2014/03/03 by Alberto Pimpinelli, Levent Tümbek, Adolf Winkler · 2 citations
Physics and Astronomy · Materials Science · Mathematics · #Theoretical and Computational Physics #Block Copolymer Self-Assembly #Quasicrystal Structures and Properties #Scaling #Exponent #Nucleation #Statistical physics #Materials science #Thermodynamics #Mathematics #Physics #Geometry #Philosophy
paper · pdf · doi:10.1021/jz500282t
openalex publication_date 2014/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21
High Resolution Image Download MS PowerPoint Slide It is known in thin-film deposition that the density of nucleated clusters N varies with the deposition rate F as a power law, N ∼ F α . The exponent α is a function of the critical nucleus size i in a way that changes with the aggregation limiting process. We extend here the derivation of the analytical capture-zone distribution function P β ( s ) = a ß · s β ·exp(- b β s 2 ) of Pimpinelli and Einstein to generic aggregation-limiting processes. We show that the parameter β is generally related to the critical nucleus size i and to the exponent α by the equality α·β = i, in the case of compact islands. This remarkable result allows one to measure i with no a priori knowledge of the actual aggregation mechanism. We apply this equality to measuring the critical nucleus size for pentacene deposition on mica. This system shows a crossover from diffusion-limited to attachment-limited aggregation with increasing deposition rates.