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Fractal analysis methods for solid alkane monolayer domains at SiO2/air interfaces.
Lydia Knüfing1, Hauke Schollmeyer, Hans Riegler
1Australian National University, RSPhysSE, Applied Mathematics, A.C.T. 0200, Australia.
Langmuir : the ACS Journal of Surfaces and Colloids
|January 26, 2005
Summary
Accurate fractal dimensions for alkane domains on surfaces require robust confidence intervals. Comparing different measures improves accuracy, with box-counting and Minkowski density methods proving most reliable for morphological analysis.
Area of Science:
- Surface Science
- Materials Characterization
- Physical Chemistry
Background:
- Studying the morphology of experimental patterns, like alkane domains on SiO(2)/air interfaces, requires reliable fractal analysis.
- Accurate determination of fractal dimensions depends on defining confidence intervals for scaling ranges.
- Existing fractal analysis methods may be susceptible to noise and finite size effects in experimental data.
Purpose of the Study:
- To systematically evaluate various fractal analysis methods for studying finite and noisy experimental patterns.
- To improve the derivation of trustworthy fractal dimensions by enhancing confidence interval determination.
- To investigate the influence of surface coverage on alkane domain morphology using reliable fractal analysis.
Main Methods:
- Comparison of scaling behavior across different morphological measures (area, boundary, curvature).
- Application and evaluation of the box-counting method for coarse-grained structures.
- Application and evaluation of the Minkowski density method and the sandbox method.
Main Results:
- Combining area and boundary data from the box-counting method provides clear confidence limits for morphological data.
- The Minkowski density method also yields reliable confidence ranges, offering more detail on scaling behavior despite a larger lower cutoff swing-in.
- Alkane domain morphology transitions from fractal dimension ~1.7 at low coverage to ~2 at high coverage, with uncertainty around 50%.
Conclusions:
- The box-counting and Minkowski density methods are recommended for reliable fractal dimension analysis of experimental patterns.
- The sandbox method is less suitable due to susceptibility to finite size effects.
- Observed changes in domain morphology are linked to a crossover in growth regimes, from diffusion-limited aggregation to annealing- and interaction-dominated growth.