A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition
Abstract
:1. Introduction
- Examination of the configurations assumed by S particles, i.e., identification of isolated particles, dimers, chains, rings and clusters;
- Examination of the configurations assumed by L particles relative to S particles in order to identify specific recurrent patterns characterized by angular and radial uniformity of L particles with respect to S particles (for instance, isolated S particles in the interstices between three L particles arranged in an equilateral triangle and between four L particles arranged in a square or S particle dimers in the interstices between four L particles arranged in a rhombus);
- Examination of the configurations assumed by S particles relative to L particles, e.g., determination of L particles “caged” by S particles and analysis of the angular and radial uniformity of S particles around L particles.
2. Materials and Methods
2.1. Colloidal Self-Assembly
2.2. Characterization and Analysis of Particle Configurations
- Isolated particles: a particle belongs to this group if , i.e., if it does not have any neighbor within a distance from its centroid;
- Dimers: two particles and belong to this group if has only the neighbor within a distance from its centroid and if has only the neighbor within a distance from its centroid;
- Chains: particles belong to a chain if they are such that each of the particles belonging to the chain has only two neighbors within a distance from its centroid (neighborhood cardinality 2) except for two particles that have just one neighbor (neighborhood cardinality 1) and such a neighbor has a neighborhood cardinality equal to 2; roughly speaking, in a chain, all the particles have two neighbors except for the particles at the two extremes of the chain that have just one neighbor;
- Clusters: particles belong to a cluster if they belong to a connected component that does not fall into any of the previous categories; within this set, we can distinguish loops; particles belong to a loop if they all have a neighborhood cardinality equal to 2, i.e., if they all have two neighbors within a distance from their centroid; a loop can be interpreted as a sort of “closed” chain or ring.
- The center of the L particle lies within the triangle;
- All sides of the triangle (i.e., the center-to-center distances of the three S nearest neighbors) are smaller than .
3. Results and Discussion
3.1. Quantitative Analysis of S Particle Configurations
3.2. Quantitative Analysis of L Particle Configurations Relative to S Particles
- Isolated S particles present alternatively in the interstices between L particles arranged in a hexagonal pattern;
- Isolated S particles present in the interstices between L particles arranged in a square pattern;
- Isolated S particles present in all the interstices between L particles arranged in a hexagonal pattern.
3.3. Quantitative Analysis of S Particle Configurations Relative to L Particles
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Lotito, V.; Zambelli, T. A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition. Nanomaterials 2019, 9, 921. https://doi.org/10.3390/nano9070921
Lotito V, Zambelli T. A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition. Nanomaterials. 2019; 9(7):921. https://doi.org/10.3390/nano9070921
Chicago/Turabian StyleLotito, Valeria, and Tomaso Zambelli. 2019. "A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition" Nanomaterials 9, no. 7: 921. https://doi.org/10.3390/nano9070921