J . Phys. Chem. 1991, 95, 1119-1124
rotation of the NH4+ ion in numerous ammonium salts have been determined3’ through studies of NMR line widths, infrared and/or Raman spectra, heat capacities, and quasi-inlastic neutron diffraction. Typically, the rotational barriers were found to be under 5 kcal mol-’, although it should not be forgotten that the barrier is affected by intracrystal interactions between adjacent NH4+ ions as well as between the cations and anions. A recent evaluated compendium38of the thermochemistry of salts in mixed solvents shows that the Gibbs energy of transfer of K+ and NH4+ into aqueous methanol is the same for the two cations within 1 kcal mol-’ across the solvent composition range (see Table V). We now recall the literature quantum chemical calculation of the interaction of ammonia and f ~ r m a l d e h y d ethat ~ ~ was used to model the enzymatic cleavage of peptides. Contrary to the explicit expectation by the authors of ref 39, the zwitterionic tetrahedral intermediate (H3N+CH20-)was shown to be unbound in the absence of some additional water molecules. However, a simple point-charge calculation assuming the total positive charge is on the nitrogen reproduced40 the surprising conclusion. It would appear that alkyl groups electronically mimic hydrogen and that even intramolecular electrostatic interactions are qualitatively (37) Parsonage and S t a ~ e l e y , ’pp ~ 31 1-361. (38) Marcus, Y. Gibbs energies of transfer into Aqueous Alcohols. Pure Appl. Chem. 1990, 61, 899. (39) Scheiner, S.;Lipscomb, W. N.; Kleier, D. A. J. Am. Chem. Soc. 1976, 95, 4770. (40) See ref 39, footnote 25.
1119
reproduced by assuming that even an ‘alkyl-substituted” ammonium ion demonstrates isotropy much as the parent NH4+ ion does. We now turn from a calculated “mimic” of biochemical reactions to experimentally measured interactions of an important biomolecule and its counterions. In particular,4’ the K+ and NH4+ salts of calf thymus DNA, in either fiber or highly crystalline film form, have nearly identical properties vis-&vis the Raman shift of the lowest observed frequency mode, the speed of the longitudinal acoustic phonon, and the elastic constant C , , . In summary, it is seen that there are numerous similarities in the interactions of K+ and NH4+ ions, whether one considers our new experimental results of the binding of clustering neutrals in the gas phase, the properties of electrolytes in solution, or interaction with counterions in the solid.
Acknowledgment. We thank Drs. Frank J. Castora, Carol A. Deakyne, Charles L. Perrin, L. Wayne Sieck, Walter J. Stevens, Herbert L. Strauss, and Deborah Van Vechten, for their helpful comments and results of unpublished studies and analyses. In addition, S.S. thanks the National Institutes of Health (NIH Grant CM36912), while J.F.L. and M.M. thank the National Institute of Standards and Technology for support and encouragement. Registry No. NH4+, 14798-03-9; C,H,, 71 -43-2; C H 3 C N , 75-05-8. ~~
~
(41) Weidlich, T.; Lindsay, S. M.; Rupprecht, A. Phys. Rev. Left. 1988, 61, 1674.
Local Field Effect in Small Semiconductor Clusters and Particles Ying Wang Central Research and Development Department, E. I . du Pont de Nemours & Company.t P.O.Box 80356, Wilmington, Delaware 19880-0356 (Received: March 28, 1990)
When small semiconductor clusters and particles are embedded in a dielectric medium with a lower refractive index (such as glasses, polymers, organic liquids, and air), the local electric field near the particle surface can be greatly enhanced compared to the incident field upon illumination. This local field enhancement effect can be important in the study of the spectroscopy and photophysical processes of semiconductor clusters and particles. Here we first present computational results on the size and wavelength dependence of the local field intensity enhancement factors for CdS and Ti02 particles, two commonly used photocatalysts. We then report an experimental attempt to observe this local field effect, manifested as structural resonances in the photoluminescence spectrum of monodisperse 1.1 bm CdS particles.
introduction The properties of a semiconductor particle depend on its size. One familiar example is the quantum confinement effect,’-4 i.e. the shift of the absorption edge of a semiconductor to the blue as the diameter of a particle approaches that of an exciton. There is another confinement effect that originates from the difference between the refractive indices of semiconductor particles and surrounding media (such as polymers, glasses, solutions, or air). This effect has received relatively little attention to date except in a few Because of the boundary established by different refractive indices between the semiconductor and the surrounding dielectric, the interaction between the light field and the particles becomes size-dependent and the field intensity near, at, and inside the particle surface can be enhanced considerably compared to the incident intensity. This enhancement in local field may be considered a result of the “dielectric confinement” effect and can be an important factor in the study of the spectroscopy, photophysics, and photochemistry of these semiconductor particles.
The idea that the microscopic electromagnetic field inside a medium can be different from the incident field is certainly not new. The classic Lorentz (for nonpolar molecules) and Onsager (for polar molecules) models allow one to calculate the local field experienced by a molecule in a dielectric continuum.’ The molecule is assumed to be a point dipole located within a cavity embedded in a continuum. These two models do not include size-dependent effects and, although useful in the small-molecule ( I ) Efros, Ai. L.; Efros, A. L.Sou. fhys.-Semicond. (Engl. Trawl.)1982,
16, 772.
(2) Rossetti, R.; Hull, R.; Gibson, J. M.; Brus, L.E. J . Chem. fhys. 1985, 82, 552.
( 3 ) Henglein, A. Top. Curr. Chem. 1988, 143, 113. (4) Wang, Y.; Herron, N.; Mahler, W.; Suna, A. J . Opf.SOC.Am. B Opt. fhys. 1989, 6 , 808. (5) Murphy, D. V.; Brueck, S. R. J. Opt. Left. 1983.8, 496. (6) Hayashi, S.; Koh, R.; Ichiyama, Y.; Yamamoto, K. fhys. Reo. Left. 1988, 60, 1085.
(7) For a review, see: Bottcher, C. J. F. Theory ofBIectric Polarization; Elsevier Scientific Publishing Co.: New York, 1973; Vols. I and 11.
‘Contribution No. 5445.
0022-3654/91/2095-1119$02.50/0
0 1991 American Chemical Society
1120 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
limit, are not suitable in the large-particle regime. For larger particles, the particle-size-dependent interaction between the light field and the particle can be calculated via the Lorenz-Mie theory.8 For particles with highly symmetric shapes, such as spheres or cylinders, there exist sharp resonances in the optical region, corresponding to the natural modes of oscillation of the structure. When the wavelength of the incident light coincides with such a resonance, large electric fields within, near, and on the surface of the particles can result, causing enhancements in various optical phenomena. This has been demonstrated in a series of experiments with water droplets in air.g For semiconductor particles, this local field enhancement effect should be more pronounced because of the larger refractive indices of inorganic semiconductors compared to organics. In this paper, we first present computational results on the size and wavelength dependence of the local field factor of Ti02 and CdS particles, two commonly used photocatalysts. The local field effect is shown to be substantial. We then report an experimental attempt to observe this local field effect, manifested as structural resonance peaks in the photoluminescence spectrum of monodisperse CdS particles. Lorenz-Mie Theory The size and wavelength dependence of the local field intensity on the surface of a dielectric sphere can be computed via the Lorenz-Mie formalism. Here we briefly review the theory: for a detailed discussion, the reader is referred to refs 8 and IO. There are three assumptions in the theory discussed below: ( I ) the particle and the surrounding medium are treated as a continuum (Le.. atomic and molecular structures are not considered); (2) the boundary between the particle and the medium is assumed to be a step function; and (3) the particle is assumed to be a sphere. The scattering efficiency, Q,,,, is defined as the ratio of the scattered intensity (at a distance far from the sphere) and the incident intensity per geometrical cross section, m2:
Wang
9.08.0-
7.0-
8
5.0 s*o:,
4.0-s
3.0-8 2 . o y 1
.o
0
/ 100
200
300
400
560
600
760
I
l6
t
I .
14t
11
12-
8 'L: 6--
where a is the particle radius and E, is the scattered electric field at distance R from the center of the sphere. Since experimentally the observation is always carried out at far field, the integration is carried out at R >> a. In terms of the scattering coefficients, a, and b,, Q,,,can be written as
41/v
2
' 0
100
200
500
400
500
800
700
cluster radius. nm where ka = 27ra/X and X is the wavelength. Similarly, Qabs is defined as the ratio of the absorbed intensity and the incident intensity per unit geometrical cross section, and the extinction efficiency, Qext, is the sum of Qabs and Q,,,: 1
0
Figure 1. Near-field enhancement factor, QNa plotted as a function of CdS particle radius at wavelengths of 515, 1061, and 614 nm. The refractive index of the surrounding medium is 1.4.
is similar to that of Q,, except that the integral is evaluated at R = a (the surface):
0
In terms of the scattering coefficientsI0 Equations 2-4 correspond to the far-field solutions of the Lorenz-Mie theory and are commonly used for calculating the scattering properties of dielectric spheres. In the near field of a sphere, the electric field is considerably different from that of the far field. In order to satisfy the surface boundary conditions, the incident plane wave is greatly distorted. The field near the surface now contains a large portion of the radial component. Messinger et a1.I0 introduced a new parameter, QNF, which gives a measure of the local field intensity at the surface. The definition of QNF (8) For a review, see: Kerker, M. The Scattering of Light and Ofher Electromagnetic Radiation; Academic Press: New York, 1969. (9) For example: Qian, S.-X.; Snow, J. B.; Chang, R. K. In Laser Spectroscopy VII; Hansch, T . W., Shen, Y. R., Eds.; Springer-Verlag: Berlin, 1985; p 204. (IO) Messinger, J.; Ulrich von Raben. K.; Chang, R. K.; Barber, P. W . Phys. Rev. B Condens. Matter 1981, 24, 649.
QNF = 2e1(an12[(n+ I)lh%(ka)12 + n= 1
where hL2)is the Hankel function of the second kind. Equation 6 provides the basis for calculating the local field on the surface of a dielectric sphere. Computational Results The computation was carried out on a Cray X-MP/28 computer. The programming codes developed by Wiscombe" for calculating the Mie coefficients, an and b,, were used. We performed the calculation for CdS and Ti02particles, two commonly used photocatalysts. The results are discussed separately below. ( I 1 ) Wiscombe, W. J . Appl. Opt. 1980, f9, 1505.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1121
Local Field Effect in Small Semiconductor Particles
"T
'O'OT
20-
15-
8 10-
5-
u IOOA
2.04.
"800
600
leT
700
800
900
1000 1100 1 2 0 0
04 500
550
600
650
700
750
800
850
t
900
Wavelength, nm
I
Figure 3. Effect of size dispersion on the structural resonances of Q N F as a function of wavelength for 5000-A-radius CdS particles embedded in a medium with n = 1.3: (solid line) u = 0.04; (dashed-dotted line) u = 0.02; (dashed line) u = 0. The size distribution is assumed to be log-normal (eq 7).
14.-
12-
When the wavelength of light is in the absorbing region (e&
-
5 1 5 nm, Figure I , top), the largest enhancement occurs in the intermediate size regime ( 1500 A for CdS). For larger particles,
10.-
8-
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--
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660
760
860
960
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12100
Wavelength, nm Figure 2. Near-field enhancement factor, QNF, plotted as a function of wavelength for CdS particle radii of 100, 1500, and 5000 A. The refractive indcx of the surrounding medium is 1.4.
CdS. The index of refraction, n, and the index of absorption, k , of CdS from 515 to 2000 nm are taken from refs 12 and 13. Isotropically averaged values are used and interpolated in the wavelength region of interest. The shortest wavelength calculated is 51 5 nm, since no reliable values of n and k can be found in the literature beyond this wavelength. Figure 1 shows the dependence of Q N F on the CdS particle radius at three wavelengths, 51 5,641, and 1061 nm, in a medium of n = I .4. For very small clusters, the intensity enhancement factor is relatively small (1-2). As the cluster size increases, the enhancement factor increases monotonically in the Rayleigh size regime (
