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Register a new userMeasurement theory of a density profile of small colloids around a large colloid: Superposition of the radial distribution functions
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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.
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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.
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.
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 spheres 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.
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.
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.
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