KR101950771B1 - Method and apparatus for analyzing of polyelectrolyte adsorbed layer in microfluidic channel - Google Patents

Abstract

The present invention relates to a method and an apparatus for calculating an accurate thickness of a polyelectrolyte adsorbed layer formed on a channel wall surface by a polymer brush when a liquid having a polyelectrolyte flows in a microfluidic channel. According to the present invention, instead of a conventional method required for high-priced equipment, an accurate thickness of a polyelectrolyte adsorbed layer can be quickly and conveniently calculated from repeated calculation to minimize a relative error between average flow velocity calculated from viscosity measured from a liquid having a polyelectrolyte dispersed with various molecular weights and concentrations and directly measured average flow velocity.

Description

TECHNICAL FIELD The present invention relates to a method and an apparatus for analyzing an electrolyte polymer adsorbent layer in a microfluidic channel,

When a polyelectrolyte solution is flowed through a microfluidic channel, flow potential and flow current are generated by the electrokinetics principle. As a result of this, as an energy conversion and harvesting technology for converting mechanical energy into electric energy, . When an electrolyte polymer solution is poured into the microfluidic channel, an adsorbed-layer of an electrolyte may be formed on the channel wall surface. As a result, the flow rate is decreased with respect to the same pressure difference. However, The charge density is increased and the maximum output and the conversion efficiency are improved.

Microfluidics is a field of study of fluid flow in microchannels, where unique phenomena and behavior are related. Recently, attention has been paid to the fact that liquid flow characteristics are changed as the wall characteristics of microfluidic channels are changed, such as adding hydrophilicity or hydrophobicity to channel walls, ultimately affecting analytical efficiency and performance.

Schlenoff and Sui [J. Schlenoff, Z. Sui, "Variable charge films for controlling microfluidic flow", US patent application (7,722,752), May 25, 2010] discloses a microfluidic channel using a characteristic of an electrolyte polymer which is sensitive to pH, A film having a thickness in the range of 1 nm to 1 [mu] m was formed inside to control the electroosmosis flow. The film formed on the channel walls was a multilayer formed by alternating cationic electrolyte polymer and anionic electrolyte polymer, and the direction and velocity of the electroosmotic flow were controlled by controlling the pH of the solution flowing through the channel in which the film was formed.

In addition, attempts have been made to obtain higher output by introducing an electrolyte polymer to the wall surface of the nanochannel in the interface electrokinetic energy conversion technology to add the chargeability of the electrolyte polymer to the ionic charge of the bulk solution.

[S. Chanda, S. Sinha, S. Das. "Soft Matter, 10, 7558, 2014], which is a new type of nanofluidic electrochemomechanical energy converters, Electric potential and electroviscous effect were analyzed. When the electrolyte polymer brush is formed on the channel wall, the change of the electric potential and the electric viscous effect against the change of the electric double layer thickness are lowered. In particular, the formation efficiency of the electrolytic polymer brush is at least several times higher than that of the electrolytic polymer brush Respectively.

Patwari et al. [J. Patfary, G. Chen, and S. Das, "Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density", Microfluid Nanofluid, 20, 37, 2016) grafts an electrolyte polymer to the channel walls. The analysis of the velocity field reflecting the drag force in the electrostatic field and the electrolyte polymer adsorbent layer taking into account the elasticity and excluded volume effect of the electrolyte polymer in the nanochannel of the solution, And pKa, which is an acid dissociation constant index, and the conversion efficiency can be improved to 5%. Here, the electrolyte polymer adsorbing layer can freely permeate ions and move around, so that the velocity distribution of the liquid flow is kept relatively uniform.

J.B. Schlenoff, Z. Sui, " Variable charge films for controlling microfluidic flow ", US patent registration (7,722,752), May 25, 2010.

 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.

It is an important problem to calculate the exact thickness of the adsorbent layer in the analysis of the electrolyte polymer adsorbent layer formed on the channel wall surface for the efficiency evaluation of the electrokinetic energy conversion technology and the performance improvement. Similarly, the length of the polymer in the form of a brush adsorbed on the channel wall surface is determined.

In the present invention, a method and an apparatus for calculating the thickness of an electrolyte polymer adsorbent layer from repeated calculations according to comparison between an average flow rate calculated from the viscosity of an electrolyte polymer solution dispersed at various molecular weights and concentrations and a direct measured average flow rate, To analyze the adsorption layer thickness.

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

(1) Calculating the average distance between the electrolyte polymers in the adsorption layer

The molar concentration of the electrolyte polymer solution in the bulk, C _PE , is multiplied by the Avogadro constant N _A, which is converted to the number concentration of the electrolyte polymer per unit volume. Assuming that the concentration of the electrolyte polymer in the bulk is adsorbed directly on the channel surface, and if a circular unit area is set around the electrolyte polymer, the average distance l _b between the electrolyte polymers in the adsorption layer can be calculated by the following equation (1).

Here, n is the degree of polymerization of the electrolyte polymer, and l _m is the length of the monomer, and nl _m means the maximum contour length of the electrolyte polymer.

(2) Calculation of Initial Thickness of Electrolyte Polymer Adsorbent Layer

Generally, the thickness h of the electrolyte polymer adsorbing layer can be calculated from the above-mentioned l _b value by the following equation (2).

Where _{k K} is the Kuhn length, N _K is the number of b _K in one electrolyte polymer chain, and a is the Flory-Huggins coefficient determined by the dissociation of the electrolyte polymer. These factors for any electrolyte polymer can be found in various documents.

In the present invention, the initial thickness of the electrolyte polymer adsorbent layer is required for the pre-recurrence calculation step, which is calculated by Equation (2) and is also referred to as h _ini , and the thickness of the electrolyte polymer adsorbent layer can be continuously changed in the iterative calculation step.

(3) Concentration distribution model selection step in the electrolyte polymer adsorption layer

Concentration distribution model of electrolytic polymer is based on the concept of statistical mechanics. In general, it can be assumed to be a homogeneous concentration model when the concentration is high and a second or tertiary function concentration model when the concentration is low. In the present invention, it is possible to freely select among uniformity, quadratic function and cubic function concentration models.

가 0 부터 W/2 까지에 대한 농도분포이고, f_y 는 채널높이 방향인 y방향 영역, 즉,

가 0 부터 H/2 까지에 대한 농도분포이며, f_xy 는 x 와 y 방향 영역이 중첩되는 구간에 대한 농도분포이다. 각 농도분포 모델은 공통적으로 채널 벽면부터 전해질고분자 흡착층 두께인 h까지의 구간에 대해 적분하면 1을 갖도록 정규화(normalization) 되어 있고, 채널 벽면에서 h 보다 멀리 떨어진 전해질고분자 흡착층 이외의 영역에서는 0 이 된다. 각 농도분포 모델은 도 3에 예시되어 있다.In Fig. 2, a channel model in which the cross-section inside the channel is a square, the channel width is W, the channel height is H, and the origin of the x, y, and z coordinate axes in the channel width, And the concentration distribution model is calculated using this channel model. Here, f _x An x-direction region which is a channel width direction, that is,

Is the concentration distribution from 0 to W / 2, f _y Direction region which is the channel height direction, that is,

Is the concentration distribution from 0 to H / 2, and f _xy Is the concentration distribution for the region where the x and y directional regions overlap. Each concentration distribution model is normalized so as to have 1 when it is integrated with respect to a section from the channel wall surface to the thickness h of the electrolyte polymer adsorption layer. In the region other than the electrolyte polymer adsorption layer, . Each concentration distribution model is illustrated in FIG.

The uniform concentration model is given by the following equation (3).

The quadratic function concentration model is given by the following equations (4) to (6).

The cubic function concentration model is given by the following equations (7) to (9).

(4) Calculation of liquid flow rate and average flow rate

When the electrolyte polymer solution flows at the velocity of u by the pressure difference? P in a rectangular channel having a length L having the initial calculated h _ini value, the flow rate of the electrolyte polymer solution to the steady state is determined by the known non-Newton (10) which is an equation of motion of a non-Newtonian fluid.

Here, τ is a viscous stress tensor that reflects the change in viscosity with shear rate in a non-newtonic fluid such as an electrolytic polymer solution, and corresponds to a product of viscosity η and shear rate of an electrolyte polymer solution do. The resistance coefficient C _d by the polymer brush in the polymer electrolyte adsorption layer is a function of the viscosity η of the electrolyte polymer solution, the average distance l _b between the electrolyte polymers in the electrolyte polymer adsorption layer, and the concentration distribution model f of the electrolyte polymer, C _d = η f / l _b ² .

From the viscosity data of the electrolytic polymer solution measured experimentally and C _d determined based on the value calculated in the previous step, it is found from the viscosity data of the electrolytic polymer solution as the solution of the partial differential equation of Equation (10) the velocity distribution u (x, y), which is a function of y, is obtained. Next, by integrating u (x, y) with respect to the channel width W and the channel height H, the flow rate of the solution flowing through the channel and the average flow velocity U divided by the cross-sectional area of the channel can be calculated.

(5) calculating the thickness of the adsorption layer by iterative calculation

The process of minimizing the error between the average flow rate calculated in the above step and the actually measured average flow rate is smaller than the tolerance is repeated. The thickness h of the electrolyte polymer adsorbing layer can be determined, and the overall process is as shown in FIG.

The method of calculating the thickness of the electrolyte polymer adsorbent layer according to an embodiment of the present invention is advantageous in that it is possible to obtain a thin film of the electrolyte polymer adsorbed layer of the electrolyte polymeric adsorbent layer in comparison with the conventional method in which expensive equipment such as an atomic force microscope It has technological competitiveness that can quickly and easily calculate the length of polymer brush with thickness.

1 is a view showing a polymer brush having a thickness h of an electrolyte polymer adsorbing layer formed on a channel wall surface.
Fig. 2 is a view showing a region to which each concentration distribution model is applied when an electrolyte polymer adsorbing layer is formed on the inner wall surface of a channel having a rectangular cross section with a constant thickness h.
FIG. 3 is a graph showing the concentration distribution in the electrolyte polymer adsorbing layer with respect to the concentration distribution model such as uniformity, quadratic function, cubic function, etc. In this case, the distance from the wall surface divided by the thickness of the adsorption layer is 1, Length.
4 is a flowchart schematically showing a process of calculating the thickness of the electrolyte polymer adsorbing layer.
FIG. 5 shows the result of measuring viscosity according to shear rate of a polyacrylic acid (PAA) solution, which is an electrolyte polymer, and curve fitting according to the viscosity model.
FIG. 6 shows the velocity distributions of the case where the adsorption layer is not formed on the channel wall surface and the case where the adsorption layer is formed for the PAA 1000 ppm solution, and the velocity distribution differs according to the electrolyte polymer concentration distribution model.
7 shows the average flow rate measured according to the concentration of the PAA solution.
FIG. 8 shows results obtained by applying the AFM-based experimental measurement values of the thickness of the electrolyte polymer adsorbing layer to the concentration of the PAA solution and the concentration distribution models from the analysis method of the present invention.

Polyacrylic acid (PAA) solutions with molecular weights of 1.25 × 10 ⁶ g / mol were prepared at 500, 1000 and 2000 ppm, respectively, and the pH of each solution was maintained at 9. The viscosity of each concentration of electrolyte polymer solution was measured by shear rate change with a double Couette cell attached to a fluid machine (model: MCR301, Anton Paar). As shown in FIG. 5, the results obtained by measuring the viscosity according to the concentration of PAA and by curve fitting according to the Bird-Carreau model can be seen.

Using the above equation (10), the velocity distribution of the solution in a given microfluidic channel can be obtained from the viscosity measurement result of the solution, which is a function of the shear rate. 6 shows a graph showing the relationship between the center of the channel and x = 0 when the PAA 1000 ppm solution was spilled on a microfluidic channel having a channel width W of 40 m, a channel height H of 10 m and a channel length L of 3.8 mm. The velocity distribution of the solution in the direction of the channel height from the point is calculated according to the concentration distribution model of the electrolytic polymer. If the calculated velocity distribution is numerically integrated in the channel width and height direction, the flow rate of the solution flowing through the channel can be calculated and the average flow rate of the solution according to the concentration distribution model can be calculated by dividing it by the cross-sectional area of the channel.

In the present invention, a chip made of glass or polydimethylsiloxane (PDMS) having a width, a height, and a length of the microfluidic channel, an inlet through which the electrolytic polymer solution enters, and an outlet through which the electrolyte polymer solution is discharged is formed , The average flow rate of the electrolyte polymer solution can be actually measured and compared with the calculated average flow rate. In one embodiment of the present invention, a 1/16 inch outer diameter plastic tubing equipped with a precision pressure gauge is installed at the inlet and outlet, and PAA solution is flowed through the channel at a constant pressure difference by a pump. When a steady state is reached after a certain period of time, the volumetric flow discharged from the spout tubing is measured, and the volumetric flow rate is divided by the cross-sectional area of the channel to obtain the experimentally measured average flow rate. The average flow rate measured according to the concentration of the PAA solution in this manner is shown in FIG.

Meanwhile, the apparatus for measuring the viscosity according to the shear rate change of the electrolyte polymer solution or the apparatus for measuring the average flow rate in the microfluidic channel may be connected to the apparatus for calculating the thickness of the electrolyte polymer adsorbent layer either online or offline.

[Example]

In order to calculate the thickness h of the electrolytic polymer adsorbent layer, the initial thickness h _ini must be calculated as described above. The parameters of the above equations 1 and 2 can be obtained from various documents. For example, in the case of 1000 ppm of PAA at a pH of 9, the Kuhn length b _k is 11.7 nm and the Fuller-Huggins The coefficient is zero. From Equation (1), the average distance l _b between the electrolyte polymers in the adsorption layer was calculated to be 31.5 nm, and the initial thickness h _ini of the electrolyte polymer adsorbent layer was calculated to be 760 nm from Equation (2).

The average flow rate of the electrolyte polymer solution of 1000 ppm of PAA was calculated to be 11.4, 11.8, and 12.4 mm / s for the concentration distribution models such as uniformity, quadratic function, and cubic function through Equations 3 to 9. Which was slightly higher than the actual measured average flow rate of 9.6 mm / s in Fig.

As shown in the flow chart of FIG. 4, it is determined whether or not iterative calculation is required by comparing the relative error obtained from the _{calculation of the} average flow velocity (U _calculation ) and the measurement value (U _measurement ) and the tolerance, and the adsorption layer thickness h _new Respectively. The number of iterations is determined by the tolerance. For example, if the tolerance is set to 3%, the iterations are performed five times. In this case, the adsorption layer thickness and average velocity of PAA 1000 ppm electrolyte polymer were calculated as 963, 1016, and 1089 nm and 9.71, 9.82, and 9.84 mm / s for the concentration distribution model of uniformity, quadratic function and cubic function, respectively .

Figure 8 shows the results for any concentration of PAA solution. As the concentration of PAA increases, the thickness h of the polymer adsorbent layer increases. In addition, a comparison between the calculated value obtained by applying each concentration distribution model and the experimental value measured by the AFM from the analytical method for the h calculation of the present invention is shown.

While the present invention has been particularly shown and described with reference to specific embodiments thereof, those skilled in the art will appreciate that such specific embodiments are merely preferred embodiments and that the scope of the present invention is not limited thereby. something to do.

Claims (12)

A method for calculating the thickness of an electrolyte polymeric adsorbent layer formed on a microfluidic channel wall surface by flowing a liquid containing a polyelectrolyte in a microfluidic channel,
Calculating an average distance between the electrolyte polymer in the electrolyte polymer adsorbing layer formed on the channel wall;
Calculating an initial thickness of the electrolyte polymer adsorbing layer;
Electrolyte Polymer Concentration Distribution Model Selection in Electrolyte Polymer Adsorption Layer;
Calculating a liquid flow rate and an average flow rate; And
A step of calculating the thickness of the electrolyte polymer adsorbing layer by repeated calculation;
The thickness of the electrolyte polymer adsorbing layer formed on the microfluidic channel wall surface. The method according to claim 1,
In the step of calculating the average distance between the electrolyte polymers in the electrolyte polymer adsorbing layer formed on the channel walls,
Wherein the concentration of the electrolyte polymer in the bulk is adsorbed on the surface of the microfluidic channel as it is and is set around the unit area of the circle around the electrolyte polymer, the adsorption of the electrolyte polymer formed on the wall of the microfluidic channel including the calculation method Method of calculating layer thickness.
[Equation 1]

(In the above equation (1), wherein l _b is the average distance between the polymer electrolyte in the adsorbent bed, the C _PE is the molar concentration of the electrolyte polymer in bulk in the liquid containing a polymer electrolyte, wherein N is _A Wherein n is the degree of polymerization of the electrolyte polymer, and l _m is the length of the single molecule. The method according to claim 1,
Wherein the step of calculating the initial thickness of the electrolyte polymer adsorbing layer is performed on the microfluidic channel wall surface including the calculating method according to Equation (2).
&Quot; (2) "

(Where h is the thickness of the electrolyte polymer adsorbing layer, l _b is the average distance between the electrolyte polymers in the adsorbing layer, b _K is the Kuhn length, N _K is one electrolyte The number of b _K in the polymer chain, and a is the Flory-Huggins coefficient determined by the dissociation degree of the electrolyte polymer. The method according to claim 1,
The electrolyte polymer concentration distribution model selection step in the electrolyte polymer adsorption layer can be selected from the concentration distribution model group consisting of a uniform concentration model, a quadratic function concentration model, and a cubic function concentration model,
Each concentration model is normalized so as to have 1 when it is integrated with respect to the section from the channel wall surface to the thickness h of the electrolyte polymer adsorption layer. In the region other than the electrolyte polymer adsorption layer, The thickness of the electrolyte polymer adsorbing layer formed on the wall surface of the microfluidic channel. 5. The method of claim 4,
Wherein the homogeneous concentration model is formed on a microfluidic channel wall surface including a calculation method according to Equation (3): " (1) "
&Quot; (3) "

(In the above Equation 3, f _x Direction region which is the channel width W direction, that is,

Is a concentration distribution from 0 to W / 2, and f _y Direction region which is the channel height H direction, that is,

Is a concentration distribution from 0 to H / 2, and f _xy Is the concentration distribution for the section where the x and y directional regions overlap.) 5. The method of claim 4,
Wherein the quadratic function concentration model is formed on a microfluidic channel wall surface including a calculation method according to Equations (4) to (6).
&Quot; (4) "

&Quot; (5) "

&Quot; (6) "

(In the above Equations (4) to (6), f _x Direction region which is the channel width W direction, that is,

Is a concentration distribution from 0 to W / 2, and f _y Direction region which is the channel height H direction, that is,

Is a concentration distribution from 0 to H / 2, and f _xy Is the concentration distribution for the section where the x and y directional regions overlap.) 5. The method of claim 4,
Wherein the cubic function concentration model is formed on a microfluidic channel wall surface including a calculation method according to the following Equations (7) to (9).
&Quot; (7) "

&Quot; (8) "

&Quot; (9) "

(In the above Equations (7) to (9), f _x Direction region which is the channel width W direction, that is,

Is a concentration distribution from 0 to W / 2, and f _y Direction region which is the channel height H direction, that is,

Is a concentration distribution from 0 to H / 2, and f _xy Is the concentration distribution for the section where the x and y directional regions overlap.) The method according to claim 1,
The flow rate and the average flow velocity of the liquid are calculated by using the following mathematical expression for the steady state when the electrolyte polymer solution flows at the velocity of u by the pressure difference DELTA P in the square channel having the length L having the initial calculated value of the thickness of the electrolyte polymer adsorbent layer A method for calculating the thickness of an electrolyte polymer adsorbent layer formed on a microfluidic channel wall surface including a calculation method according to formula (10).
&Quot; (10) "

In Equation (10), τ is a viscous stress tensor that reflects a change in viscosity according to a shear rate in a non-newtonic fluid such as a liquid containing an electrolyte polymer, the viscosity η and the shear rate corresponding to the product of (shear rate), wherein C _d is the average distance between the electrolyte viscosity of the electrolyte polymer solution from the polymer adsorption layer is a resistance coefficient of the polymer brushes η, electrolyte polymer electrolyte polymer in the adsorbed layer l _b , And as a function of the concentration distribution model f of the electrolyte polymer, C _d = η f / l _b ² . The method according to claim 1,
The step of calculating the thickness of the electrolyte polymer adsorbent layer through the iterative calculation may be carried out by repeating the calculation until the error between the flow rate of the liquid and the average flow rate obtained through the average flow rate calculation step is smaller than the tolerable error, A method for calculating the thickness of an electrolyte polymer adsorbent layer formed on a channel wall surface. In order to calculate the thickness of the electrolyte polymer adsorbent layer formed on the wall surface of the microfluidic channel, the steady state in the case where the electrolyte polymer solution flows at the speed of u by the pressure difference? A viscosity measuring device according to a change in shear rate of a liquid containing a certain concentration of an electrolyte polymer for measuring a viscosity? Of an electrolyte polymer solution required for calculating a velocity u of an electrolyte polymer solution; And
In order to compare the error between the flow rate of the liquid from the calculated velocity u and the average flow rate obtained through the average flow rate calculation step, a device for measuring the actual average flow rate in the microfluidic channel of the liquid containing the electrolyte polymer at a constant concentration ;
The thickness of the electrolyte polymer adsorbing layer formed on the wall surface of the microfluidic channel.
&Quot; (10) "

In Equation (10), τ is a viscous stress tensor that reflects a change in viscosity according to a shear rate in a non-newtonic fluid such as a liquid containing an electrolyte polymer, the viscosity η and the shear rate corresponding to the product of (shear rate), wherein C _d is the average distance between the electrolyte viscosity of the electrolyte polymer solution from the polymer adsorption layer is a resistance coefficient of the polymer brushes η, electrolyte polymer electrolyte polymer in the adsorbed layer l _b , And as a function of the concentration distribution model f of the electrolyte polymer, C _d = η f / l _b ² . 11. The method of claim 10,
An apparatus for measuring an actual average flow rate in a microfluidic channel of a liquid containing a certain concentration of the electrolyte polymer
An inlet through which the liquid containing the electrolyte polymer enters;
A microfluidic channel through which a liquid containing an electrolyte polymer flows;
An outlet through which liquid containing the electrolyte polymer is discharged;
A chip made of glass or polydimethylsiloxane (PDMS) material on which the inlet, the microfluidic channel, and the outlet are formed;
A pump for flowing a liquid containing an electrolyte polymer in a microfluidic channel to a constant pressure difference? P; And
Tubing with precision pressure gauge;
The thickness of the electrolyte polymer adsorbing layer formed on the microfluidic channel wall surface. 11. The method of claim 10,
Wherein the apparatus for measuring the average average flow rate in a microfluidic channel of a liquid containing a certain concentration of the electrolyte polymer or a viscosity measuring apparatus according to a change in shear rate of the liquid containing the electrolyte polymer at a certain concentration includes: Of-line < / RTI > or offline,
The apparatus for calculating the thickness of the electrolyte polymer adsorbent layer may include a concentration distribution model of the electrolyte polymer; And
The thickness of the electrolyte polymer adsorbent layer is calculated by iterative calculation until the error between the average flow rate calculated from the viscosity measured by the viscosity measuring device and the actual average flow rate by the device for measuring the actual average flow rate becomes smaller than the tolerance doing,
An apparatus for calculating the thickness of an electrolyte polymer adsorption layer formed on a wall surface of a microfluidic channel.

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