Stories from the Microscale: Simulating the Dance of the Molecules

Christophe Vaillant, PhD

28 July 2021

Many of the properties we observe in the matter around us are a direct result of what is happening on the molecular scale. As molecules bounce off each other, react, change their shapes, etc., their behavior can have a big impact on what happens on the human scale. The dynamics of these molecules become especially important when they can gather (or self-assemble) together to form larger structures, such as micelle formation in surfactants. For example, in order to make grease dissolve in water one must add a detergent (which is usually just a surfactant). At different relative concentrations, the mixtures can form very different molecular structures, which may or may not lead to the desired solubility. Molecular insights into this process would therefore allow us to deduce why and how the solubility changes as a function of how much detergent we add to our dishwater. Of course, these types of microscopic simulations can get very complicated, so how do people go about doing this in general, and how are we bringing these simulations to RheoCube?

Electrons, atoms and molecules

Our story starts with quantum mechanics. In principle, Schrödinger’s equation (the equation that is the cornerstone of the quantum world) could be used to calculate all the properties of matter. In practice, however, doing these calculations is hard. Very hard. The difficulty lies not in how clever we are at doing pen-and-paper algebra, but rather how good our algorithms are at solving the equations in a reasonable time frame. So we do the only thing we can do: we simplify. Molecules are basically built out of two types of particles: tiny and dense, positively-charged nuclei surrounded by a cloud of very light, negatively charged electrons. The forces between the molecules come about mainly because of the electric fields acting between all the particles.

The first simplification comes when we realize that electrons are at least a factor of 2000 lighter than the nuclei, which means electrons move a lot faster. We can therefore split our problem up into two separate, easier problems: heavy nuclei that move slowly subject to effective forces determined by the dance of the fast electrons. The nuclei are heavy enough that we can typically ignore quantum mechanics altogether, and so we can employ classical mechanics. Unfortunately, however, there’s no getting around the quantum nature of electrons. A full quantum simulation of these electrons involves what we would call “ab initio” methods, or quantum chemistry. Thankfully, though, those electrons tend to behave in a similar way across different molecules. Broadly speaking, the interactions are very repulsive when too close, giving molecules their size (“excluded volume”), and otherwise weakly attractive (“cohesive energy”). This allows us to create something called a “force field” (also known as an interaction potential). A force field is a simplified, time-averaged model of the electronic forces, which we can use to calculate the forces and chemical interactions that are acting on our atoms and molecules. 

Putting this all together means that all we need to do is use our force field to calculate the forces between our particles, and take small steps in time while making sure the nuclei move according to classical mechanics (i.e. Newton’s laws). This type of simulation is known as molecular dynamics, or simply MD.

Practical Molecular Dynamics and Coarse Graining

Now, the story is far from over, as MD is still a computationally intensive technique. For every atom, you have to calculate the force between that atom and every other atom in your system. Bearing in mind that there are hundreds of thousands of atoms in that system, things quickly get out of hand. Thankfully, there are sophisticated techniques for solving these issues, and modern MD simulations are done routinely in both academic and industrial research.

Figure 1: Molecular dynamics simulations can represent molecules at different levels of complexity: “ab initio” (i.e. using ab initio quantum chemistry methods), all-atom force fields (which explicitly include all the atoms), and coarse-grained force fields (where different atoms are grouped together into beads). In the above diagram, the black circles denote carbon atoms and the blue circles denote hydrogen atoms, with red dots, lines and colored ellipses corresponding to electrons, bonds, and coarse-grained beads, respectively.

However, there are many systems out there (think of proteins, or complex fluids, or even viruses) where we simply could not simulate every single atom without having to wait a century for useful results. This is where the concept of “coarse graining” comes in very handy. The idea is that, despite the complexity of the physics at play, perhaps some details are unnecessary. For example, a polymer is basically a long chain that can flex and coil itself up, and the specific details of how each atomic bond vibrates is not crucial to the overall physics. If we therefore simplify the structure of a molecule, for example by collecting together groups of atoms into “beads” (as shown in the bottom part of Figure 1), then we can retain the important molecular-scale physics, while reducing the amount of computer power needed to run the simulation. A simulation based on grouping atoms together into “coarse-grained beads” is known, rather logically, as coarse-grained molecular dynamics (CGMD).

There are two philosophies behind coarse graining, known as “bottom-up” or “top-down”. In “bottom-up” coarse graining, one first runs an all-atom simulation to get some reference results. An algorithm is then used to work out what can be thrown away without compromising the accuracy of the results. In the “top-down” procedure, however, we begin by defining the beads beforehand, and the forces between these beads are determined by the requirement to get the best results for as large a number of systems as possible. There is an increasing number of “top-down” type coarse-graining procedures and force fields, with popular examples including the MARTINI and SPICA  force fields. We are now beginning work on incorporating these sophisticated models into the microscale simulations offered by RheoCube, thereby pushing the boundary of accuracy for our clients.

A force field from solubility parameters

Coarse-graining procedures, of course, rely on some pretty crucial information: molecular structure. Many formulation scientists in industry, however, simply do not have access to this information. For this reason, we have developed an in-house method that can automatically generate a coarse-grained representation of molecules, along with the corresponding force field needed to run a MD simulation. The idea is based on the Hansen Solubility Parameters (HSPs), which are three parameters that characterize how soluble a fluid may be with other fluids (click here for more details). The information contained within these parameters, however, can also be combined with more approximate theories. We use a version of lattice fluid theory to extract information about the forces acting between individual coarse-grained beads. With minimal information, we can therefore prepare sophisticated coarse-grained molecular dynamics without knowing the exact molecular structure of every species!

Our in-house process is, of course, not without caveats. We can only capture simpler polymers and surfactants, and the act of translating HSPs to force fields can introduce significant errors. Nevertheless, we find that our procedure performs remarkably well (albeit with some occasional manual tuning of parameters needed) across a variety of different types of systems. Although we will be making the next leap in accuracy for our simulations by moving toward more sophisticated force fields, we will retain our HSP-based force fields for the particular cases where detailed molecular structures are unavailable.

Rheology and the dance of the molecules

Understanding the different phenomena that can affect the rheology of a fluid can be very tricky. Structures that self-assemble on the microscale because of complex molecular interactions can lead to wild variations in behavior seen in the lab. Without some kind of simulation to gain insights into these molecular processes, tedious trial-and-error procedures could easily become very time consuming, and perhaps even lead some teams on a wild-goose chase. For example, we compare a water-decane-surfactant mixture in Figure 2, with a slight change in relative concentrations. This change is enough for a switch in the phase behavior, which might only be visible to our eyes as a slight change in opacity.

Figure 2: CGMD simulations of a mixture of water, decane and C12EO6 (a common non-ionic surfactant), where orange and purple beads are the hydrophilic and hydrophobic parts of the surfactant, the pink beads are decane; the water is not shown. A small change from (a) 85%/5%/10% water/decane/C12EO6 volume fractions to (b) 70%/10%/20% completely changes the self-assembled structure from spherical micelles to a kind of hexagonal micellar phase.

Changes in phase behavior like those in Figure 2 can be hard to understand using only experimental tools. With the unique microscale solutions that are being developed in RheoCube, formulation scientists can therefore get a better understanding of the chemistry behind their products. The insights gained from these CGMD simulations are likely to reduce experimental trial-and-error, ultimately cutting down on the time spent making new products.

Final Note

Not a RheoCube user yet and interested in how simulation software can progress your product development? Reach out to request your demo and speak with one of our experts today.

Author
admin
Category
Blog Post
Date
Jul 28, 2021