Using dice, fuzzy or not, to move molecules

This post has been a long tine coming... I wrote it back in May 2015, and somehow in the middle of things, I forgot to hit "publish." While we have done quite a bit of work with this model since then, maybe you'll still enjoy our crazy analogy to playing dice with particles at the mesoscale...

Some time ago, I published what might seem as yet another paper describing the properties of our model for (coarse-grained) large-scale macromolecules. A critical part of the model is that we roll dice every time these particles collide so as to decide whether they bounce or go through each other. They can overlap, because at intermediate length scales, they don't behave like rocks even if they occupy space. Despite our simple (and dicey) model, in our earlier papers, we showed that our particles give rise to the same structure as the corresponding particles that would interact through typical (so-called soft) interactions. But Einstein's famous quote about God not playing dice with the universe (albeit in a different context) serves as a warning that our particles might not move in analogous ways to those driven by Newton's deterministic laws. In our most recent paper, we confirmed that our particles (if they live in one dimension) do recover deterministic dynamics at sufficiently long (that is, coarse-grained) length scales. That's a baby step towards using our model in human-scale (three) dimensions. So there are more papers to come!

The work was performed (and the paper was written) with my recent Ph.D. graduate, Dr. Galen Craven, and a Research Scientist, Dr. Alex Popov. It's basic research and I'm happy to say that It was supported by the National Science Foundation. The title of the article is "Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties," and it was recently published at J. Chem. Phys. 142, 154906 (2015).

Building Pillars of MesoScale Particles on a Surface

Let’s build layers of (macromolecular) material on a surface. If the material were lego pieces, then the amount of coverage at any given point would be precisely the number that fell there and connected (interlocked). In the simplest cases, you might imagine the same type of construction on a macromolecular scale surface with nano sized bricks. The trouble is that at that small length scale, particles are no longer rigid. The possibility of such softness allows for higher density layers and even a lack of certainty as to which layer you are in. This leads to a roughness in the surface due to the fact that the soft legos stack more in some places than others. Moreover, there will be regions without any legos at all which means that the surface will not be completely covered. This led us to ask: What is the surface coverage as a function of the amount of macromolecular material coated on the surface and the degree of softness of that material?

As in our recent work using tricked-up hard particles, we wondered whether we could answer this question without using explicit soft particle interactions. It does, indeed, appear to work in the sense that we are able to capture the differences in coverage of the surface between a metastable coverage in which particles once trapped at a site remain there, and the relaxed coverage in which particles are allowed to spread across the surface. We also found that relaxation leads to reduced coverage fractions rather than larger coverage as one might have expected a spreading of particles due to the relaxation.

This work was performed by my graduate student, Dr. Galen Craven, in collaboration with a research scientist in my group, Dr. Alex Popov. The title of the article is "Effective surface coverage of coarse grained soft matter.” The work was funded by the NSF. It was published on-line in J. Phys. Chem. B back in July, and I’ve been waiting to write this post hoping that it would hit the presses. Unfrotunately, it’s part of a Special Issue on Spectroscopy of Nano- and Biomaterials which hasn’t quite yet been published. But I hope that it will be soon! Click on the doi link to access the article.

Soft materials made up of tricked-up hard particles

Materials are made of smaller objects which in turn are made of smaller objects which in turn… For chemists, this hierarchy of scales usually stops when you eventually get down to atoms. However, well before that small scale, we treat some of these objects as particles (perhaps nano particles or colloids) that are clearly distinguishable and whose interactions may somehow be averaged (that is, coarse-grained) over the smaller scales. This gives rise to all sorts of interesting questions about how they are made and what they do once made. One of these questions concerns the structure and behavior of these particles if their mutual interactions is soft, that is when they behave as squishy balls when they get close to each other and unlike squishy balls continue to interact even when they are far away. This is quite different from hard interactions, that is when they behave like billiard balls that don’t overlap but don’t feel each other when they aren’t touching.

I previously blogged about our work showing that in one-dimension, we could mimic the structure of assemblies of soft particles using hard particles if only the latter were allowed to overlap (ghostlike) with some prescribed probability. In one dimension, this was like looking at a system of rods on a line. We wondered whether this was also possible in two dimensions (disks floating on a surface) or in three dimensions (balls in space). In our recent article, we confirmed that this overlapping (i.e. interpenetrable) hard-sphere model does indeed mimic soft particles in all three dimensions. This is particularly nice because the stochastic hard-sphere model is a lot easier to simulate and to solve using theoretical/analytical approaches. For example, we found a formula for the effective occupied volume directly from knowing the “softness” in the stochastic hard-sphere model.

The work was done in collaboration with my group members, Galen Craven and Alexander V. Popov. The title is "Structure of a tractable stochastic mimic of soft particles" and the work was funded by the National Science Foundation. It was released just this week at Soft Matter, 2014, Advance Article (doi:10.1039/C4SM00751D). It's already available as an Advance Article on the RSC web site, though this link should remain valid once it is formally printed.