Stefanus - it can be as simple as taking a close-up photo of the drop on the crystal (take the image a few seconds after applying the liquid due to evaporation) and using a protractor (software-based or physical) to measure the angle manually from the picture. Adjust the lighting beforehand so you can get good contrast between the drop and the background. It may even be possible to do the whole thing by smartphone by taking a picture and using an angle measure app. Won't be the most accurate but will give you an idea.
The best way to do it is by using a goniometer device, which involves a camera and an image processing software. This device will give you an accurate contact angle.
Similar to what was suggested by Karl. You would need a high-resolution imaging device, a levelled stage and a diffused backlight. I would imagine the droplet such that the camera is not pointing at the surface at an angle. Your image should show clear interfaces between the liquid, solid and air. After the imaging process, a simple matlab code can be used to find the liquid-air interface and fit a circle to the droplet which gives the coordinate for the centre of the circle (assuming the droplet is under the capillary length and takes the shape of a spherical cap). A line can be manually drawn (or automatically with a few more lines of matlab code) along the baseline (the surface). You can then calculate the contact angle using the formula: Theta(e) = pi - acos(h/R), where Theta(e) is the contact angle, h is the distance from the centre of the fitted circle to the baseline (y coordinate of the centre of the circle minus the y coordinate of the baseline) and R is the radius of the fitted circle.
You don't necessarily need a high-resolution camera. Perhaps a good camera on a smartphone would suffice. What kind of camera do you have? As long as you can see the drop and the bottom surface clearly then I think you should be able to measure the contact angle.
I'm submitting to the journal CrystEngComm a manuscript in which we propose a simple and cheap method to measure (with high accuracy) the contact angle of saturated solution droplets on calcite cleavage faces. At the beginning of the next week I'll be able to send you a pre-print of this paper, if you are intersted in.
You can trying finding its equivalent contact angle reading for its bulk material and you can use it to draw a relationship. eventhough at the nanoscale the properties might be different that the best possible way
@stefanus, kindly get a material with high CaCO2 content like limestone modified it the same way as you did to the nanoparticle. Afterwards, you can conduct contact angle experiment to find its hydrophobicity.
Or
Compress the nanocrystals into a bulky material under pressure and conduct contact angle measurement to find out.
Your problem may have been solved but someone else might need this.
Well, You can take a clear picture of the droplet using any type of camera as long as the picture is clear when converted into gray-scale. Then you can measure the contact angle accurately using the plugin "Low-Bond Axisymmetric Drop Shape Analysis" (LBADSA) in imagej software.
imagej software is available for free for everyone as well as the LBADSA plugin.
Please read the plugin manual carefully to get accurate results.
You will find everything you need in the following link:
I think that there was a method - you pack a thin glass column with your powder, and put the bottom end in your liquid. The capillary rise depends on the contact angle and the size of the pores. The tricky part is how to determine the size of the pores from the size of the nanoparticles.
U can use digital microscope available on Amazon online shopping. With this product up to 1000x magnification and a cd software will be provided. After installation software connect digital microscope and take droplet image. The contact angle can be measured by using product cd software or by plug in Image J software