JP2014134396A - Measuring method for viscoelasticity coefficient of substance - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a measuring method for a viscoelasticity coefficient that: enables information on the viscoelasticity of an adsorbing substance in the atmosphere and in solution to be represented by a coefficient generally used for representation of viscoelasticity; and further enables viscoelasticity coefficient to be calculated in real time.SOLUTION: A measuring method for a viscoelasticity coefficient measures a frequency change amount, and, with calculation using the change amount and a variable in response to a measurement environment, measures a viscoelasticity coefficient.

Description

  The present invention uses a sensor used in the field of chemistry, physics, biochemistry, pharmacy, materials, etc., for measuring the amount of adsorption of a substance and evaluating physical properties in the atmosphere or with both sides or one side of a piezoelectric element immersed in a solution. The present invention relates to a method for measuring the mass and thickness of a substance and the viscoelastic coefficient.

ところが、大気中や溶液中で粘弾性の性質を持つ物質の測定においては、Sauerbreyの式が成り立たず、従来のQCMで測定できる共振周波数F_Sの周波数変化は、吸着物質による質量負荷と吸着物質自体の粘弾性効果を含んだ値、溶液中では更に溶液の粘性負荷も一緒に測定してしまい、それぞれを分離することはできていなかった。
そこで、我々は特許文献１に記載した発明により、上記のF_Sの周波数変化量に含まれる３つの要素を分離し、それを周波数変化量としてそれぞれ算出することが可能なことを見出した。
しかしながら、分離した質量負荷による周波数変化から上記Sauerbreyの式を使って質量を換算することができても、分離した粘弾性要素から吸着物質の粘弾性係数を算出することはできなかった。
そこで、溶液中においては特許文献１記載の発明により、各N倍波の各周波数変化ΔF_S,ΔF₂、ΔF_Wを質量負荷項、粘性負荷項及び粘弾性項にそれぞれ分離して得られた各要素の周波数変化量から、物質の粘弾性を表す変数として一般的なG’、G”値を算出する方法を可能とする発明を先に提案した。(文献２：特願2010-235657）
しかし、文献２においては、溶液中の粘弾性物質の粘弾性係数の算出だけを可能とするもので大気中において適用することは出来なかった。また、溶液中の粘弾性物質の測定においても、粘弾性の性質をあまり持たない剛体に近い物質の場合は、粘弾性係数の算出が出来なかったり、精度よく係数を求めることが困難であった。
また、一般的な粘弾性計測装置では、１μｍ以下の厚みをもつ試料の粘弾性測定は困難とされていた。
なお、ここでいう剛体とは密に出来たたんぱく質やポリマー等をさすこととする。 The relationship between the frequency change ΔF due to the adsorption of the QCM and the mass load Δm is the Sauerbrey equation shown below.

However, when measuring substances with viscoelastic properties in the atmosphere or in solution, the Sauerbrey equation does not hold, and the frequency change of the resonance frequency F _{S that} can be measured by the conventional QCM The value including the viscoelastic effect of itself and the viscous load of the solution were also measured together in the solution, and each could not be separated.
Accordingly, the present invention described in Patent Document 1, to separate the three elements included in the frequency variation of the above F _S, found that it is possible to calculate each of them as a frequency variation.
However, even if the mass can be converted from the change in frequency due to the separated mass load using the Sauerbrey equation, the viscoelastic coefficient of the adsorbed material cannot be calculated from the separated viscoelastic element.
Therefore, in the solution, the frequency changes ΔF _S , ΔF ₂ , and ΔF _W of each N-th harmonic wave were obtained by separating the mass load term, the viscous load term, and the viscoelastic term, respectively, according to the invention described in Patent Document 1. An invention that enables a method for calculating general G ′ and G ″ values as variables representing viscoelasticity of a substance from the frequency variation of each element has been proposed previously (Reference 2: Japanese Patent Application No. 2010-235657).
However, in Document 2, it is only possible to calculate the viscoelastic coefficient of a viscoelastic substance in a solution and cannot be applied in the atmosphere. Also, in the measurement of viscoelastic substances in solution, it was difficult to calculate the viscoelastic coefficient or to obtain the coefficient with high precision in the case of a substance close to a rigid body that does not have viscoelastic properties. .
Moreover, with a general viscoelasticity measuring apparatus, it has been difficult to measure viscoelasticity of a sample having a thickness of 1 μm or less.
The rigid body here refers to a dense protein, polymer, or the like.

Japanese Patent No. 4669649

Therefore, the present invention makes it possible to represent the viscoelasticity information of the adsorbed material both in the atmosphere and in the solution by the coefficients G ′ and G ″ that are generally used for representing the viscoelasticity. It is another object of the present invention to provide a method for measuring the viscoelastic coefficient of a substance capable of calculating the viscoelastic coefficient in real time, and to provide accuracy even in the case of a substance close to a rigid body that does not have viscoelastic properties. The purpose is to calculate the viscoelastic coefficient well, calculate the viscoelastic rigidity and viscosity of the adsorbed material from the obtained viscoelastic coefficient, and simultaneously calculate the mass and film thickness of the adsorbed material.
Furthermore, the viscoelastic coefficient of a material having a thickness of 1 μm or less, which is difficult to measure with a conventional viscoelasticity measuring apparatus, is calculated.

（ロ）溶液中の場合

（上記（イ）又は（ロ）において、G’：貯蔵弾性率（動的弾性率）（Pa）、G”：損失弾性率（動的損失）（Pa）、ω：角周波数、h₁：吸着した物質の厚み（m）、ρ₁：吸着した物質の密度（kg/m³）、η₂：溶液の粘度（Pa・s）、ρ₂：溶液の密度（kg/m³）、r_sw=ΔF_s1/ΔF_w1である。）
を含むことを特徴とする。
また、請求項２記載の本発明は、請求項１記載の発明において、前記関数A(α)は、以下の数５で表され、

（イ）大気中の場合において、
前記関数C(α,A(α))は以下の数６で表され、

前記補正関数のΔF_S,N’(C(α,A(α))及び半値半幅の変化の補正関数ΔF_W,N’(C(α,A(α))は、以下の数７及び数８で表され、

（ロ）溶液中の場合において、
前記関数C(α,A(α))は以下の数９で表され、

補正関数のΔF_S,N’(C(α,A(α))及び半値半幅の変化の補正関数ΔF_W,N’(C(α,A(α))は、以下の数１０及び数１１で表され、

ることを特徴とする。
請求項３記載の本発明は、請求項２記載の発明において、前記N倍波は３倍波とし、大気中の場合の前記測定環境変数αは、９＜α≦８１であり、溶液中の場合の前記測定環境変数αは、１＜α≦９であることを特徴とする。
請求項４記載の本発明は、請求項１乃至３の何れか１項に記載の発明において、前記粘弾性係数G'を使用し、前記物質の剛性率μ及び前記物質の粘性率ηの少なくとも何れかを測定することを特徴とする。
請求項５記載の本発明は、請求項４に記載の発明において、前記剛性率μ又は前記粘性率ηの測定は、前記共振周波数の変化ΔF_S,1及び前記N倍波の共振周波数の変化ΔF_S,Nの測定とともに行うことを特徴とする。
請求項６記載の本発明は、請求項１乃至５の何れか１項に記載の発明において、前記物質の質量と膜厚とを、前記粘弾性係数G'及びG''とともに算出することを特徴とする。
請求項７記載の本発明は、請求項１乃至６の何れか１項に記載の発明において、前記圧電素子は、水晶振動子、APM（ACOUSTIC PLATE MODE SENSOR）、FPW(FLEXURAL PLATE-WAVE SENSOR)又はSAW(SOURFACE ACOUSTIC-WAVE SENSOR)であることを特徴とする。 In order to solve the above-mentioned problem, the first solving means of the present invention is the surface of the piezoelectric element in the solution by a sensor using a piezoelectric element immersed on the both sides or one side in the atmosphere or in the solution, or A method of measuring a viscoelastic coefficient in a system in which a film is formed by adsorbing a substance to a film fixed on the piezoelectric element, the following steps (1) to (4):
(1) A step of setting a fluctuation range in the atmosphere or a fluctuation range in a solution as a fluctuation range of the measurement environment variable α in which the sensor is arranged;
(2) the change [Delta] F _S in the resonant frequency of the change in the resonant frequency of the fundamental wave of said sensor [Delta] F _{S, 1} and N harmonic (N = 3, 5, 7 · · _·), the _N measured during the measurement, these ΔF _{S, N} ′ (C (α, A (α)) of correction function of change in resonance frequency of N harmonic based on values ΔF _{S, 1} and ΔF _{S, N} and correction function ΔF _W of change in half width at half maximum _{, N} ′ (C (α, A (α))
(Note that A (α) is determined by ΔF _{S, 1} and ΔF _{S, N} , half-width changes ΔF _{W, 1} and ΔF _{W, N} obtained by ΔF _{S, 1} and ΔF _{S , N} and a variable α. C (α, A (α)) is a function based on the variable α and the function A (α), and the half width at half maximum F _{W, k} (k = 1, 3, 5,... .N) is a frequency F _{1, k} , F _{2, k} (F _{1, k} <F _{2, k} ) that is a conductance value that is half the conductance of the resonance frequency F _{S, k.} (The difference from the frequency F _{1, k} or F _{2, k} shall be said.)
(3) A correction function for a change in the resonance frequency of the N-th harmonic wave, which is a minimum error, with respect to the change ΔF _{S, N} of the resonance frequency of the N-th harmonic wave and the change in half-width half width ΔF _{W, N} obtained therefrom. ΔF _{S, N} ′ (C (α, A (α))) and half-width change correction function ΔF _{W, N} ′ (C (α, A (α))) Substituting into function C (α, A (α)) to calculate value C,
(4) calculating viscoelastic coefficients G ′ and G ″ according to step (b) or (b) separately for the following cases;
(I) In the atmosphere

(B) In solution

(In the above (a) or (b), G ′: storage elastic modulus (dynamic elastic modulus) (Pa), G ″: loss elastic modulus (dynamic loss) (Pa), ω: angular frequency, h ₁ : Adsorbed substance thickness (m), ρ ₁ : Adsorbed substance density (kg / m ³ ), η ₂ : Solution viscosity (Pa · s), ρ ₂ : Solution density (kg / m ³ ), r _sw = ΔF _s1 / ΔF _w1 .)
It is characterized by including.
Further, in the present invention according to claim 2, in the invention according to claim 1, the function A (α) is expressed by the following equation (5):

(I) In the case of the atmosphere,
The function C (α, A (α)) is expressed by the following formula 6,

ΔF _{S, N} ′ (C (α, A (α)) of the correction function and the correction function ΔF _{W, N} ′ (C (α, A (α)) of the change in half width at half maximum are the following equations 7 and 8 and

(B) In solution,
The function C (α, A (α)) is expressed by the following formula 9,

The correction function ΔF _{S, N} ′ (C (α, A (α)) and the half-width half-width change correction function ΔF _{W, N} ′ (C (α, A (α)) are expressed by the following equations 10 and 11. Represented by

It is characterized by that.
According to a third aspect of the present invention, in the second aspect of the present invention, the N harmonic is a third harmonic, and the measurement environment variable α in the atmosphere is 9 <α ≦ 81, In this case, the measurement environment variable α is 1 <α ≦ 9.
According to a fourth aspect of the present invention, in the invention according to any one of the first to third aspects, the viscoelastic coefficient G ′ is used, and at least the rigidity μ of the substance and the viscosity η of the substance are at least. Any one of them is measured.
According to a fifth aspect of the present invention, in the invention according to the fourth aspect, the rigidity μ or the viscosity η is measured by changing the resonance frequency change ΔF _{S, 1} and the N harmonic resonance frequency. It is characterized by being carried out together with the measurement of ΔF _{S, N.}
The invention according to claim 6 is the invention according to any one of claims 1 to 5, wherein the mass and film thickness of the substance are calculated together with the viscoelastic coefficients G ′ and G ″. Features.
The present invention according to claim 7 is the invention according to any one of claims 1 to 6, wherein the piezoelectric element includes a crystal resonator, an APM (ACOUSTIC PLATE MODE SENSOR), and an FPW (FLEXURAL PLATE-WAVE SENSOR). Or SAW (SOURFACE ACOUSTIC-WAVE SENSOR).

Since conventional can only measure only the resonance frequency F _S containing elements of viscoelasticity of the adsorbed material with mass load due to the adsorption, it was not accurately obtained information viscoelasticity. Moreover, although it was possible to obtain | require and isolate | separate each element of mass, viscosity, and a viscoelasticity by the invention proposed in patent document 1, it was only able to represent it as a frequency change amount.
However, according to the present invention, it is possible to calculate a general G ′, G ″ value as a variable representing viscoelasticity from the frequency change amount of each element obtained in the air or in a solution. This also makes it possible to obtain viscoelastic coefficients G 'and G''in real time while measuring the amount of frequency change, and instantly acquire physical information other than frequency (loss coefficient, elastic modulus, viscosity). As a result, the physical properties of the adsorbed material can be evaluated more accurately.

The graph which shows the relationship between the frequency and conductance of the fundamental wave of this invention, and N times harmonic (N = 3,5,7 ...) Explanatory drawing of the device configuration of the embodiment of the present invention Frequency change due to trypsin adsorption Results of viscoelasticity analysis according to Reference 2 (Japanese Patent Application 2010-235657) Results of viscoelasticity analysis according to the present invention

式（４）において、

のとき、式（４）のtan項をテーラー展開し、式（４）は、下記の式（５）に近似することができる。

更に、式（５）は、下記の式（６）に変形される。

このとき水晶振動子の直列共振周波数の変化ΔF_Sは、下記の式（７）で表される。

更に、半値半幅の変化ΔF_Wは、式（８）で表される。

また式（７）及び式（８）から、F₂の変化量ΔF₂が求められる。

（１−ｂ）溶液中の測定の場合は、Martin らの伝送理論（V.E.Granstaff,S.J..Martin,J.Appl.Phys. 1994,75,1319）により粘弾性膜が溶液中で水晶振動子に吸着した場合のインピーダンスZの変化は、式（１０）で表される。

式（１０）から、共振周波数の変化ΔF_Sは下記の式（１１）、半値半幅の変化ΔF_Wの変化は式（１２）で表される。

また、式（１１）、式（１２）から、周波数変化ΔF₂が求められる。

The measurement principle of the present invention will be described below.
(1) As shown in FIG. 1, for each of the fundamental wave and N harmonic wave (N = 3, 5,...) Obtained by measurement, the resonance frequency is F _s and the conductance value is half the conductance value of the resonance frequency. F ₁ , F ₂ (F ₂ > F ₁ ), and the half width obtained using two of them is F _W (F _W = (F ₁ -F ₂ ) / 2, F _W = F ₁ -F _S or F _W = F _S -F ₂ ). Moreover, what added "(DELTA)" before these values shall say the variation | change_quantity in predetermined time.
(1-a) When measuring in the atmosphere, according to R. LUCKLUM, et al (Meas, Sci. Technol, 12, 1854-1864 (2003)) The acoustic load impedance of the load by this thin film is expressed by the following equation (4).

In equation (4),

, The tan term of equation (4) is Taylor-expanded and equation (4) can be approximated to equation (5) below.

Further, the equation (5) is transformed into the following equation (6).

At this time, the change ΔF _{S in} the series resonance frequency of the crystal resonator is expressed by the following equation (7).

Further, the change in half width at half maximum ΔF _W is expressed by Expression (8).

Also from equation (7) and (8), the change amount [Delta] F ₂ of F ₂ is obtained.

(1-b) In the case of measurement in solution, the viscoelastic film is adsorbed on the quartz crystal resonator in solution according to Martin et al.'S transmission theory (VEGranstaff, SJ.Martin, J.Appl.Phys. 1994,75,1319). In this case, the change in impedance Z is expressed by equation (10).

From the equation (10), the change ΔF _{S in the} resonance frequency is expressed by the following equation (11), and the change in the half-value half width ΔF _W is expressed by the equation (12).

Further, equation (11), from equation (12), the frequency change [Delta] F ₂ is determined.

(2) Here, the Voigt model often used as a model of the viscoelasticity of the film is applied to G ′ and G ″.
The Voigt model in which the spring G of the elastic element and the dashpot η are connected in parallel is expressed by the following equation (14).

  Here, by setting ωη = Cμ (C: constant, μ: rigidity, η: viscosity), C has the meaning of C = G ″ / G ′. In viscoelastic analysis, G ″ / G ′ is called tan δ (loss factor), and is known to be a viscoelastic variable representing the hardness of an object.

この式（数２５）で求めた値A(α_L)を、測定環境に応じて、下記の式（数２６又は数２７）に代入することで、関数C(α,A(α))の具体的な値C_L(L=１〜M)値が算出される。
（３）大気中で粘弾性係数を測定する場合

（４）溶液中で粘弾性係数を測定する場合

（５）次に、関数C(α,A(α))から、値ΔF_S,1及びΔF_S,Nに基づいたN倍波の共振周波数の変化の補正関数のΔF_S,N’(C(α,A(α))及び半値半幅の変化の補正関数ΔF_W,N’(C(α,A(α))を求める。具体的には、求められた値C_L(L=１〜M)を使用してN倍波の共振周波数変化ΔF_S,Nの補正値ΔF_S,N´と半値半幅の変化ΔF_W,Nの補正値ΔF_W,N´を求める。それぞれの補正値を求める式（数２８又は数２９）を以下に示す。尚、以下の式において、C(α,A(α))は具体的な値であるC_L(L=１〜M)となる。
（５−ａ）大気中で粘弾性係数を測定する場合

（５−ｂ）溶液中で粘弾性係数を測定する場合

（６）次に、測定して得られたN倍波の共振周波数の変化ΔF_S,Nと半値半幅の変化ΔF_W,N、更にα値を各測定雰囲気により各指定範囲内で設定して求めた補正値のΔF_S,N´とΔF_W,N´から、測定値と補正値の相対誤差を求める。
α値の設定毎の測定値と補正値の相対誤差を求め、その相対誤差が最小になったときのα値で求めた値A，値Cを使用して、測定環境に応じて下記の式（数３２及び数３３、又は、数３４及び数３５）から粘弾性係数を算出する。
（６−ａ）大気中で粘弾性係数を測定する場合

（６−ｂ）溶液中で粘弾性係数を測定する場合

（式中においてG’：貯蔵弾性率（動的弾性率）（Pa）、G”：損失弾性率（動的損失）（Pa）、ω：角周波数、h₁：吸着した物質の厚み（m）、ρ₁：吸着した物質の密度（kg/m³）、η₂：溶液の粘度（Pa・s）、ρ₂：溶液の密度（kg/m³）、r_sw=ΔF_s1/ΔF_w1である。） In order to obtain the value C, first, the value A is calculated by the following function A (α) (Equation 25). Α (a value not limited to an integer) is a measurement environment variable that is set according to the environment in which the sensor is arranged, and its variation range is set separately for the atmosphere and the solution. If it is a thing, there will be no restriction | limiting in particular. In the example described below, the fundamental wave and the third harmonic are used, the setting range of the measurement environment variable α in the atmosphere is 9 <α ≦ 81, and the measurement environment variable α in the solution is set. Is set to 1 <α ≦ 9.
Measure the change in the resonance frequency of the fundamental wave ΔF _{S, 1} and the change in the resonance frequency of the N harmonic (N = 3,5,7 ...) ΔF _{S, N} during the measurement. Half-width change ΔF _{W, 1} and N half-wave half-width change ΔF _{W, N} are calculated, and these values are changed within the set range by measuring environment variable α (value α _L , L is and 1 to M. the) are substituted into equation (25) below, to obtain M values a (alpha _{1 to M).} The half width at half maximum F _{W, k} (k = 1, 3, 5,... N) is the frequency F _{1, k} , F _{2 at which} the conductance value is 1/2 of the conductance at the resonance frequency F _{W, k. , k} (F _{1, k} <F _{2, k} ) _, and the difference between the resonance frequency F _{W, k} and the frequency F _{1, k} or F _{2, k} is assumed.

By substituting the value A (α _L ) obtained by this equation (Equation 25) into the following equation (Equation 26 or 27) according to the measurement environment, the function C (α, A (α)) A specific value C _L (L = 1 to M) is calculated.
(3) When measuring the viscoelastic coefficient in the atmosphere

(4) When measuring the viscoelastic coefficient in solution

(5) Next, from the function C (α, A (α)), the correction function ΔF _{S, N} ′ (C of the resonance frequency change of the N harmonic based on the values ΔF _{S, 1} and ΔF _{S, N} A correction function ΔF _{W, N} ′ (C (α, A (α)) for the change of (α, A (α)) and the half width at half maximum is obtained. Specifically, the obtained value C _L (L = 1˜1) is obtained. use M) N times wave of the resonant frequency change [Delta] F _S, the correction value [Delta] F _S of _{N, N} 'change [Delta] F _W with half width at half _maximum, the correction value [Delta] F _W of _{N, N'} Request. the respective correction values The equation (Equation 28 or 29) to be obtained is shown below, where C (α, A (α)) is a specific value C _L (L = 1 to M).
(5-a) When measuring the viscoelastic coefficient in the atmosphere

(5-b) When measuring viscoelastic coefficient in solution

(6) Next, the resonance frequency change ΔF _{S, N} and the half-value half-width change ΔF _{W, N} obtained by measurement, and the α value are set within each specified range according to each measurement atmosphere. A relative error between the measured value and the correction value is obtained from ΔF _{S, N} ′ and ΔF _{W, N} ′ of the obtained correction value.
Calculate the relative error between the measured value and the correction value for each α value setting, and use the values A and C calculated with the α value when the relative error is minimized. The viscoelastic coefficient is calculated from (Expression 32 and Expression 33, or Expression 34 and Expression 35).
(6-a) When measuring the viscoelastic coefficient in the atmosphere

(6-b) When measuring viscoelastic coefficient in solution

(In the formula, G ′: storage elastic modulus (dynamic elastic modulus) (Pa), G ″: loss elastic modulus (dynamic loss) (Pa), ω: angular frequency, h ₁ : thickness of adsorbed substance (m ), Ρ ₁ : Adsorbed substance density (kg / m ³ ), η ₂ : Solution viscosity (Pa · s), ρ ₂ : Solution density (kg / m ³ ), r _sw = ΔF _s1 / ΔF _w1 .)

Note that the frequency measurement of F _S , F ₁ , F ₂ of each N harmonic used in the above measurement method is a method obtained by an oscillation circuit method or a frequency sweep from an external device such as an impedance analyzer or network analyzer. As long as the resonance frequency F _s and 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, the measurement method is not limited.
As an example of an apparatus used for the measurement method, as shown in FIG. 2, a sensor 1 having a piezoelectric element is connected to a network analyzer 2 via a network analyzer 2, a control means for the network analyzer 2, a measurement means, an arithmetic means such as a CPU. And a control means 3 such as a personal computer provided with a storage means such as a memory. In the illustrated example, in order to adjust the temperature of the sensor 1, the temperature control means 4 such as a Peltier element is provided on the lower surface of the sensor 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-described formula, the fundamental wave and the third harmonic wave are used. However, the present invention can be used as long as any two of 1, 3, 5, 7.

Further, from the value C obtained by the above method, it is possible to measure at least one of the rigidity μ and the viscosity η from the relational expression of ωη = Cμ (μ: rigidity, η: viscosity). Become. The calculation for obtaining the value C, and the measurement of at least one of the rigidity μ and the viscosity η are the measurement of the change ΔF _{S, 1} of the resonance frequency and the change ΔF _{S, N} of the resonance frequency of the N harmonic. It can be done at the same time (in real time).
Similarly, the thickness (film thickness) (h ₁ (m)) of the adsorbed substance and the density (ρ ₁ (kg / m ³ )) of the adsorbed substance are also calculated by the above formula (Equations 32 to 35). Measurements can be made.

  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.

下記式（数３７）にα_Lを代入してC_Lを演算手段により求め記憶手段に記憶した。

下記式（数３８及び数３９）にC_Lを代入して、３倍波の共振周波数変化ΔF_S,3の補正値ΔF_S,3´と半値半幅の変化ΔF_W,3の補正値ΔF_W,3´を演算手段により求め、記憶手段に記憶した。

そして、得られた補正値と、実測値との相対誤差を求めて、その相対誤差が最小になったときのα_Lから、値A及びCを決定して、上記実施の形態で説明した方法により、粘弾性係数として貯蔵弾性率（動的弾性率）G’（Pa）、損失弾性率（動的損失）G”（Pa）、損失係数（tanδ）及び膜厚（nm）を算出した。その結果を表１に示す。比較の為に同試料の膜厚をエリプソ測定により測定した結果も表１に示した。 In this example, a crystal unit having a circular gold electrode provided at the center of each of both surfaces of a circular crystal plate is used, and the measured frequency change is a fundamental wave and a third harmonic wave. The frequency. In addition, PDMS attached in the following used Sylgard 184 manufactured by Toray Dow Corning, and the ellipsometer used was ULVAC, Laser Ellipsometer, ESM-1AT. Moreover, the thing of the structure shown in FIG. 2 was used for the measurement of the apparatus used by this measurement.
(1) Measurement example in the atmosphere Samples 1 to 3 were obtained by forming a thin film on one side of a 27 MHz quartz crystal resonator with a spin coater, and a thin film was not formed with the same quartz crystal resonator. Were prepared, and the resonance frequencies F _S , ₁ and F _S , ₃ of the fundamental wave and the third harmonic wave of Samples 1 to ₃ were measured and stored in the storage means. At the same time, the half-widths _{FW, 1} and _FW , ₃ of the fundamental wave and the triple wave were obtained by the computing means and stored in the storage means. In addition, in order to obtain the changes ΔF _S , ₁ and ΔF _S , ₃ of the resonance frequency of the fundamental wave and the third harmonic, and the changes ΔF _{W, 1} and ΔF _W , ₃ of the half wave half width of the fundamental wave and the third harmonic, A comparison operation with the one not formed was performed and stored by the storage means.
Further, the changes ΔF _S , ₁ and ΔF _S , ₃ of the resonance frequency of the fundamental wave and the third harmonic stored in the storage means and the changes ΔF _{W, 1} and ΔF _W , ₃ of the half width at half maximum of the fundamental wave and the third harmonic are stored. Then, as α _L , 9 <α _L ≦ 81, and values obtained by equally dividing 1000 within that range are substituted as α _L into the following equation (Equation 36) to obtain A (α _L ) in the storage means. I remembered it.

Substituting α _L into the following equation (Equation 37), C _L was obtained by the calculation means and stored in the storage means.

Substituting C _L into the following equations (Equation 38 and Equation 39), the correction value ΔF _{S, 3} ′ of the resonance frequency change ΔF _{S, 3} of _{the third} harmonic wave and the correction value ΔF _{W of the} half-value half width ΔF _{W, 3 , 3} 'was obtained by the calculation means and stored in the storage means.

Then, the relative error between the obtained correction value and the actual measurement value is obtained, and the values A and C are determined from α _L when the relative error is minimized, and the method described in the above embodiment Thus, storage elastic modulus (dynamic elastic modulus) G ′ (Pa), loss elastic modulus (dynamic loss) G ″ (Pa), loss coefficient (tan δ), and film thickness (nm) were calculated as viscoelastic coefficients. The result is shown in Table 1. For comparison, the result of measuring the film thickness of the sample by ellipsometry is also shown in Table 1.

  From this result, according to the present invention, it was found that the viscoelastic value of a thin film of 100 nm or less in the atmosphere can be calculated by measuring the frequency change. Further, as a result of performing ellipso measurement on the prepared sample, it is almost the same value as the film thickness calculated by the method of the present invention. Therefore, in the conventional viscoelasticity measuring apparatus, the viscosity of a substance having a thickness of 1 μm or less is obtained. Although it is difficult to measure elasticity, it has been found that viscoelasticity measurement of a substance having a thickness of 1 μm or less is sufficiently possible by using the method of the present invention.

下記式（数４１）にα_Lを代入してC_Lを演算手段により求め記憶手段に記憶した。

下記式（数４２及び数４３）にC_Lを代入して、３倍波の共振周波数変化ΔF_S,3の補正値ΔF_S,3´と半値半幅の変化ΔF_W,3の補正値ΔF_W,3´を演算手段により求め、記憶手段に記憶した。

そして、得られたそれぞれの補正値と、対応する実測値との相対誤差を求めて、その相対誤差が最小になったときのα_Lから、値A及びCを決定して、上記実施の形態で説明した方法により、粘弾性係数として貯蔵弾性率（動的弾性率）G’（Pa）、損失弾性率（動的損失）G”（Pa）、損失係数（tanδ）及び膜厚（nm）を算出した。
以上の測定、演算をリアルタイムで行い、その結果を図５に示した。
トリプシンは振動のエネルギー損失をほとんど起こさない剛体に近い物質の為、特許文献２（特願2010-235657）に開示した従来の解析方法では解析できない。このことを示すために、貯蔵弾性率（動的弾性率）G’（Pa）及び損失弾性率（動的損失）G”（Pa）の解析を文献２に開示される方法により行った例を図４に示した。
図４及び図５を比較すれば明らかな通り、本発明の方法では、１８００秒辺りまで粘弾性の解析ができているのに対して、特許文献１開示の方法では、３００秒を経過した時点で解析ができないことがわかった。 (2) Measurement Example in Solution After washing the gold electrode of the 27 MHz crystal resonator, it was fixed as a sensor on the cell bottom. Then, 500 μL of Buffer solution was put into the cell, and it waited for the frequency change to stabilize. When the frequency was stabilized, 5 μL of 1 mg / mL trypsin (protein) was added, and the amount adsorbed on the gold electrode was measured. .
As shown in FIG. 3, the resonance frequency of the fundamental wave ((a) ΔF _{S, 1} ) and the half width at half maximum ((b) ΔF _{W, 1} ), and the resonance frequency of the third harmonic wave ( (c) ΔF _{S, 3} ) and half width at half maximum ((d) ΔF _{W, 3} ) were obtained by measurement or calculation and stored in the storage means.
Further, the changes ΔF _S , ₁ and ΔF _S , _{3 of} the fundamental and third harmonic resonance frequencies stored in the memory means in real time and the changes ΔF _{W, 1} and ΔF _W , half-widths of the fundamental and third harmonics, _{Using 3} as α _L , 1 <α _L ≦ 9, and values obtained by dividing the range into 1000 equal parts are assigned as α _L to the following equation (Equation 40) to obtain and store A (α _L ) Memorized in the means.

Substituting α _L into the following equation (Equation 41), C _L was obtained by the calculation means and stored in the storage means.

Substituting C _L into the following equations (Equation 42 and Equation 43), the correction value ΔF _{S, 3} ′ of the resonance frequency change ΔF _{S, 3} of _{the third} harmonic and the correction value ΔF _W of the change of half width at half maximum ΔF _{W, 3 , 3} 'was obtained by the calculation means and stored in the storage means.

Then, a relative error between each of the obtained correction values and the corresponding actual measurement value is obtained, and values A and C are determined from α _L when the relative error is minimized, and the above embodiment is performed. According to the method described above, the storage elastic modulus (dynamic elastic modulus) G ′ (Pa), loss elastic modulus (dynamic loss) G ″ (Pa), loss coefficient (tan δ), and film thickness (nm) are used as viscoelastic coefficients. Was calculated.
The above measurement and calculation were performed in real time, and the results are shown in FIG.
Since trypsin is a substance close to a rigid body that hardly causes vibrational energy loss, it cannot be analyzed by the conventional analysis method disclosed in Patent Document 2 (Japanese Patent Application No. 2010-235657). In order to show this, an example of analyzing the storage elastic modulus (dynamic elastic modulus) G ′ (Pa) and the loss elastic modulus (dynamic loss) G ″ (Pa) by the method disclosed in Reference 2 This is shown in FIG.
As is clear from comparison between FIGS. 4 and 5, the method of the present invention can analyze viscoelasticity up to about 1800 seconds, whereas the method disclosed in Patent Document 1 has a time when 300 seconds have passed. It was found that analysis was not possible.

1 cell 2 measuring means (network analyzer)
DESCRIPTION OF SYMBOLS 3 Control means 4 Temperature control means 5 Temperature control adjustment means 6 1st calculating part 7 2nd calculating part 8 Display part

Claims (7)

A system in which a substance is adsorbed on the surface of the piezoelectric element or a film fixed on the piezoelectric element by a sensor using a piezoelectric element that is immersed in the atmosphere or in a solution on both sides or one side. A method for measuring a viscoelastic coefficient in the following steps (1) to (4):
(1) A step of setting a fluctuation range in the atmosphere or a fluctuation range in a solution as a fluctuation range of the measurement environment variable α in which the sensor is arranged;
(2) the change [Delta] F _S in the resonant frequency of the change in the resonant frequency of the fundamental wave of said sensor [Delta] F _{S, 1} and N harmonic (N = 3, 5, 7 · · _·), the _N measured during the measurement, these ΔF _{S, N} ′ (C (α, A (α)) of correction function of change in resonance frequency of N harmonic based on values ΔF _{S, 1} and ΔF _{S, N} and correction function ΔF _W of change in half width at half maximum _{, N} ′ (C (α, A (α))
(Note that A (α) is determined by ΔF _{S, 1} and ΔF _{S, N} , half-width changes ΔF _{W, 1} and ΔF _{W, N} obtained by ΔF _{S, 1} and ΔF _{S , N} and a variable α. C (α, A (α)) is a function based on the variable α and the function A (α), and the half width at half maximum F _{W, k} (k = 1, 3, 5,... .N) is a frequency F _{1, k} , F _{2, k} (F _{1, k} <F _{2, k} ) that is a conductance value that is half the conductance of the resonance frequency F _{s, k.} (The difference from the frequency F _{1, k} or F _{2, k} shall be said.)
(3) A correction function for a change in the resonance frequency of the N-th harmonic wave, which is a minimum error, with respect to the change ΔF _{S, N} of the resonance frequency of the N-th harmonic wave and the change in half-width half width ΔF _{W, N} obtained therefrom. ΔF _{S, N} ′ (C (α, A (α))) and half-width change correction function ΔF _{W, N} ′ (C (α, A (α))) Substituting into function C (α, A (α)) to calculate value C,
(4) calculating viscoelastic coefficients G ′ and G ″ according to step (b) or (b) separately for the following cases;
(I) In the atmosphere

(B) In solution

(In the above (a) or (b), G ′: storage elastic modulus (dynamic elastic modulus) (Pa), G ″: loss elastic modulus (dynamic loss) (Pa), ω: angular frequency, h ₁ : Adsorbed substance thickness (m), ρ ₁ : Adsorbed substance density (kg / m ³ ), η ₂ : Solution viscosity (Pa · s), ρ ₂ : Solution density (kg / m ³ ), r _sw = ΔF _s1 / ΔF _w1 .)
A method for measuring a viscoelastic coefficient. The function A (α) is expressed by the following formula 5,

(I) In the case of the atmosphere,
The function C (α, A (α)) is expressed by the following formula 6,

ΔF _{S, N} ′ (C (α, A (α)) of the correction function and the correction function ΔF _{W, N} ′ (C (α, A (α)) of the change in half width at half maximum are the following equations 7 and 8 and

(B) In solution,
The function C (α, A (α)) is expressed by the following formula 9,

The correction function ΔF _{S, N} ′ (C (α, A (α)) and the half-width half-width change correction function ΔF _{W, N} ′ (C (α, A (α)) are expressed by the following equations 10 and 11. Represented by

The method for measuring a viscoelastic coefficient according to claim 1.   The N harmonic is a third harmonic, the measurement environment variable α in the atmosphere is 9 <α ≦ 81, and the measurement environment variable α in the solution is 1 <α ≦ 9. The method for measuring a viscoelastic coefficient according to claim 2.   4. The substance according to claim 1, wherein at least one of a rigidity modulus μ of the substance and a viscosity coefficient η of the substance is measured using the viscoelastic coefficient G ′. 5. Measuring method of viscoelastic coefficient. 5. The measurement of the rigidity μ or the viscosity η is performed together with the measurement of the change ΔF _{S, 1} of the resonance frequency and the change ΔF _{S, N} of the resonance frequency of the N harmonic wave. Method for measuring the viscoelastic coefficient of a material.   The method for measuring a viscoelastic coefficient of a substance according to any one of claims 1 to 5, wherein the mass and the film thickness of the substance are calculated together with the viscoelastic coefficients G 'and G' '.   7. 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 viscoelastic coefficient of the substance described in the item.

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