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Duke University materials scientists have devised a simplified method for calculating the attractive forces that cause nanoparticles to self-assemble into larger structures.
With this new model, accompanied by a graphical user interface that demonstrates its power, researchers will be able to make previously impossible predictions about how nanoparticles with a wide variety of shapes will interact with each other. The new method offers opportunities to rationally design such particles for a wide range of applications, from harnessing solar energy to driving catalytic reactions.
The results appear online November 12 in the journal Horizons on the nanoscale.
“Faceted nanoparticles can lead to new assembly behaviors that have not been explored in the past,” said Brian Hyun-jong Lee, a graduate student in mechanical engineering and materials science at Duke and first author of the paper. “Cubes, prisms, rods and so on show distinct interparticle interactions dependent on distance and orientation that can be used to create unique particle groups that cannot be achieved through self-assembly of spherical particles.”
“Every time I read the latest published series of articles on nanotechnology, I see some new applications of these types of nanoparticles,” added Gaurav Arya, associate professor of mechanical engineering and materials science at Duke. “But accurately calculating the forces that bind these particles at very close distances is extremely expensive from a computational standpoint. We have now demonstrated an approach that speeds up these calculations millions of times while losing only a small amount of accuracy.”
The forces at work between the nanoparticles are called van der Waals forces. These forces arise due to small temporary changes in the density of electrons orbiting atoms according to the complex laws of quantum physics. Although these forces are weaker than other intermolecular interactions such as coulombic forces and hydrogen bonds, they are omnipresent and act between each atom, often dominating the net interaction between particles.
To adequately account for these forces between particles, it is necessary to calculate the van der Waals force that each atom of the particle exerts on each atom of a neighboring particle. Even if both particles in question were tiny cubes less than 10 nanometers in size, the number of calculations that add up all these interatomic interactions would be in the tens of millions.
It’s easy to see why trying to do this over and over for thousands of particles located in different locations and with different orientations in a multiparticle simulation quickly becomes impossible.
“A lot of work has been done to come up with a sum that comes close to an analytical solution,” Arya said. “Some approaches treat particles as being made up of infinitely small cubes stuck together. Others try to fill space with infinitely thin circular rings. While these volume discretization strategies have enabled researchers to obtain analytical solutions for interactions between simple particle geometries. such as parallel plane surfaces or spherical particles, such strategies cannot be used to simplify interactions between faceted particles due to their more complex geometries. “
To get around this, Lee and Arya took a different approach by making several simplifications. The first step is to represent the particle as composed not of cubic elements, but of rod-shaped elements of various lengths stacked together. The model therefore assumes that rods whose projections fall outside the projected boundary of the other particle contribute negligibly to the overall interaction energy.
It is also assumed that the energies provided by the remaining rods are equal to the energies of the rods of uniform length located at the same normal distance as the actual rods, but with zero lateral offset. The final trick is to approximate the distance dependence of the rod-particle energy using power law functions that have closed-form solutions when the distances vary linearly with the lateral position of the actual rods, as in the case of interacting flat surfaces. of particle facets.
After all these simplifications have been made, it is possible to obtain analytical solutions for the interparticle energies by allowing a computer to traverse them. And while they may appear to introduce a great deal of error, the researchers found that the results were on average only 8% less than the actual response for all particle configurations and only 25% different at worst.
Although the researchers worked primarily with cubes, they also showed that the approach works with triangular prisms, square rods, and square pyramids. Depending on the shape and material of the nanoparticles, the modeling approach could impact a wide range of fields. For example, silver or gold nanocubes with edges close to each other can harness and focus light into tiny “hot spots”, creating an opportunity for better sensors or catalyzing chemical reactions.
“This is the first time anyone has proposed an analytical model for van der Waals interactions between faceted particles,” said Arya. “While we have yet to apply it to compute interparticle forces or energies within molecular dynamics or Monte Carlo simulations of particle assembly, we expect the model to accelerate such simulations up to ten orders of magnitude.”
This research was supported by the National Science Foundation (CMMI 1636356 award, ACI-1053575).
Source of the story:
Materials provided by Duke University. Original written by Ken Kingery. Note: The content can be changed by style and length.
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