L470 Surface Science 171 (1986) L470-IA78 North-Holland, Amsterdam

SURFACE SCIENCE LETTERS

FOe ON S I L V ~ SOL PAITIO.J~

Ping JIANG, Chunping ZHANG and Guangyin ZHANG

Department of Physics, Nankai University, Tianfin, People's Rep. of China

Received 18 July 1985; accepted for pubfication 31 October 1985

In this paper, under the approximate condition of a static electrical field, the Raman depolarization ratios for the breathi_4a $ vibran~ modes of pyri~ac adsorbed on silver sol particles are caloalatcd. B i ~ a l coordinates are ~ ~ ~ i t s indicate that the distortion of the incident field which is caused by the collo~ aUrega ~ contributes to an increase in the Raman depolarizatlon ratio. It is also indicated by calculation that although the variation of the distance betwc¢~ two spheres has a strong effect on the ~ i o n ratio, the orientation of the adsorbed pyridine has a minimal effect when the chemical adsorption is not considered. The ca!culated results are in good a4p'cemcnt with the experimental results.

In the pyridine normal Raman spectra, the breathing vibrant modes (992 and 1028 cm -1) exhibit depolarization ratios near zero (0 < 0.05); whereas in the experiment of surface enhanced Raman scattering (SERS), the depolariza- tion ratios of the pyridine molecule adsoxbed on metal surface are p > 0.5. The reasons for this increase are not yet clear. In ref. [I] it is considered that the ma$nitude of dclaotaxi~tion ratio is related to the orieatation of pyridine adsorbed on a metal surface; however, Creighton infexrod that the increase in the ~ f i o n ratio is due to the d q a o t ~ g egfect of the anisotropy of the colloid agg~q~tes [2]. We can see there is a contradiction between these two papas. The conclusion of ref. [2] is that pyridine is adsorbed face-on to the metal surface, it is considered in inf. [1], however, that pyridine in a face-on adsorption configuration will have a depolarization ratio of zero for a totally symmetric mode. We must state that all these opinions are based on conjecture, they are not explained clearly by theory.

Using classical thoary, and simplifying each sol particle to be a small isolated metal sphere (radius R ~ wavelcagth h), Creighton has calculated the depolarization ratio of the pyridine m o ~ adsorbed On the colloid particles [2]. The results of his calculation show O = 0.125 (corresponding to an isotropic breathing vibration of a u = 0t22 ~-a33 ). This is much smaller than the experi- mental value of p > 0.5. It can be seen by comparing the traasmission electron

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micrographs of silver sol [3] before and after adding pyridine, that the colloids with pyridine aggregate into strings of particles rather than a single sphere. In this paper, considering two spheres each with a radius of R (R ~: ~), we utilize bisphcrical coordinates. According to Aravind's method [4], we inspect the effect of the colloid aggregates on the d e p o l ~ ratio, and examine whether or not the orientation of molecules adsorbed on the surface of silver sol particles affect the Raman depolarization ratio~ From the pyridine SER spectra we can infer that the symmetry of adsorbed molecules is not in any obvious way distorted, therefore chemisorption is not considered. The free pyridine Raman tensor is used in our calculations.

The bispherical coordinate system (/~, 71, ~) is given in ref. [5]. In ref. [4] the solution of the Laplace equation for bispherical systems is given. The c6mpo- nents of the electric field of the bispherical system E~, E~, E~ are give n in the appendix. The pyridine molecule is considered to be located at the spherical surface point M,. as shown in fig. 1.

c0,s) i s t h e complex dielectric constant of the metal at .the scattered light frequency ~,~. c m is the dielectric constant o f the surrounding medium, The molecular dipole p = aTE, where a T is the Raman tensor o f the free pyridine molecule and E is the local field of the bispherical system at point M, The dipole moment of the system sphere 2 plus a molecule is p '= A(vs) p [6], where

1 12] is the enhancement factor of a single sphere system [2]. The intensity of the Raman scattering field is given by Es=kAO,s)aTE, where k= k'vs 2, and k'ffi const. In order to make the calculated results comparable with the experimental results, the coordinate components for the scattered field must be transformed,

r= E, = r 2 r , , (1)

Er Er

where/ '! and T 2 (see appendix) are the transformation m a u ~ from biepheri- cal coordinates (~t, 71, ep) to Cartesian coordinates (x,y~ z) and from Carte- sian coordinates to spherical coordinates (#, ~, r), respectively. It should be noted that on the surface of sphere 2 p =/t 0.

As shown in fig. 11, the orientation of the adsorbed molecules on the surface of sphere 2 is such that the angle between the molecular C2-axis and the

L472 P. Jiang et al. / Pyridine on silver sol particles

. . . . . . . . ~ i~ j'

Z

, r y 0 , ,

X

Fig. 1. ~ s y r i a , The ~ molecule is adsorbed at point M on the surface of sphere 2. MP s ~ for~ the molecular plane.

P, Jtang et al. / Py~'tdifJe ~ sllver s~ l~vcfcl~ I.A73.

normal of the surface is ~, and the angle between the molecular plane and the direction of e0 (see fig. 1) is ~k.

It is known that the Raman tensor components of a~ pyridine modes, in the coordinates by which the molecular C2-axis is defined! as z-axis are a ~ , ¢tyy, azz, are named a~l, a[2, a[3 here. In spherical coordinates (0, % r ) t h e Raman tensor is named a T.

a TffiT an ai2 T, T f l c o s ~ s i n ~ cos~ s in~s in

°t33 L - s i n ~ 0 cos

is the transposed matrix of intensity of scattered fields is given by

E~z E,.

(2)

T. In Cartesian coordinates (x, y, z) the

(3)

The coordinates x, y, z are fixed on the bispherical system, with the z-axis chosen along the line passing through the centers of the two spheres, shown in fig. 2. The electric vector of the external field E o is directed along the polar angle 0 0 and the azimuthal angle %. The observation direction is perpendicular to the direction of propagation of the incident laser beam. The electric vector of the inOdent beam is perpen~culur to the scattered plane,

The depolarization ratio is given by

O± (~ /2) -- I E, [ 2/l E± [ 2 = I , , / I , ; (4)

Esx, Esy, E~:, which are solve! in ~1. (3), are projected on the direction perpendicular to and parallel to the scattered plane; E± and E. can be obtained, respectively:

I , = I E,, I s ffi sin2%E,2x + c o s % E , - 2 sin % cos % z , x E , , , (sa)

I . ffi I E± I z ffi (sin 00 cos %Esx): + 2 sine00 sin % cos % E , xE, y

+(sin 00 sin %E,y)2 + 2 sin 00 cos 0o cos %E,~E~

+2 sin 00 cos 00 sin %EsyE~ + (cos 00Esz) 2. (Sb)

The following hypotheses are made in our calculations: (1) The pyridine molecules are adsorbed on the surface of the silver particles in a single layer and homogeneously.

L474 P. Jiang et al. / Pyridine on silver sol particles

Z

01// t '

' " " o o

x 01

B-y

Fig. 2. Geometry of Raman scattering. 01 and 02 are the centers of sphere 1 and 2. The direction of observation (marked by OB in the figure) is perpendicular to the direction of propagation of the incident laser beam (marked by i in the figure).

(2) The angle ~b can be takon as an arbitrary value from 0 to 2,r, i.e. the mot~ular plane on the surface ~ a random orientation. (3) 0 o and 9o can be taken as arbitrary values from 0 to ,r and 0 to 2,r, respectively, i.e. the orientation of the line passing through the centers of the two spheres with respect t o the external field E o is random.

Based on these hypotheses we can average I , and I± by integrating them over 0, q0, q~, 0o, q'o.

[ .,'2~" r *r r2~ e *r t2qr ,~ tJo JoJo JoJo I"sinOsinO°d~bdOd~dO°d*°) R/(4~')3

c ,-o -o -o ,o ,o I ± sin e sin 0 o d~ dO dq0 dO o d¢o)R/(4qr)a"

The results of our calculations are shown in fig. 3.

(6)

P: Jiang et at / Py~d~ne on silver Sol ~tlcl~s I.,475

o

o.1

(a)

(b)

(c)

b • w - D/a

Fig. 3. The calculated results of p versus D/R for three different incident laser frequencies~ a~l - a~2 "ffi a~3. (a) to •l.9 eV; (b) to m 2.4 eV; (c) to •- 2.95 eV.

In aqueous sol, the didectric constant of water is taken to be (,, ffi 1.78. The complex dielectric constant of siiver is taken from ref. [7].

In order to inspect the effect 'of the colloid a g g r ~ on the value of O, the variation of # with the ratio D / R (for the definition of D and R see fig. 1) is calculated. In figs. 3a and 3b we plot p as a function of D / R for different wavelengths of the incident field, all ffi a ~ ffi a~3 is assumed in the calculation. It can be seen from fig. 3, when the ratio D / R is big enough, the depolariza- tion ratio p reaches the "fimit 0.14, this is approxin~tely the same value as a single sphere, 0.125. When the ratio D / R reaches the .limit 0;5, ~ p reaches its maximum value p >I 0,5. When t h e ratio D / R < 0.5, then P tends to decrease.

It can be seen from the transmission electron micrographs of silver sol in ref. [3] that the distance between spheres is no t constant and has a definite

L476 P. Jiang et al. / Pyridine on silver sol particles

d t .*, , I

Fig. 4. 0 versus D / R for two different molecular orientations: ( = 900; 2a{l = oti2 = ot~3 is assumed.

) £=o°; ( - - - - - - )

distribution. Therefore we estimate that, for the bispherical system, the ex- istence of metal spheres leads to a depolarization ratio increasing to ~ 0.4. This value is much closer to the experimental results than the single spherical value. This result proves that Creighton's assumption [2] was correct.

We can also calculate the change of p as a function of the ratio D / R for two extreme molecular orientations, ~ =-0, ~r/2, i.e. when the molecular C2-axis is parallel to the normal of the spherical surface and perpendicular to the normal. The calculated results are shown in fig. 4. The curves in fig. 4 seem to imply that for the bispherical system, the molecular orientation has no obvious effect on the Raman depolarization ratio.

The following conclusions are indicated from our calculated results: (a) The colloid aggregates cause the depolarization ratio to increase. (b) The molecular orientation has no obvious effect on the depolarization ratio when the chemjsorption is not considered (the R ~ tensor used in the calculation is that of free pyrimne molecules), (c) For different excitation ~ e s , P remains basically constant.

Appendix

In reL [4], the potzntial outside the ,sph~es 1 and 2, • is given. We can calculate the electric fietd outside the sphzrcs from

1 a% E i = h i ai ' i = # , Ti, q~.

P. Yiang et al. / Py~i~b~e on silver soI particles L477

Therefore

E~ l ~-~o = E ; . , o - A ° F , / 2 sinh + cosh

~ ( [ sinh p° sinh((n + ½)Po ) + A°~ F~/2

+ 2(n + ½)F 1/2 cosh((n + ½)Po) Y°(cos ~, ~)

( 2 n + 1 1'/2[ sinh pp cosh((n + ½)Po ) +2a~ 4.,.,,(,., + 1) ] [ F~/2

+2(n+ ½)F '/~ sinh((n + ½)~o)]e" cos(,~-,o)]},

E, = E i F / ~o sin 71 . , , - , , o , ,

[ 0 s,.h((,. + + ~ A,, F1/2Y/ , + 2 F ~/u n--1

• , / s i n a i ,

E, I.-.o-- E; I~-~,o q a sin" 11 n~.l 4,~n(n + 1) A: cosh((n + ½)Pro)

xeg sin(~ - ,~), where F ffi cosh Po - cos 7.

The transformation matrices T~ and T2 are 8iven by

sinh t~ sin 1,1 cos q~ (cosh p cos 11 - !) cos ¢~ - sin q~ cosh ~ - cos ~ cosh ~ - cos

sinh/~ sin ~ sin~ (cosh ~ cos 71 - 1) cps ~ cos ~ , T~ = cosh p - cos 71 cosh ~t - cos

1 - cosh p cos ~! sinh t~ sin ~1 - 0

cosh p - cos 71 cosh p - cos 1'1

cosOcosq~ cos~s inq~ - s i n S ] T 2 = - s i n q~ cos ¢p 0 ].

sin 8 cos ¢p sin 0 sin ¢p cos 8

[.478 P. Jiang et aL / Pyridine on silver sol particles

References

[1] D.L. Jeanmaire and R.P. Van Duyne, J. Electroanal. Chem. 84 (1977) 1. [2] J.A. Creighton, Surface Sci. 124 (1983) 209. [3] T.E. Furtak and R.K. Chang, Eds., Surface Enhanced Raman Scattering (Plenum, New York,

1982) p. 318. [4] P.K. Aravind, Surface Sci. 110 (1981) 189. [5] R. Ruppin, Phys. Rev. B26 (1982) 3440. [6] Ref, [3], p. 99. [7] P.B. Johason and R.W. Christy, Phys. Rev. 156 (1972) 4370.