KR102564147B1 - Method and system for estimating of grafting density of polyelectrolyte brush-layer - Google Patents

Abstract

The present invention relates to a method and system capable of calculating the grafting density of a brush layer formed by grafting an electrolyte polymer to a channel wall. According to the present invention, the average length of the brush and the grafting density of the brush layer can be calculated from numerical quantification of the image data of the surface of the brush layer obtained through observation with an optical microscope. Compared to conventional methods that require expensive measuring devices such as atomic force microscopes (AFMs) and complex experimental procedures, calculations can be made more simply and accurately, as well as comparative verification with experimental values by these measuring devices. possible.

Description

Method and system for estimating of grafting density of polyelectrolyte brush-layer}

The present invention relates to a method and system capable of calculating the grafting density of a brush-layer formed by grafting a polyelectrolyte to a channel wall.

Microfluidics is a technical field related to fluid flow in microchannels, and unique phenomena and behaviors are related to it. Recently, great attention has been paid to the fact that the behavior of liquid flow changes depending on physicochemical properties such as hydrophilicity/hydrophobicity or charge of microchannel walls, ultimately affecting analysis and separation performance or sensing efficiency.

Shurenov and Sui [J. Schlenoff, Z. Sui, “Variable charge films for controlling microfluidic flow”, US patent registration (US 7,722,752 B2), 2010.5.25] uses the characteristics of electrolyte polymers that change sensitively to pH A film layer having a thickness of ㎛ was formed to control the electro-osmosis flow. The film formed on the wall of the channel is a multilayer formed by alternating cationic and anionic electrolyte polymers, and the speed and direction of the electroosmotic flow were controlled by adjusting the pH of the solution flowing through the channel in which the film was formed.

In the nanochannel, in the micro-energy conversion technology based on the principle of electrokinetics, the electrolytic polymer is introduced into the channel wall to add charge of the electrolyte polymer to the ionic charge in the bulk solution, thereby increasing the conversion efficiency. ) and attempts to obtain an improvement in output have been reported.

Chanda et al. [S. Chanda, S. Sinha, S. Das. "Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters", Soft Matter, 10, 7558, 2014] shows the flow under conditions of low surface potential in nanochannels grafted with high concentrations of electrolyte polymers. The potential and electroviscous effect were analyzed. They reported that when an electrolyte polymer brush is formed on the channel wall, the conversion efficiency increases by at least several times due to the change in the flow potential and the electrical viscosity effect for the change in the thickness of the electric double layer.

Patwari et al. [J. Patwary, G. Chen, S. Das, "Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density", Microfluid Nanofluid, 20, 37, 2016] grafting an electrolyte polymer onto the channel wall By analyzing the flow field reflecting the drag force in the brush layer and the electrostatic field considering the elasticity of the electrolyte polymer and the excluded volume effect in the Shikin nanochannel, pH and acid, which are the proton concentration index of the solution (acid) It has been reported that the flow potential increases according to the pKa value, which is the dissociation constant index, and the conversion efficiency can be improved up to the 5% level. Here, since ions can freely permeate in the brush layer region, the velocity distribution of the liquid is kept limited.

As described above, when a brush layer is formed by grafting a charged polymer, such as polyelectrolyte, on the channel wall, various industrial applications can be achieved by changing and controlling surface charge. As an example, when a solution flows through a microchannel, which is a key element of microfluidics, flow potential and flow current are generated by the interfacial electromotive principle, and mechanical energy is converted into electrical energy. In this case, when a microchannel grafted with an electrolyte polymer brush is introduced, the flow rate is reduced for the same pressure difference, and the maximum output and conversion efficiency can be expected to be improved by adjusting the charge density, which is the charge characteristic of the channel wall. there is

The electrolyte polymer brush layer may naturally be formed on an open surface such as a substrate or particles as well as an inner wall of a closed channel. As its applications, there are specific stimuli-response materials such as pH-sensitivity and redox-sensitivity, drug delivery, biosensing, and functional particles.

In the above case, the calculation or evaluation of the grafting density, which is defined as the number of brushes per unit area in the brush layer formed on the open surface or the inner wall of the channel, is a very important basis for material development, property prediction, processing, and process. It is information.

J. Schlenoff, Z. Sui, “Variable charge films for controlling microfluidic flow”, US patent registration (US 7,722,752 B2), 2010.5.25.

S. Chanda, S. Sinha, S. Das. "Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters", Soft Matter, 10, 7558, 2014. J. Patwary, G. Chen, S. Das, "Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density", Microfluid Nanofluid, 20, 37, 2016.

Important information in the grafting of the electrolyte polymer to the channel wall is the grafting density, which is the number of brushes per unit area in the brush layer formed as shown in FIG. It is required.

An object of the present invention is to provide a method and system capable of accurately calculating the grafting density from data processing of light intensity obtained by dyeing a brush layer and observing the dyed surface with an optical microscope. In addition, an object of the present invention is to provide a method and system capable of verifying the reliability of the result by comparing the average length of the brush and the grafting density calculated therefrom with the experimental value by a measuring device.

Meanwhile, as shown in FIG. 1B, various types of electrolyte (eg, KCl) solutions or electrolyte polymer solutions may exist in the bulk region inside the channel under various conditions (eg, concentration, pH, etc.). If the grafting density for various conditions is calculated, the average distance between the brushes and the average length of the brushes can be calculated, and from this, a model in the brush layer is introduced, and the electrostatic field relation and Nernst-Planck ion movement The charging characteristics of the brush layer can be obtained by repetitively calculating the flux relational equations simultaneously. Here, the charge characteristics are determined by the distribution of electrostatic potential to a space a certain distance from the channel wall, the surface potential determined from the distribution of electrostatic potential, and the net charge density, which is the amount of charge per unit volume. all.

The object of the present invention is not limited to the object mentioned above. The objects of the present invention will become more apparent from the description that follows, and will be realized by means and combinations thereof set forth in the claims.

A description of each step for solving the task is as follows.

A method for calculating the grafting density of a brush layer formed by grafting an electrolyte polymer on a channel wall according to an embodiment of the present invention includes quantifying light intensity on a surface of a dyed brush layer through optical microscope observation; Calculating an average distance between brushes formed in the brush layer; Calculating an average length of brushes formed on the brush layer; Calculating the grafting density of the brush layer; and introducing a concentration distribution function model in the brush layer and evaluating charge characteristics of the brush layer. can include

The overall process of the above calculation method is shown in FIG.

(1) quantifying the light intensity of the dyed brush layer surface by optical microscope observation

Referring to FIG. 2 , the step may include the following detailed steps.

The brush layer formed by grafting the electrolyte polymer is dyed with an appropriate dye, and as shown in FIG. 3, an image data screen of the dyed brush layer surface can be obtained with an optical microscope camera. In one embodiment, the microchannel made of a transparent material may be formed as a space surrounded by mutually parallel upper and lower wall surfaces and two mutually parallel sidewall surfaces. As shown in FIG. 1B, this microchannel has a rectangular cross section having a depth H , which is the separation distance between the upper and lower walls, and a width W , which is the separation distance between the two sidewall surfaces, and the depth H and the width W are smaller than the length L. can be formed

A brush layer formed on an inner wall of the channel may be dyed, and the transparent channel may be photographed by a photographing device (eg, a CCD or CMOS camera). At this time, it is preferable to measure so that the focal volume determined by the focal depth of the objective lens is located on the upper or lower surface of the channel.

Next, the image data may be processed to obtain the intensity of light from the image data. The image data processing process may be performed by an arithmetic device such as a computer. In addition, the processing of image data may be performed using any software that is known or to be developed in the future, running on a computer. For example, the process of processing the image data may be performed by commercial software, MATLAB (Mathworks, MA), but is not limited thereto.

In the image data processing process, first, image data obtained for the surface of the brush layer may be digitized according to light intensity to form data consisting of one color. In one embodiment, the acquired image data may be numerically matrixed according to light intensity in units of pixels by selecting a light color suitable for a dye color. An averaging process may be performed to reset the value of each element of the numerical matrix of one color to a value obtained by averaging the value of the corresponding element and values of elements adjacent to the corresponding element. As a result, the average value of the light intensity of all pixels of the given image data can be obtained using the averaged numerical matrix.

A specific numerical calculation method will be described in detail below.

Image data according to an embodiment has the number of pixels determined according to the performance of a camera. In the following description, it will be assumed that image data has m pixels vertically and n pixels horizontally (m and n are natural numbers). The image data of the color selected according to the dye color can be represented and analyzed as an m×n numerical matrix for m vertical and n horizontal pixels, respectively.

It can be expressed as an m×n matrix G _mn whose element is g, the pixel intensity for the selected color. Since the color intensity is not constant according to the pixel position, it can be averaged as the average of the values of the matrix elements. For example, a 3×3 matrix G _{L ,ij including elements around a point (i,j) of an arbitrary element g ij} of the matrix G mn as _a center is defined as in Equation 1 below.

[Equation 1]

For each element of the matrix G _mn , a local average value can be obtained by applying an arbitrary first order moment. For example, the regional average value g _A,ij at the point (i,j) can be expressed as Equation 2 below.

[Equation 2]

By extending the regional average value g _A,ij calculated above to all elements g _A,mn of the G _mn matrix, which is all pixels of the given image data, the overall average value G _A of light intensity on the surface of the brush layer is obtained by Equation 3 can be obtained as

[Equation 3]

(2) Calculating the average distance between brushes formed in the brush layer

The surface on which the brush layer is not formed at all (i.e., grafting degree: 0%) is completely achromatic as it is not dyed at all, and the surface completely covered with the brush layer (i.e., grafting degree: 100%) shows the dye color itself. Therefore, a calibration curve representing the relationship between this value and the degree of grafting can be drawn as shown in _FIG . Using the correction curve, it is possible to know the degree of grafting with respect to the overall average value G _A of arbitrary light intensities obtained from given image data, and then to calculate the grafting density, which is the number of brushes per unit area.

The horizontal and vertical lengths of the image data of the microscope camera are A and B , respectively, and the size of a square pixel can be determined by the magnification of the objective lens and camera conditions. The number of pixels N _F of the grafted region can be determined in Equation 4 below from the value of α , which is the degree.

[Equation 4]

One or more brushes exist in one pixel, and the number can be determined from the diameter according to the chemical structure of the electrolyte polymer chain. If the number of brushes present in one pixel is β , the total number of grafted brushes is βN _F Therefore, lb , which is the average distance between the brushes _, can be calculated from Equation 5 below.

[Equation 5]

(3) calculating the average length of the brushes formed on the brush layer

Referring to FIGS. 1A and 1B , the average length of brushes formed on the electrolytic polymer brush layer is substantially equal to the thickness of the brush layer. Therefore, calculating the average length of the electrolytic polymer brush is substantially the same as calculating the thickness of the brush layer.

The average length of the brush (ie, the thickness of the brush layer) can be calculated according to Equation 6 below using the average distance ( lb ) _between the electrolyte polymer brushes.

[Equation 6]

In Equation 6, h is the thickness of the brush layer, b _k is the Kuhn length, N _k is the number of b _k in one electrolyte polymer chain, and N _k b _k is the maximum length of the electrolyte polymer chain Correspondingly, a is the Flory-Huggins coefficient determined by the degree of dissociation of the electrolyte polymer. These factors for any electrolyte polymer can be obtained through various literature information, which can also be input through the client.

On the other hand, the calculated average length can be compared with the average length of experimental brushes obtained using a measuring device.

(4) Calculating the grafting density of the brush layer

In the electrolyte polymer brush layer, the grafting density, which is the number of brushes per unit area of the channel wall, may vary depending on the shape of the unit area around the brush.

The grafting density σ when the periphery of each electrolytic polymer brush grafted on the channel wall is set as a square unit area is the average distance l _b between the brushes in Equation 7 below can be calculated from

[Equation 7]

On the other hand, the grafting density σ when the periphery of each electrolytic polymer brush grafted on the channel wall is set as a circular unit area is the average distance l _b between the brushes in Equation 8 below. can be calculated from

[Equation 8]

Therefore, the grafting density σ of the brush layer from Equations 7 and 8 above may have a range as shown in Equation 9 below.

[Equation 9]

The grafting density can be measured experimentally or obtained from literature information. The above measurement values or literature information can be input through a separate client accessible by the user.

(5) introducing a concentration distribution function model in the brush layer and evaluating the charging characteristics of the brush layer

The concentration distribution function f of the electrolyte polymer can be obtained by molecular modeling, and in most cases, except for exceptional cases where the concentration is considerably high, it can be reasonably assumed as a quadratic function model.

FIG. 5 illustrates each area to which the concentration distribution function model of the brush layer is applied on the wall surface of a microchannel having a rectangular cross section. Specifically, f _x , which is the concentration distribution function for the x direction, which is the width direction inside the rectangular channel, and the height direction, It shows a section to which f _y , a concentration distribution function in the y direction, and f _xy , a concentration distribution function in an area where the width and height directions overlap, are applied.

These concentration distribution function models are normalized to have 1 when integrated over a section from the channel wall to h , the thickness of the brush layer, and become 0 in sections other than the brush layer.

The concentration distribution function f _x is expressed by Equation 10 below, and is an area in the x- direction, which is the width ( W ) direction of the channel, | x | represents the concentration distribution for the region from 0 to W /2.

[Equation 10]

In Equation 10, h is the thickness of the brush layer and W is the width of the channel.

On the other hand, the concentration distribution function f _y is expressed by Equation 11 below, and as an area in the y direction, which is the height ( H ) direction of the channel, | y | represents the concentration distribution for the region from 0 to H /2.

[Equation 11]

In Equation 11, h is the thickness of the brush layer, and H is the height of the channel.

Meanwhile, the concentration distribution function f _xy is expressed by Equation 12 below.

[Equation 12]

When the channel wall surface is charged, due to the movement of electrolyte polymer ions in the liquid, counter-ions with opposite charge signs of the wall surface gather around the wall surface, forming an electric double layer and electrostatic potential distribution.

The thickness of the electric double layer is a measure of the electrostatic interaction and is inversely proportional to the square root of the concentration of ions present in the liquid. In other words, in distilled water having an extremely low ion concentration of 10 ^-7 mol (M), the electric double layer is the thickest at the maximum level of 1 μm, so the wall charge is very strong, and as the ion concentration increases, the electric double layer becomes thinner and the wall charge becomes weaker. .

The step of calculating the electrostatic potential distribution may be iterative calculation by associating an electrostatic field relational expression and a Nernst-Planck ion movement flux relational expression.

The electrostatic field relational expression shows that when the brush layer is formed on the channel wall in contact with the solution, the mobile charge in the electric double layer around the wall and the fixed charge in the brush layer due to the dissociation of the electrolyte polymer In consideration of this, the relationship between the electrostatic potential and the total charge density may be derived and expressed from the Poisson equation.

On the other hand, the flux of i ions in the brush layer originates from diffusion by the concentration gradient and migration by the potential gradient, which can be quantified using the Nernst-Planck ion migration flux relation. Bar, This is a boundary-value problem of partial differential equations, and can be solved if the boundary conditions in the channel wall and the bulk region are given.

When the concentration distribution function model in the brush layer is introduced as described above, the charging characteristics of the brush layer can be evaluated through the above steps. That is, if the electrostatic potential distribution from the channel wall to a space at a certain distance is calculated, the surface potential Ψ _s defined at the point of the channel wall can be obtained, and then the unit volume by the fixed charge of the electric double layer and the brush layer The total charge density for each can be obtained.

Surface potential is an important measure of electrostatic interaction, and the larger its absolute value, the stronger the charge on the wall. The calculated surface potential can be compared with the experimentally measured zeta potential. Typically, the zeta potential value corresponds to about 70-80% of the absolute value of the surface potential.

A system for calculating the grafting density of the electrolytic polymer brush layer formed on the channel wall surface according to an embodiment of the present invention may include an optical microscope and a server that performs the above-described calculation method. Each module included in the server may perform each of the aforementioned steps. The calculation system may further include a client that allows a user to input necessary information and is connected to the server.

In addition, the calculation system may include a measuring device capable of measuring and comparing the average length and grafting density of brushes formed on the wall surface of the channel by incising the channel, which is an atomic force microscope (AFM) , a spectroscopic ellipsometer, a Fourier transform infrared-attenuated total reflection (FTIR-ATR) spectrometer, and the like. For example, the roughness of the original material of the channel and the roughness of the brush layer formed on the channel wall by cutting the channel can be measured by AFM, and the differences can be compared with the average length of the brushes experimentally obtained.

The grafting density calculated in the present invention can determine the degree of grafting and is important information in evaluating electrostatic potential distribution, surface potential, and total charge density, which are charge characteristics of the brush layer.

In addition, in calculating the average length and grafting density of the electrolyte polymer brush layer, it can be calculated more simply and accurately than conventional methods that require expensive measuring devices such as AFM and complicated experimental procedures, and these measuring devices It can take the technical competitiveness that it is possible to compare and verify with the experimental values by

The effects of the present invention are not limited to the effects mentioned above. It should be understood that the effects of the present invention include all effects that can be inferred from the following description.

FIG. 1A shows electrolyte polymer brushes formed by grafting on the channel wall, and FIG. 1B shows a state in which a brush layer is formed on the inner wall of the channel and a potassium chloride (KCl) solution or an electrolyte polymer solution is filled in the bulk area inside the channel. it is a drawing
2 is a view sequentially showing the process of calculating the grafting density of the electrolytic polymer brush layer grafted on the channel wall and subsequently evaluating the charging characteristics of the brush layer.
3 is a diagram illustrating a process of obtaining an image data screen photographed by an optical microscope and a camera for a dyed brush layer formed on an inner wall of a transparent channel.
FIG. 4 is a diagram showing a calibration curve showing the relationship between the relative light intensity obtained from the image data for each case of grafting (ie, the light intensity based on the maximum overall average value) and the degree of grafting.
5 is a concentration distribution function in the channel width direction according to the average length of the electrolyte polymer brush for each area to which the concentration distribution function model of the electrolyte polymer brush layer is applied on the wall of the microchannel having a rectangular cross section and the pH change of the solution is a drawing representing
6 is a graph showing the relationship between the degree of dissociation of polyacrylic acid and the Flurry-Huggins coefficient ( a ), which varies according to the hydrogen ion concentration index (pH).
7 is an optical microscope photograph of an ultraviolet (UV) irradiation process for forming a polyacrylic acid brush layer on a channel wall and a transparent microchannel and a polyacrylic acid brush layer of a microchannel stained with toluidine blue, respectively. is a drawing showing
8 is a graph showing the result of the grafting density calculated for the average length ( h ) of polyacrylic acid (PAA) brushes, which is an electrolyte polymer, according to the pH of the solution.

The above objects, other objects, features and advantages of the present invention will be easily understood through the following preferred embodiments in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments described herein and may be embodied in other forms. Rather, the embodiments introduced herein are provided so that the disclosed content will be thorough and complete and the spirit of the present invention will be sufficiently conveyed to those skilled in the art.

Like reference numerals have been used for like elements throughout the description of each figure. In the accompanying drawings, the dimensions of the structures are shown enlarged than actual for clarity of the present invention.

In this specification, terms such as "include" or "have" are intended to designate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, but one or more other features It should be understood that it does not preclude the possibility of the presence or addition of numbers, steps, operations, components, parts, or combinations thereof. In addition, when a part such as a layer, film, region, plate, etc. is said to be "on" another part, this includes not only the case where it is "directly on" the other part, but also the case where another part is present in the middle. Conversely, when a part such as a layer, film, region, plate, etc. is said to be "under" another part, this includes not only the case where it is "directly below" the other part, but also the case where another part is in the middle.

Unless otherwise specified, all numbers, values and/or expressions expressing quantities of components, reaction conditions, polymer compositions and formulations used herein refer to the number of factors that such numbers arise, among other things, to obtain such values. Since these are approximations that reflect the various uncertainties of the measurement, they should be understood to be qualified by the term "about" in all cases. Also, when numerical ranges are disclosed herein, such ranges are contiguous and include all values from the minimum value of such range to the maximum value inclusive, unless otherwise indicated. Furthermore, where such ranges refer to integers, all integers from the minimum value to the maximum value inclusive are included unless otherwise indicated.

Hereinafter, an embodiment in which the grafting density of the brush layer formed on the channel wall surface is calculated by the above-described calculation method according to the present invention will be described in detail.

In the present invention, polyacrylic acid having a molecular weight in the range of 3×10 ⁴ g/mol to 5×10 ⁴ g/mol was considered as an electrolyte polymer grafted on the channel wall, and 0.01 mM as a bulk solution present inside the channel. A KCl solution at a concentration or a polyacrylic acid solution at a concentration of 0.4 wt % with a molecular weight of 4.5×10 ⁵ g/mol was considered.

Polyacrylic acid selected as the electrolyte polymer in the present invention has a chain structure with a degree of polymerization of 6,245 if the molecular weight of the monomer acrylic acid (CH ₂ -CHCOOH) is 72.06 g/mol, for example, the molecular weight is 4.5×10 ⁵ g/mol. It is a polymer with Since there is one carboxylic acid anionic group per single molecule, a total of 6,245 anionic groups exist when one polyacrylic acid chain is completely dissociated. If the acrylic acid single molecule is RCOOH, the dissociation constant Ka from the dissociation reaction (ie, RCOOH → H ⁺ + RCOO ^- ) is expressed by Equation 13 below.

[Equation 13]

Ka = [H ⁺ ][RCOO ^- ]/[RCOOH]

Here, the degree of dissociation, which is the fraction occupied by charged single molecules in one polyacrylic acid chain, is expressed by an expression related to pH and pKa. If the degree of dissociation is 0.8, a total of 4,996 (= 6,245 × 0.8) anionic groups exist in one polyacrylic acid chain.

Various factors of Equation 6 can be obtained through various literatures, the Kuhn length ( b _k ) is 0.64-11 nm depending on the pH condition, and the Flurry-Huggins coefficient ( a ) is the hydrogen ion concentration It is determined according to the degree of dissociation in the brush layer and bulk solution of polyacrylic acid, which changes according to the index (pH), and this relationship can be obtained as shown in FIG. 6 from literature values.

7 shows a grafting polymerization process by ultraviolet (UV) irradiation for filling the inside of the microchannel with an acrylic acid solution and forming a polyacrylic acid brush layer on the channel wall, and a transparent microchannel and toluidine blue, a blue dye, to the channel These are pictures taken with an optical microscope of the polyacrylic acid brush layer of the microchannel dyed by flowing into the inside.

A microfluidic chip with microchannels having a structure having a width ( W ) of 60 μm, a height ( H ) of 50 μm, and a length ( L ) of 0.8 cm was manufactured. It was considered that it was made of dimethylsiloxane (polydimethylsiloxane: PDMS) material, but other transparent materials such as glass and silicon may be considered.

From the result of the grafting density calculated for the average length ( h ) of the polyacrylic acid brush, which is an electrolyte polymer, according to the pH of the solution in FIG. 8, it can be seen that the grafting density increases as the average length increases. On the other hand, in the average length of a given brush, it can be seen that as the pH of the solution increases, the degree of dissociation increases, and the polyacrylic acid chain spreads due to the electrostatic repulsive force of more acrylic acid anions, increasing the grafting density. According to the conditions in the present invention, the grafting density ( s ) is about 0.02/nm ² to 0.15/nm ² range.

On the other hand, the calculated average length of the brush formed on the channel wall and the grafting density of the brush layer can be compared with experimental values obtained by measuring devices such as AFM, ellipsometer, and FTIR-ATR after cutting the microchannel.

For reference, the acrylic acid ion concentration is the product of the concentration of the electrolyte polymer, the degree of dissociation according to the pH of the electrolyte polymer, and the degree of polymerization of the electrolyte polymer, and the concentration of the electrolyte polymer is the grafting density ( σ ), the concentration distribution function model ( f ) and It is determined by the average length ( h ) of the electrolyte polymer.

As above, the experimental examples and examples of the present invention have been described in detail, the scope of the present invention is not limited to the above-described experimental examples and examples, and the basic concept of the present invention defined in the following claims Various modifications and improvements made by those skilled in the art are also included in the scope of the present invention.

Claims (18)

In the method for calculating the grafting density of a brush layer formed by grafting an electrolyte polymer on a channel wall,
quantifying the light intensity of the surface of the dyed brush layer by observation with an optical microscope;
Calculating an average distance ( _lb ) between the brushes formed in the brush layer;
Calculating an average length ( h ) of brushes formed in the brush layer; and
Calculating the grafting density ( σ ) of the brush layer,
The step of quantifying the light intensity of the surface of the brush layer dyed by the optical microscope observation,
A detailed step of acquiring an image data screen with an optical microscope camera for the surface of the dyed brush layer;
a detailed step of forming data consisting of one color by numerically matrixing the acquired image data according to light intensity;
an averaging sub-step of resetting the value of each element of the numerical matrix consisting of one color to a value obtained by averaging the value of the corresponding element and values of elements adjacent thereto; and
A method for calculating the grafting density of a brush layer, including a detailed step of calculating an overall average value of light intensity for all pixels of given image data using an averaged numerical matrix.
delete According to claim 1,
The detailed steps of forming data consisting of one color by numerically matrixing the acquired image data according to light intensity are:
A method of expressing the image data of the color selected according to the dye color as an m×n numerical matrix for m vertical and horizontal n pixels (m, n are natural numbers), respectively.
According to claim 1,
In the averaging sub-step of resetting the value of each element of the numeric matrix of one color to the average value of the value of the element and its adjacent elements,
Calculation _method of averaging with the average of the values of the matrix elements since the intensity of the color is not constant depending on the pixel location.
According to claim 4,
A calculation method in which a 3 × 3 matrix G _{L,ij including elements around the point (i, j) of an arbitrary element g ij of the} matrix G _mn is defined as in Equation 1 below.
[Equation 1]

Here _, a local average value can be obtained by applying an arbitrary first-order moment to each element of the matrix G _mn .
[Equation 2]

According to claim 1,
The detailed steps of calculating the overall average value of the light intensity for all pixels of the given image data using the averaged numerical matrix are:
By extending the calculated regional average value g _A,ij for all elements g _A,mn of the G _mn matrix, which is all pixels of the given image data, the overall average value G _A of light intensity on the surface of the brush layer is obtained by Equation 3 Calculation method obtained as follows.
[Equation 3]

According to claim 6,
The step of calculating the average distance between the brushes formed in the brush layer,
A calibration curve representing the relationship between this value and the degree of grafting is shown by making the overall average value of light intensity G _A for each grafted case dimensionless as the maximum light intensity, and obtained from the given image data using the calibration curve. A method of calculating the grafting density, which is the number of brushes per unit area, after knowing the degree of grafting for the overall average value G _A of any light intensity.
According to claim 7,
The horizontal and vertical lengths of the microscope camera's image data are A and B, respectively, and the size of a square pixel is determined by the objective lens magnification and camera conditions. The number of pixels N _F of the grafted area is determined from the value of α in Equation 4 below,
[Equation 4]

One or more brushes exist in one pixel, and the number is determined from the diameter according to the chemical structure of the electrolyte polymer chain. If the number of brushes present in one pixel is β , the total number of grafted brushes is βN _F Therefore, l _b , which is the average distance between the brushes, is calculated from Equation 5 below.
[Equation 5]

According to claim 1,
Calculating the average length of the brushes formed in the brush layer,
Calculation method comprising _the step of calculating the average length of the brush (ie, the thickness of the brush layer) according to the following Equation 6 using the average distance ( lb ) between the electrolyte polymer brushes.
[Equation 6]

In Equation 6, h is the thickness of the brush layer, b _k is the Kuhn length, N _k is the number of b _k in one electrolyte polymer chain, and N _k b _k is the maximum length of the electrolyte polymer chain Correspondingly, a is the Flory-Huggins coefficient determined by the degree of dissociation of the electrolyte polymer.
According to claim 1,
The step of calculating the grafting density of the brush layer,
Setting a square unit area around the electrolytic polymer brush, and calculating the grafting density of the square unit area by Equation 7 below;
[Equation 7]

Setting a circular unit area around the electrolyte polymer brush, and calculating the grafting density of the circular unit area by Equation 8 below; and
[Equation 8]

A calculation method comprising the step of having the same range as Equation 9 below from Equation 7 and Equation 8.
[Equation 9]

Calculating an average length of brushes formed on the brush layer calculated according to claim 1; and
A method for calculating the grafting density of a brush layer comprising introducing a concentration distribution function model in the brush layer and evaluating charging characteristics of the brush layer.
According to claim 11,
The step of introducing the concentration distribution function model
Inside a channel with a rectangular cross section, f _x is the concentration distribution function in the x direction, which is the width direction, f _y is the concentration distribution function in the y direction, which is the height direction, and f is the concentration distribution function in the area where the width and height directions overlap. Apply _xy ,
The concentration distribution functions are normalized to have 1 when integrated over a section from the channel wall to h , the thickness of the brush layer, and become 0 in sections other than the brush layer.
According to claim 12,
The concentration distribution function f _x is expressed by Equation 10 below, and is an area in the x- direction, which is the width ( W ) direction of the channel, | x | represents the concentration distribution for the region from 0 to W / 2,
[Equation 10]

(In Equation 10, h is the thickness of the brush layer and W is the width of the channel)
The concentration distribution function f _y is expressed by Equation 11 below, and as an area in the y- direction, which is the height ( H ) direction of the channel, | y | represents the concentration distribution for the region from 0 to H / 2,
[Equation 11]

(In Equation 11, h is the thickness of the brush layer, H is the height of the channel)
The concentration distribution function f _xy is a calculation method expressed by Equation 12 below.
[Equation 12]

According to claim 11,
The step of evaluating the charge characteristics of the brush layer,
The electrostatic field relation and the Nernst-Planck ion movement flux relation are combined and repeatedly calculated to calculate the electrostatic potential distribution from the channel wall to a space at a certain distance, from which the surface potential Ψ _s defined at the channel wall Obtaining, and then obtaining total charge densities per unit volume due to fixed charges of the electric double layer and the brush layer, respectively.
According to claim 14,
The above electrostatic field relation is that when the brush layer is formed on the channel wall in contact with the solution, the mobile charge in the electric double layer around the channel wall and the fixed charge in the brush layer due to the dissociation of the electrolyte polymer Calculation method comprising the step of deriving from Poisson's equation in consideration of.
According to claim 1,
A microfluidic chip made of transparent polydimethylsiloxane (PDMS) with microchannels having a predetermined width, height and length is manufactured,
An acrylic acid solution is filled inside the channel, and a polyacrylic acid brush layer, an electrolyte polymer, is formed on the channel wall by a grafting polymerization technique by UV irradiation, and toluidine blue, a blue dye, is applied to the inside of the channel. A calculation method of dyeing the brush layer by shedding.
optical microscope; and
A system for calculating the grafting density of a brush layer formed by grafting an electrolyte polymer to a channel wall including a server performing the calculation method according to any one of claims 1 and 3 to 16.
According to claim 17,
The brush layer formed by grafting an electrolyte polymer to the channel wall including a measuring device capable of measuring and comparing the average length of the brush formed on the wall of the channel and the grafting density of the brush layer by cutting the channel. Rafting Density Calculation System.