Calculation of light transmittance in a film: considerations of the coating geometry, the agent distribution, and its probability density distribution

Transmittance is an important parameter for various films such as sunscreen films and creams, biofilms, coating materials, etc. Even if amounts of a sunscreen agent are the same, the transmittance greatly changes depending on the coating geometry (CG) and the agent distribution (AD) in the film. In this study, we calculate the transmittance considering CG and AD. In addition, we associate the transmittance with probability density distribution of the thickness of the film. We found analytical and numerical solutions of the transmittance in several model cases. It can be used for prediction of performance of the sunscreen film and for a fair comparative evaluation. Mathematical techniques in calculation of the transmittance are also explained in detail

Theoretical study of solvent-mediated Ising-like system: A study for future nanotechnology

We theoretically study physical properties of one-dimensionally and regularly placed solutes. The solute is rigid-body, has arrow-like shape, and changes its direction up or down. If the solutes are immersed in continuum solvent, nothing happens in the system. However, the property of the directions differs in granular solvent (e.g., hard-sphere solvent). Depending on distance between the nearest-neighbor solutes, the directional property periodically changes as follows: "ferromagnetic-like" \leftrightarrow "random" \leftrightarrow "antiferromagnetic-like". Furthermore, the directional property decays into "random" as the distance increases. Studying a newly created nano-system theoretically, it is able to discover a new or interesting property hiding in nano-material world. We believe that such an approach gives physics research a new direction and contributes to nanotechnology.Comment: Main Text (9 pages & 4 figures), Supplemental Material (4 pages & 1 figure

Measuring Method of a Surface Property inside the Pore: Application of Kelvin's equation

Surface analyses inside the nanopore, micropore, and a very narrow pipe are important topics for development of the chemical engineering. Here, we propose a measuring method which evaluates the surface coverage of the chemically modified pore surface and the corrosion rate of the inner surface of the narrow pipe, etc. The method uses Kelvin's equation that expresses saturated vapor pressure of a liquid in the pore (pipe). The surface coverage and the corrosion rate are calculated by measuring saturated vapor pressure of the liquid in the pore and the pipe, respectively. In this letter, we explain the concept of the method briefly.Comment: 4 pages, this is a short lette

Measurement theory of a density profile of colloid particles on a flat surface: Conversion of force acting on a colloidal probe into pressure on its surface element

Recently, we proposed a method that converts the force between two-large colloids into the pressure on the surface element (FPSE conversion) in a system of a colloidal solution. Using it, the density distribution of the small colloids around the large colloid is calculated. In a similar manner, in this letter, we propose a transform theory for colloidal probe atomic force microscopy (colloidal probe AFM), which transforms the force acting on the colloidal probe into the density distribution of the small colloids on a flat surface. If measured condition is proper one, in our view, it is possible for the transform theory to be applied for liquid AFM and obtain the liquid structure. The transform theory we derived is briefly explained in this letter

An improved transform theory for estimation of number density distribution of colloidal particles on a surface: A method for colloidal-probe atomic force microscopy

In the short letter, we explain an improved transform theory for colloidal-probe atomic force microscopy (CP-AFM). CP-AFM can measure a force curve between the colloidal probe and a wall surface in a colloidal dispersion. The transform theory can estimate the normalized number density distribution of the colloidal particles on the wall from the force curve measured by CP-AFM. The transform theory is important for study of the stratification of the colloidal particles on the wall, which is related to fundamental studies of colloidal crystal and glass

Measurement theory of a density profile of small colloids around a large colloid: Superposition of the radial distribution functions

We propose a transform theory for calculating a density profile of small colloids around a large colloid from a force curve between the two-large colloids. In the colloid solution, there are many small colloids and two or several large colloids. The force curve between the two-large colloids can be measured by laser tweezers. In this letter, the transform theory is derived in detail, where a superposition approximation of the radial distributions of the density profiles and rigid-body approximation are introduced. In our opinion, if the experimental condition is satisfied, the transform theory can be used not only for the laser tweezers, but also for surface force apparatus and colloid probe atomic force microscopy. Furthermore, the transform theory is to calculate a density profile of micelles around a large spherical surface

A method for calculating solvation structure on a sample surface from a force curve between a probe and the sample: One-dimensional version

Recent surface force apparatus (SFA) and atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in solvent. The force curve is thought as the solvation structure in some articles, because its shape is generally oscilltive and pitch of the oscillation is about the same as diameter of the solvent. However, it is not the solvation structure. It is only the force between the probe and the sample surface. Therefore, this brief paper presents a method for calculating the solvation structure from the force curve. The method is constructed by using integral equation theory, a statistical mechanics of liquid (Ornstein-Zernike equation coupled by hypernetted-chain closure). This method is considered to be important for elucidation of the solvation structure on a sample surface.Comment: Solvation Structure, Hydration Structure, SFA, AFM, Integral Equation Theor

Measurement theory of a density profile of small spheres on a cylindrical surface: Conversion of force curve measured with surface force apparatus into pressure on its surface element

Recently, in an ensemble of small spheres, we proposed a method that converts the force between two large spheres into the pressure on the large sphere's surface element. Using it, the density distribution of the small spheres around the large sphere can be obtained experimentally. In a similar manner, in this letter, we propose a transform theory for surface force apparatus, which transforms the force acting on the cylinder into the density distribution of the small spheres on the cylindrical surface. The transform theory we derived is briefly explained in this letter.Comment: 3 figure

A method of comparison between a force curve measured on a solvated surface and the solvation structure

Recent atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in solvent. The force curve is thought as the solvation structure in some cases, because its shape is generally oscilltive and pitch of the oscillation is about the same as diameter of the solvent. However, it is not the solvation structure. It is just only a mean force between the probe and the sample surface. A theoretical relation between the mean force and the solvation structure is not clearly known. Therefore, the relation must be elucidated theoretically to deepen understanding of the mean force measured by the AFM. In this letter, we briefly explain the relation and a method for comparing the measured mean force and the solvation structure (that obtained by a simulation, a liquid theory, or a x-ray reflectivity) by using basic statistical mechanics of liquid

Relation between a force curve measured on a solvated surface and the solvation structure: Relational expressions for a binary solvent and a molecular liquid

Recent atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in several solvents. The force curve is thought as the solvation structure in some cases, because its shape is generally oscilltive and pitch of the oscillation is about the same as diameter of the solvent. However, it is not the solvation structure. It is just only a mean force between the probe and sample surface. Since theoretical relation between the mean force and the solvation structure had not been clearly known, we have recently derived a relational expression within a simple liquid. Although we have derived the relational expression within the simple liquid, the relational expressions for a binary solvent and a molecular liquid have still not known clearly. Hence, we try to obtain the relational expressions in the two types of the solvents. In this letter, we briefly derive the relations and explain a method for comparing the mean force measured by liquid AFM and the solvation structure (obtained by a simulation, a liquid theory, or a x-ray reflectivity). The derivations of the relational expressions are performed in the basis of classical statistical mechanics of liquid