Fringes Of Equal Chromatic Order Research Articles

Surface Forces Characterization of Concentrated PMMA Brush Layers under Applied Load and Shear.

Concentrated polymer brushes (CPBs) are known to exhibit excellent lubrication properties. However, the frictional behaviors of CPBs vary, depending on their preparation and operating conditions. In order to understand such complicated properties, it is necessary to determine their structures and correlate them with their properties, during shear motion. In this study, we employed surface forces and resonance shear measurement (RSM) as well as refractive index measurement using fringes of equal chromatic order (FECO) for studying the structure of the CPBs of poly(methyl methacrylate) (PMMA) in toluene. The obtained elastic (ks) and viscous (bs) parameters based on the RSM for the PMMA-PMMA were higher than those obtained for PMMA-silica over the entire distance range. With the increasing shear amplitude on the PMMA-PMMA under an applied load, the bs value first increased and then decreased while the ks value monotonically decreased. These behaviors were consistent with those of the thicker CPBs reported in a previous paper (Soft Matter, 2019). Thus, the dynamics of the CPBs under the applied load and shear were not dependent on the thickness of the polymer brushes in this case. The density distribution of the swollen PMMA brushes along the distance in the thickness direction of the brush layer was estimated by using the measured refractive index values, showing that the fraction of the PMMA brushes in the outer region from the surface (20% in the thickness) was ca. 10%. This lower density region near the surface of the swollen CPBs enabled them to interpenetrate with each other. Changes in the refractive index value under shear were observed, indicating that the interpenetrated PMMA chains were pulled out with increasing shear amplitude. These results demonstrated that broader applications of CPBs are possible by regulating the friction between them under different operating conditions, even for usually lubricious CPBs.

Dual-image multiple-beam fringes of equal chromatic order for dynamic characterization of fibers

In this paper, we present a modification of one of the common systems for producing multiple-beam fringes of equal chromatic order (FECO). This modification allows us to capture two FECO patterns of different polarizations simultaneously during dynamic investigations of fibers. Using this modified system, the dispersion curves in cases of parallel and perpendicular polarizations can be measured simultaneously. Also, dispersion of birefringence values along the visible spectrum can be calculated using a single FECO pattern.

Structure and Dynamics of Confined Liquids: Challenges and Perspectives for the X-ray Surface Forces Apparatus.

The molecular-scale structure and dynamics of confined liquids has increasingly gained relevance for applications in nanotechnology. Thus, a detailed knowledge of the structure of confined liquids on molecular length scales is of great interest for fundamental and applied sciences. To study confined structures under dynamic conditions, we constructed an in situ X-ray surface forces apparatus (X-SFA). This novel device can create a precisely controlled slit-pore confinement down to dimensions on the 10 nm scale by using a cylinder-on-flat geometry for the first time. Complementary structural information can be obtained by simultaneous force measurements and X-ray scattering experiments. The in-plane structure of liquids parallel to the slit pore and density profiles perpendicular to the confining interfaces are studied by X-ray scattering and reflectivity. The normal load between the opposing interfaces can be modulated to study the structural dynamics of confined liquids. The confinement gap distance is tracked simultaneously with nanometer precision by analyzing optical interference fringes of equal chromatic order. Relaxation processes can be studied by driving the system out of equilibrium by shear stress or compression/decompression cycles of the slit pore. The capability of the new device is demonstrated on the liquid crystal 4′-octyl-4-cyano-biphenyl (8CB) in its smectic A (SmA) mesophase. Its molecular-scale structure and orientation confined in 100 nm to 1.7 μm slit pores was studied under static and dynamic nonequilibrium conditions.

Preparation of stable silica surfaces for surface forces measurement.

A surface forces apparatus (SFA) measures the forces between two surfaces as a function of the surface separation distance. It is regarded as an essential tool for studying the interactions between two surfaces. However, sample surfaces used for the conventional SFA measurements have been mostly limited to thin (ca. 2-3 μm) micas, which are coated with silver layers (ca. 50 nm) on their back, due to the requirement of the distance determination by transmission mode optical interferometry called FECO (fringes of equal chromatic order). The FECO method has the advantage of determining the absolute distance, so it should be important to increase the availability of samples other than mica, which is chemically nonreactive and also requires significant efforts for cleaving. Recently, silica sheets have been occasionally used in place of mica, which increases the possibility of surface modification. However, in this case, the silver layer side of the sheet is glued on a cylindrical quartz disc using epoxy resin, which is not stable in organic solvents and can be easily swollen or dissolved. The preparation of substrates more stable under severe conditions, such as in organic solvents, is necessary for extending application of the measurement. In this study, we report an easy method for preparing stable silica layers of ca. 2 μm in thickness deposited on gold layers (41 nm)/silica discs by sputtering, then annealed to enhance the stability. The obtained silica layers were stable and showed no swelling in organic solvents such as ethanol and toluene.

Nanotribological Characterization of Lubricants between Smooth Iron Surfaces.

We performed the resonance shear measurement (RSM) for evaluating the nanorheological and tribological properties of model lubricants, hexadecane and poly(α-olefin) (PAO), confined between iron surfaces. The twin-path surface forces apparatus (SFA) was used for determining the distance between the surfaces. The obtained resonance curves for the confined lubricants showed that the viscosity of the confined hexadecane and PAO increased due to liquid structuring when the surface separation (D) decreased to a value less than 24 and 20 nm, respectively. It was also determined that the iron surfaces were lubricated by the hexadecane when normal load (L) was less than 1.1 mN, while the confined hexadecane behaved almost solid-like and showed poor lubricity when L was greater than 1.1 mN. In contrast, PAO between the iron surfaces showed high lubricity even under the high load (L > 2 mN). The surface separation of hexadecane and PAO at a hard wall contact between the iron surfaces was determined to be 4.6 ± 0.5 and 5.0 ± 0.4 nm by applying the fringes of equal chromatic order (FECO) for half-transparent iron films deposited on mica surfaces as substrates. We also characterized hexadecane and PAO confined between mica surfaces for studying the effect of substrates on the confined lubricants.

Use of optical interferometry to measure gold nanoparticle adsorption on silica

Adsorption of metal nanoparticles is at the heart of many chemical and biosensor techniques, but there are few approaches that can provide quantitative characterisation of individual nanoparticle films fabricated at different times and/or under different conditions. Using synthesised gold nanoparticles (Au NPs) as a model, the nanoparticle films were investigated using an optical interferometry technique known as fringes of equal chromatic order (FECO), which was further systematically validated against both in situ quartz crystal microbalance (QCM) and ex situ atomic force microscopy (AFM) measurements. The results indicate that the FECO wavelengths has a quantifiable red shift with increasing particle densities, making it possible to quantify the degree of surface coverage via the analysis of the fringe shift at a fixed fringe order. Moreover, the calculated formula between the FECO shifts and the surface coverage allows quantitative analysis of the whole adsorption kinetics investigated. Particularly, the as-proposed FECO technique can successfully monitor the Au NP adsorption in situ, which could be a new versatile technology platform for ⿿online⿿ monitoring method, for example in biosensor applications using Au NP-tagged analytes.

The Formation of Fringes of Equal Chromatic Order across Double Clad Fiber in the Presence of High Power Lasers

Multiple-beam fringes of equal chromatic order interferometry is a powerful technique to extract optical properties over a continuous range of spectrum. In this paper we develop a theory for the spectral shape of the fringes of equal chromatic order (FECO) that are formed across a double-clad fiber. The modified single term Sellmeier dispersion formula is used to construct the refractive index dispersion curves for the liquid, claddings, and core. Expressions for the paraxial optical path length for several rays passing through the fiber and the liquid are developed. The condition of bright fringe is applied to get an analytical expression for the spectral shape of the FECO across a double-clad fiber with an elliptical/circular inner cladding. A potential application of this theory is to determine the dispersion of Kerr constant of the claddings and the core of the fiber. To illustrate the theory and its application, simulation examples are provided and discussed.

A new method for calculating the refractive index of semiconductor thin films retrieved from their transmission spectra

A simple new method to calculate the refractive index dispersion n(λ) from the transmission spectrum of a semiconductor thin film is presented. The proposed method is based on analyzing the fringes of equal chromatic order (FECO) of thin film by solving the interference equation of light waves interfering coherently at two successive minimum and the one maximum between them. A direct relations for FECO order p, refractive index dispersion n(λ) at each FECO peaks and refractive index variation δn(λ) from one FECO peak to the next one are explicitly obtained. The method of calculation is successively applied to a fixed thickness ZnO, ZnS, ZnSe, ZnTe and SiO2 as well as wedge-shape As30Se70 semiconducting thin films. The obtained refractive index dispersion data for all aforementioned semiconducting thin films agree very well with the previously reported data. In wide wavelength range (500–2500 nm), the obtained refractive index dispersions n(λ) data are fitted to Cauchy dispersion function with relative errors in calculating refractive index of order 5.4 × 10−3 at λ = 800 nm and 5.6 × 10−3 at λ = 2500 nm, respectively. Our calculation procedure yields refractive index data agree very well with the refractive index data calculated from the well known Swanepoel method. Finally, a procedure to calculate the film geometrical thickness t is also presented.

Low-Friction Adsorbed Layers of a Triblock Copolymer Additive in Oil-Based Lubrication.

The tribological properties of the dilute solution of an ABA triblock copolymer, poly(11-acrylamidoundecanoic acid)-block-poly(stearyl methacrylate)-block-poly(11-acrylamidoundecanoic acid (A5S992A5), in poly(α-olefin) (PAO) confined between mica surfaces were investigated using the surface forces apparatus (SFA). Friction force was measured as a function of applied load and sliding velocity, and the film thickness and contact geometry during sliding were analyzed using the fringes of equal chromatic order (FECO) in the SFA. The results were contrasted with those of confined PAO films; the effects of the addition of A5S992A5 on the tribological properties were discussed. The thickness of the A5S992A5/PAO system varied with time after surface preparation and with repetitive sliding motions. The thickness was within the range from 40 to 70 nm 1 day after preparation (the Day1 film), and was about 20 nm on the following day (the Day2 film). The thickness of the confined PAO film was thinner than 1.4 nm, indicating that the A5S992A5/PAO system formed thick adsorbed layers on mica surfaces. The friction coefficient was about 0.03 to 0.04 for the Day1 film and well below 0.01 for the Day2 film, which were 1 or 2 orders of magnitude lower than the values for the confined PAO films. The time dependent changes of the adsorbed layer thickness and friction properties should be caused by the relatively low solubility of A5S992A5 in PAO. The detailed analysis of the contact geometry and friction behaviors implies that the particularly low friction of the Day2 film originates from the following factors: (i) shrinkage of the A5S992A5 molecules (mainly the poly(stearyl methacrylate) blocks) that leads to a viscoelastic properties of the adsorbed layers; and (ii) the intervening PAO layer between the adsorbed polymer layers that constitutes a high-fluidity sliding interface. Our results suggest that the block copolymer having relatively low solubility in a lubricant base oil is effective at forming low-friction adsorbed layers in oil-based lubrication.

Mercury Vapor Sorption and Amalgamation with a Thin Gold Film.

Understanding the amalgamation mechanisms between mercury and gold is of fundamental interest and importance to many mercury sensing applications. However, there is only limited and piecemeal discussion in the literature of the mechanisms by which Au-Hg amalgams are formed on thin Au films. Here, we present a comprehensive description of a series of morphological changes occurring in a thin polycrystalline Au film during Au-Hg amalgamation investigated by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), and atomic force microscopy (AFM). These microscopic investigations enable us to offer a coherent explanation for the features and the mechanisms of amalgamation of Hg with Au in the film. We also use an optical technique (fringes of equal chromatic order, FECO) to observe changes in optical thickness and reflectivity of the film. Amalgamation reactions in the film render it inhomogeneous, thus making optical techniques unsuitable as a method for quantitative monitoring of Hg vapor using Au films of this type.

Interferometry of surfaces with well-defined topography in the surface force apparatus

We studied the multiple beam interferometry of surfaces with well-defined microscale features in the surface force apparatus (SFA). The structures investigated consist of hexagonal arrays of microscale cylindrical posts made out of the photoresist SU-8. The ability of the SFA to visualize the profile and topography of the interacting surfaces leads to the observation of discontinuities in primary fringes of equal chromatic order that are caused by the microscale structural features. The shift in wavelengths has been analyzed to extract the post height and compared to independent profilometry measurements. The analysis based on the shift in wavelength is shown to be viable only when the order of the fringe and the position of the discontinuity is precisely known and within the field of view. Analysis of the full profile of the interacting surface for two orthogonal 2-dimensional slices can be used to determine how the surface lattice is oriented within the point of closest approach. Finally, we discuss cases in which the structural features detrimentally affect the spatial resolution of the SFA.

Large Area, Molecularly Smooth (0.2 nm rms) Gold Films for Surface Forces and Other Studies

Using large-area (cm2) single-crystal mica sheets as the templating substrate, we have created correspondingly large template-stripped (TS) gold films (thickness 82 +/- 2 nm) that appear smooth to within 0.2 nm rms roughness over their entire area. These gold films, created without the use of any releasing solvent, are characterized using AFM, X-ray diffraction, multiple beam interferometric fringes of equal chromatic order (FECO), and contact angle measurements. Being molecularly smooth over large areas and (adjustably) semitransparent, these films are especially suitable for use in the surface force balance (SFB), as shown by measurements of the normal force (F) versus distance (D) profiles between such a flat gold surface and a bare mica surface in water. The F(D) profiles are in good agreement with DLVO theory down to molecular contact and indicate that the gold surface is negatively charged under water.

Group refractive index measurement by fringes of equal chromatic order

Fringes of equal chromatic order in transmission across a thin liquid or a thin solid sample inside a wedge interferometer, followed with a grating spectrograph, are produced. A single-shot interferogram of the air and sample regions is recorded. Locations of fringes maxima in the air region are fitted in a numerical procedure based on Cauchy's dispersion function. Then it is used for measuring the interferometric gap thickness. The order of interference in the sample region is represented by a third-order polynomial in the wavenumber for deducing the sample group refractive index. An error analysis of the measured group refractive index is given. The method is applied for measuring the group refractive index of water and mica samples across the visible spectrum. The method measures both the sample thickness and its group refractive index. It is static with no moving parts and suitable for thin liquid or solid samples without immersion liquids.

Group refractive index measurement by fringes of equal chromatic order

Group refractive index measurement by fringes of equal chromatic order

Platinum Nanoparticles at Mica Surfaces

We report a systematic study of factors that influence the incidence of platinum (Pt) nanoparticles produced by the standard method of cutting mica sheets into shapes using a hot platinum wire. Related findings in prior literature are confirmed. Characterization by AFM (atomic force microscopy) shows that fewer particles were produced the thinner the Pt wire and that the density and size of particles were substantially less when using Pt wire not previously used to cut mica. In optimal cases, using 0.0125 in. diameter wire, we obtained ∼0.1% surface coverage; the mean particle height of particles was ∼2.3 nm, and the mean diameter, 15 nm. After detachment from a backing sheet, the particle abundance was reduced by a factor of roughly 2. For Pt wires of the same diameter, the abundance of particles as a function of mica thickness and location relative to the wire was studied. The identification of these particles as Pt was confirmed using a combination of TEM (transmission electron microscopy) and Rutherford backscattering (RBS). After applying normal loads relevant to conditions in the surface forces apparatus, up to 5 MPa, we conclude from AFM characterization that the particles were not deformed by normal load and that their indentation into the underlying mica substrates was negligible. Cutting mica with hot iridium (Ir) rather than Pt wire also produced nanoparticles. Finally, FECO interference fringes (fringes of equal chromatic order) between cleaved mica sheets in close contact were contrasted with and without nanoparticles present. Implications for surface forces measurements are discussed tentatively.

Thickness and refractive index measurements using multiple beam interference fringes (FECO)

We report on the use of optical interferometry employing fringes of equal chromatic order (FECO) in a surface force apparatus (SFA) to determine film thicknesses and refractive indices of confined media for a wide range of separations. In particular, we show how to calculate the surface separation (film thickness) based on two fringes whose contact position was not measured. We discuss the measurement accuracy, and though the theoretical accuracy is 1 Å for all separations, we show that in practice, for large separations, it is very hard to get to this accuracy.

N-Octadecyltriethoxysilane Monolayer Coated Surfaces in Humid Atmospheres: Influence of Capillary Condensation on Surface Deformation and Adhesion

We have investigated the effect of humidity on surface deformation and adhesion of mica surfaces coated with n-octadecyltriethoxysilane self-assembled monolayers using a surface forces apparatus. The Maugis model of contact elasticity based on linear elastic fracture mechanics is used to analyze the results. The Laplace pressure is assumed to act in the “Dugdale” zone outside the contact area to account for capillary condensation. We measure the radius of the contact area as a function of applied load and use the model to obtain the surface energy and elastic constant of these surfaces for humidities ranging from 0 to 99%. The limiting values in dry and near-saturated conditions are as expected from well-known theories. A significant result is that we also obtain the surface energy for intermediate humidities. Increasing humidity modifies the deformed shape of the surfaces in contact due to capillary condensation. The sharp bifurcation at the edge of the contact zone for low humidities (JKR-type contact) is replaced by rounded edges (DMT-type contact) with increasing humidity. This is predicted by the Maugis model and is experimentally observed using optical interference fringes of equal chromatic order. We are able to separate the capillary condensation and solid−solid contributions to the adhesive force because the Maugis model allows a direct calculation of the area on which the Laplace pressure acts. At humidities approaching saturation the forces due to capillary condensation dominate monolayer−monolayer adhesion. At lower humidities both capillary condensation and direct monolayer−monolayer interaction contribute to the overall adhesion.

Interferometric determination of refraction and dispersion of human blood-serum, saliva, sweat and urine

Multiple-beam interference fringes of equal chromatic order are produced in air and liquid sample interferometric gaps. The two gaps are of the same thickness and simultaneously enclosed in a wedge interferometer. A single shot interferogram containing fringes in the two gaps is sufficient to deduce the needed experimental data. Locations of the fringe maxima, in the two gaps, are introduced in a non-numerical procedure for determining the gap thickness and the liquid-phase refractive indices across the visible spectrum. The method has been used for measuring the phase refractive indices of human blood-serum, saliva, sweat, urine and water liquids. A third-order polynomial dispersion relation is applied for fitting the measured phase indices. Group refractive indices have been derived and fitted to the same dispersion formula.

Application of fringes of equal chromatic order for investigating the effect of temperature on optical parameters of a GRIN optical fibre

Multiple-beam white light interference fringes across a GRIN optical fibre immersed in a liquid wedge interferometer placed in front of a grating spectrograph are produced. They are used to investigate the effect of temperature on the optical fibre parameters of both the cladding (pure SiO2) and the core (GeO2-doped SiO2). A two-term Sellmeier dispersion relation is adopted and fitted to the experimental refractive index data. Then a temperature-dependent Sellmeier formula is deduced to study the effect of temperature on the refractive index of the fibre and its dispersion in addition to all of its optical parameters. These parameters are the average energy gap, the variation of the thermo-optic coefficient with photon energy, the refractive index difference, the numerical aperture, the normalized frequency (V-number), the number of modes, the material dispersion and the zero-dispersion wavelength.

Interferometric determination of refraction and dispersion of a birefringent material: numerical procedure

Air, liquid and solid sample interferometric gaps of the same thickness and simultaneously enclosed in a wedge interferometer are used to produce fringes of equal chromatic order. A mica sample of dimensions 2×5 mm 2 and an immersion liquid of the same refractive index are used. A single shot interferogram containing fringes in the three gaps is sufficient to deduce the needed experimental data. Locations of fringe maxima are introduced in a numerical procedure to retrieve the sample and liquid refractive indices across the visible spectrum. The numerical procedure is based on a simple dispersion function of wavelength and wavenumber. A modified two-term Sellmeier dispersion formula has been used for fitting the experimental data and deducing the needed dispersion parameters.