrate, pyridine, and other molecules adsorbed on Ag colloids, the Raman excitation profiles and the absorption spectra have been measured and correlated with the particle sizes and degrees of aggregati~n.~-’O Whereas Weits et al.’ were able to explain the excitation profile in terms of the classical electromagnetic effect, the relevant importance of the charge-transfer mechanism has been suggested!*s-” Surface enhancement for chromophores in resonance with the exciting line [surface-enhanced resonance Raman scattering (SERRS) effect] has been also observed, especially for biological molecule^.^^^^'^^'^ However, the way of combination of the surface and resonance enhancements is still unclear. This is due to the fact that, apart from experiments in limited frequency ranges,I3 the only systematic study of SERRS excitation profiles performed until now, to our knowledge, was concerned with the 202-cm-’ band of crystal violet adsorbed on a smooth Au surface.I4 For this case, the excitation profiles in the spectral region of the electronic intramolecular absorption are well characterized for both the free and adsorbed m ~ l e c u l e , ’but ~ , ~the ~ spectral region corresponding to the metal-adsorbate electronic transition could
* Author
to whom correspondence should be addressed.
0022-3654/90/2094-2540$02.50/0
not be observed since it occurs at too low a frequency for Au. SERRS spectra of some antitumor anthracyclines adsorbed on Ag colloids have been recently reported.I6J7 These molecules that are formed by an anthraquinone chromophore and a sugar residue are good candidates for a systematic analysis of the excitation profiles for several vibrational modes. In fact, they give rise to S E R R S spectra of good quality (where the strong fluorescence is completely quenched), the chromophoric portion being directly attached to the Ag surface. In addition, the modes (1) Weits, D. A.; Moscovits, M.; Creighton, J. A. In Chemistry and Structure at Interfaces; Hall, R. B., Ellis, A. B., W.;VCH: Deerfield Beach, FL, 1986; p 197-243. (2) Cotton, T. M. In Aduances in Spectroscopy; Clark, R. G. H., Hester, R. E., Eds.; Wiley: New York, 1987; Vol. 15. (3) Koglin, E.; Sequaris, J. M. In Topics in Current Chemistry; Spring er-Verlag: New York, 1986; Vol. 134, p 1-57. (4) Otto, A. In Light Scattering in Solids; Cardona, M., Guntherodt, G., Eds.; Springer-Verlag: New York, 1986; Vol. 4, p 289. ( 5 ) Brotman, A,; Burstein, E.; Jiang, J. D. Surf. Sci. 1985, 158, 1. (6) Pettenkofer, C.; Mrozek, I.; Borneman, T.; Otto, A. Sur!. Sci. 1987, 188, 519. ( 7 ) Fornasiero, D.; Grieser, F. J . Chem. Phys. 1987, 87, 3213. (8) Creighton, J. A,; Blatchford, C. G.; Albrecht, M . G. J . Chem. SOC., Faraday Trans. 2 1979, 75, 790. (9) Blatchford, C. G.; Campbell, J. R.; Creighton, J. A. Surf. Sci. 1982, 120, 435. (10) Siiman, 0.;Burnan, L. A.; Callaghan, R.; Blatchford, C. G.; Kerkar, M. J . Phys. Chem. 1983, 87, 1014. (1 1) Takahashi, M.; Furukawa, H.; Fujita, M.; Ito, M . J . Phys. Chem. 1987, 91, 5940. (12) Smulevich, G.; Spiro, T. G . J . Phys. Chem. 1985, 89, 5168. (13) De Groot, J.; Hester, R. E. J . Phys. Chem. 1987, 91, 1693. (1 4) Jiang, J. D.; Burnstein, E. Indian J . Pure Appl. Phys. 1988, 26, 1 12. Raman effect diamond jubilee issue. (1 5) Angeloni, L.; Smulevich, G.; Marzocchi, M. P. J . Raman Spectrosc. 1979, 8 , 305; J . Mol. S t r u t . 1980, 61, 331. (16) Smulevich, G.; Feis, A. J . Phys. Chem. 1986, 90, 6388. ( I 7) Smulevich, G.; Feis, A.; Mantini, A. R.; Marzocchi, M. P. Indian J . Pure Appl. Phys. 1988, 26, 207. Raman effect diamond jubilee issue.
0 1990 American Chemical Society
