Preparation of a Non-Evaporating Contact Angle Part 4

CHAPTER VI DISCUSSION The measurement of the contact angle of a liquid on a surface is related to wettability and surface energy information. The literature study confirmed that although many of the adaptations were primitive, three theories could be combined with improvements in digital imaging and computing to bring contact angle measurements to the modern coating or adhesive production facility. The three primary approaches to looking at a drop; the side-on (Young), top-down (Bikerman) and reflected angle (Langmuir) methods present their own challenges and advantages when measuring a drop. In order to effectively compare these methods, several standard reference materials were created. The first step in the contact angle method comparisons was to determine the accepted contact angle for each of the standards. Table 1 described the mean contact angle for each of the standards as analyzed using the images taken using the side-on approach with the digital microscope and the contact angle calculated using the Manual Points Procedure. The calculations revealed, after five measurements, that the uncertainty in each of the measurements was very low. Goniometer measurements in industry typically have a resolution of between 0.01and 0.1 degrees for contact angle, while the measurements using the lab accepted technique has a resolution of between 0.3 and 0.6 degrees. 34, 35 Although the data collected here had lower resolution, it is still comparable to the goniometer. The side-on, microscope, Manual Points Procedure analysis was chosen as this approach most closely relates to the lab practice goniometer methods. The Manual Points Procedure also has the advantage of the drop not needing to be level before analysis. Since the DinoLite microscope has the highest resolution and there are five points taken into account in analysis, the edge of the drop is clearly outlined by the user without needing to alter any threshold values allowing for optimum measurement of the tri-phase point. These values then can be used as the accepted lab standard for which all the methods will be compared. Side-on Methods and Standards Once the accepted contact angle was measured, the two approaches to the side-on method were analyzed. As Williams, et al., 24 explained, the side-on method with the camera placed perpendicular to the drop works for contact angles of greater than or less than 90 degrees. Therefore, the first attempt of the side-on method was made to use a ruby ball mounted in a gage card to simulate a sessile drop. Both the ruby ball and the gage card on which it is mounted are well machined, giving a profile similar to a sessile drop. Unfortunately, due to the thickness of the gage card, the neither ball could be mounted in the gage card to mimic a contact angle of less than 90 degrees as Figure 24 illustrates. The left side shows a view of the ruby ball so that the gap between the ball and gage card can be seen while the right side shows how the ball was held in the gage card. Figure 24. Ruby Ball in Gage Card at Less than 90 Degrees The ball cannot provide a clear tri-phase point when mounted under the gage card as the gage card appeared to be far too thick for the under-mounting approach. The ruby ball was then only used for contact angles over 90 degrees. The half-angle and Brugnara methods were applied to the images of the ruby ball using the microscope with and without the mirror as well as with the iPod with the mirror. The prism was removed as a method because the prism did not provide a clear enough image for analysis as shown in Figure 25. There are rings present in the image that are internal reflections within the prism which cause cloudiness in the image. Figure 25. Example of Image Taken with the Prism Specifications for the mirror and its placement were optimized here as well. The mirror used was a 15 mm by 15 mm highly polished piece of stainless steel bent 90 degrees to form the mirror, supplied by our colleague Dr. Anslem Kuhn in the United Kingdom. In regards to placement relative to the standard, the mirror was placed one inch from the edge of the standard. The microscope lens was 2.22 cm from the top of the drop while the iPod, with its 0.64 cm thick lens, was 4.13 cm away from the standard. These values were not optimized, but merely used to maintain consistency in this experiment. If the mirror was placed further away, or the microscope or iPod placed higher, then the distance from the standard would be increased causing less resolution in the image. In Figure 20, the less than 90 degree standards measured with a mirror were about two degrees lower and the greater than 90 degree standards were measured almost four degrees lower. It is appropriate to differentiate between the systematic and random error seen throughout the data presented here. For example, the systematic error seen in Figure 20 lies with the fact that the mirror images produced contact angle values decisively lower than the zero point value. The random error laid within the variance among the image measurements since not all were low. The random error can most likely be attributed to the combination of the contact angles provided by the half-angle, Manual Points, and Circle Best Fit procedure being used during the analysis of the less than 90 degree standards and just the half-angle and Manual Points procedures in the greater than 90 degree standards. The systematic error can be attributed to either the analyst or the placement of the mirror. By improving measurement technique, the analyst’s contribution could be removed. To correct for the mirror, an analysis of the attributes of the mirror including natural reflectance could be measured. Analyzing the attributes of the mirror and optimizing its placement in relation to the standard and the iPod or microscope can also decrease the error seen in measuring the contact angle of the standards. Even checking into how much light is being added to the image by the mirror could help to alleviate any problems with contrast in the images. A simple screen eliminating the amount of light hitting the mirror and an optimized placement of the mirror could decrease both the systematic and random error seen in the analysis of the images taken using the mirror. By replacing the gage card with a piece of a punched aluminum sheet, __ micrometers in thickness, the steel ball could mimic the less than 90 degrees contact angle with a more distinct tri-phase point. The images in Figure 26 illustrate the suggested approach. The thinner sheet of aluminum allows the small crevice created between the ball and gage card, as seen on the left in Figure 26, to be minimized. Figure 27 is an image of the steel ball in the piece of aluminum with a hole punched in it. Ball Mounted on Underside of Gage Card Ball Mounted on Underside of Thin Aluminum Sheet Figure 26. Comparison of the Gage Card and Punched Thin Aluminum Sheet Figure 27. Under-mounted Steel Ball in Punched Aluminum To try to improve on the punched aluminum, several attempts were made to mount the balls in a plastic. Mounting the ball in plastic would have allowed the creation of a rugged standard prototype. Table B1 in Appendix B shows the images of the attempts made. All of the attempts proved to be ineffective as the plastic either created a meniscus too far up on the ball or air pockets, both of which prevented a clear view of the tri-phase point. The data from all four standards were analyzed using the images taken with the microscope, the microscope with the mirror, and the iPod with the mirror. Once the data was imported into MiniTab, Table 2 was generated to describe the error in the three different approaches to the side-on methods. The error calculations were done using the Manual Points Procedure and half-angle method for all four standards, while the less than 90 degree contact angle standards were also measured with the Circular Best Fit approach. The Circular Best Fit approach uses edge detection by the computer while the Manual Points Procedure uses the naked eye as the edge detector. The Circular Best Fit approach worked poorly on the images taken using the mirror, causing the higher variance seen in the contact angles measured in Table 2. The table suggests that even though the lab accepted value was the side-on method, the mirrors still had a high amount of variance. The boxplot in Figure 15 compares all of the standards with all three measurement methods. The Brugnara Manual Points Procedure method was chosen as the preferred method for side-on analysis, and Figure 20 and Table 7 showed that the microscope without the mirror provided the lowest average error. By partitioning the data by standard, method, and technique, the analysis shows that the contact angle measurements are very dependent on the image analysis. The worst analysis method was with the iPod and mirror set-up on the under-mounted steel ball analyzed with the Circular Best Fit approach as described in Figure 17 and Table 4. When looking at the image, it was clear that the reflection on the edge of the ball made it too hard for the computer to see and appropriately measure the edge. The Manual Points approach allowed the analyst to pick the edge of the standard which removed the need for the threshold values and the possibility of the computer not recognizing the actual edge. Almost all of the other measurements lied within a five degree range above and below the zero point, which then became the accepted range of values to determine if an analysis method was done accurately. Those measurements that lie outside were taken using the mirror set-up as seen in Figure 20 and Table 7. Even though the direct side-on approach was the lab accepted standard, the mirror had too much variability in measurements, even though the majority lie within a 10 degree range as shown in Figure 16 through Figure 19 and Table 2 through Table 6. In Table 3 and Figure 16, the pressed aluminum standard when measured using the iPod and mirror had a greater amount of random error no matter which analysis technique. Although the side-on approach with the Manual Points procedure was chosen as the lab accepted value, the mirror approach using the microscope had more precision across all three analysis techniques, but the values were right around two degrees lower than the zero point. The under-mounted steel was difficult to analyze with the iPod as well, with the Circular Best Fit approach having an average error of 11 degrees from the zero point. The reason for this can be attributed to the computer being unable to accurately find the edge of the ball due to poor contrast. The side-on approach had the lowest deviation across all three analysis methods, with the mirror with the microscope not too far behind, as seen in Figure 17 and Table 4. The data presented in Figure 18 and Table 5 outline that for the ruby ball both the mirror methods measured the contact angle right around five degrees lower than the zero point. The microscope also had the highest amount of random error in the contact angle measurements. Even though the side-on approach was the preferred method, the iPod had lower variance than the microscope without the mirror. Through analysis of the steel ball data as shown in Figure 19 and Table 6, it can be discerned that the steel ball needed better contrast for the images taken with the iPod and microscope with the mirror. The amount of variance, although under the five degree limit, was still rather large compared to the side-on approach. All the analysis done on the images with the mirror and with the strict side-on approach asserted that the mirror accounted for some of the systematic error visible in the measurements. The systematic error can be attributed to the distance created from reflecting the image to the camera and the lighting on the standards that could have come from the mirror reflecting excess room light into the image. The excess light and distance were not explored in this study. Since the lighting played a big role in the image quality, the lighting of the drop became one of the primary concerns when looking at the contact angle error. Figure 21 and Table 8 when analyzed confirmed that by using a screen to block light the problems with blurry edges in the images are eliminated. In some images, the tri-phase point was too unclear from shading caused by the gage card or aluminum that the standard was resting on or in. The unclear edges and tri-phase point prevent one from effectively being able to apply the drop shape analysis techniques to the images which make any measurement made likely to be high in error. The use of diffuse light from directly behind provided a much clearer image for the steel ball, aluminum, and ruby ball standards. The under-mounted steel ball standard showed almost no error dependency on the presence of a screen. Top-Down Methods and Standards Since the tri-phase point could not be used to measure the contact angle, the Bikerman method and Top-Down Calculator spreadsheet were applied. The methods require the placement of a calibration object in the image. In this study, a metal washer provided the calibration object. The internal circumference of the metal washer was measured with a caliper. This allowed a conversion between pixels and millimeters so that the volume of each standard could be calculated properly for use in Equation 3. The initial images were taken with the digital microscope as done in the side-on methods. The Top-Down Calculator spreadsheet allows for the analysis of drops only when the volume is known. The second round of images used a cell phone camera rather than a microscope. The approach used in the Williams 25 paper was recreated using the ruby ball, steel ball and aluminum standard. With all three standards, the cell phone cameras provided pictures that were of good enough quality to apply the Bikerman method and measure the contact angles. Figure 22 showed that the top-down method had a higher error associated with it which was not brought on by the use of either device since in the boxplot both devices were very close in the angles measured, but were way off the zero line. The top-down method only worked well for the aluminum standard, it worked very poorly for the under-mounted steel ball. The aluminum standard was measured right around five degrees lower than the accepted value while the under-mounted steel ball was closer to 13 degrees lower. The five degrees of the aluminum standard is still consistent with the five degrees seen in the side-on approaches. The issue with the steel might be due to the ball not sitting perfectly flush with the punched aluminum which can create a gap that the Bikerman equation cannot account for. As stated previously, the average error among industry methods is between 0.01 and 0.1 degrees, so the top-down method had a very high variability as compared to the industry standard. Reflected Angle Methods and Standards In order to mimic the Contact-θ-Meter, a small fiber-optic light was used to highlight the drop in a similar fashion so the iPod could be used as the viewing tube. The Theodolite application measured the elevation of the iPod through focusing the optical center line of the camera on the tri-phase point facing the light. The application provided an elevation instantaneously, which must then be plugged into Equation 6 for φ, providing an excellent imitation of the Contact-θ-Meter. Figure 23 demonstrated the error of the Contact-θ-Meter and the iPod. The reflection on the aluminum prevented a good analysis with the Contact-θ-Meter which caused the higher contact angle measurements, even though all the measurements were still under the five degree error in the other methods. The iPod and the Contact-θ-Meter both analyzed the under-mounted steel ball a tad bit lower than the accepted contact angle value, but still were under the previously measured five degree error. The Contact-θMeter values were all very close to each other suggesting that the Contact-θ-Meter was more consistent than the iPod, but the iPod still was within the error range. The iPod and Contact-θ-Meter were very similar in error demonstrating that the iPod might be an acceptable substitute for the Contact-θ-Meter in the field. Three standards showed promise as non-evaporating standards. The fragility of the aluminum foil prevents its use as a standard because the dome-shaped protrusion is easily dented. One improvement would be to pour liquid aluminum into some type of mold so that the low cost would be maintained, but the problems with deformability could be eliminated. The ruby ball would be a fair standard, but due to its higher cost it is not ideal for use in the field. The steel ball is a lower cost alternative to the ruby ball and does not show any problem with being used to mimic contact angles of greater than or less than 90 degrees. The preferred size for the steel ball is relative to the contact angle measurement required. The smaller the contact angle one wants to mimic, the smaller the size of the ball. A series of these balls could be mounted in such a way to mimic a variety of contact angles at one time with one type of standard. The main requirement is that the appropriate ball-hole combination be chosen to mimic theta.