JP6344119B2 - Method and apparatus for determining thermophoretic conditions - Google Patents

Description

  The present invention relates to a thermophoretic condition for forming a concentration distribution of a solute using a thermophoresis of the solute accompanying a temperature gradient in a mixed fluid containing a solute as a specific substance in a solvent. The present invention relates to a determination method and a determination apparatus for thermophoretic conditions.

  Thermophoresis is a phenomenon in which a specific substance (solute) in a mixed fluid migrates in one direction to a high temperature side or a low temperature side under a temperature gradient. By utilizing this thermophoresis phenomenon and applying a temperature gradient to the mixed fluid to cause the specific substance to segregate at a specific location, the specific material can be aggregated at a specific location in the mixed fluid. Examples of applications include DNA / RNA separation / concentration, removal of harmful substances, segregation (capture) of functional molecules at specific locations (see, for example, Patent Document 1).

  If the molecule to be thermophoresed is called a solute and the other molecules are called a solvent, whether the solute migrates to the high temperature or low temperature side (where it segregates) depends on the type of solvent and solute. Also depends on temperature range, solvent-solute interaction, solute concentration. FIG. 4 (Source: Non-Patent Document 1) shows the solubility of multiple types of salts in water in the temperature range of 0 ° C. to 100 ° C., and monotonically increases, monotonously decreases, and maximums depending on the type of solute. There are various temperature dependencies such as Therefore, in order to obtain the optimum thermophoretic conditions (temperature range in which segregation occurs), it has to be determined experimentally through trial and error while changing the solvent species, solute species, and solute concentration as parameters.

  As a technique related to the present invention, Patent Document 2 discloses a method for calculating a chemical potential at high speed in a simulation for obtaining the affinity between a molecular assembly and a solute. Patent Document 3 discloses a method for efficiently calculating solvation free energy in a solvent effect calculation method.

WO2009 / 110237A1 JP 2009-80803 A JP 2010-182077 A

the Handbook of Chemistry and Physics, 27th edition, Chemical Rubber Publishing Co., Cleveland, Ohio, 1943.

  Determination of thermophoretic conditions for segregating solutes at specific locations can be made by calculating the chemical potential in the diffusion equilibrium state. However, since the chemical potential depends on the interaction between the solvent and the solute and the concentration of the solute, if any one of the parameters changes, the temperature condition for obtaining an appropriate thermophoresis also changes. In the prior art, a method for determining thermophoresis conditions in consideration of the solvent-solute interaction and the solute concentration has not been established, and it is difficult to obtain appropriate thermophoresis conditions. It was.

  The present invention has been made in view of the above circumstances, and its purpose is to easily obtain appropriate thermophoretic conditions for the solute to segregate at a specific location in consideration of the solvent-solute interaction and the solute concentration. It is an object of the present invention to provide a determination method and determination apparatus for thermophoresis conditions that make it possible.

In order to achieve the above object, the method for determining thermophoretic conditions of the present invention utilizes the thermophoresis of the solute accompanying the application of a temperature gradient to a mixed fluid containing a solute as a specific substance in a solvent. In the method of determining the thermophoretic conditions for forming the concentration distribution of the solute by a process executed by a computer , the type of solvent constituting the mixed fluid, the type of solute, the concentration of solute, and the temperature gradient are given. Based on calculating the chemical potential of the solute, using molecular simulation, with the temperature condition as a parameter, to determine the conditions of thermophoresis where the solute segregates at a specific location ,
In a state in which the fluid mixture is sealed in a sealed container, assuming that achieves a one-dimensional temperature gradient varies monotonically in the sealed container (T _L ~T _H), each temperature when it reaches the diffusive equilibrium The chemical potential (μ (T)) of the solute at (T) is constant (μ (T) ≡μ ₀ ),
The chemical potential (μ ₀ ) is divided into the ideal gas contribution portion ignoring the interaction between the solvent and the solute, and the excess chemical potential (Δμ (T)) of the solute. Expressed and calculated by
μ ₀ = k _B Tln [{λ (T)} ³ ρ (T)] + Δμ (T) (1)
Where k _B is the Boltzmann constant, λ (T) is the thermal de Broglie wavelength of the solute at temperature (T), and ρ (T) is the substance quantity concentration of the solute at temperature (T).
Furthermore, the calculation of the thermophoretic conditions is as follows:
A first step of setting parameters for the solvent type, the solute type, the solute concentration, and the temperature gradient ( _TL , _TH );
A second step of calculating an excess chemical potential (Δμ (T)) of the solute by molecular simulation;
A third step of calculating the chemical potential (μ (T)) in consideration of the excess chemical potential (Δμ (T));
A fourth step of calculating a substance concentration (ρ (T)) of the solute at temperature (T) therefrom,
It is characterized in that the processes of the first to fourth steps are repeated until appropriate thermophoresis conditions are obtained .

In addition, the thermophoretic condition determining apparatus of the present invention uses a thermophoresis of the solute accompanying a temperature gradient to a mixed fluid containing a solute as a specific substance in a solvent to determine the concentration distribution of the solute. In the apparatus (1) for determining the conditions of thermophoresis at the time of formation, input means for inputting the type of solvent constituting the mixed fluid, the type of solute, the concentration of solute, and the temperature condition for imparting a temperature gradient (3), molecular simulation execution means (5) for executing molecular simulation using the solvent type, the solute type, the solute concentration, and the temperature as parameters, and the chemistry of the solute calculated by the molecular simulation. Calculation means (6, 7) for calculating a thermophoretic condition in which a solute segregates at a specific location based on a potential ;
In a state in which the fluid mixture is sealed in a sealed container, assuming that achieves a one-dimensional temperature gradient varies monotonically in the sealed container (T _L ~T _H), each temperature when it reaches the diffusive equilibrium The chemical potential (μ (T)) of the solute at (T) is constant (μ (T) ≡μ ₀ ),
The calculation means (6, 7) includes the chemical potential (μ ₀ ), the ideal gas contribution portion ignoring the interaction between the solvent and the solute, and the solute calculated by the molecular simulation execution means (5). Divided by the excess chemical potential (Δμ (T)) and calculated by the following equation (1):
μ ₀ = k _B Tln [{λ (T)} ³ ρ (T)] + Δμ (T) (1)
Where k _B is the Boltzmann constant, λ (T) is the thermal de Broglie wavelength of the solute at temperature (T), and ρ (T) is the substance quantity concentration of the solute at temperature (T).
Furthermore, the calculation of the thermophoretic conditions is as follows:
A first step of setting parameters of the solvent type, the solute type, the solute concentration, and the temperature gradient (T _L , T _H ) by the input means (3) ;
A second step of calculating an excess chemical potential (Δμ (T)) of the solute by the molecular simulation execution means (5);
A third step of calculating the chemical potential (μ (T)) in consideration of the excess chemical potential (Δμ (T)) by the calculating means (6, 7);
A fourth step of calculating the substance concentration (ρ (T)) of the solute at the temperature (T) therefrom by the calculating means (6, 7),
It is characterized in that the processes of the first to fourth steps are repeated until appropriate thermophoresis conditions are obtained .

  According to the above configuration, by using the molecular simulation, it is possible to calculate the chemical potential of the solute using the solvent type, the solute type, the solute concentration, and the temperature condition for imparting the temperature gradient as parameters. . By this molecular simulation, it is possible to obtain an appropriate thermophoretic condition in which the solute segregates at a specific location in consideration of the solvent-solute interaction and the solute concentration. As typical molecular simulation methods, a thermodynamic integration method, a free energy perturbation method, a particle insertion method, an energy display method, and the like are known, and these can be used.

The block diagram which shows one Example of this invention and shows schematically the electrical structure of the determination apparatus of thermophoresis conditions The figure which shows the example of the airtight container and segregation Flow chart showing processing procedure for determination of thermophoresis conditions Characteristic diagram showing the temperature dependence of the solubility of various salts in water

  Hereinafter, an embodiment embodying the present invention will be described with reference to FIGS. 1 to 3. FIG. 1 schematically shows the configuration of a thermophoretic condition determining apparatus 1 according to this embodiment. This determination apparatus 1 is a thermophoresis for forming a concentration distribution of a solute by using a thermophoresis of the solute accompanying a temperature gradient to a mixed fluid containing a solute as a specific substance in a solvent. In this embodiment, for example, a general-purpose computer system is used.

  The determination device 1 includes a processing device 2 and an input device 3 and an output device 4 connected to the processing device 2. Of these, the input device 3 includes, for example, a keyboard and a mouse, and functions as an input means. The user operates the input device 3 to instruct the processing device 2 to execute thermophoresis condition determination processing or to input necessary parameters as described later. . The output device 4 includes, for example, a display, a printer, and the like, and is configured to output a result of an operation executed by the processing device 2.

The processing device 2 is composed of, for example, a computer including a CPU, a memory, and the like, and has functions as a molecular simulation unit 5, a chemical potential calculation unit 6, and an optimum condition determination unit 7 depending on its hardware configuration and software configuration. As a result, the processing device 2 inputs the type of the solvent constituting the mixed fluid, the type of the solute, the concentration of the solute (average substance amount concentration n), and the temperature conditions for providing the temperature gradient, which are input by the input device 3. The molecular simulation is performed by the molecular simulation unit 5 using (the lowest temperature T _L and the highest temperature T _H ) as parameters.

  Then, the processing apparatus 2 calculates the chemical potential of the solute by the chemical potential calculation unit 6 using the result of the molecular simulation, and based on the calculated chemical potential, the optimum condition determination unit 7 segregates the solute at a specific location. Determine the conditions for thermophoresis. Therefore, the molecular simulation unit 5 functions as a molecular simulation execution unit, and the chemical potential calculation unit 6 and the optimum condition determination unit 7 function as a calculation unit. As typical molecular simulation methods, a thermodynamic integration method, a free energy perturbation method, a particle insertion method, an energy display method, and the like are known, and these can be used.

In this embodiment, when the processing apparatus 2 determines the thermophoretic conditions, more specifically, as shown in FIG. 2, the cross-sectional area is constant and uniaxial direction (Z-axis direction, that is, the vertical direction in the figure). It is assumed that a one-dimensional (linear) temperature gradient (T _{L to} T _H ) that monotonously changes in the uniaxial (Z-axis) direction is realized in a state where the mixed fluid is sealed in the sealed container 8 extending in the vertical direction. In this case, in a rectangular parallelepiped sealed container 8 having a bottom surface and a top surface (square and area S) parallel to the XY plane and long in the Z-axis direction (vertical direction in the figure), the bottom surface is the temperature (T _L ) and the top surface is Assume that the temperature (T _H ) is higher than that.

At this time, when the inside of the sealed container 8 reaches diffusion equilibrium, the chemical potential (μ (T)) of the solute at each temperature (T) from the temperature (T _L ) to the temperature (T _H ) is constant ( μ (T) ≡μ ₀ ), the chemical potential (μ ₀ ) is an ideal gas contribution part ignoring the solvent-solute interaction, and the excess chemical potential (Δμ (T)) of the solute. It is expressed by the following equation (1).
μ ₀ = k _B Tln [{λ (T)} ³ ρ (T)] + Δμ (T) (1)
Where k _B is the Boltzmann constant, λ (T) is the thermal de Broglie wavelength of the solute at temperature (T), and ρ (T) is the substance quantity concentration of the solute at temperature (T).

Then, as will be described in the following explanation of the action (description of the flowchart), the calculation of the thermophoresis conditions performed by the processing apparatus 2 is to provide the type of solvent, the type of solute, the concentration of solute (n), and the temperature gradient. A first step of setting parameters of temperature conditions (T _L , T _H ), a second step of calculating an excess chemical potential (Δμ (T)) of the solute by molecular simulation, and an excess chemical potential (Δμ (T) ), A third step of calculating the chemical potential (μ (T)), and a fourth step of calculating the solute mass concentration (ρ (T)) at the temperature (T) therefrom, The processes of the first to fourth steps are repeated until appropriate thermophoresis conditions are obtained.

Next, the operation of the above configuration will be described with reference to FIG. The flowchart of FIG. 3 shows a processing procedure for determining the optimum conditions for thermophoresis, which is executed by the processing device 2 of the determining device 1. That is, first, in step S1 as the first step, parameters of solvent type, solute type, solute concentration (n), and temperature conditions (T _L , T _H ) are set. This parameter setting is performed by a user's operation input on the input device 3, or a part thereof is automatically performed.

In step S2 as the second step, molecular simulation is executed by the molecular simulation unit 5 based on the parameters set in step S1, and an excess chemical potential (Δμ (T)) is calculated. More specifically, the calculation of the excess chemical potential (Δμ (T)) by molecular simulation is performed based on the following equation (2).
Δμ (T) = − k _B Tln <exp (−v / k _B T)> (2)
Where v is the solvent-solute interaction, and <exp (−v / k _B T)> is the ensemble average of exp (−v / k _B T) in a pure solvent system.

但し、ｎは溶質の平均物質量濃度、Ｄは密閉容器８の一軸（Ｚ軸）方向の長さである。 In step S3 as the third step, the chemical potential (μ (T)) is calculated in consideration of the excess chemical potential (Δμ (T)) calculated in step S2. Specifically, the chemical potential μ ₀ is calculated by searching for μ ₀ that satisfies the following equation (3).

However, n is the average substance amount concentration of the solute, and D is the length in the uniaxial (Z-axis) direction of the sealed container 8.

In this case, the above equation (3) is obtained as follows. That is, the number of solute particles (molecules) in the sealed container 8 is N (a constant value), and the number N of particles is obtained by the following equation (11) by volume integrating the substance concentration (ρ (T)). Desired.

When the cross-sectional area of the sealed container 8 is S (constant value), the following equation (12) is obtained from the equation (11).

Further, when the above equation (1) is converted into an equation for obtaining the substance concentration (ρ (T)) and substituted into the equation (12), the following equation (13) is obtained.

Since the average substance amount concentration n of the solute is the number of particles N / (cross-sectional area S × length D), the equation (13) is transformed into the equation (3).
In the above equation (3), μ ₀ can be determined by searching for μ ₀ whose right side integral value matches n * D.

Here, dZ / dT is a factor determined from the thermal conductivity of the solvent. Within the _{T L} <T <T _H, when the negligible temperature dependence of the thermal conductivity, since the _{dZ / dT = d / (T} H -T L), a (3), the following equation (4) It can simplify like Formula.

In step S4 as a fourth step, step S2, the [Delta] [mu (T) and mu ₀ determined in step S3, amount of substance concentration of solute at a temperature (T) (ρ (T) ) is calculated. This calculation can be obtained by the following equation (14) obtained by modifying the above equation (1).

  In the next step S5, it is determined whether or not appropriate segregation has been obtained in the processing in steps S1 to S4. If appropriate segregation is not obtained (No in step S5), the process returns to step S1, and the processing (calculation) in steps S2 to S4 is performed after the parameters are changed automatically or manually. Thus, the process of step S1-step S4 is repeated until the suitable thermophoresis conditions are obtained, and a process is complete | finished when the suitable thermophoresis conditions are obtained (it is Yes at step S5).

As described above, according to the present example, the chemistry of the solute is determined using molecular simulation using the parameters of the type of solvent constituting the mixed fluid, the type of solute, the concentration of the solute, and the temperature condition for imparting the temperature gradient. Based on the calculation of the potential (Δμ (T) and μ ₀ ), the conditions of thermophoresis in which the solute segregates at specific locations were determined. This makes it possible to easily determine appropriate thermophoresis conditions for the solute to segregate at a specific location, taking into account the solvent-solute interaction and the solute concentration.

  In the above embodiment, a rectangular parallelepiped container is assumed as the sealed container, but a cylindrical sealed container having a constant cross-sectional area may be used. In addition, the present invention is not limited to the above-described embodiments. For example, various methods can be applied as a molecular simulation method, and the calculation formula is not limited to the above-described one, and can be modified. For example, the present invention can be implemented with appropriate modifications within a range not departing from the gist.

  In the drawings, 1 is a determination device, 2 is a processing device, 3 is an input device (input means), 5 is a molecular simulation unit (molecular simulation execution unit), 6 is a chemical potential calculation unit (calculation unit), and 7 is an optimum condition determination. Reference numeral 8 denotes a closed container.

Claims (8)

The computer determines the thermophoretic conditions for forming the concentration distribution of the solute using the thermophoresis of the solute accompanying the application of a temperature gradient to the mixed fluid containing the solute that is the specific substance in the solvent. In the method of determining by the processing to be executed ,
Based on calculating the chemical potential of the solute using molecular simulation, with the parameters of the type of solvent constituting the mixed fluid, the type of solute, the concentration of the solute, and the temperature condition for imparting a temperature gradient, solute a shall seek conditions thermophoretic segregated to particular locations,
In a state in which the fluid mixture is sealed in a sealed container, assuming that achieves a one-dimensional temperature gradient varies monotonically in the sealed container (T _L ~T _H), each temperature when it reaches the diffusive equilibrium The chemical potential (μ (T)) of the solute at (T) is constant (μ (T) ≡μ ₀ ),
The chemical potential (μ ₀ ) is divided into the ideal gas contribution portion ignoring the interaction between the solvent and the solute, and the excess chemical potential (Δμ (T)) of the solute. Expressed and calculated by
μ ₀ = k _B Tln [{λ (T)} ³ ρ (T)] + Δμ (T) (1)
Where k _B is the Boltzmann constant, λ (T) is the thermal de Broglie wavelength of the solute at temperature (T), and ρ (T) is the substance quantity concentration of the solute at temperature (T).
Furthermore, the calculation of the thermophoretic conditions is as follows:
A first step of setting parameters for the solvent type, the solute type, the solute concentration, and the temperature gradient ( _TL , _TH );
A second step of calculating an excess chemical potential (Δμ (T)) of the solute by molecular simulation;
A third step of calculating the chemical potential (μ (T)) in consideration of the excess chemical potential (Δμ (T));
A fourth step of calculating a substance concentration (ρ (T)) of the solute at temperature (T) therefrom,
The method for determining thermophoresis conditions , wherein the processes of the first step to the fourth step are repeated until suitable thermophoresis conditions are obtained . The method for determining thermophoretic conditions according to claim 1 , wherein the calculation of the excess chemical potential (Δμ (T)) by the molecular simulation is performed based on the following equation (2) .
Δμ (T) = − k _B Tln <exp (−v / k _B T)> (2)
Where v is the solvent-solute interaction, and <exp (-v / k _B T)> is the ensemble average of exp (-v / k _B T) in a pure solvent system . The calculation of the chemical potential μ ₀ adds a condition that the closed container has a cross-sectional area (S) constant and a shape extending in a uniaxial direction,
3. The method for determining thermophoretic conditions according to claim 1, wherein the determination is made by searching for μ ₀ satisfying the following expression (3) .

Here, n is the average substance concentration of the solute, and D is the length in the uniaxial direction of the closed container. The calculation of the chemical potential μ ₀ is performed by searching for μ ₀ satisfying the following expression (4) by adding a linear temperature gradient condition in the expression (3). The method for determining the thermophoretic conditions described .

An apparatus for determining the conditions of thermophoresis when forming a concentration distribution of the solute using thermophoresis of the solute accompanying the application of a temperature gradient to the mixed fluid containing the solute as a specific substance in the solvent In (1),
An input means (3) for inputting the type of solvent constituting the mixed fluid, the type of solute, the concentration of the solute, and temperature conditions for imparting a temperature gradient;
A molecular simulation execution means (5) for executing a molecular simulation using the type of the solvent, the type of the solute, the concentration of the solute, and the temperature as parameters;
Based on the chemical potential of the solute calculated by the molecular simulation, calculating means (6, 7) for calculating conditions of thermophoresis in which the solute segregates at a specific location;
With
In a state where the mixed fluid is sealed in a sealed container, a one-dimensional temperature gradient (T _L ~ T _H ), The chemical potential (μ (T)) of the solute at each temperature (T) when diffusion equilibrium is reached is constant (μ (T) ≡μ ₀ )age,
The calculation means (6, 7) is configured such that the chemical potential (μ ₀ ) Is divided into the ideal gas contribution portion ignoring the interaction between the solvent and the solute, and the excess chemical potential (Δμ (T)) of the solute calculated by the molecular simulation execution means (5). (1)
μ ₀ = K _B Tln [{λ (T)} ^Three ρ (T)] + Δμ (T) (1)
Where k _B Is the Boltzmann constant, λ (T) is the thermal de Broglie wavelength of the solute at temperature (T), and ρ (T) is the mass concentration of the solute at temperature (T).
Furthermore, the calculation of the thermophoretic conditions is as follows:
By the input means (3), the type of the solvent, the type of the solute, the concentration of the solute, the temperature gradient (T _L , T _H ) The first step of setting the parameters,
A second step of calculating an excess chemical potential (Δμ (T)) of the solute by the molecular simulation execution means (5);
A third step of calculating the chemical potential (μ (T)) in consideration of the excess chemical potential (Δμ (T)) by the calculating means (6, 7);
A fourth step of calculating the substance concentration (ρ (T)) of the solute at the temperature (T) therefrom by the calculating means (6, 7),
The apparatus for determining thermophoresis conditions, wherein the processes of the first to fourth steps are repeated until an appropriate thermophoresis condition is obtained. 6. The thermophoretic condition determining apparatus according to claim 5, wherein the calculation of the excess chemical potential (Δμ (T)) by the molecular simulation executing means (5) is performed based on the following equation (2).
Δμ (T) = − k _B Tln <exp (−v / k _B T)> (2)
However and, v is the solvent - the interaction between the solute is ensemble average of <exp (-v / kB T) > exp of the pure solvent system (-v / kB T). The calculation of the chemical potential μ ₀ by the calculation means (6, 7) adds a condition that the sealed container has a shape with a constant cross-sectional area (S) and extending in a uniaxial direction,
7. The thermophoretic condition determining apparatus according to claim 5 , wherein the determination is made by searching for μ ₀ satisfying the following expression (3) .

Here, n is the average substance concentration of the solute, and D is the length in the uniaxial direction of the closed container. The calculation of the chemical potential μ ₀ by the calculating means (6, 7) is performed by searching for μ ₀ satisfying the following expression (4) by adding a linear temperature gradient condition in the expression (3). The apparatus for determining thermophoresis conditions according to claim 7.

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