JP2012208007A - Method for measuring water content - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for measuring water content for calculating mass of water contained in a film of an absorption film and mass of only an adsorbed material, and water content ratio of the absorption film in real time in solution even without measuring dry weight of the adsorbed material.SOLUTION: In a system that a material is adsorbed to the surface of a piezoelectric element of which the both sides or one side are immersed in solution, or a film fixed on the piezoelectric element in the solution, and the film is formed by a sensor using the piezoelectric element, any two of variations (ΔF, ΔF, ΔF) of a resonance frequency F, half-value frequencies Fand F(F>F) having conductance values of a half of a conductance value of the resonance frequency is measured, on the basis of frequency variation (Δ(F-F)/2)/ΔFs in the maximum adsorption of a reference material to the sensor, compared with frequency variation (Δ(F-F)/2)/ΔFs of a measuring object, and mass of water which the measuring object contains is calculated.

Description

  The present invention relates to a method for evaluating a thin film having viscoelasticity in the fields of chemistry, physics, biochemistry, materials, and the like, and more specifically, the moisture content relative to the adsorbed material when a piezoelectric element is used as a sensor. And relates to a method for measuring the water content of the adsorbed material.

The following Sauerbrey equation is used for the relationship between the frequency change of the QCM and the mass load.

  It has been reported that the frequency change due to adsorption in the solution shows a larger frequency change because the solution is included in the adsorbate material, unlike when measured in the atmosphere. In fact, the amount of frequency change due to adsorption in solution is estimated to be about twice as large as the frequency change due to the mass of protein alone, and about 6 times the frequency change due to the mass of DNA alone in the case of DNA. It was.

  In order to know exactly the amount of adsorbed material that does not contain water, remove the solution after adsorption in the solution, return it to the atmosphere, measure the frequency, and subtract the frequency in the atmosphere that was measured before the adsorption in advance. There is a method for obtaining the mass of the adsorbed substance (dry weight measurement method). However, there are problems such as complicated operations, some substances that are adsorbed during drying and cannot be measured accurately, and some substances that lose activity after drying. In addition, the film may have several layers due to repeated adsorption of substances, and this method is not effective for all measurements.

  It is possible to determine the mass of water contained in the membrane of the adsorbed membrane, the mass of the adsorbed material alone, and the moisture content of the adsorbed membrane in real time without measuring the dry weight of the adsorbate. Provide a method for measuring the amount of water.

The water content measuring method of the present invention is the method of claim 1, wherein a sensor using a piezoelectric element immersed on both sides or one side in a solution is used to measure the surface of the piezoelectric element in the solution or on the piezoelectric element. In a system in which a film is formed by adsorbing a substance to a film fixed to the resonance frequency F _s , the half-value frequencies F ₁ and F ₂ (F ₂ > F ₁ having a conductance value that is half the conductance value of the resonance frequency) ) Is measured (ΔF _s , ΔF ₁ , ΔF ₂ ) and the frequency change amount (Δ (F ₁ −F ₂ ) / at the time of maximum adsorption of the reference substance to the sensor is measured. 2) By using / ΔFs as a reference, the mass change amount of the measurement object (Δ (F ₁ −F ₂ ) / 2) / ΔFs is compared with the amount of water contained in the measurement object. To do.
According to a second aspect of the present invention, in the method for measuring water content according to the first aspect, the amount of frequency change at the time of maximum adsorption of the reference substance to the sensor is defined as (G ′ / | G | ² ) It is characterized by calculating.
According to a third aspect of the present invention, in the method for measuring moisture content according to the first or second aspect, the frequencies used during the measurement are fundamental wave and overtone (third harmonic, fifth harmonic, seventh harmonic ·・ ・) Is one of the above.
According to a fourth aspect of the present invention, there is provided the method for measuring mass load and viscoelasticity of a substance according to any one of the first to third aspects, wherein the piezoelectric element is a crystal resonator, an APM (ACOUSTIC PLATE MODE SENSOR). , FPW (FLEXURAL PLATE-WAVE SENSOR) or SAW (SOURFACE ACOUSTIC-WAVE SENSOR).

  In the conventional method using QCM, the amount of adsorption (mass load) in the solution includes water, so it was necessary to measure the dry weight to obtain the correct value. However, the measurement of dry weight is complicated, and some substances cannot be measured due to peeling. In addition, the moisture content of the adsorption membrane could not be determined while following the reaction in real time in the solution. According to the present invention, the adsorption amount (mass) of a substance in a solution can be obtained in real time without using a dry weight measurement method.

Explanatory drawing of the apparatus structure for enforcing the measuring method of this invention The graph which shows the measurement result of this invention and the conventional dry weight method of description in one embodiment of this invention The graph which shows the measurement result of QCM of one example of the present invention The graph which shows the water content ratio computed from the frequency change in the Example The graph which shows the relationship between the mass of the measuring object of the same Example, and the mass of water Explanatory drawing of measurement frequencies, such as N harmonic of one embodiment of the present invention

In QCM sensors in solution, it is generally known that the change in frequency when a thin film is adsorbed on the sensor is expressed by the following equations 2 and 3 when the Forked model is applied to the thin film. Yes.
Where G: complex elastic modulus (MPa), G ′: storage elastic modulus (dynamic elastic modulus) (MPa), G ″: loss elastic modulus (dynamic loss) (MPa), ω: angular frequency, ρ ₂ : Density of solution (g / cm ³ ), η ₂ : Viscosity of solution (Pa · S), h _f : Thickness (nm) of formed pre-film, ρ ₁ : Density of pre-formed film (g / cm ³ ), η ₁ : Viscosity (Pa · S) of the formed membrane, f ₀ : Fundamental frequency (Hz), z _q : Shear mode acoustic impedance (gm / sec / cm ² ) of quartz .

At this time, ΔFs is a frequency change value of the resonance frequency Fs, and ΔFw is a frequency change value of Δ (F ₁ -F ₂ ) / 2. ΔFs can also be obtained from Δ (F ₁ + F ₂ ) / 2.

Further, when there is no change in the viscosity of the solution, the viscous load term is eliminated, and in Equation 2, the viscoelastic term 1 is sufficiently smaller than the mass load term, and generally, the biomolecule film contains a lot of water in the solution. Therefore, the density of the film can be approximated as almost the same as the density of the solution. By dividing Equation 3 by Equation 2 based on this approximation, ΔF _w / ΔF _s can be summarized as Equation 4 below.

We found from the experimental results that the number 4 is related to the moisture content of the adsorbed material.
As an example, when the adsorption to a gold electrode in a solution of 50 nm latex beads is tested, the typical values at the maximum adsorption are as shown in Table 1 for a sensor using a 27 MHz crystal resonator.

  According to the dry weight measurement method at this time, the frequency change of Fs is −2514 Hz, and by subtracting this from the frequency change of Fs in the solution −5020 Hz, the mass of water contained in the film −2506 Hz is obtained. It can be seen that the latex beads formed an adsorption film containing the same amount of water in the solution as the latex beads themselves.

  That is, the moisture content when latex beads form an adsorption film in a solution is 1 (or 100%). The water content ratio indicates a value obtained by dividing the mass of water contained in a substance by the mass of the substance (solid), and indicates the ratio of water contained in the substance.

Since the sensitivity of the 27 MHz crystal resonator is 0.62 ng / cm ² per −1 Hz, the mass per unit area is −2514 Hz × 0.62 ng / cm ² . When the adsorption area is multiplied by this, the mass of the beads attached to the sensor surface can be calculated.

Since the value of Δfw / Δfs = 0.069 in the latex bead solution is a value when the water content ratio of the adsorption film is 1, the water content ratio of the adsorption film is obtained from the frequency change based on 0.069. The method is defined as (ΔF _w / ΔF _s ) /0.069.

Table 2 and Fig. 2 show the water content ratio of each substance adsorbed in the solution based on the dry weight measurement method and the water content ratio ((ΔF _w / ΔF _s ) /0.069) determined by the above definition. . It was obtained from the experimental data that the water content agreed well.

The reference substance is not limited to latex beads. Any structure can be used as long as it has a simple structure, a depth of penetration of less than about 100 nm in a 27 MHz solution, and a dry weight that is reproducible.
The “penetration depth” refers to the distance at which the thickness shear vibration of the crystal resonator is transmitted to the solution in contact and attenuates, and can be derived from the following equation (5).

  Next, a method for calculating the mass of water contained in the adsorbed film, the mass of only the adsorbed substance, and the water content ratio of the adsorbed film from the viscoelastic coefficients G ′ and G ″ values will be described.

The viscoelastic term coefficients G ′ and G ″ of the film are obtained by the method described in detail in Method 1 and Method 2 below.
The resulting G ', G "G from value' / | G | .G calculates a ^binary '/ | G | ² values but constants in the right term of Equation 4, the difference to the number 4 of the right term, Since it does not include the angular frequency ω and the viscosity η ₁ of the solution, it becomes a value represented only by the information of the adsorbed film.Therefore, using this value, the mass of water contained in the adsorbed film more accurately and its adsorption It becomes possible to calculate the mass of only the membrane and the moisture content of the adsorbed membrane.

(Method 1 of calculating viscoelastic term coefficients G ′ and G ″ of the film)
According to Martin et al.'S transmission theory (VEGranstaff, SJ. Martin, J. Appl. Phys. 1994, 75, 1319), the change in impedance Z when the viscoelastic film is adsorbed to a quartz crystal resonator in solution is It is represented by
From Equation 6, the change in resonance frequency F _s is expressed by Equation 7, and the change amount of (F ₁ −F ₂ ) / 2 (= F _w ), which is half the half-value frequency, is expressed by Equation 8.
Further, from Equation 7 and Equation 8, the change amount of the frequency F2 can be obtained as shown in Equation 9.
Where G: complex elastic modulus (MPa), G ′: storage elastic modulus (dynamic elastic modulus) (MPa), G ″: loss elastic modulus (dynamic loss) (MPa), ω: angular frequency, ρ ₂ : Density of solution (g / cm ³ ), η ₂ : Viscosity of solution (Pa · S), h _f : Thickness (nm) of formed pre-film, ρ ₁ : Density of pre-formed film (g / cm ³ ), η ₁ : Viscosity (Pa · S) of the formed membrane, f ₀ : Fundamental frequency (Hz), z _q : Shear mode acoustic impedance (gm / sec / cm ² ) of quartz .

Here, the Voigt model often used as a model of the viscoelasticity of the film is applied to G ′ and G ″.
A model in which the spring G of the elastic element and the dashpot η are connected in parallel is expressed by the following equation.
Here, if ωη = Cμ (C: constant, μ: rigidity (MPa)), Equation 7 can be modified as follows.
In the case of the Nth harmonic wave, the following equation is obtained.
By dividing the value of ΔF _w of each of the two frequencies, an approximate expression including a constant C is obtained.

The above equation is an equation in the case of using the frequency variation F _w of the fundamental wave (N = 1) and third harmonic (N = 3).
The following constant C can be calculated by substituting A for the value obtained by dividing the frequency variation F _w3 obtained by measurement by F _w1 and substituting that value A into the left side of the above equation.

From the calculated value C and the measured frequency changes ΔF ₂ , ΔF _w , ΔF _{s of} the fundamental wave, the frequency change of each term represented by the following equations 15 to 17 is obtained. At this time, the measurement is performed under the condition that no viscous load of the solution occurs.

First, since ΔF _w is established only by the viscoelastic term (2),
Viscoelastic term (2) = ΔF _w
It becomes.

Next, the viscoelastic term (1) is obtained by the following equation. Since the constant C can be expressed by G ″ / G ′, the viscoelastic term (1) can be calculated by substituting C = G ″ / G ′ and multiplying by the viscoelastic term (2).
Viscoelastic term (1) =-(1 + C) * Viscoelastic term (2)
Mass load term is obtained by substituting the values of viscoelasticity term obtained above in equation ΔF ₂ (1).
Mass load term = ΔF ₂ -Viscoelastic term (1)
Finally, the viscoelastic term (3) is obtained by substituting the value of the mass load term obtained above into the equation for ΔF _s .
Viscoelastic term (3) = ΔF _s -Mass load term

Further, the viscoelastic coefficients G ′ and G ″ are calculated from the following formula using the mass load term and the frequency change amount of the viscoelastic term (2) obtained above. In the formula, ω: angular frequency, ρ ₂ : Solution density (g / cm ³ ), η ₂ : Solution viscosity (Pa · S), ρ ₁ : Film density (g / cm ³ ).
G ″ = C * G ′

(Method 2 for calculating the viscoelastic term coefficients G ′ and G ″ of the film)
When a substance such as protein, DNA or sugar chain is synthesized with water in a solution, and the substance is adsorbed in the form of a thin film on the electrode of the piezoelectric element, the fundamental wave and overtone (3rd harmonic, 5th harmonic) , 7th harmonic, etc., as described in Patent Document 1, each term of Equations 2 and 3 (mass load term, viscous load term, viscoelastic term 1, Table 1 below shows the viscoelasticity term 2) obtained by the Voigt model, and the viscoelastic coefficients G ′ and G ″ calculated from the value and the density of the adsorbate.

From this result, it can be seen that the beam converges on a straight line of G ″ = G ′ / 2. Therefore, when there is no viscous load of the solution, the fundamental wave is used by using the relationship of G ″ = G ′ / 2. , Measure the frequency variation of any one of the overtones (3rd harmonic, 5th harmonic, 7th harmonic ...) and separate any one of mass load, viscous load and viscoelasticity from the remaining load To measure.
When there is no change in the viscosity of the solution, Equation 19 becomes the following equation.
The value of the viscoelastic term (2) is obtained from the amount of change of Δ (F ₁ −F ₂ ) / 2.
When there is no change in the viscosity of the solution, the following equation is established.
From G ″ = G ′ / 2, the viscoelastic term (3) of Equation 22 is obtained, and further, the mass load term can be obtained by substituting the actual change amount into ΔF _s .

From the above, the viscoelastic term (2) of the system is Δ (F ₁ −F ₂ ) / 2, the viscoelastic term (3) of the system is Δ (F ₁ −F ₂ ) / 4, The mass load of the system can be determined independently as Δ (F ₁ −F ₂ ) / 4−ΔF _s .
The above is the case where the fundamental wave of a 27 MHz crystal resonator is used, and C in the relationship of G ″ = CG ′ is almost ½, but the overtone (N = 3, 5, 7,...) When used, G ′ has no frequency dependence, and C is approximately N / 2 due to the relationship of G ″ = ωη (ω: angular frequency, η: viscosity of the solution). From this, G ′ and G ″ can be obtained.

Using the above method, G 'and G "of each film were obtained with the fundamental wave and 3rd harmonic of a 27 MHz crystal resonator. Water content ratio when 50nm latex beads formed an adsorbed film in solution Since it has been experimentally determined that the ratio is 1 as G ′ / | G | ² = 0.350 when the water content ratio is 1, a method for obtaining the water content ratio of the adsorbed film from the viscoelastic coefficient (G ′ / | G | ² ) /0.350.

The frequency of F _s , F ₁ , F ₂ used in the above measurement method is measured by the resonance frequency F, such as a method using an oscillation circuit or a method obtained by frequency sweep from an external device such as an impedance analyzer or a network analyzer. _{If s} is a half-value frequency F ₁ , F ₂ (F ₂ > F ₁ ) having a conductance value that is half the conductance value of the resonance frequency, the measurement method is not limited.
As an example of an apparatus used in the measurement method, as shown in FIG. 1, a cell 1 equipped with a piezoelectric element is connected to a network analyzer 2 via a network analyzer 2 to control, measure and calculate a personal computer or the like. It is configured by connecting to the control means 3. In the illustrated example, in order to adjust the temperature of the cell 1, the temperature control means 4 such as a Peltier element is provided on the lower surface of the cell 1, and the temperature adjustment means 5 for adjusting the temperature control means 4 is similarly provided. Control is performed by the control means 3.
In the above description, the fundamental wave and the third harmonic wave are used. However, the present invention is used if the frequency is at least two of the overtone frequencies including the fundamental wave as shown in FIG. can do.

  In addition, the piezoelectric element used in the present invention is not limited as long as it can measure the target frequency, and is a crystal resonator, APM (ACOUSTIC PLATE MODE SENSOR), FPW (FLEXURAL PLATE-WAVE SENSOR) or SAW. (SOURFACE ACOUSTIC-WAVE SENSOR) can also be used.

Using the apparatus described in the above embodiment, a crystal resonator was used as the piezoelectric element, and an experiment was performed in which Neutravidin (protein) was adsorbed on the gold electrode surface.
FIG. 3 is a time-dependent change in resonance frequency change (ΔFs) obtained by normal QCM measurement.

As a result of analyzing the measurement data of FIG. 3 by the method of the present invention, the water content ratio of the Neutravidin membrane was calculated in real time (FIG. 4), and the mass of water contained in the Neutravidin membrane and the mass of Neutravidin itself ( FIG. 5) is possible.
It was found that the Neutravidin membrane in solution had a low water content when the amount of adsorption was small, and the water content increased as it approached the maximum amount of adsorption (saturated adsorption amount).

1 cell 2 network analyzer 3 control means 4 temperature control means 5 temperature adjustment means

Claims (4)

A system in which a film is formed by adsorbing a substance on a surface of the piezoelectric element in the solution or a film fixed on the piezoelectric element in the solution by a sensor using a piezoelectric element immersed on both sides or one side in the solution. In
The amount of change (ΔF _s , ΔF ₁ , ΔF ₂ ) of any one of the resonance frequency F _s and the half-value frequencies F ₁ , F ₂ (F ₂ > F ₁ ) having a conductance value that is half the conductance value of the resonance frequency Measure and
Frequency change amount of measurement object (Δ (F ₁ -F ₂ ) with reference to frequency change amount (Δ (F ₁ −F ₂ ) / 2) / ΔFs at maximum adsorption of the reference substance to the sensor / 2) A method for measuring water content, wherein the mass of water contained in the object to be measured is obtained in comparison with / ΔFs. The method for measuring water content according to claim 1, wherein the amount of change in frequency at the time of maximum adsorption of the reference substance to the sensor is calculated as (G '/ | G | ² ).   The frequency used in the measurement is any one of a fundamental wave and an overtone (third harmonic, fifth harmonic, seventh harmonic, ...). Measuring method.   4. The piezoelectric element according to claim 1, wherein the piezoelectric element is a crystal resonator, an APM (ACOUSTIC PLATE MODE SENSOR), an FPW (FLEXURAL PLATE-WAVE SENSOR), or a SAW (SOURFACE ACOUSTIC-WAVE SENSOR). A method for measuring a mass load and viscoelasticity of the substance according to the item.