Colloidal gels are used in applications such as water purification, skin creams, and also show up in some food products such as jellies and jams. In food, colloidal gels modify the texture and shelf-life stability of the food. Our NASA-funded study of colloidal gels should improve our understanding of long-term stability of colloidal gels, as well as how they initially form.

One project we are pursuing is the study of colloidal gels made from highly polydisperse particles: particles of a wide range of sizes. This is more realistic for industrial materials, as compared to a lot of prior work which studied particles that were are nearly the same size. Thus, our work will help understand the structure of these more realistic, easier to make colloidal gels.

Colloids are small (micron-sized) particles in a liquid. In these experiments, the particles are made to be sticky, so they stick together into a network of tendrils of particles. This is the colloidal gel state. The ACE-M-1 experiment was done on the International Space Station so that the colloidal gels could be studied in microgravity conditions. The reason microgravity is important is that, as the particles begin to stick together, they form heavy clusters that can sink in normal gravity. This ultimately limits the shelf life of a colloidal gel, but also changes the overall structure. We wish to understand what the gel structure would be like if this limit is overcome in microgravity conditions.

RESULTS FOR MICROGRAVITY DATA: The ACE-M-1 data set has nine distinct experiments on 8 different samples, where the different samples are made with different levels of attractive interaction – that is, different levels of particle stickiness. Undergraduate student Swagata Datta studied the ACE-M-1 data in 2022 working with the Principal Investigator (PI) Eric Weeks, and subsequent analysis in the past year was primarily done by the PI. We have determined that of the nine experiments, four are suitable quality to be fully analyzed. These experiments have 50-60 hours of data each. Fortunately, these four experiments include the one with the highest attractive interaction, and also the one with the lowest attractive interaction, thus spanning the entire range. The samples are composed of equal amounts of small (1.8 micron diameter) and large (2.2 micron diameter) particles.

Much of our analysis and results was reported in last year’s annual report. We briefly reprise the key points here. First, the colloidal gel samples show aging: the dynamics slow down as a function of time. Second, the slowing of dynamics is related to particles sticking together over time. That is, even particles stuck in a gel still undergo some Brownian motion, and this can cause coarsening of the gel: particles occasionally rearrange into more stable configurations.

In the past year, we have elaborated on this analysis by examining the role of freely diffusing particles. Initially, when the samples are first formed, the samples that have colloidal gels present at the earliest stages of observation also have some freely diffusing particles; this is about 10 – 40% of the small particles. Over the course of tens of hours, these particles become incorporated into the gels. Even separating out these particles from the analysis, the particles that are in the gels – whether initially or at long times – also slow down over time. This indicates that the gel partially restructures itself into more stable configurations, or perhaps that as the free particles are added to the gel, they do so in a way that makes the entire gel more rigid.

Additionally, in last year’s NASA Task Book Report, we noted that for the non-gel forming sample (with the least amount of depletant polymer, and thus least attractive interactions), the number of particles observed over time decreased dramatically. A conversation with Prof. John Crocker (University of Pennsylvania) shed light on the problem: he pointed out that they are most likely sticking to the sample chamber walls due to the depletion force. The depletion force is twice as large between a particle and a wall as between two particles; so while the depletion force is not sufficient to stick the particles together to form a gel, it is enough to cause particles to stick to the walls.

NEW GROUND-BASED EXPERIMENTS: Two years ago we started ground-based experiments on colloidal gels, and in the past year this effort has been led by lab technician Ben Lonial. Ben earned his undergraduate degree in physics (with honors) from Emory University in May 2023. He took a gap year and spent it focusing on the NASA project. Ben made colloidal gels with particles with extreme size polydispersity.

Our goal is to understand how the mixture of particle sizes changes the gel structure. While the ACE-M-1 data uses two different particle sizes, they are fairly similar in size (1.8 micron and 2.2 micron diameter) and the gel structure does not vary a huge amount due to these sizes. On the other hand, with the larger range of sizes in Ben’s new samples, we see differences. The size distribution is roughly log-normal, with the largest particles more than 15 times the size of the smallest particles. The volume fractions studied ranged from 0.01 to 0.50; at the latter, half of the volume of the sample is solid particles and the other half the liquid solvent.

Our motivating question is to understand how random the structure is: What geometric constraints influence the structure? For example, particles are not all equal. We verify that larger particles have more contacts. Surprisingly, this is not proportional to surface area. The number of neighboring particles scales as approximately R0.8 rather than R2, which would be the case if the surface area was the key factor. Additionally, samples at higher volume fractions result in all particles having more neighbors, which makes sense. But even at the lowest volume fractions (down to 0.01), nearly all particles are stuck to at least one other particle. This is because this particular colloidal sample was composed of highly attractive particles, so that if any two come into close proximity they will stick permanently.

Graduate student David Meer has been doing complementary simulations of random close packed circles or spheres. One set of simulations uses the exact same size distribution as seen in Ben’s experimental data. In this case, the number of nearest neighbor particles in the simulation, as a function of particle radius, is the same overall shape as the experimental colloidal gel data. This suggests that the contact numbers are set by geometry and the particle size distribution, rather than anything physically different between the different particle sizes.

Ben also looked at tetrahedral structures in his data: places where four particles are mutually touching. He finds that the larger particles act as hubs for the formation of tetrahedra; but this is in large part because they generally have more neighbors, as discussed in the previous paragraph, so it is easier for them to have more mutually touching neighbors that thus form a tetrahedron.

We have written up this work on highly polydisperse colloidal gels for publication, and a preprint is available at arXiv: 2406.10321. [Ed. Note: See Bibliography.] This was submitted to Phys. Rev. E, and we are now revising the manuscript in response to the referee concerns. We are also nearly finished writing up the paper analyzing the ACE-M-1 data and expect to post a preprint on arXiv soon.

Another happy outcome during the course of this grant is that summer undergraduate researcher Swagata Datta is now a graduate student in mathematical physics at the University of Alberta, and undergraduate/lab technician Ben Lonial is now a graduate student in physics at the University of California/Santa Barbara.

Colloidal gels are used in applications such as water purification, skin creams, and also show up in some food products such as jellies and jams. In food, colloidal gels modify the texture and shelf-life stability of the food. Our NASA-funded study of colloidal gels should improve our understanding of long-term stability of colloidal gels, as well as how they initially form.

We have learned several interesting facts about the data. First, the colloidal gel samples show aging: the dynamics slow down as a function of time. Mean square displacement curves taken from different time points in the sample show that particles diffuse slower than normal diffusion: the curves rise with lag time dt showing that particles diffuse slightly, but as dt^(0.3) rather than dt^(1.0). The dynamics are noticeably slower as the sample ages from 2 hours to 56 hours since preparation. For the non-gel sample, the mean square displacement curves taken at different time points are essentially the same, and the curves rise as dt^(1.0), indicating the particles diffuse normally rather than being stuck together.

There are also structural differences between the colloidal gel samples and the non-gel sample. We can measure structural differences with the pair correlation function g(r), which measures the likelihood of finding particles a certain distance from each other. Samples with stronger attractions have higher peaks. Moreover, the peak height grows slowly over the course of the experiment for the gel samples. This relates to the slowing of the dynamics: both changes (slower dynamics, stronger peak height) indicate that particles are becoming more stuck together. This means the gel is stronger; for example, macroscopically, the sample would have a higher viscosity, or higher elastic modulus, or both.

NEW GROUND-BASED EXPERIMENTS: This past year we have additionally done ground-based experiments on colloidal gels. This work is being done by graduate student Waad Paliwal, lab technician Ben Lonial, and PI Eric Weeks. Ben earned his undergraduate degree in physics (with honors) in May 2023. He is now taking a gap year, continuing work in the Weeks Lab, and focusing on the NASA project.

In 2021-22, Waad made mixtures of colloids, solvent, and “depletant.” A depletant is a polymer added to the liquid which causes particles to stick together. By controlling how much depletant is added, we control how sticky the particles are. Waad and Eric then took confocal microscopy movies of these colloidal gels. Subsequently, Ben learned these techniques from Waad and Eric.

In this past year (2023), Waad has investigated what can be seen in three-dimensional images of the gels (imaged using confocal microscopy) as compared to two-dimensional images. This is to help us calibrate the ACE-M-1 data, which are only 2D images. The question she (Waad) is studying in particular is to understand how 2D observations are related to 3D reality. For example, suppose initially we see in a 2D gel image that each particle is stuck to two other particles on average. Waad finds that in the 3D data, this generally means that a particle has six neighboring particles on average; that is, the measurements differ by roughly a factor of three. Unfortunately, we’re finding that this calibration factor (three) varies quite a bit from experiment to experiment, ranging from two to four. We have not found any obvious sign as to what the calibration factor will be from looking at 2D images. Thus, we cannot be certain what the calibration factor should be for the ACE-M-1 data.

Additionally, Ben Lonial has begun making colloidal gels with particles with extreme size polydispersity. Our goal is to understand how the mixture of particle sizes changes the gel structure. While the ACE-M-1 data uses two different particle sizes, they are fairly similar in size (1.8 micron and 2.2 micron diameter), so we do not expect the gel structure to vary a huge amount due to these sizes. On the other hand, with the larger range of sizes in Ben’s new samples, we should be able to see differences. For example, the larger particles should have significantly larger numbers of neighboring particles that stick to them. We will determine how the number of attached neighbors scales with the particle size.

Colloidal gels are used in applications such as water purification, skin creams, and also show up in some food products such as jellies and jams. In food, colloidal gels modify the texture and shelf-life stability of the food. Our NASA-funded study of colloidal gels should improve our understanding of long-term stability of colloidal gels, as well as how they initially form.

Colloids are small (micron-sized) particles in a liquid. In these experiments, the particles are made to be sticky, so they stick together into a network of tendrils of particles; this is the colloidal gel state. The ACE-M-1 experiment was done on the International Space Station, so that the colloidal gels could be studied in microgravity conditions. The reason microgravity is important is that as the particles begin to stick together, they form heavy clusters which can sink in normal gravity. This ultimately limits the shelf-life of a colloidal gel, but also, changes the overall structure. We wish to understand what the gel structure would be like if this limit is overcome in microgravity conditions. The ACE-M-1 data set has 9 distinct experiments on 8 different samples, where the different samples are made with different levels of attractive interaction – that is, different levels of particle stickiness.

Undergraduate student Swagata Datta studied the ACE-M-1 data this past year, working with the Principal Investigator (PI) Eric Weeks. In our analysis of the microscope images, we have learned several useful things. First, we observe that the stickier particles form stronger gels – not surprisingly, there are more particles stuck together, which we can measure from the microscope images. Second, we can observe the increase in aggregated particles over time. The experiments have up to 60 hours of data, and a gradual increase in touching particles is observable in most experiments. The exception is the least sticky particles, which do not form a gel.

In addition to this structural information, we also study the Brownian motion of the particles. As expected, the stickier particles have less Brownian motion, especially as they stick together more strongly in the gel structure. We can see the particle motion slows down as the gels change over the 60 hours of observation. This slowing is more dramatic for the stickiest particles, but still apparent even for some less sticky particles, although the least stickiest particles do not change their motion, consistent with them not forming a gel.

This past year we have additionally done new ground-based experiments on colloidal gels. This work is being done by graduate student Waad Paliwal and PI Eric Weeks. Waad made mixtures of colloids, solvent, and “depletant.” A depletant is a polymer added to the liquid which causes particles to stick together. By controlling how much depletant is added, we control how sticky the particles are. Waad and Eric then took confocal microscopy movies of these colloidal gels. Waad’s analysis of these movies shows similar behaviors to what are described above in the ACE-M-1 data.

Additionally, Waad is investigating what can be seen in three-dimensional images of these gels (made using confocal microscopy) as compared to two-dimensional images. This is to help us calibrate the ACE-M-1 data, which are only 2D images. The question she is studying in particular is to understand how 2D observations are related to 3D reality. For example, suppose initially we see in a 2D gel image that each particle is stuck to two other particles on average. Perhaps in the 3D data, we’ll be able to see that, in reality, the particle is stuck to five other particles on average – with those “extra” particles being out-of-plane, and thus unseen in the 2D image. Waad’s experiments will help us better understand the 3D structure underlying the 2D ACE-M-1 images.

Our plans for the upcoming year are to finish the analysis of all 530 GB of ACE-M-1 images. We will continue taking and analyzing new confocal microscopy images of our lab’s newly created colloidal gels. Finally, we hope to do new experiments looking at gels composed of mixtures of particles with much different sizes to see how their structures might differ from gels composed of identical particles and/or particles of similar sizes.