Adsorption of 4-biphenylmethanethiolate (BPMT) has been studied for different-sized gold nanoparticles, with mean diameters of 6, 11, 15, 27, 35, 43, and 97 nm, using surface-enhanced Raman scattering (SERS). Transmission electron microscopy (TEM) images and UV−visible absorption spectra were obtained to examine the monodispersity and BPMT derivatization of the gold nanoparticle samples. Changes in the UV−vis spectra indicated that BPMT-derivatized gold particles appeared to aggregate more extensively with increasing mean diameter. The SERS enhancement was found to be weak in diameter ranges smaller than 11 nm. BPMT was assumed to adsorb on gold, with a standing geometry on the surface, from the presence of the ν2 mode at ∼3065 cm-1 in the SERS spectra of 35-, 43-, and 97-nm particles. The disappearance of the νas(CH2) band in the SERS spectra of all the gold particle samples denoted a preference of sp3 hybridization for the sulfur atom in BPMT on gold particle surfaces. The TEM images showed that monodisperse 15-nm gold nanoparticles derivatized with BPMT could be arranged in a two-dimensional close-packed array. The results of simulated annealing molecular dynamics simulations showed that the close-packed structures of BPMT on a Au(111) surface exhibit ordered herringbone arrangements with almost vertical orientations.

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Rainfall kinetic energy has been linked to linear, exponential, logarithmic, and power-law functions using rainfall intensity as an independent variable. The power law is the most suitable mathematical expression used to relate rainfall kinetic energy and rainfall intensity. In evaluating the rainfall kinetic energy, the empirical power laws have shown a larger deviation than other functions. In this study, universal power law between rainfall kinetic energy and rainfall intensity was proposed based on the rainfall power theory under an ideal assumption that drop-size is uniformly distributed in constant rainfall intensity. An exponent of the proposed power law was 11/9 and coefficient was estimated at 10.3 from the empirical equations of the existing power-law relation. The rainfall kinetic energy calculated by universal power law showed >95% concordance rate in comparison to the average values calculated from exponential and logarithmic functions used in soil erosion model such as USLE, RUSLE, EUROSEM, and SEMMA and <5% relative difference as compared to the average rainfall kinetic energies calculated by other empirical functions. Therefore, it is expected that power law of ideal assumption may be utilized as a universal power law in evaluating rainfall kinetic energy.