Thin films refraction from

In 2007, a team led by Professor E. Thomas of Massachusetts Institute of Technology (MIT) developed a smart gel based on the cephalopod s skin structure. The team used a self-assembling block copolymer thin film made from layers of polystyrene and poly-2-vinyl-pyridine. The thickness of the layers controls the refractive indices and thus the color of the reflected light. The poly-2-vinyl-pyridine layer is designed to alter its thickness in response to stimuli such as pH and salt concentration thus changing the gel s color. 

The degree of deviation of the thin-film approximation from the exact spectral simulations depends upon the refractive indices of the immersion medium and the substrate 113, the oscillator strength of the film, and on the angle of incidence (Pi. The deviation can be more than 10% for a 50-nm film and several percent for a 1-nm film (Sections 2.2, 2.5, 3.3, and 3.10). 

We found that the surface morphology of thin films derived from mixture of TEOS and MTES sols can be controlled by changing molecular weights of siloxane polymers in TEOS and MTES (Takahashi, 1997). We describe the method to produce low refractive index film and discuss the mechanism of formation of different surface morphologies. A new layer to reduce the reflection of the automotive windshield for drivers has been developed by sol-gel method. 

Lee, L.H. and Chen, W.C. (2001) High refractive-index thin films prepared from trialkoxysilane-capped poly(methyl methacrylate)-titania materials. Chem. Mater., 13, 1137-1142. 

We are now in a position to calculate the reflections from multiple mterfaces using the simple example of a thin film of material of thickness d with refractive index n.2 sandwiched between a material of refractive index (where this is generally air witii n = ) deposited onto a substrate of refractive index [35, 36], This is depicted in figure Bl.26.9. The resulting reflectivities for p- and s-polarized light respectively are given by ... 

For thin-film samples, abrupt changes in refractive indices at interfrees give rise to several complicated multiple reflection effects. Baselines become distorted into complex, sinusoidal, fringing patterns, and the intensities of absorption bands can be distorted by multiple reflections of the probe beam. These artifacts are difficult to model realistically and at present are probably the greatest limiters for quantitative work in thin films. Note, however, that these interferences are functions of the complex refractive index, thickness, and morphology of the layers. Thus, properly analyzed, useful information beyond that of chemical bonding potentially may be extracted from the FTIR speara. 

Spherical rollers were machined from AISI 52100 steel, hardened to a Rockwell hardness of Rc 60 and manually polished with diamond paste to RMS surface roughness of 5 nm. Two glass disks with a different thickness of the silica spacer layer are used. For thin film colorimetric interferometry, a spacer layer about 190 nm thick is employed whereas FECO interferometry requires a thicker spacer layer, approximately 500 nm. In both cases, the layer was deposited by the reactive electron beam evaporation process and it covers the entire underside of the glass disk with the exception of a narrow radial strip. The refractive index of the spacer layer was determined by reflection spectroscopy and its value for a wavelength of 550 nm is 1.47. 

Upon selective absorption of analyte molecules from the ambient environment, the zeolite thin film increases its refractive index. Correspondingly, release of adsorbed molecules from the zeolite pore results in the decrease of its refractive index. The absorption/desorption of molecules depends on the molecule concentration in the environment to be monitored. Therefore, monitoring of the refractive index change induced phase shift in the interference spectrum can detect the presence and amount of the target analyte existing in the environment. 

The factor f reduces the oscillation amplitude symmetrically about R - R0, facilitating straightforward calculation of polymer refractive index from quantities measured directly from the waveform (3,). When r12 is not small, as in the plasma etching of thin polymer films, the first order power series approximation is inadequate. For example, for a plasma/poly(methyl-methacrylate)/silicon system, r12 = -0.196 and r23 = -0.442. The waveform for a uniformly etching film is no longer purely sinusoidal in time but contains other harmonic components. In addition, amplitude reduction through the f factor does not preserve the vertical median R0 making the film refractive index calculation non-trivial. 

An instrument known as a refractometer has been used for many years to measure the refractive index of liquids and liquid solutions for the purpose of both quantitative and qualitative analysis (see Chapter 15). A refractometer measures the degree of refraction (or bending) of a light beam passing through a thin film of the liquid. This refraction occurs when the speed of light in the sample is different from a reference liquid or air. The refractometer measures the position of the light beam relative to the reference and is calibrated directly in refractive index values. It is rare for any two liquids to have the same refractive index, and thus this instrument has been used successfully for qualitative analyses. 

This very useful method also has the advantage that the equations do not contain anything about the material or diffraction conditions other than the Bragg angle and geometry. The independence from material parameters arises because the refractive index for X-rays is very close to unity. The equations are, of course, similar to those for optical interference from thin films, since the physics is the same, but in the optical case we do need to know the refractive index. 

To obtain a measure of the dielectric constant and anisotropy of thin films, the refractive index of thin film samples was measured. It has been shown that the measured dielectric constant is approximately the square of the refractive index at 633 nm wavelength [the actual relationship is roughly e (refractive index) -i- 02.] and the anisotropy is obtained from the difference between the in-plane and out-of-plane refractive index [97]. The measured anisotropy of foamed polyimides is lower than that observed for non-foamed polyimides. In addition, a drop in refractive index of the samples was observed upon foaming. The polyimide PMDa/3FDA has a measured dielectric constant of ca. 2.9 at 70 °C. A foamed sample of PMDA/3FDA derived from copolymer 6f showed a drop in dielectric constant of 2.3 [97]. 

Ellipsometiy is unrivaled for the measurement of the properties of thin films, particularly those on electrodes in solution. It has extraordinary sensitivity and can measure films from submonolayers up to films having a thickness near to that of the wavelength of the light incident upon the electrode surface. Moreover, ellipsometiy gives not only the thickness of the film but also its refractive index and, in the case of conducting films, the absorption coefficient. 

Amorphous polymers characteristically possess excellent optical properties. Unlike all the other commercially available fluoropolymers, which are semicrystalline, Teflon AF is quite clear and has optical transmission greater than 90% throughout most of the UV, visible, and near-IR spectrum. A spectrum of a 2.77-mm-thick slab of AF-1600 is shown in Figure 2.5. Note the absence of any absorption peak. Thin films of Teflon AF have UV transmission greater Ilian 95% at 200 mm and are unaffected by radiation from UV lasers. The refractive indexes of Teflon AF copolymers are shown in Figure 2.6 and decrease with increasing FDD content. These are the lowest refractive indexes of any polymer family. It should be noted that the abscissa could also be labeled as glass transition temperature, Tg, since Tg is a function of the FDD content of the AF copolymer. Abbe numbers are low 92 and 113 for AF-1600 and AF-2400. 

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