Showing 1–15 of 15 results for author: Amano, K

Introduction of Probability Density Alternation Method for Inverse Analyses of Integral Equations in Surface Science

Authors: Keito Hashidate, Rieko Iwayasu, Takumi Otake, Ken-ichi Amano

Abstract: Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed inverse calculations to obtain the pressure between parallel plates from measured interaction forces. These inverse analyses were used to reconstruct solvation st… ▽ More Integral equations frequently arise in surface science, and in some cases, they must be treated as inverse problems. In our previous work on optical tweezers, atomic force microscopy, and surface force measurement apparatus, we performed inverse calculations to obtain the pressure between parallel plates from measured interaction forces. These inverse analyses were used to reconstruct solvation structures near solid surfaces and density distribution profiles of colloidal particles. In the course of these studies, we developed a method that enables inverse analyses through a unified and systematic procedure, hereafter referred to as the Probability Density Alternation (PDA) method. The central idea of this method is to reformulate a given integral equation in terms of probability density functions. In this letter, we demonstrate the validity of the PDA method both analytically and numerically. While the PDA method is less advantageous for single integral equations, it becomes a convenient and powerful approach for inverse analyses involving double or higher-order integral equations. △ Less

Submitted 11 January, 2026; originally announced January 2026.

Introduction of Additive Particle Theory for Path Integral Approaches

Authors: Ken-ichi Amano

Abstract: Path integral approaches have been used for boson and fermion systems. The path integral approach has been successful in the many-boson system. However, in the many-fermion system, the path integral approach is not feasible due to the sign problem. In this letter, I introduce additive particle (AP) theory in order to generate an approximation method that avoids the sign problem. The AP theory cons… ▽ More Path integral approaches have been used for boson and fermion systems. The path integral approach has been successful in the many-boson system. However, in the many-fermion system, the path integral approach is not feasible due to the sign problem. In this letter, I introduce additive particle (AP) theory in order to generate an approximation method that avoids the sign problem. The AP theory considers one electron as a string polymer, and virtual particles are added into the system. The AP theory is an approximation, but it is constructed to be able to generate the pair distribution function between free electrons and the density of states of the free electrons at an arbitrary temperature. Hence, when the electrostatic interactions are decreased, the AP theory converges to the free electron system. On the other hand, it deviates from the actual system when the electrostatic interactions are increased. Star polymer approximation and extended star polymer approximation are also introduced. △ Less

Submitted 14 July, 2026; v1 submitted 22 November, 2024; originally announced December 2024.

Strategy of a separation technique for different particles with the same size and zeta potential: Application of non-additive Asakura-Oosawa theory

Authors: Ikuma Ogasawara, Ken-ichi Amano

Abstract: In this letter, we use knowledge gained from our recent study to present a technique for separation of nanoparticles such as exosomes, anticancer drugs, and vaccines. The technique involves adding non-adsorptive polymers to a system in which two types of nanoparticles with the same size and zeta potential are dispersed. The different types of nanoparticles can be separated based on differences in… ▽ More In this letter, we use knowledge gained from our recent study to present a technique for separation of nanoparticles such as exosomes, anticancer drugs, and vaccines. The technique involves adding non-adsorptive polymers to a system in which two types of nanoparticles with the same size and zeta potential are dispersed. The different types of nanoparticles can be separated based on differences in their hydrophobicities and softness of the polymer. Using the non-additive Asakura-Oosawa theory and assuming a realistic model system, we were able to separate the two types of the particles with the same size and zeta potential in the model system. △ Less

Submitted 25 April, 2024; originally announced April 2024.

Strategies for deliveries of anti-cancer drugs from perspectives of a measurement theory and an adsorption theory

Authors: Ken-ichi Amano, Takumi Otake

Abstract: In this letter, we present anti-cancer drug delivery strategies using knowledges obtained from our recent studies. We have conducted inverse analyses of "density distributions of colloidal particles near a focused surface" and "pair potentials between the surface and the colloidal particle" using data measured by optical tweezers (OT) and atomic force microscopy (AFM). Non-additive Asakura-Oosawa… ▽ More In this letter, we present anti-cancer drug delivery strategies using knowledges obtained from our recent studies. We have conducted inverse analyses of "density distributions of colloidal particles near a focused surface" and "pair potentials between the surface and the colloidal particle" using data measured by optical tweezers (OT) and atomic force microscopy (AFM). Non-additive Asakura-Oosawa (NAO) theory and a lattice theory in statistical mechanics of simple polymers have been also our research topics. Summarizing the knowledges, we propose two strategies to increase the delivery rate of capsule shaped anti-cancer drugs to cancer cells. We consider that enhanced repulsion between the normal cell and the drug accelerates the attraction between the cancer cell and the drug, which can be named enhanced repulsion and accelerated adsorption (ERAA) effect. To realize the ERAA effect, we propose a supporting method for measuring the interactions using OT and AFM. In the second strategy, dose of water-soluble polymers is considered to realize adsorptions of the drugs and cancer cell derived exosomes onto the cancer cells, which we call non-specific and selective adsorption (NSSA) effect. In the main text, we explain the NSSA effect using the NAO theory. Moreover, we explain that structural stabilities of normal dispersed proteins around the cancer cells are not largely destroyed by the dosed polymers from the viewpoint of the lattice theory. △ Less

Submitted 17 April, 2023; originally announced April 2023.

Comments: 12 pages, 3 figures

Interaction between substrate and probe in liquid metal Ga: Experimental and theoretical analysis

Authors: Ken-ichi Amano, Kentaro Tozawa, Maho Tomita, Hiroshi Nakano, Makoto Murata, Yousuke Abe, Toru Utsunomiya, Hiroyuki Sugimura, Takashi Ichii

Abstract: Understanding the interaction between two bodies in a liquid metal is important for developing metals with high stiffness, strength, plasticity, and thermal stability. We conducted atomic force microscopy measurements in liquid Ga and performed a theoretical calculation in which the statistical mechanics of a simple liquid containing a quantum effect was used. The experiment and theory showed unus… ▽ More Understanding the interaction between two bodies in a liquid metal is important for developing metals with high stiffness, strength, plasticity, and thermal stability. We conducted atomic force microscopy measurements in liquid Ga and performed a theoretical calculation in which the statistical mechanics of a simple liquid containing a quantum effect was used. The experiment and theory showed unusual behaviours in the interactions between the probe and substrate in the liquid metal. In the interactions, there were relatively numerous oscillations and large amplitudes. Furthermore, the interaction ranges were relatively long. From the theoretical calculations, we found an asymmetric property that when the probe is solvophilic and the substrate is solvophobic, the interaction tends to be repulsive; when the solvation affinities are exchanged, the interaction tends to be attractive in the close position. Our findings will be useful for understanding and controlling dispersion stabilities of nanoparticles and chemical reactions in liquid metals. △ Less

Submitted 18 May, 2022; originally announced May 2022.

Non-additivities of the particle sizes hidden in model pair potentials and their effects on physical adsorptions

Authors: Ken-ichi Amano, Satoshi Furukawa, Rina Ishii, Ayane Tanase, Masahiro Maebayashi, Naoya Nishi, Tetsuo Sakka

Abstract: It is important to understand mechanism of colloidal particles assembly near a substrate for developments of batteries, heterogeneous catalysts, paints, and cosmetics. Knowledge of the mechanism is also important for crystallizations of the colloidal particles and proteins. In this study, we calculated the physical adsorption of colloidal particles on a flat wall by using the integral equation the… ▽ More It is important to understand mechanism of colloidal particles assembly near a substrate for developments of batteries, heterogeneous catalysts, paints, and cosmetics. Knowledge of the mechanism is also important for crystallizations of the colloidal particles and proteins. In this study, we calculated the physical adsorption of colloidal particles on a flat wall by using the integral equation theory, wherein small and large colloidal particles were employed. In the calculation system, electric double layer potentials were used as the pair potentials. In some cases, it was found from the calculation results that the small particles are more easily adsorbed. The result is unusual from the viewpoint of the Asakura-Oosawa theory: we call it "reversal phenomenon". Then, we investigated mechanism of the reversal phenomenon. As a result, it was found that the inversion phenomenon originates from the non-additivities of the particle sizes. In addition, we invented the method to analyze the non-additivity in the pair potentials. The method will be useful for checks of various simulation results and developments of force fields for simulations of the colloidal particles and proteins. △ Less

Submitted 17 May, 2022; originally announced May 2022.

Theoretical correction methods for optical tweezers: Acquisition of potentials of mean forces between colloidal particles in a bulk and on a surface

Authors: Ken-ichi Amano, Rikako Suzuki, Madoka Takasu

Abstract: It is known that line optical tweezers (LOT) can measure potential of mean force (PMF) between colloidal particles in the bulk. However, PMF obtained with LOT is empirically modified before showing the result of the final form in order to correct the potential rise at long distances. In the present letter, we derive theoretical correction methods for acquisition of PMF by using statistical mechani… ▽ More It is known that line optical tweezers (LOT) can measure potential of mean force (PMF) between colloidal particles in the bulk. However, PMF obtained with LOT is empirically modified before showing the result of the final form in order to correct the potential rise at long distances. In the present letter, we derive theoretical correction methods for acquisition of PMF by using statistical mechanics. Using the new methods, PMF can be obtained without the empirical fitting equation. Through the new methods, external potential acting on the trapped two colloidal particles induced by LOT can also be obtained. As an additional study, we explain two methods for obtaining PMF between colloidal particles on a substrate surface, in which a normal single optical tweezers with a fixed focal point is used, and for obtaining PMF between colloidal particles trapped by dual-beam optical tweezers in the bulk. These methods can also obtain the external potential acting on the trapped two colloidal particles. △ Less

Submitted 25 July, 2025; v1 submitted 24 March, 2020; originally announced March 2020.

Comments: In version 4, the correction method for dual-beam optical tweezers was added. In version 5, Eq. (40) was corrected

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

Authors: Ken-ichi Amano, Taira Ishihara

Abstract: 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… ▽ More 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. △ Less

Submitted 19 December, 2017; originally announced December 2017.

A theory for calculating the number density distribution of small particles on a flat wall from pressure between the two walls

Authors: Kota Hashimoto, Ken-ichi Amano

Abstract: Surface force apparatus (SFA) and atomic force microscopy (AFM) can measure a force curve between a substrate and a probe in liquid. However, the force curve had not been transformed to the number density distribution of solvent molecules (colloidal particles) on the substance due to the absence of such a transform theory. Recently, we proposed and developed the transform theories for SFA and AFM.… ▽ More Surface force apparatus (SFA) and atomic force microscopy (AFM) can measure a force curve between a substrate and a probe in liquid. However, the force curve had not been transformed to the number density distribution of solvent molecules (colloidal particles) on the substance due to the absence of such a transform theory. Recently, we proposed and developed the transform theories for SFA and AFM. In these theories, the force curve is transformed to the pressure between two flat walls. Next, the pressure is transformed to number density distribution of solvent molecules (colloidal particles). However, pair potential between the solvent molecule (colloidal particle) and the wall is needed as the input of the calculation and Kirkwood superposition approximation is used in the previous theories. In this letter, we propose a new theory that does not use both the pair potential and the approximation. Instead, it makes use of a structure factor between solvent molecules (colloidal particles) which can be obtained by X-ray or neutron scattering. △ Less

Submitted 9 February, 2017; originally announced February 2017.

Conversion of a force curve between chemically the same surfaces into the number density distribution of the particles on the surface using a structure factor

Authors: Ken-ichi Amano, Kota Hashimoto, Ryosuke Sawazumi

Abstract: Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a transform theory to obtain the number density distribution of the small colloidal particles on the large colloidal particle from the force curve. In this short l… ▽ More Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a transform theory to obtain the number density distribution of the small colloidal particles on the large colloidal particle from the force curve. In this short letter, we propose another method which utilizes Ornstein-Zernike equation coupled with a closure equation instead of Kirkwood superposition approximation. The new transform theory uses a structure factor measured by x-ray or neutron scattering, and applies Nelder-Mead method to find the solution. Since it is known that Ornstein-Zernike equation coupled with the closure equation is accurate compared with Kirkwood superposition approximation, the new transform theory is theoretically better than the previous methods when the structure factor and the closure equation are reliable. △ Less

Submitted 17 December, 2016; originally announced December 2016.

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

Authors: Kota Hashimoto, Ken-ichi Amano

Abstract: 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… ▽ More 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. △ Less

Submitted 22 July, 2015; originally announced July 2015.

Comments: 3 figures

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

Authors: Ken-ichi Amano

Abstract: 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 pro… ▽ More 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. △ Less

Submitted 19 August, 2016; v1 submitted 17 May, 2015; originally announced May 2015.

Measurement theory of a density profile of small colloids around a large colloid: Conversion of force between two-large spheres into pressure on the surface element

Authors: Ken-ichi Amano, Kota Hashimoto, Ryosuke Sawazumi

Abstract: We suggest a transform theory for calculating a density distribution of small colloids around a large colloid from a force curve between the two-large colloids. The main idea (calculation process) is that the force curve between the two-large colloids is converted into the pressure on the surface element of the large colloid. This conversion is different from the celebrated Derjaguin approximation… ▽ More We suggest a transform theory for calculating a density distribution of small colloids around a large colloid from a force curve between the two-large colloids. The main idea (calculation process) is that the force curve between the two-large colloids is converted into the pressure on the surface element of the large colloid. This conversion is different from the celebrated Derjaguin approximation. A numerical matrix calculation is performed in the conversion to calculate it more precisely. Subsequently, the pressure on the surface element is transformed into the density distribution of the small colloids around the large colloid by using a transform theory for surface force apparatus proposed by Amano. In this letter, the process of the transformation is explained and a prototype result of the transformation is shown. △ Less

Submitted 8 November, 2015; v1 submitted 16 May, 2015; originally announced May 2015.

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

Authors: Ken-ichi Amano, Kota Hashimoto

Abstract: 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 super… ▽ More 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. △ Less

Submitted 15 May, 2015; v1 submitted 12 May, 2015; originally announced May 2015.

A Transform Method of a Force Curve Obtained by Surface Force Apparatus to the Density Distribution of a Liquid on a Surface: An Improved Version

Authors: Ken-ichi Amano, Eisuke Tanaka

Abstract: We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is mo… ▽ More We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is more realistic compared with the rigid potential applied in our earlier work. The introduction of the model potential is the improved point of the present transform method. The transform method is derived based on the statistical mechanics of a simple liquid where the simple liquid is an ensemble of small spheres. To derive the transform method, Kirkwood superposition approximation is used. It is found that the transformation can be done by a sequential computation. It is considered that the solvation structure can be obtained more precisely by using the improved transform method. △ Less

Submitted 8 December, 2014; v1 submitted 8 August, 2014; originally announced August 2014.

Comments: Measurement theory for surface force apparatus