Quantitative Comparative Techniques of Infrared - American Chemical

Chapter 15

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Quantitative Comparative Techniques of Infrared Spectra of a Thin Film Takeshi Hasegawa* Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan *E-mail: [email protected].

Fundamentals of infrared (IR) spectroscopy for analysis of molecular adsorbates or a thin film on a flat surface are described in terms of surface spectroscopy. To fully understand IR spectra of a thin film deposited on a surface, theoretical backgrounds (such as both quantum mechanics and electrodynamics) of spectroscopy are necessary. Especially when an interface is taken into account, the electrodynamic approach is inevitable. In recent days, the ATR technique has spread over a wide range of research fields. In this situation, a very important matter must be known that the band position and relative band intensity of an ATR spectrum cannot be compared to those of a spectrum obtained by another technique such as the transmission and reflection-absorption (RA) spectrometries. Without an appropriate knowledge on this matter, incorrect discussion is generated, which makes the thin-film analysis highly confused. In this chapter, quantitative comparison of spectra is described by using some application studies.

© 2015 American Chemical Society In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Infrared Spectroscopy for Surface Adsorbates Fourier transform infrared (FT-IR) spectrometry (1–3) is one of the most common spectroscopic tools spread over a wide variety of fields in chemistry. Unfortunately, the power of FT-IR is not fully recognized in many cases, even if much chemical information is necessary for chemical discussion. This situation is quite discouraging. FT-IR can provide more information than the primary chemical structure as well as molecular interaction via a quantitative analysis of the IR spectra. Absorption spectra provide molecular information through the band location (ordinate) and intensity (abscissa). Molecular vibration is measured by the interaction of a vibrating dipole moment with the oscillating electric field of IR ray (3, 4). This physical process is theorized in two manners of quantum mechanics and electrodynamics. The quantum-mechanical treatment yields a very important conclusion of “Fermi’s golden rule,” which is the starting point of discussing absorption spectroscopy, and it also provides an important concept of polarization analysis of “molecular orientation.” Oriented molecules are often found in a thin film, and FT-IR is quite suitable for analyzing the thin film due to the uniquely high sensitivity. To analyze a thin film, however, only the quantum-mechanics approach is insufficient, and another theoretical framework on electrodynamics is definitely necessary, since “an interface” comes up in the thin-film analysis (5). In this chapter, through some recent analytical examples, the spectroscopic concepts on the two approaches are described, so that IR spectra obtained by different techniques can directly be compared in a quantitative manner.

Fundamentals on Quantum Mechanics IR spectroscopy is one of the absorption spectroscopies that rely on the absolute principle of Fermi’s golden rule. This rule is a conclusion deduced from a physical model that a dipole along a chemical bond (or a chemical group) at a steady state is perturbed by oscillating electric field of light, which is described in an ordinary procedure using Schrödinger equation. The finally obtained golden rule is known as:

The left-hand side corresponds to peak area or absorbance, which is proportional to the squared transfer integral, , where the wave functions indexed by j and k respectively correspond to the initial and final . Dirac’s delta states of the transition induced by the perturbation operator, function means the conservative energy absorption between the two quantized energy levels. In the case of molecular vibrations observed by IR spectroscopy, 304 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


can be employed with a good approximation. Here, p(= er) and E are the dipole moment and the electric field applied to the moment, respectively. As a result, the transfer integral can be a dot product of the transition moment and the electric field (Eq. (1)).

Since the wavelength of the IR light is generally much longer than the length of the dipole, r, E can be treated as a constant value in the integral, and it can be put outside the integral. Fortunately, IR spectroscopy can be recognized to measure a vibrational transition from the ground state only. In this situation, the group theory tells us that the transition moment has the same direction as that of the normal mode. Therefore, Eq. (1) indicates that the absorption intensity becomes greater when the direction of the normal mode is parallel to the electric field; whereas no peak appears when they are orthogonal to each other. This is the fundamental of the orientation analysis using IR spectroscopy.

Fundamentals on Electrodynamics Eq. (1) provides a very simple principle for the orientation analysis of a molecule in vacuum. To quantitatively analyze the spectra of molecules adsorbed on a surface, however, only quantum mechanics is very insufficient, and electrodynamics is necessary to evaluate the electric field near the surface (4, 5). This is true of not only the orientation analysis, but all the analyses of the absorption spectra measured at an interface. The simplest example is presented by transmission measurements with the normal incidence of a thin film deposited on an IR transparent substrate. The absorbance, ATr, is defined as:

Here, Isample and IBG are single-beam spectra of the sample and background (BG) measurements, respectively. The BG spectrum can be interpreted as the apparatus function. On looking at this definition, one may consider that the chemical/physical information of the substrate is readily canceled to leave the information of the thin film only. Unfortunately, however, this expectation is denied when referring to Table 1.

305 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Table 1. Transmission Absorbance, ATr, of an LB Film on an IR Transparent Substrate Calculated at 2900 cm-1. n3 Is the Refractive Index of the Substrate (Phase 3). substrate

n3

ATr/10-3

ATr/ATr(air)

air

1.000

4.14

1.00

CaF2

1.415

3.43

0.83

KRS-5

2.380

2.46

0.59

ZnSe

2.455

2.40

0.58

Si

3.429

1.88

0.45

Ge

4.034

1.65

0.40

When an identical thin film is deposited on a different substrate, the absorbance (peak intensity) varies a lot. For example, the film on CaF2 exhibits a very strong peak more than twice that on Ge. This straightforwardly implies that the influence of the substrate still remains even after the division by the BG spectrum. To deduce the analytical expression of the transmission measurements, Isample and IBG are theorized by using the three- and two-phase optical models (Figure 1), respectively, and boundary conditions of the electric and magnetic fields are considered. As a result, the following equation (4) is obtained using a thin-film approximation

:

Here, d2 is the film thickness, and εx,2 is the surface-parallel component of the complex electric permittivity of the film. Here, no details is described for mj, but Eq. (2) apparently tells us that the absorbance is influenced by the optical parameter of the phase 3 (substrate). Another important point is that the transmission spectrum relies on Im(εx,2) that is called TO (transverse optic) energy-loss function.

Figure 1. A schematic of IR transmission measurements of a thin film on an IR transparent substrate. 306 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Note that the TO-driven spectra cannot be compared to a spectrum measured by the KBr pellet technique. The KBr-pellet spectra are free from the influence of an optical interface. As a result, the absorbance, AKBr, is physically represented as:

This is another expression of Beer’s law, and the KBr spectrum provides an “α-spectrum.” Here, d is the path length, and n″ is the imaginary part of the refractive index (n = n′ + in″)of the absorbing material (i.e., sample). Since the relationship of ε = n2 = (n′2 − n″2) + i2n′n″ holds, the function of Im(ε) = 2n′n″ is influenced not only by n″, but also by n′. In other words, IR bands in the transmission spectrum of a “thin film” are distorted by the dispersion curve of n′ with respect to the corresponding KBr spectrum. This explicitly shows an important character of “surface spectroscopy.”

Surface Selection Rules for Thin-Film Analysis Surface spectroscopy is a fundamental concept, which should be discriminated from normal spectroscopy on a bulk sample with no interface. Once the relationship between the surface and normal spectroscopy is understood, molecular adsorbates and a thin film can readily be discussed to reveal the molecular conformation, packing and orientation. In the previous section, the transmission spectra of a thin film depend on the TO energy-loss function of the surface-parallel component of the complex electric permittivity of the film. In short, this means that the surface parallel molecular vibrations appear in the transmission spectra. This rule is called “surface selection rule (SSR)” of transmission spectrometry. In other words, the surfaceperpendicular component is missed in the transmission spectra.

Figure 2. A schematic of IR RA measurements of a thin film on a metallic substrate using the p-polarized IR ray. To measure the surface-perpendicular molecular vibrations, the film should be put on a metallic surface, which is subjected to a grazing-angle reflection measurement. This grazing-angle technique on a metallic surface is called “reflection-absorption (RA)” spectrometry (Figure 2) (1, 4). The grazing angle is often set to near 80° from the surface normal. Note that reflection measurements on a “nonmetallic surface” are categorized into the “external reflection (ER)” 307 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


spectrometry (1, 4), which is strictly distinguished from the RA technique, since the analytical expressions are totally different from each other (4). The analytical expression of the RA technique is known as (4):

Here, the incident light comes through the air phase with the angle of incidence of θ1. The imaginary part of the inversed electric permittivity is called the LO energy-loss function, which determines the band shape of the RA spectrum. Although the TO and LO energy-loss functions look largely different from each other, the simulated spectra always yield very similar shapes, but they accompany some “band shift” especially for a strong absorption band. This claims an important point that the band position of an RA spectrum cannot directly be compared to a transmission spectrum, even if the analyte is a common compound. Of course, it cannot be compared to a KBr pellet spectrum, either. Eq. (4) indicates that the surface-normal (z) component of the molecular vibrations is selectively observed in the RA spectra, which is called the SSR of the RA spectrometry. In this manner, the SSRs of the transmission and RA spectrometries are complimentary with each other. In other words, the orientation of a transition moment is readily revealed by looking at the band appeared in the two spectra. Figure 3 presents IR RA and transmission spectra of a 7-monolayer LangmuirBlodgett (LB) film (6). Since the cadmium stearate is known to form a highly stable monolayer independent of the substrate, it is useful to compare the two techniques. We note that the anti-symmetric and symmetric CH2 stretching vibration (νa(CH2) and νs(CH2), respectively) bands appear in the transmission spectrum at 2916 and 2850 cm-1, respectively. These “band locations” respond to the “molecular conformation,” and the two values are typically found for the all-trans zigzag conformation of the alkyl chain (7). In other words, the chain should have a straight-line structure, which suggests that the molecules are highly packed. This is supported by the CH2 bending vibration (δ(CH2)) band, which is split into doublet at 1472 and 1462 cm-1. This splitting (factor-group splitting, or Davydov splitting (6, 8)) is known to be a good marker of the orthorhombic subcell packing of the alkyl chains. With the conformation and the crystallinity, the molecular orientation is expected to be nearly perpendicular to the surface. In fact, the νa(CH2) and νs(CH2) bands are both strong in the transmission spectrum; whereas they are largely suppressed in the RA spectrum. Judging from the SSRs of the two techniques, they consistently indicate that the transition moments are both nearly parallel to the substrate, which further indicates that the molecular axis is nearly perpendicular to the surface. This is supported by the band progression that is a coupled oscillation of the synchronous CH2 wagging (ωCH2) modes along the alkyl chain (9). The band progression is a proof of a highly ordered molecular configuration, and the appearance in the “RA spectrum only” indicates that the alkyl chain is nearly perpendicular to the surface. In this manner, the vibrational modes relating to the alkyl chain are all discussed in a 308 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


consistent manner, and a highly plausible model is reached. The discussion based on SSRs is a great benefit of using IR spectroscopy.

Figure 3. IR RA and transmission spectra of a 7-monolayer LB film of cadmium stearate deposited on a silver substrate (single side) and a ZnSe one (both sides), respectively. Adapted with permission from Reference (6). Copyright 1990 the American Chemical Society. In a similar manner, the terminal carboxylic group adds more information to the chemical structure. Since the group is fully anionized by the interaction with the cadmium cation, the C=O stretching vibration band disappears, and instead two bands of the anti-symmetric and symmetric COO- stretching vibration (νa(COO-) and νs(COO-), respectively) bands appear at 1543 and 1433 cm-1, respectively. The νs(COO-) band appears dominantly in the RA spectrum, while the νa(COO-) strongly appears in the transmission spectrum, which consistently indicates that the COO- group stands nearly perpendicular to the surface. In this manner, a chemical image of the molecule in the LB film has been obtained. To quantitatively discuss the orientation angle, a quantitative comparison of transmission and RA spectrometries is necessary, which requires the refractive indices of the film and the IR transparent substrate. This strategy is for obtaining the ratio of the surface-parallel and –perpendicular components of the electric permittivity, so that the molecular orientation would be calculated. In practice, the two components have different refractive index of the sample, which is close 309 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.

to impossible to obtain without using the orientation angle of the molecule. Therefore, the quantitative analysis is possible only when the optical parameters are fortunately ready at hand, and the dispersion of the refractive index can be ignored.


ATR Spectrometry Attenuated total reflection (ATR) spectrometry has rapidly spread in a recent decade, which is overwhelming the conventional KBr pellet technique. Note that, however, a KBr spectrum cannot be replaced by an ATR spectrum as shown later. ATR spectrometry is one of the internal reflection techniques: IR light traveling in a higher refractive-index matter reflects at an interface face to a lower refractive-index matter.

Figure 4. Optical scheme of the ATR spectrometry.

When the angle of incidence, , is greater than the critical angle, , the IR light is totally reflected at the interface (Figure 4), but only the electric field of the light is penetrated across the interface into the sample. Since the electric field oscillation is necessary to measure the absorption by the sample as presented in Eq. (1), this technique enables us to measure the sample near the interface only. The penetration depth of the electric field into the sample is about one tenth of the wavelength, which results in ca. 1 μm or less. An ATR spectrum has a component formulated as (4):

Here, and A is referred to literature (4). As found in the equation, ATR spectra depend on both TO and LO energy-loss functions. This is the reason an ATR spectrum has a distorted band shape and position in comparison to the corresponding KBr spectrum (Eq. (3)). Therefore, if we find a different band position in an ATR spectrum from the KBr spectrum, we should not conclude that the molecules are in a different chemical situation. As described in the next section, an appropriate conversion should be applied to the ATR spectrum to have a pure TO and LO function spectra for direct comparison to the transmission and RA spectra, respectively. This is particularly important for analyzing a strongly absorbing band, which is commonly found in perfluoroalkyl compounds. 310 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Application Study Using a Combined Technique of RA and ATR Spectrometries Here, an example study using IR RA spectrometry is described. A thin film of a perfluoroalkyl compound is employed as the analyte. A perfluoroalkyl (Rf) group is a fluorine-substituted alkyl group on all hydrogen atoms, and the character of an Rf group is often recognized on an extended line of the corresponding normal alkyl group. The material characters of an Rf compound is, however, totally different from those of a normal hydrocarbon. The uniquely high melting point (327°C for Teflon) (10) is, for example, a representative characteristic, which is not found in a normal hydrocarbon material. This Rf-specific property is attributed to the spontaneous molecular aggregation property of the Rf groups, which depends on the number of CF2 groups (Rf length) (11, 12). To discuss the molecular aggregation, IR spectroscopy works powerfully, since the aggregation influences the molecular conformation. Speaking of van der Waals force, one may consider London’s dispersive force (13). In fact, the dispersive force is the main factor accounting for the hydrophobic interaction between the normal hydrocarbons. Of Rf compounds, however, this concept is not true (11). The major factor of the van der Waals force between Rf groups is not the dispersive force, but the “orientation (or dipole-dipole interactive) force.” As a result of the spontaneous molecular aggregation due to the orientation force, the Rf groups are put together to generate a two-dimensional molecular aggregate, i.e., a monolayer film (12). In Figure 5, a myristic acid (MA) molecule having an Rf group at the terminal of the tail (MA-Rf(n); n is the number of CF2 groups) is illustrated. An Rf group is characterized by a twisted structure with a constant rate: the direction of the CF2 group is twisted by 180° over twelve C–C bonds (14, 15). In the case of an Rf group of n = 9, the twisted angle is thus 120° as in Figure 5.

Figure 5. A model compound, MA-Rf(n), having n CF2 groups. When a CF2 group is represented by a single dipole for simple visibility, the dipoles are easily found to be aligned linearly in the closest packing of the molecules, and a dipole array is generated over the hexagonal assembly (Figure 6). As a result, the MA-Rf(n) molecules spontaneously make a molecular aggregate with the hexagonal packing. This model is a result of the orientation force due to the “permanent dipoles,” which readily accounts for the high melting point of an Rf compound. In addition, the summation of the dipoles in various directions over 311 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


the molecular aggregate results in a low polarization density (11), under which a character of a low “bulk polarizability” appears, which further yields a low electric permittivity (11). This molecular aggregation model is named “stratified dipole-arrays (SDA)” model (12).

Figure 6. A top view of a molecular aggregate of the MA-Rfn=9 molecules in a hexagonal manner. To examine the SDA model, a series of Rf compounds, CF3(CF2)n(CH2)mCOOH denoted as MA-Rf(n), are prepared (n + m = 12). According to the SDA model in phase II (below 19°C), a short Rf chain would exhibit a dipole-interactive character; whereas an Rf chain of n = 7 or longer would exhibit a spontaneous molecular aggregation, in which the molecules would have a perpendicular stance to the water surface (Figure 7).

Figure 7. Schematic image of MA molecules with (a) n=3 and (b) n= 7 on the water surface. 312 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


The expectation on the SDA model was examined by using a Langmuir monolayer of each model compound on a water surface, which was transferred at a surface pressure of 15 mN m-1 onto a gold-evaporated glass surface to be an LB film. The surface pressure was chosen because the molecules with n = 7 or longer are expected to be aggregated “spontaneously” (12). IR RA spectra of the LB films are presented in Figure 8.

Figure 8. IR RA spectra of single monolayer LB films of MA-Rf(n) on gold. Adapted with permission from Reference (12). Copyright 2014 Wiley. As found in the figure, RA spectrometry is powerful to obtain high-quality IR spectra of a monolayer-level thin film on a metallic surface. The spectra are obtained by 2000 accumulations using a liquid nitrogen-cooled MCT detector (1). Here, it is of note that the spectral pattern largely depends on the Rf length. In general, normal alkyl compounds yields a nearly identical spectral shape except the methyl-related bands on a change of the chain length (16), and therefore the spectral change of the Rf compounds may look unusual (17). The most understandable band is the CF3 symmetric stretching (νs(CF3)) vibration band that appear at 1343 cm-1 for MA-Rf(9). Since only one CF3 group is available at the terminal end of the Rf group for all the compound, the orientation of the CF3 group equals to the orientation of the Rf group (12). In short, the band is useful for molecular orientation analysis of the Rf group. 313 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Here, let us remind the SSR of RA spectrometry: only the surfaceperpendicular component of a transition moment appears in the spectra. The IR RA spectra show that the νs(CF3) band strongly appears for n = 9 at 1343 cm-1 while it is suppressed for n = 3 at 1301 cm-1. This result straightforwardly implies that the molecules of n = 9 stand nearly perpendicularly to the surface while the molecules of n = 3 lie on the surface, which agrees with the expectation on the SDA model. On the other hand, the CF2 stretching vibration bands are difficult to be discussed. Since an Rf chain has a twisted structure, each CF2 group has different direction with a different tilt angle when the Rf group is tilted to the surface. This means that the bands cannot be employed for molecular orientation analysis. Instead, fortunately, the modes are still useful for discussing the molecular packing, since it is sensitive to the molecular conformation. For the analysis, the CF2 symmetric stretching vibration (νs(CF2)) band is used, since this band is separated from another band. Since the band location depends on the Rf length (17), IR spectra of bulk (un-oriented) solid samples are necessary. In recent days, for that purpose, the ATR technique is quite often conveniently employed.

Figure 9. IR ATR spectra of bulk compounds of MA-Rf(n) after converted to the LO energy-loss functions. Adapted with permission from Reference (12). Copyright 2014 Wiley. 314 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


IR ATR spectra of MA-Rf(n) are shown in Figure 9, in which the Rf-related bands appear. Here, we have to note that an ATR spectrum cannot directly be compared to an RA spectrum. An ATR spectrum involves a p-polarization component, which is a linear combination of both TO and LO energy-loss functions. Since an RA spectrum depends on the LO function only, the contribution of the TO function involved in the ATR spectrum must be removed for the mutual comparison especially for discussing the band location. To do that, a spectrum conversion available on a recent spectrometer is quite useful. For example, “Advanced ATR Correction” is the most useful function on a Thermo’s FT-IR, which generates an α-spectrum from an ATR spectrum (Eq. (3)), as if a film with a thickness of 2.303 (= ln10) μm is measured by the transmission technique having no influence by the air/film interfaces. The α-spectrum is defined as:

as found in Eq. (3).With this equation, the n″ spectrum is obtained, which can further be converted to be the real part of the refractive index, n′, by using the Kramers-Kronig relationship (18) with the limiting refractive index ( for an Rf compound, for example). With the complex refractive-index, the complex electric permittivity, ε, is readily obtained as:

which further yields the LO energy-loss function. Figure 9 is obtained in this manner. Now, the LO spectra of the bulk solid are ready to be compared to the RA spectra of the monolayers on gold. The νs(CF2) mode appears at the same position of 1153 cm-1 for both LO and RA spectra, which straightforwardly implies that the molecules in the monolayer have a highly condensed packing as found in the bulk solid. In this manner, the spontaneous molecular aggregation of the long Rf group with n = 9 has experimentally be proved. On the other hand, the same mode of the compound of n = 3 is located at 1138 cm-1 in the RA spectrum, which is higher than that of the LO spectrum at 1128 cm-1 by 10 cm-1. The higher wavenumber shift means that the molecular packing is loose in the monolayer, which agrees with the expectation on the SDA model. In this manner, an appropriate spectral conversion is necessary for precise comparison of the bulk and film samples.

IR External Reflection Spectrometry When a thin film deposited on a nonmetallic (dielectric) surface is measured by a reflection technique (Figure 10), the measurement is strictly discriminated from the RA technique, and it is called “external reflection (ER)” technique (1, 2, 4). 315 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Figure 10. A schematic of IR ER measurements of a thin film on a nonmetallic substrate using the s- (gray arrow) and p-polarizations (solid arrow).

On the contrary to the RA measurements, the electric field of the s-polarization still remains on the surface, since the nonmetallic surface does not generate the mirror image beneath the interface (1, 2, 4). As a result, a totally different SSR is obtained for the ER spectrometry. To discuss the ER technique, absorbance and reflectivity should both be taken into account. The absorbance on a three-phase system is represented by the following equations.

Here, only the film phase (the 2nd layer) has a thickness while the rest phases have infinite thickness. The details of the coefficients, Cy and Cz, are referred to literature (4), but Eq. (6) apparently tells us that the ER spectra are of the TO and LO functions. One of the outstanding characteristics of ER spectrometry is that Cz can be both positive and negative. As a result, the p-polarized ER spectrum comprises both positive and negative bands. This character is intuitively understood by using Hansen’s approximation equations (2, 4, 19, 20). This approximation is based on the thin-film approximation and a non-absorbing substrate.

Here, can be calculated by Eqs.

. The ideally surface-parallel orientation (7) and (9); whereas the surface-perpendicular 316

In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


orientation is reflected in Eqs. (8) and (10). With these equations, band intensities of the s- and p-polarization measurements are readily calculated as presented in Figure 11.

Figure 11. Band intensity of a thin film on a GaAs substrate at 2850 cm-1. The thickness of the film is 22.5 nm. When a thin film on a single-side polished GaAs substrate (3-phase system) is subjected IR p-polarized ER spectrometry, for example, the surface-perpendicular component (Apz) of a transition moment yields a positive absorbance for a small angle of incidence, but it turns into negative when the angle is larger than Brewster’s angle ( (18)). On the other hand, the surface-parallel component yields negative band for the s-polarization, which is also indicated by Eq. (5).

Figure 12. Reflectance on the angle of incidence at a silicon surface for both polarizations. 317 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


This is the SSR of ER spectrometry, and both polarizations are useful. Figure 11 implies that a p-polarized spectrum is highly sensitive when the angle of incidence is near Brewster’s angle, but we have to pay attention to another issue, i.e., reflectance on the surface. The reflectance on a silicon surface for each polarization is presented in Figure 12. Since the p-polarization exhibits an extremely low reflectance near Brewster’s angle, the quality of the spectra using an angle of incidence near Brewster’s angle is degraded. As a result, we have to choose a well-balanced angle for obtaining high-quality ER spectra for the p-polarization. Figure 13 presents an IR ER spectrum of a self-assembled monolayer (SAM) of octadecylsilane (ODS) (21). The band positions of both νa(CH2) and νs(CH2) modes indicates a well-ordered packing of the alkyl chains having the all-trans zigzag conformation in the SAM. Since the angle of incidence is chosen as 60° that (Figure 11), the negative-absorbance bands indicate that the is less than transition moment of the two modes are both nearly parallel to the surface. This implies that the chain axis stands nearly perpendicular to the film surface. This discussion is supported by the rest two positive bands at 2966 and 2877 cm-1, which are assigned to the in-skeleton asymmetric CH3 stretching vibration (νs(CH3)IS) and the symmetric CH3 stretching vibration (νs(CH3)) bands, respectively (22).

Figure 13. IR ER spectrum of a SAM of ODS on a silicon substrate measured by using an angle of incidence of 60° (< θB). Adapted with permission from Reference (21). Copyright 2013 Japan Society for Analytical Chemistry.

IR p-polarized ER spectrometry has thus a benefit that molecular information of both surface-parallel and -perpendicular components is simultaneously obtained on a single spectrum. Although the signal-to-noise ratio can be inferior to the other techniques because of the low reflectance, the SSR of ER spectrometry is quite powerful. 318 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


IR MAIRS Spectrometry The ER technique has a limit that a transition moment with an oblique tilt angle gives no band, which is caused by overlapping the positive and negative bands. As an example, an IR p-polarized ER spectrum of a dip-coated film of linear polyethyleneimine (LPEI) on a silicon wafer is presented in Figure 14 (23). Since the angle of incidence (50°) is less than the Brewster angle (ca. 73°), the surfaceparallel and perpendicular components of a transition moment appear as negative and positive bands, respectively, due to the SSR. Of note is that there is no band in the circled area that is for the CH2 stretching vibration bands. Since LPEI has a number of CH2 groups, the bands must aappear in the wavenumber region. The disappearance is a result of an oblique tilting of the transition moment, but it is a quite ambiguous result.

Figure 14. IR p-polarized ER spectrum of a dip-coated film of LPEI on a single-side polished silicon wafer. Adapted with permission from Reference (23). Copyright 2008 American Chemical Society.

To overcome the limitation, the MAIRS (multiple-angle incidence resolution spectrometry (24–29)) technique is powerful. MAIRS is built on a unique concept that the surface-perpendicular component of a transition moment is measured by using a virtual light, in which the electric-field oscillation is parallel to the traveling direction of the IR light. IR MAIRS measurements are performed by using an IR transparent substrate with oblique-incidence transmission measurements as illustrated in Figure 15. A light intensity (single beam) spectrum is decomposed into two independent components, SIP and SOP. The single-beam spectrum of SOP corresponds to a virtual measurement using the virtual light, but it can be calculated by collecting single-beam spectra at multiple angles. 319 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Figure 15. A schematic image of MAIRS: an oblique-incidence transmission measurements are decomposed into two normal-incidence transmission measurements denoted by SIP and SOP.

The collected single-beam spectra at various angles of incidence are stored in the matrix, S. These spectra involves a linear combination of the SIP and SOP spectra with weighting factors in R, which is presented by Eq. (11) involving a two-column matrix.

Regardless, other complicated components such as reflection of the substrate surface and multiple reflections in the substrate are not involved in the linear combination. This can readily be formulated by using a multivariate analysis formulated by Eq. (12).

This type of formulation is called classical least squares (CLS) regression, and the nonlinear response to R is automatically discarded into the undescribed matrix, U, by obtaining the least squares solution as Eq. (13).

As a result, two sets of SIP and SOP are obtained by the sample and background measurements, which yield two explicit absorbance spectra:



Figure 16 presents IR MAIRS spectra of an LPEI dip-coated film on a doubleside polished germanium substrate (23). If the film is the same as that for Figure 14, the MAIRS-IP and –OP spectra would correspond to the negative and positive bands in the ER spectra, respectively. Although the CH2 stretching vibration bands disappear in the ER spectrum due to oblique orientations, they are apparently found in the MAIRS spectra: the νa(CH2) and νs(CH2) modes at 2908 and 2928 cm-1, respectively, in both IP and OP spectra with a nearly the same intensity. This is the reason, in the ER spectrum, the positive and negative bands are overlapped to make the bands disappeared.

Figure 16. IR MAIRS spectra of the LPEI film dip-coated on a germanium substrate. Adapted with permission from Reference (23). Copyright 2008 American Chemical Society.

Figure 17. A schematic of double helix of LPEI standing perpendicularly on a Ge substrate. Adapted with permission from Reference (23). Copyright 2008 American Chemical Society. 321 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


In addition, the surface-parallel orientated moment at 1247 cm-1 appears in the IP spectrum only; whereas the surface-perpendicular oriented moment at 1281 cm-1 appears in the OP spectrum only. Since these moments are known to parallel and perpendicular to the double-helix of LPEI, respectively (30), the MAIRS spectra straightforwardly implies that the double helices stand on the Ge substrate perpendicularly as illustrated in Figure 17 (23). Another notable band is the N–H stretching vibration (ν(N–H)) band found at 3222 and 3212 cm-1 in the IP and OP spectra, respectively, which exhibits a large shift of 10 cm-1. If this shift is caused by the TO-LO splitting (Berreman’s effect (31, 32)), the OP band should exhibit a higher wavenumber shift to the LO band. The opposite result to the TO-LO splitting is readily explained by the factorgroup splitting (33). When two closest N–H groups on the double helix vibrate symmetrically, the vibration mode has a lower vibration energy than that of the corresponding anti-symmetric vibration. Since the symmetric and anti-symmetric vibration are directed along and perpendicular to the helix, the shift in the MAIRS spectra implies again that the helix stands perpendicularly on the Ge surface. In this manner, IR MAIRS is quite useful for discussing molecular structure in a thin film. The MAIRS technique has a limitation, however, that only a high refractiveindex substrate can be employed for the measurements (26). Although a silicon substrate has a high refractive index of ca. 3.4 in the IR wavelength region, the oxidized surface has a low refractive index of ca. 1.4, which makes the MAIRS measurements largely degraded. To overcome this limitation, the s-polarization must be removed (26), and the following renovated weighting matrix, , is used.

This improved MAIRS technique is named pMAIRS, since only p-polarization is used. Unless otherwise stated nowadays, pMAIRS is strongly recommended to be used, since pMAIRS has a great advantage that the lowest limit of the analytical wavenumber region is down to 700 cm-1 (34, 35), while the original MAIRS is limited by 1100 cm-1. One of the most successful application studies using pMAIRS is the structural analysis of a spin-coated film of poly(3-alkylthiophene) (P3HT; Figure 18) on a silicon surface (35). P3HT is an extensively studied p-type organic semiconductor, which consists of polythiophene hanging a hexyl-chain tail on each thiophene ring. Thanks to the hexyl chain, it can easily be dissolved in various organic solvents, which can be subjected to the spin-coating to yield a thin film on a solid surface. After being spread on a solid surface, the molecular planarity along the polythiophene chain is improved to have a long π-π conjugation. In this situation, an exciton is created by irradiating visible light, which is suitable for a solar cell. Therefore, the “face-on” orientation of the compound has long been considered 322 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


to have a piled-up lamellar structure parallel to the film surface. In fact, this speculation was supported by an X-ray diffraction (XRD) analysis. Nevertheless, a spin-coated P3HT film having the face-on orientation often exhibits a very poor crystallinity, which yields an ignorable XRD peak. In this situation, the textbook image of the lamellar structure cannot be employed. To a thin film having poor crystallinity, IR pMAIRS works powerful.

Figure 18. Primary chemical structure of P3HT. pMAIRS has already been fully analyzed on electrodynamics to have mathematical expressions, which are also linear combinations of the TO and LO energy-loss functions (36). For the IP spectrum, for example, optimal parameters should be employed to make the weighting factor of LO function adequately small to leave the IP function only. The optimal parameters correspond to the optimized experimental condition. For example, for a quantitative analysis, the pMAIRS spectra require the condition: the angle of incidence is varied from 9° through 44° by 5° steps (35).

Figure 19. IR pMAIRS spectra of a spin-coated film of P3HT on a Si substrate. Adapted with permission from Reference (35). Copyright 2015 Royal Society of Chemistry. With the optimal experimental condition, IR pMAIRS spectra of a thin film of P3HT spin-coated on a silicon substrate are obtained as presented in Figure 19 (35). The left higher-wavenumber panel is of the hexyl chain. The locations of the νa(CH2) and νs(CH2) bands appear at 2927 and 2856 cm-1 are specific to the gauche 323 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


conformer, and the hexyl chain is found to have a largely disordered structure. The MAIRS shift (37) of the νs(CH2) band between the IP and OP spectra (2856 and 2857 cm-1) supports this discussion, too. In the lower-wavenumber panel, two useful bands are available: the anti-symmetric thiophene-ring (νa(C=C)) vibration at 1511 cm-1 and the C–H out-of-plane deformation vibration on the thiophene ring (γ(C–H)) at 826 cm-1 (34, 35). The νa(C=C) band appears stronger in IP than OP; whereas the γ(C–H) band exhibits the opposite relative intensity. Since the νa(C=C) has a transition moment along the long axis of the polythiophene and the γ(C–H) has a moment perpendicular to the thiophene ring, the pMAIRS spectra apparently indicate that the polymers are stacked in the face-on fashion. Since the film exhibited no XRD diffraction peak on a laboratory equipment (35), pMAIRS is powerful for the amorphous film. Another benefit of using pMAIRS is that the orientation angle, , is obtained quantitatively after the optimization of the measurement condition.

Here, IIP and IOP are band intensities of an identical vibrational mode appeared in the IP and OP spectra, respectively. In the same manner, the two key bands on the thiophene ring are analyzed for four kinds of similar polymer with a tail with a different length as found in Table 2.

Table 2. Molecular Orientation Angles Obtained by IR pMAIRS Spectra. (Adapted with permission from Reference (35). Copyright (2015) Royal Society of Chemistry.)

B, H, O and DD involved in a compound name stands for butyl, hexyl, octyl and dodecyl, respectively. IR pMAIRS reveal that the molecular orientation is greatly changed as a function of the tail length only. The spin-coating condition and the solvent are commonly fixed to all the samples. 324 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.


Figure 20. Geographical relationship of the γ(C–H)) and νa(C=C) modes.

The ring-perpendicular orientation (γ(C–H)) is influenced by both short and long axis of the thiophene ring. If the short axis is fixed parallel to the surface (Figure 20), however, the angle of the γ(C–H) mode simply depends on the orientation of the νa(C=C) mode. In this case, as depicted in Figure 20, the summation of the orientation angles of the γ(C–H) and νa(C=C) modes should be equal to 90°. As found in Table 2, all the face-on type film yields the summation near 90° as expected, which paradoxically implies that the short axis of the polythiophene ribbon is kept unchanged parallel to the film surface; whereas the polymer chain exhibits a nearly random orientation (φC=C ≈ 55°). Since these “face-on” spin-coated films exhibit no XRD peak, the polythiophene film with the face-on orientation can be concluded to be not driven by the crystallinity, but by the planer interaction keeping the parallel orientation of the short axis (Figure 21).

Figure 21. A schematic of molecular piling of the face-on type polythiophene compounds. Adapted with permission from Reference (35). Copyright 2015 Royal Society of Chemistry. 325 In Recent Progress in Colloid and Surface Chemistry with Biological Applications; Wang, Chengshan, et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2015.

This schematic image is largely different from that of the edge-on film of P3BT, in which the molecules are highly crystallized yielding an apparent XRD peak even on a laboratory-use X-ray equipment. In this manner, IR pMAIRS is quite useful to provide molecular orientation, which can be used for finer discussion of the film structure irrespective of the crystallinity of the film.


Concluding Remarks IR spectroscopy has a great potential to reveal structural information in a thin film, and the sensitivity is also good enough to discuss a monolayer-level thin film. Since a vibrational spectrum provides plural number of absorption bands due to the 3N − 6 rule, a plausible chemical model can be constructed by discussing as many bands as possible. When we consider that a thin film always accompanies an optical interface, the SSR of each spectrometry works powerfully to help the discussion of the many bands. For quantitative discussion of the band locations, the mathematical expressions of the spectrometries are highly useful, and an appropriate spectral conversions considering the TO and LO energy-loss functions enable us to step into a deep insights of the thin films. Of another importance is that an IR analysis can be made on any sample irrespective of the degree of crystallinity, which suggests that IR spectroscopy should be the first choice for analyzing the thin film at hand. Since FT-IR has already spread over many chemical laboratories, the spectral data are expected to be analyzed more deeply to make the best use of the chemical information involved in the spectra.

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Quantitative Comparative Techniques of Infrared - American Chemical

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