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At Duke University, materials scientists have developed a simple technique for calculating the attractive forces that allow nanoparticles to assemble on their own into larger structures.
This latest model, featuring a graphical user interface that shows its power, will allow scientists to make predictions about how different forms of nanoparticles will interact with each other, a feat that wasn’t previously possible.
The new technique offers new possibilities for the rational development of these particles for a variety of applications, from driving catalytic reactions to harnessing solar energy. The study results appeared online in Horizons on the nanoscale on November 12th, 2020.
Faceted nanoparticles can lead to new assembly behaviors that have not been explored in the past. 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.
Brian Hyun-jong Lee, first author of the study and graduate student in mechanical engineering and materials science, Duke University
Gaurav Arya, associate professor of mechanical engineering and materials science at Duke University, added: “Whenever I look at the latest series of published articles on nanotechnology, I see some new applications of these types of nanoparticles. But the accurate calculation of the forces that join these particles at very close distances is extremely expensive from a computational point of view.“
Arya continued, “We have now demonstrated an approach that speeds up these calculations millions of times while losing only a small amount of accuracy. “
The working forces between the nanoparticles are referred to as van der Waals forces. Such forces are caused by slight, fleeting shifts in the density of electrons that rotate atoms in accordance with the intricate laws of quantum physics.
Although such forces are weaker than other intermolecular interactions, such as hydrogen bonds and coulombic forces, they are pervasive and act between all atoms, usually governing the net interaction that occurs between particles.
To accurately explain these Van der Waals forces between particles, it is important to calculate these forces which are exerted by all atoms in the particle on all atoms in a neighboring particle. Even if both target particles were tiny cubes less than 10 nm in size, the number of calculations that summarize these interatomic interactions would be in the tens of millions.
It’s easy to see why trying to do this repeatedly for dozens of particles in various orientations and located in various positions in a multiparticle simulation quickly becomes impossible.
A lot of work has been done to formulate a summation that comes close to an analytical solution. Some approaches treat particles as being made up of infinitely small cubes stuck together. Others try to fill the space with infinitely thin circular rings.
Gaurav Arya, Associate Professor of Mechanical Engineering and Materials Science, Duke University
Arya continued, “Although these volume discretization strategies have enabled researchers to obtain analytical solutions for the 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 smaller geometries. complex. “
To overcome this problem, both Lee and Arya adopted a different method by making a number of simplifications. In the initial stage, the team showed that instead of cubic elements, the particle is made up of different lengths of rod-shaped elements arranged together.
The model subsequently assumes that the rods whose projections fall beyond the estimated margin of the other particle contribute insignificantly to the overall interaction energy. The remaining rods bring energies that are also believed to balance the energies of the rods of equal length. These rods are located at the same regular distance as the real rods, but with zero lateral offset.
The final trick is to approximate the distance dependence of the energy between the rod and the particle using the power law functions. These functions have closed-form solutions, especially when the distances differ linearly with the lateral position of the real rods, as in the case of the interacting flat surfaces of the faceted particles.
Once all these simplifications have been realized, it is possible to obtain analytical solutions aimed at interparticle energies, allowing a computer to go through them. While these solutions may appear to introduce a significant amount of errors, the team noted that the results were on average only 8% lower than the actual solution for all particle configurations and only 25% different at worst. .
While the researchers mostly used cubes for their study, they noted that the method also works with square pyramids, square rods, and triangular prisms.
Based on the material and shape of the nanoparticles, the new modeling method can affect a variety of fields. For example, gold or silver nanocubes with edges proximal to each other can exploit and direct light into tiny “hot spots”. This can provide an opportunity to catalyze chemical reactions or to develop more improved sensors.
This is the first time that anyone has proposed an analytical model for van der Waals interactions between faceted particles. Although we have yet to apply it to calculate interparticle forces or energies within molecular dynamics or Monte Carlo particle assembly simulations, we expect the model to accelerate such simulations up to ten orders of magnitude.
Gaurav Arya, Associate Professor of Mechanical Engineering and Materials Science, Duke University
The study was funded by the National Science Foundation (CMMI 1636356 award, ACI-1053575).
Journal reference:
Lee, BH-J., (2020) Analytical van der Waals Interaction Potential for faceted nanoparticles. Horizons on the nanoscale. doi.org/10.1039/d0nh00526f.
Source: https://pratt.duke.edu/
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