Theoretical prediction of the structure of nanoparticle (NP) based thin films via atomistic simulations is challenging, due to computational limitations. To overcome these limitations, we are developing a meso-scale technique that integrates atomistic and microscopic scale methods. Herein, as a first step, we propose an approach that encompasses the random nature of NP deposition, which results in a statistical cancellation of individual sintering mechanisms between coalescing NPs upon deposition. As a result, we present a simple and intuitive analytical method that describes the average coalescence behavior of NPs, regardless of constituent element or crystallinity, emphasizing only the predominant coalescence dependencies on temperature and size-dependent NP melting points. When two NPs touch each other (i.e. impact in flight, soft-land on one another or surface-diffuse on a substrate) a part of them melts due to free surface annihilation, forming a region that, when re-solidified, binds the two NPs together. The exact configuration may depend on many parameters (such as relative orientation, defect content, constituents of the nanoparticles, etc.) and can be quite complex, but the thesis of our proposed model is that it mainly depends on the melting temperature of the NP: the lower it is, the bigger the portion of the NP that melts. In other words, if the NP melting temperature as a function of size is known, no other physical properties are needed in order to describe the sintering, and thus one can circumvent the complex physics involved and simulate the NP deposition on a much coarser scale. Typically, NP melting temperatures follow a Tm (1-constant/diameter) dependence with size, approaching asymptotically the bulk melting temperature above a certain size threshold.
We assess our model using molecular dynamics (MD) computer simulations of dissimilar systems, and find good agreement between its predictions and the MD results. Its simplicity makes our model a suitable starting point for the development of a meso-scale simulation technique that can describe the growth of nanoparticulated films and the prediction of their properties such as structure, porosity, and percolation threshold.
 “Simple analytical model of nanocluster coalescence for porous thin film design”
P. Grammatikopoulos, E. Toulkeridou, K. Nordlund, M. Sowwan
Modelling Simul Mater Sci Eng 23 (2015) 015008.