Balls of ice cream

When you go to your local ice cream shop, you likely ponder the question of how many scoops you wish to order. I, on the other hand, prefer to order balls of ice cream. The scoop corresponds to the void that is to be filled, but a ball corresponds to the filling. It seems to me that I'd rather order balls of ice cream rather than empty space. My wife suggests that this is just a matter of my literal mistranslation of "bolas de helado" rather than any deeper significance over the ontology of balls verses scoops. As an optimist, I certainly prefer for them to be more than half-filled, and hence naturally prefer balls of ice cream to voids, that is scoops.

This argument extends to the nanoscale. Are the properties of a particle driven by itself or by the space which it occupies? If the latter, then its properties are independent of the nanoparticle aside from its shape. As a chemist, this is a disappointing possibility because I would like to tailor the properties of the particles, such as how they assemble, by changing the atoms or molecules at the surface (and the interior). The good news is that such control can be exercised. That is why we have been studying so-called Janus particles and other patchy particles. In our rendering, they look like ice cream balls made of blueberry and strawberry ice cream halves or layers.  The blueberry faces like to face the strawberry faces (because they correspond to charges and opposites attract), and this gives rise to their interesting patterns and response to changes from the outside.

Check out our some of our recent papers on Janus and striped particles and stay tuned for the next ones!

M. C. Hagy and R. Hernandez, "Dynamical simulation of electrostatic striped colloidal particles," J. Chem. Phys. 140, 034701 (2014). (doi:10.1063/1.4859855)
M. C. Hagy and R. Hernandez, "Dynamical simulation of dipolar Janus colloids: Dynamical properties," J. Chem. Phys. 138, 184903 (2013). (doi:10.1063/1.4803864)
M. C. Hagy and R. Hernandez, "Dynamical Simulation of Dipolar Janus Colloids: Equilibrium Structure and Thermodynamics," J. Chem. Phys. 137, 044505 (2012). (doi:10.1063/1.4737432)

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.

The relaxation of striped spheres… ( #AIP_JCP #justpublished )

When was the last time that you took a bunch of pool balls, suspended them in a thick oil, and watched how they assembled? Pool balls being what they are, they will simply stack on themselves, though there is some question as to how efficiently they do so. If you start to shake the container, thereby maintaining some average kinetic energy (that is, temperature), they probably started to jiggle. They probably won't rotate much. Even if they do, it won't matter much because they collide with each other in the same way no matter what. So now take the balls and paint them with some pattern of red and blue paint, and suppose that there is a difference in the forces between the spheres depending on which colored surfaces are near each other. Now when they collide with each other, they have preferred relative orientation. The emergence of structure (or patterns in the positions and orientation) of the pool balls should presumably be very sensitive to how you painted them.

This is precisely the problem that Matthew Hagy and I have been studying over the past couple of years. Our pool balls are actually colloidal particles of a couple hundred nanometers in diameter. The paint corresponds to the charges encoded on the surface of the colloids. Opposite charges attract. Initially we studied Janus particles that literally have two faces, one hemisphere is positively charged and the other negative. (If interested, you can also check out my earlier blog post on the dynamics of Janus particles.) In the work that was just published in the Journal of Chemical Physics, we now consider the case in which the spheres are coated in stripes of alternating charge. This generalizes the surface pattern of the Janus particles to three, four, five, six, and more stripes. The funny thing is that very little happens to the packing of the particles because that property is so strongly dominated by the shape of the particles. But their motion, and the timescales in which they relax from a given deformation is highly sensitive to the number of stripes and perhaps also to how they are striped. In a sense, this says that if you want to maintain their behavior, you can fatten them up a little but you can't change their stripes.

The title of the article is "Dynamical simulation of electrostatic striped colloidal particles," and the work was funded by the NSF. It was released recently at J. Chem. Phys. 140, 034701 (2014), and featured on the cover!  Click on http://dx.doi.org/10.1063/1.4859855 to access the article.

Tricking hard collisions into soft interactions(#AIP_JCP #justpublished)

One of the simplest ways to describe atoms or molecules is to pretend that they are balls with some effective diameter (roughly on the order of nanometers.) If you ignore the fact that they can collide, you recover the ideal gas law you might remember from college chemistry classes. On the other hand, because they occupy space, they must collide. These collisions can be "hard" if the balls are treated like billiard balls that hit each other without changing their shape. But actual molecules are more like tennis balls in that they deform during the collision and the nearest approach depends on their velocities. That is, molecular-scale particles undergo soft interactions. Unfortunately, it takes a lot more computational effort to simulate soft particles and we'd like to avoid the extra expense. The question my coworkers and I asked is whether we could mimic soft particles using a model in which the particles moved like hard particles some of the time and like ideal particles the rest of the time. It's a little tricky because the ideal gas particles don't occupy space so we had to calculate the effective density of a given system as a function of the degree to which the particles collided with each other as hard or soft. Meanwhile, the comparison between our model and corresponding soft particle systems with the same density gave us similar structure! We intend to use this model to understand more complicated reactions, and the degree to which we can understand the behavior of complex solvents that interact with the reacting system at comparable time scales.

The title of the article is "Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order" and the work was funded by the National Science Foundation. It was released just this week at J. Chem. Phys. 138, 244901 (2013). (doi:10.1063/1.4810807).

On the dynamics of Janus colloids (#JChemPhys)

Janus colloids are particles that like the Roman god, Janus, have two faces. Chemically, the two faces in a Janus colloid correspond to different interactions based on what is coating the surface of each of the two halves. (In principle, they don't have to be spherical. There's some recent work on cylinders emerging as well.) We, and others, have been curious about whether a container of Janus particles would have different structure than spherically attractive particles. We showed in earlier work that, at equilibrium, such containers can indeed be quite similar. This was disappointing, in part, because it meant that you couldn't make new equilibrium structures by carefully making Janus particles. It may not be surprising to you, though, because it simply means that if you are in a room filled with people, then most of the time, you can turn your head so that you are facing someone you like. As such, you can ignore the direction you don't like. Similarly we can, for the most part, ignore the unhappy contacts in a container of Janus colloids (in the fluid regime.)

But what about the motion of this system? It turns out that this is indeed highly dependent on the Janus particle interaction strengths. Equally interesting is the fact that if you try to remove degrees of freedom from this system, you get some crazy results. First of all, if you get rid of them without doing anything else, then the particles move too quickly. (This is a known problem in coarse-graining.) If you trick the system to get the rates of particle diffusion right (as is often done), then other stuff breaks down. We found in the Janus colloids, that the association of the particles (that is which are neighbors are next to which) is highly dependent on the Janus particle interactions strengths. This means that performing coarse-grained molecular dynamics simulations to model the motion of large assemblies of molecules is more difficult to do correctly(!) than we had anticipated...

These latter findings are available, in far too much detail, in our second article on Janus Colloids which just appeared on line in J. Chem. Phys. (doi:10.1063/1.4803864).