Aperture total internal reflection (A-TIR) for contact angle measurement

Abstract

Recently, aperture total internal reflection (A-TIR) was proposed to characterize the microdroplet patterns, such as the coverage fraction of the droplet, by placing the aperture just in front of the detector in classical total internal reflection (TIR). However, the reflection from the curved liquid-air interface was simulated using simple two-dimensional modeling, causing inaccuracy in A-TIR measurement. In addition, the reflectance dependency on the aperture size and the working distance of the aperture was not investigated, hindering its applications. In this study, the simulation based on three-dimensional (3-D) ray tracing with Fresnel equation modeling was successfully developed and verified to explain the internal reflection from the curved droplet liquid-air interface. With this developed 3-D modeling, A-TIR characteristics were explored using the parameters of the aperture size and the working distance of the aperture as well as the droplet surface coverage fraction, which shows a good agreement between the experiment and the simulation. Furthermore, it was for the first time demonstrated that the droplet contact angle can be effectively determined by obtaining the droplet thickness from the analytic quadratic solution by subtracting the measured reflectance at the two different sized apertures and using the spherical profile relation. Low contact angles in the range of 1∼ 15° were determined experimentally for the micro- and macro-sized droplets with a droplet diameter of 70 ∼ 7000 µm by the measured thickness of 1 ∼ 450 µm using A-TIR and compared with Fizeau interferometry and side-view imaging to show a good agreement. The simulation shows that A-TIR can be a new optical diagnostic tool to measure the contact angles 0 ∼ 90° regardless of the droplet diameter by adjusting the aperture size and the working distance. In addition, A-TIR can effectively determine the small contact angles less than 5°, even ultrasmall contact angles less than 1° for the submicron thickness, not requiring the complicated microscope setup. Thus, we can observe a sessile droplet's drastic contact angle change during wetting phenomena from 90° to 0° on the same A-TIR setup. Additionally, A-TIR can be used for a single or an array of micro or nanodroplets with a microscope objective by reducing the laser beam size and scanning methodology.

Investigating the origin of the far-field reflection interference fringe (RIF) of microdroplets

“…2(a) has the dual convex-concave profile to form interference fringe on the screen away from the droplet as in Figs. 1(a 25 and Fig. 1(c).…”

“…The microdroplets are prepared by microcontact printing (μCP) and syringe methods on the representative oleophilic, plain, and oleophobic coated SF 10 glasses (substrates), which are provided by CEKO, Co. Ltd. 25,37 The interference fringe is formed on the far-field screen away from the droplet in internal reflection configuration with an equilateral triangle prism (SF10, n p = 1.732 at 633 nm; Esco Optics) below the critical angle. 25,37 The indexmatching liquid (Cargille Labs) is put between the glass substrate and the prism. 36,37 The study shows that the substrate material and the shape would not affect the interference fringe formation.…”

“…4,5,11 Furthermore, the measurement of the geometric shape of droplets is substantial in applications, such as the spreading of droplets, 4,5 the evaporation/condensation of sessile droplets, [12][13][14] microfluidics, 15 inkjet printing, 10 and microlens array. 16 There have been various methods for droplet profile measurement, such as the droplet height or thickness, and the contact angle, based on goniometry, 17 interferometry, 6,8,[18][19][20][21][22][23][24] total internal reflection microscopy (TIR), 25,26 atomic force microscopy (AFM), [27][28][29] ellipsometry, 30 and optical microscopy. 31,32 The interferometry, AFM, and ellipsometry can measure the droplet profile on a nanometer to sub-micrometer scale, enabling the profile determination in the intermediate region of the droplet.…”

“…36 The droplet height is determined by counting the fringe numbers in the OPD relation, showing a linear dependency on the fringe numbers and an excellent agreement with the experimental measurements and the ray tracing simulation. Furthermore, a raytracing simulation was performed based on the custom-designed MATLAB program 25,37 to provide the details of the droplet profiles. The interfering rays reflected near the inflection point in the intermediate region produce the outermost fringe of the concentric interference pattern on the screen, away from the sample droplet.…”

“…The reflecting rays from the convex and the concave profiles of the droplet are projected on the far-field screen to form interference fringe patterns. The reflected rays are diverged at a larger area because of the droplet lens effect, 25,37 to facilitate counting the fringe number (FN) and radius.…”