Nonlinear Agglomeration of Bimodal Colloids under Microgravity

Colloidal suspensions are discrete mixtures of two or more materials that interact to form two or more immiscible phases. One phase must be continuous while the other phases are discontinuous and remain stabilized within the continuous phase. The phases may be solid, liquid, or gas, thus creating many variations. Consumer products based on colloidal systems include, but are not limited to, paints (Tadros, 2010), ceramics (Lewis, 2000), foams (Kontogeorgis and Kiil, 2016), personal care products (Tadros, 2008), and pharmaceutical formulations (Sinko and Martin, 2006). These examples, among others, require that the dispersed phase remain stable over the lifetime of the product, in which the solution does not separate or form agglomerates. Thus, fundamental investigations into long-term colloidal stability are applicable toward improved shelf-life and consistent performance of everyday products.

Long-term colloidal stability depends on a series of carefully balanced interaction forces (Lyklema, 2000). While the mechanisms for stabilization can vary, most require balancing the attractive and repulsive forces within the system (Grządka, 2015). The attractive forces within a colloidal suspension vary from system to system, but the main sources of attraction are from van der Waals forces. Van der Waals forces, which include London dispersion forces, dipole-dipole interactions, and dipole-induced dipole interactions, tend to only act at close distances of <10 nm, and decrease in magnitude with increasing distance (Hiemenz, 1972; Ottewill, 1997). Since they are predominantly attractive, they must be counteracted by repulsive forces to maintain system stability (Israelachvili, 2011).

The source of repulsive forces in colloids also varies between systems. One of the simplest is electrostatic repulsion, in which particles of like charge experience Coulombic repulsion, thus counteracting the attractive van der Waals forces (Walz and Sharma, 1994). Of particular importance to this study is charge regulation, an electrostatic stabilization method (Bakhshandeh et al., 2020; Ninham and Parsegian, 1971). Charge regulation relies on a charged double-layer effect to repel other particles: charged microparticles suspended in an electrolyte adsorb to the particle surface creating an ion layer, and counter-ions gather to create a second ion layer suspended just outside the inner layer. If the electrical potential between the double layers of two particles is greater than the attractive van der Waals forces present between them, the system will remain stable (Ottewill, 1997).

Of recent interest, nanoparticle haloing (NPH) can also be utilized to effectively counter the attractive van der Waals forces. This colloidal stabilization technique manipulates properties of particles in a binary mixture that was first described by Tohver et al. (2001). The size of one population of particles is on the order of micrometers and the other on the order of nanometers. The zeta potential of the larger particles is set at its isoelectric point, in which the only intermolecular forces acting upon the microparticles are van der Waals forces, while the nanoparticles are highly charged. At particular proportions of nano- and microparticles, nanoparticles both adhere to and form halos around the microparticles to create an effective electrostatic repulsive barrier to screen the van der Waals forces and stabilize the suspension (Moradi et al., 2019a). At this state, the suspension is metastable and forms an ordered crystalline solid phase.

The surface charge of a particle submerged in a colloidal solution creates two parallel layers of alternating positive and negative ions, referred to as the electric double layer. The first layer is due to the chemical interactions of the surface charge adsorbing ions of the opposite charge of the surface charge. The second layer, called the Stern Layer, is created due to Coulombic forces of the first layer. The ions within this Stern Layer are not as strongly bonded as the first layer but have the same charge as the particle's surface. The zeta potential is found on the surface of this double layer, called the slipping plane, determined by the difference in potential of the medium and potential of the double layer attached to the particle (Hunter et al., 2013). Zeta potential on an absolute scale is directly proportional to the stability of the colloidal solution – a greater magnitude of zeta potential enhances colloid stability, preventing particle aggregation. For example, zeta potentials near ±15 mV may experience rapid aggregation, whereas zeta potentials in the range of ±40–60 mV could remain stable long-term, depending on the interactions present and respective sizes of the colloidal particles (Kumar and Dixit, 2017).

Where NPH requires negligibly charged microparticles and highly charged nanoparticles within a very narrow concentration range, bimodal systems only require that the two particles be of different sizes. One of the earliest models of bimodal colloids was pioneered by Asakura and Oosawa (1958) with their introduction of the depletion region – spaces between large particles small enough to exclude smaller particles are subjected to osmotic pressure pushing the large particles together, due to the entropic tendency for the small particles to reduce the concentration difference between the interparticle space and the bulk. Later models included a wide range of effects due to variables such as dissymmetrical species, concentration differences, long-range electrostatics, polydispersity, polymers, and more (Chatterjee and Schweizer, 1998a, 1998b; Chu et al., 1996; Shah et al., 2003; Walz and Sharma, 1994; Weight and Denton, 2018). In addition to thermodynamic metrics such as potential energy balances, changes in enthalpy, and partition functions, other options have been explored for controlling colloidal stability. A team of researchers from University of Washington exploring the effects of altering particle ratios were able to limit particle transport enough to temporarily halt the agglomeration of thermodynamically unstable systems (Liu et al., 1991; Yasrebi et al., 1991). Another group in 2016 found that attractive and unstable systems could remain stable as long as the entropy of mixing resulted in strong enough negative free-energy to discourage phase separation (Mo et al., 2016).

The colloidal suspension observed in this study is a suspension of like-charged particles at a nanoparticle–microparticle size ratio of 60:1, microparticle volume fraction of 10⁻², and nanoparticle volume fractions between 10⁻³ and 10⁻⁴. Experiments performed by Moradi et al. confirmed that only sub-monolayer adsorption of nanoparticles occurs within this volume fraction and size ratio for NPH systems. The significant difference between this system and NPH systems is that the microparticles in this system are charged. Since the micro- and nanoparticles are like-charged, electrostatic interactions between particles disfavors adsorption even more strongly than in NPH systems. Consequently, there are free nanoparticles in solution to contribute to depletion interactions and cause phase separation.

Cluster size analysis is a basic 2D mathematical model used to describe a binary image as a series of aggregated clumps. The model developed for this analysis uses a local thresholding algorithm coupled with a watershed algorithm to convert the images to a binary format in which white pixels represent particle agglomerates. From the binary image, connected regions of white pixels are identified as clusters. Use of local as opposed to global thresholding minimizes the sensitivity of such size analysis on specific thresholding parameters.

Particles that can be visualized using a standard microscope (diameters >1 μm) typically sediment within seconds or minutes, unless their density is matched with the suspending medium (Wiederseiner et al., 2011). Gravity hinders the observation of fundamental physical mechanisms guiding particle interactions, including identifying particularly the self-assembly of such structures. Thus, over the past few decades there has been a thrust in microgravity colloid research on the ISS (Ansari et al., 1999; Swan et al., 2012; Veen et al., 2012). In response to the growing interest, NASA established the Advanced Colloids Experiment (ACE) program to coordinate future efforts on the ISS. Specifically, this study is part of the Advanced Colloids Experiments-Heated-2 (ACE-H-2) series of experiments. The Light Microscopy Module (LMM) was developed to visualize the colloidal interactions in this experiment. The LMM on the ISS is an automated microscope that has been built in stages (Lant and Resnick, 2000). It allows flexible imaging (e.g., bright field, dark field, phase contrast, confocal microscopy) for physical and biological experiments and can be commanded from the ground. The LMM accommodates sample changeout and fluid containment and includes a glovebox for on-orbit sample manipulation. This unique capability can support a large set of experiments that require visual imaging of a small test sample.

For our experiments forming part of the ACE-H-2, benzyl chloride functionalized silsesquioxane microspheres (600 nm, synthesized using the method described by Moradi et al. (2019b) at 0.01 volume fraction) were suspended along with three different concentrations (0.1%, 0.05%, 0.01% by volume) of charged zirconia (ZrO₂) nanoparticles (from Nyacol Nano Technologies Inc., Ashland, MA, USA). The manufacturer-reported diameter of the nanoparticles was 10 nm, with a Gaussian size distribution in the range of 5–15 nm. The media was an aqueous solution of nitric acid (Fischer Scientific, Pittsburgh, PA, USA) set at 1.5 pH, intended to reach the silsesquioxane microparticles’ isoelectric point. According to NPH literature, these volume fractions provide the greatest stability range while allowing visibility of individual clusters via confocal microscopy (Tohver et al., 2001). However, later testing found that the functionalized silsesquioxane's isoelectric point was not equal to that of silica as advertised, but 2.8 pH, making this system bimodal, and not a NPH system (Moradi et al., 2019b). Fifteen samples (five of each nanoparticle concentration) were sealed in 2.5 mm diameter, 0.2 mm depth disc-shaped circular wells with a stainless-steel mini-rod, as shown in Figure 1. Our samples launched on Atlas V OA-4 on December 6, 2015.

Figure 1

Prior to observation, an astronaut manually mixed each sample well by agitating the mini-rod using a magnetic wand for 2 minutes before loading the sample into the LMM. Samples were illuminated from the side to induce scattering since the particles were not fluorescent. The sample wells were observed over the course of 12 days at an approximate rate of 10 images per day per well. The image files were labeled with a timestamp and magnification level, stored in the station's computers, and analyzed by methods as described later in the paper. Not all of the wells were analyzed, as some were compromised (excessive bubble formation, inadequate mixing, etc.). Additionally, an undocumented time of long as 5–8 h passed between mixing and the start of imaging. Nine of the fifteen uncompromised wells were analyzed: three low-concentration wells at 0.01% ZrO₂, three intermediate-concentration wells at 0.055% ZrO₂, and three high-concentration wells at 0.1% ZrO₂. Figure 1 shows one well at the beginning and end of imaging. The two large circles inside of the well are air bubbles introduced during sample transport to the ISS and were unavoidable.

Python (Python, 2021) is a high-level programming language used in a wide range of scientific applications, and is most commonly coupled with external, open-source Python libraries. Colloidspy (Cecil, 2021), an image analysis package, was developed to analyze the images in this study. The analysis methods are a simple Python implementation of methods used by ImageJ for particle detection (Papadopulos et al., 2007), with the notable addition of local thresholding to minimize threshold sensitivity.

Colloidspy (Cecil, 2021) utilizes NumPy (Harris et al., 2020), SciPy (Virtanen et al., 2020), pandas (McKinney, 2010), scikit image (Van Der Walt et al., 2014), and OpenCV (Bradski, 2000) Python packages. Package construction, design, and assumptions are discussed in detail in the following thesis and corresponding GitHub page: Cecil (2021).

A region of interest (ROI) was selected for a series of images. All the images in the series were cropped to that ROI; then a local thresholding algorithm was applied to convert the image to binary, leaving only clusters in the frame. The images were cleaned to remove single-pixel noise, and a watershed and contour detection algorithm was applied to separate discrete clusters that appeared to be touching in the image. Finally, individual cluster data, including area, perimeter, convexity defects, and circularity were extracted and exported for further analysis. A visual example of this analysis progression is shown in Figure 2. As another visual aid, Figure 3 shows sample images of average particle sizes of 800 μm², 1100 μm², and 1400 μm².

Figure 2

Figure 3