Reflection Spectroscopy of Adsorbed Layers BY WILFORD N. HANSEN Utah State University Logan Utah 84321 U.S.A. Received 14th September 1970 General approximate equations are presented for the change in reflectance of a stratified medium due to the presence of an absorbing adsorbed layer. These equations which represent reflection spectra are simple functions of the optical characteristics of the adsorbed species. Experimental examples of monolayer spectra illustrate the sensitivity of reflection methods and the validity of the equations. Band shapes of reflection spectra differ from but are as representative as transmission spectra. The shapes usually depend on polarization but often do not depend on angle of incidence. Intensity is usually linear in absorption coefficient and thickness when the approximate equations are valid.In order to bring the powerful techniques of absorption spectroscopy to full use in the study of surface chemistry and physics it is necessary to obtain spectra of thin layers with ease and accuracy. This paper is concerned with the understanding of reflection spectra from the interfacial region of a three-or-more-phase plane- bounded system. Such a system might represent an organic dye on glass a pro- tective organic film on a metal or some species adsorbed on an electrode immersed in an electrochemical cell. The discussion will be limited to films much thinner than a quarter wavelength typifying adsorbed layers. The idea is to obtain spectra by simple procedures which are characteristic of the molecular species involved (not a fickle function of experimental parameters) and which bear a simple relation- ship to the optical properties especially the absorption coefficient a.Exact equations for reflectance R and reflectance absorbance A = -log, R in a stratified medium can be found in the literature. Here we will use the nomen- clature and exact theory of ref. (1). This theory is extremely useful whenever the real system corresponds close enough to the model assumed. In this case the model is an ideal stratified medium i.e. a stack of parallel plane-bounded layers. The exact equations are far too complicated however to give direct physical insight for multi-phase systems. For this reason we have derived simple approximate equations for reflectance changes caused by very thin films such as absorbing adsorbed layers. The equations are simplest for a thin film on a dielectric or at the surface of a highly reflecting metal.Both internal and external reflection are considered. With some increase in complexity absorbing intermediate and final phases in addition to the one whose spectrum is sought can be accommodated. It will also be seen that reflection methods are sensitive enough to deal with fractions of monolayers. Some aspects of this subject have been discussed in the literature in a different context. Harrick has discussed first-order attenuated total reflection (ATR) theory for thin films on transparent substrates. Francis and Ellison and others 4-6 have discussed reflection from a filmed mirror. Their work was significant in the formulation of the present theory. 27 28 REFLECTION SPECTROSCOPY OF ADSORBED LAYERS THIN FILM O N NON-ABSORBING SUBSTRATE External reflection is considered first.In this case the refractive index of the incident phase n, is less than the index n3 of the final semi-infinite phase. If the exact equations for reflectance in a three-phase system [eqn (3) and (8) of ref. (l)] are expanded in terms of film thickness we obtain to first order and The subscripts refer to the phase phase 2 being the absorbing film phase 3 the sub- strate and phase 1 the incident phase which is usually air. The I and 11 subscripts refer to perpendicular and parallel polarization. For any phase j 5 = A cos ej = (A3-nZ sin2 el)* where A is the complex index of refraction n+ik 6 is the angle of refraction in phasej and k is the extinction coefficient. The angle 8,> is complex if k,> 0 and/or 6 > O, where OC is the critical angle.(This latter condition is possible only for internal reflection where n3 <n,.) The absorption coefficient a which is the quantity directly measured by transmission methods is related to the extinction coefficient by a = 471k/R where R is the wavelength in vacuo h2 is the film thickness in units such that ah is dimensionless; tj+l is complex in general. It is evaluated by taking the complex square root above. The rule in choosing roots is that both Re t,>O and Im t,>O. The &st factor of each equation is the reflectance in the absence of phase 2 and is valid even if phase 3 is absorbing. (Phase 1 is always non-absorbing). In fact eqn (1) and (2) are valid for an absorbing final phase so long as k3 < 1 if Img3 is ignored in the second factor.Experimentally it is most convenient to measure reflection spectra as the change in reflection absorbance (AA = log, (Ro/R)) caused by the presence of the film. (Ro is the reflectance in the absence of the film.) For the present case of external reflection with the first phase air and the final phase transparent we have from (1) and C9 . .- bA = -(-')n2u2h2 4 case In 10 n,2-1 (3) Note that the absorbance will always decrease for I polarization (RI will increase) as the film is added. For 11 polarization it may either increase or decrease. At 8 large but less than Brewster's angle the (n; + k i ) 2 factor which varies greatly through a typical absorption band will determine the behaviour. When this factor is large say 40 its term is small and the next term dominates making AAll negative.When it is much less than unity as it sometimes is AAI will be positive. The reverse is true when 8 is greater than Brewster's angle. To compare spectral shapes of AA with the ones obtained by transmission through thick samples we note that a transmission spectrum in terms of transmission absorbance is a quantity proportional to a and h. So the spectrum of AAl has the same shape as a transmission spectrum multiplied by n2 except for sign ; AA 11 has the same shape as AAL so long as the first term in square brackets can be ignored. When it becomes equal to the second term however the spectrum crosses the no-film axis and becomes positive. WILFORD N. HANSEN 29 For intense bands this will happen on the short wave-length side where n2 becomes low sometimes even less than unity and k2 is also low.Now consider internal reflection where n3<n,. Eqn (1) and (2) still apply. The refractive index of phase 1 is always greater than unity and that of phase 3 is usually so. We therefore write These equations are valid even if phase 3 is absorbing with k3 4 1 and it is noteworthy that they are valid at angles less than and greater than the critical angle. Thus a AA spectrum is continuous in shape as we pass through the critical angle. is obvious. The behaviour of (6) is more complicated. At normal incidence (6) reduces to (5) as it must and AAII is positive. We recall that for n3>n it was negative. As 8 is increased to Brewster's angle O, the denominator inside the parentheses goes to zero making the sensitivity very large but at the same time the energy of the system becomes very small.As 0 passes through Brewster's angle the denominator changes from negative to positive and AA II also changes sign. From OB to OC the radiant power increases to a maximum. At OC the second term in square brackets goes to zero and The behaviour of eqn (5) with and for I polarization AAL = L-(-)n2ct2h2 1 (8 = &). In 10 n cos O1 At angles greater than OC < is negative so that all terms in eqn (6) are positive. Thus in the ATR region the terms in square brackets add and the second term iiicreases in importance as 8 becomes larger. The first term is due to fields normal to the interface while the second term is due to fields parallel to the interface. Eqn (1)-(8) are first order in thickness over wavelength.Nothing is assumed with regard to n2 or k2 so long as the film is thin enough for A A 4 1. (Actually eqn (3)-(8) apply to higher radiant power absorption than eqn (1) and (2).) Thus they are even valid for very thin metal films. The derivation assumes that the thin film is isotropic and homogeneous but these restrictions can be relaxed considerably. For I polarization the electric field vector is always in the plane of the film so the only optical constants involved are those components lying in that plane and per- pendicular to the plane of incidence. For 11 polarization at & the fields are entirely perpendicular to the interfacial plane. Then only those components are effective. When =i= OC both components are effective and different values of n2 and/or a would apply to the two terms of eqn (6).Also eqn (1)-(8) are all valid for an absorbing final phase provided k3 4 1. In fig. 1 are shown four different reflection spectra of a monolayer on a transparent substrate-crystal violet adsorbed on one face of an optical glass prism (n = 1.52). The upper curves were taken per internal reflection near the critical angle. The lower pair were of the same film but per external reflection. Only a single reflection was used in a standard double-beam spectrophotometer. For the upper curves 0 = 43" n = 1.52 n3 = 1. For the lower curves O1 = 45" nl = 1 n3 = 1.52. 30 REFLECTION SPECTROSCOPY OF ADSORBED LAYERS Three of the curves are similar in shape while AAli (internal) is quite different having its maximum at shorter wavelengths. This is as predicted by eqn (6) or (7) and results from the (n2 +k2) factor.A reasonable range for this quantity in the present case is from about 10 at 620 nm to 1 at 490 nm. Also AAII (external) crosses the no-film axis at the left end. This will happen according to eqn (4) whenever the first term in the square brackets dominates over the second. (The denominator in parentheses is negative in the present case.) On the other hand AAII (internal 0,20,) can never cross the no-film axis. A comparison of eqn (3) and (5) shows that the two AAL curves should have the same shape with a ratio AAl (internal)/AAl (external) = - 1.52. This ratio holds for the experimental data at about 580 nm but the ratio is not constant with wavelength. Evidently higher order terms in the original expansion are large enough to be seen.The AAl curves indicate a value of 0.064 for n2k2h2/A at 580 nm. Using this value and guessed values for n2 and k of 1.6 and 1.0 eqn (4) gives -0.57 for AAll (external) compared with the value of -0.62 measured. Such good agreement in absolute intensity will not be found outside the central region of the absorption band. wavelength (nm) FIG. 1.-Reflection spectra of crystal violet monolayer on BK-7 optical glass n~ = 1.52. Upper curves are ATR spectra single reflection at 43". Lower curves are external reflection spectra single reflection at 45". THIN FILM I N A MULTILAYER SYSTEM The rate of absorption of radiant energy at any position in a medium is given by where S is Poynting's vector 0 is the high frequency conductivity and ( E 2 ) is the mean square electric field at the position.This can be made the basis of a powerful method of deriving approximate equations for reflectance in a multilayer system. Values of <E2> can be calculated exactly for any point in a stratified medium.' (rate of energy absorption) = -V . S = a(E2) W/m3 (9) WILFORD N. HANSEN 31 For most cases (E') is affected little by the presence of a very thin film nearby and when the effect is appreciable it can often be accounted for by the decrease in radiant pDwer caused by the absorption in the film. (E2) in the film itself will be continuous for tangential components and (n2 + k2)2 ( E 2 ) will be continuous for normal com- ponents. For simple systems ( E 2 ) values can be predicted as a function of angle of incidence and polarization. For complicated systems curves can be prepared by computer.The general method is to derive approximate equations which give the reflectance in terms of ( E 2 ) which is calculated in the absence of the thin film whose spectrum is sought or with a transparent film in its place to approximate more closely the film-present case. By this scheme eqn (5) and (6) can be derived for the attenuated total reflection (ATR) region where there is no refracted beam. The scheme often fails however when large fractions of the radiant power are lost to absorption or refraction in neighbouring phases. By the above method the fractional change in radiant power in a stratified medium due to absorption in phase j is given by where (E2) is the space-time average field in film j . This equation is exact. For the equation to be useful however we must be able to calculate the (E2) without knowing the a of the film whose spectrum we seek.The R of the equation should also correspond to experimental reality. In some experiments such as the electro- chemical adsorption and removal of a monolayer on a thin metal film electrode the R (most conveniently measured as AA = -log,&) refers to a film-present film- absent situation. In other cases such as an adsorbed film with a strong band in the infra-red but non-absorbing at neighbouring wavelengths AA corresponds to the change in A with wavelength providing absorption by all other phases is relatively constant. We now alter eqn (10) so as to use an ( E 2 ) for vanishingly thin film j or transparent film j where no energy is absorbed. This leads to the following equation njajhj In 10 Ronl cos 6 AAj = (E2> g where Ro is the reflectance when film j does not absorb.This equation is approximate for we have assumed that (E2) M ((l+R,)/2) (E2)g and that AA = 2(1-R,)/ In 10 (1 +R,). Eqn (11) accounts for the absorption in phases other than j but it assumes that this absorption does not depend on the absorption in film j . It is also possible to correct for this latter effect. This leads to the equation njajhj AAj = (E2>q (1 +Ao)Ro In 10 nl cos where A . is the absorbance of the system in the absence of absorption in phase j multiplied by 2.312. This latter factor is usually unimportant and is omitted to sim- plify the eqations. Eqn (12) applies for either polarization. But for I polarization ( E 2 ) is continuous across an interface while for the normal component of 11 polariza- tion it is (n2+k2)2 ( E 2 ) that is continuous.Thus one approach would be to substitute a standard reference film s of similar index and thickness and a = 0 in place of film j for calculation purposes. With reference to this standard state our equations finally become 32 REFLECTION SPECTROSCOPY OF ADSORBED LAYERS and where It and the fields apply to the standard state film. These equations account for absorption in surrounding phases including the final semi-infinite phase. These phases may even be metallic in some cases. While these equations have been found to be valid for a variety of cases the full range of their validity is as yet unknown. They do not take into account changes in phase caused by the presence of film j . Thus eqn ( 5 ) and (6) at 61>6c follow directly from eqn (13) and (14) but not for 6 < OC.Likewise eqn (3) and (4) for external reflection do not follow by the present scheme because phase changes dominate. Eqn (13) and (14) show immediately the nature of a reflection spectrum. Within the range of their validity absorbance is linear in a and h. This implies that a rule analogous to Beer's law is followed and that the spectral intensity is proportional to the amount of absorbing species involved. Thus the absorbances of two thin films are additive and the distribution of absorbing species can be inhomogeneous without affecting the spectrum. The significance of this point becomes clear when we consider that at a molecular level adsorption of molecules on a glass surface might be much like a layer of snow on the Rocky Mountains.In fig. 2 are shown spectra of crystal violet adsorbed on a thin film gold electrode. I I 1 I 4 5 0 5 00 5 5 0 6 0 0 6 5 0 700 wavelength (nm) FIG. 2.-Internal reflection spectra of crystal violet adsorbed on a gold film electrode. Single reflection at slightly greater than critical angle. The first phase is glass which supports a gold film about lOOA thick. The gold film constitutes the second phase. The final phase is aqueous electrolyte containing a small amount of crystal violet. The solution is so dilute that the ATR spectrum of the crystal violet cannot be seen but is sufficiently concentrated to cause adsorption on the gold a condition easily attained. The angIe of incidence was near critical. It is remarkable that the spectra closely resemble ATR spectra even though the optical properties of gold vary widely through this spectral range and the gold is highly absorbing.Another unexpected feature is that the sensitivity is higher for WILFORD N. HANSEN 33 parallel polarization when the film is present than when it is absent. The reason is that ( E 2 ) 11 is greater when the film is present even though the radiation must penetrate through the film! Calculation of ( E 2 ) values for this multiphase system using the equations of ref. (1) confirms this fact. (E2)L is much smaller and the sensitivity is much smaller as indicated by the equtions. THIN FILM ON A METAL Eqn are now derived for the absorbance change due to the presence of a thin film on the specular surface of bulk metal. The most powerful approach is simply to use eqn (12) which is valid even if the metal is not a good reflector and even if it is already covered with a thin oxide layer plus other very thin films.To use the equation effectively we must have knowledge about (E2)g which must be calculated by computer in the general case. For good reflectors however the situation is especially simple. As a general rule all metals are good reflectors in the infra-red and some are good reflectors in the visible. For these metals the mean square fields at the surface relative to those in the incident beam are given by (E2) x 4 ~ 0 s ' 81/k2 (16) where the z direction is normal to the interface and the y direction is normal to the plane of incidence. BB is the pseudo-Brewster Angle. Just how well these equations hold is illustrated by comparison with exact calculations.For the present let n = 3 k = 30 (typical for a metal in the infra-red). At 60" eqn (15) gives 3.00 for (S')~,,. The exact calculation gives 2.95. Eqn (15) gives 4.44 x for (Ez)llx at all angles. The value calculated using exact equations is 4.37 x at = 0" and 4.33 x at = 60". Eqn (16) gives 4 . 4 4 ~ for (E2)1 at 8 = 0" 1.11 x at 60" and 5.40 x at 88". The values from exact calculations are 4.37 x at 0" 1.10 x at 60° and 5.36 x at 88". Substituting the above equation for (Ez)llz into eqn (12) letting Ro = 1 and neglecting ( E ) \Ix we have or The factor in parentheses is the sensitivity and is constant from metal to metal. The sensitivity can be increased rapidly by increasing nl. For perpendicular polarization we can substitute eqn (16) into eqn (12) and similarly obtain The sensitivity is diminished by a factor of l/k2 which is cu.for the metal discussed above. The above equations make clear the physics of the reflection process show what a spectrum will look like relative to an absorption spectrum and show that except for changes in n j absorbance will be proportional to the amount of absorbing S4-2 34 REFLECTION SPECTROSCOPY OF ADSORBED LAYERS material at the interface. This will be true even if the discreteness of the absorbing material is considered. The way to get an intense spectrum is clearly to use parallel polarization alone since any perpendicular component present acts like stray light. With equations written in the form given above the case of multiple reflection is easy to handle. For a single polarization the absorbance at each reflection simply adds to the total.If the sample is uniform and there are Nreflexions A j T = NAj (20) where A, is the overall absorbance. In this case the sensitivity in the above equations is increased by a factor of N. This will not be true however if perpendicular radiation is allowed to come through along with parallel since the ratio of the two will change from point to point. In fact Aoll may be so large compared to AOL that after a number of reflections the light is mostly I which swamps the signal. Polmizers are desirable for quantitative work. A molecular layer of silicone oil was adsorbed on an aluminium mirror and the reflection spectrum of the layer was recorded in the infra-red using a multiple reflection apparatus adjusted to give 100 reflections.The layer formed quickly and reproducibly when a dilute toluene solution of silicone oil was contacted by the mirror. The resulting reflection spectrum is shown in fig. 3 along with a transmission spectrum scaled to give about the same intensity at the 1250 cm-l peak. One curve is shifted vertically relative to the other to aid visual comparison. t I I On30 ' 13bo 1200 I100 1000 9 wavenumber cm- 0 FIG. 3.-Silicone oil adsorbed on aluminium mirror 100 external reflections parallel polarization. Dashed curve is transmission spectrum. First we note the qualitative features. They will be determined by eqn (17). The angle of incidence was 45" and n = 1. Since h is fixed the only remaining factor varying with wavelength is [nj/(n3 + k3)2]aj which determines the shape of WILFORD N.HANSEN 35 the spectrum. From known spectral behaviour and from our determination of the optical constants of silicon oil kj gets very large about unity in the most intense regions. Therefore (Anj)max is also large with low values of n (below unity) to the left of large absorption regions and large to the right. The above equations predict therefore that the reflection spectrum will be more intense to the left of the main absorption bands and less intense to the right. The side bands show that to be just what happens. There are not enough data in the present example to analyze the spectrum in every detail. For example there may be some band distortion in the adsorbed material with consequent spectral changes but this effect is evidently small. Even such a simple spectrum which is easily obtained contains a great deal of information.It is instructive to make an absolute calculation of the thickness of the film from the experimental data. At A = 7.9 pm we take our measured bulk values n = 1.0 kj = 0.27 (giving a = 4200 cm-l) and 8 = 45". From eqn (17) we then have for a single reflection All = 4500 h,. The measured absorbance at 7.9 pn is 0.15 or 0.0015 per reflection for the 100 reflections used. That gives hj = 34 .$ a reasonable answer. The author is greatful to the National Science Foundation for the financial support of Grant no. GP 13767 and to Research Corporation for help in purchasing experi- mental equipment. W. N. Hansen J. Opt. SOC. Amer. 1968,58 380. N. J. Harrick Internal Reflection Spectroscopy (Interscience Publishers 1967). S. A. Francis and A. H. Ellison J. Opt. Soc. Amer. 1959,49,131. R. G. Greenler J. Chem. Phys. 1969,50 1963. G. W. Poling J. Electrochem. SOC. 1969 116,958. Harvey Pobiner Anal. Chem. 1967,39,90.