Method for measuring viscoelastic modulus of substance, and apparatus for measuring viscoelastic modulus of substance

摘要

[Problem] A method for measuring a viscoelastic modulus of a substance and an apparatus for measuring the viscoelastic modulus of the substance are provided for allowing information on viscoelasticity of an adsorption substance to be expressed by moduli G′ and G″ which are generally used when expressing viscoelasticity, and for further allowing calculation of the viscoelastic modulus in real time.;[Solution] In a system for forming a film by adsorbing a substance to the surface of a piezoelectric element or to a film fixed onto the piezoelectric element in a solution, at least two of N-th waves of the piezoelectric element are used, and at least two of a resonance frequency Fs, and half-value frequencies F1 and F2 (F2>F1) having half conductance values of a conductance value of the resonance frequency in each N-th wave are used to calculate a mass load term, a viscoelastic term (1), a viscoelastic term (2), and a viscoelastic term (3), and to calculate viscoelastic moduli G′ (storage elastic modulus) and G″ (loss elastic modulus) of the film.

主权项

1. A method for measuring a viscoelastic modulus of a substance comprising the steps of:
submerging both sides or one side of a sensor with a piezoelectric element in a solution; adsorbing the substance to a surface of the piezoelectric element or to a film fixed onto the piezoelectric element in the solution; measuring at least two of a resonance frequency Fs, and half-value frequencies F1 and F2 (F2>F1) having half conductance values of a conductance value of the resonance frequency in each of at least two of N-th waves (N=1, 3, 5 . . . (N=2n+1)) of the piezoelectric element by a method based on an oscillating circuit or a method obtained from external equipment including an impedance analyzer or a network analyzer; and executing first to sixth calculation steps by using the values measured in the measuring step to calculate the viscoelastic modulus of the adsorbed substance by an arithmetic means, wherein the first calculating step is a step calculating a constant C based on an equation obtained by a value obtained by making division of respective ΔFWN of two N-th waves represented by Equation 1 and a value obtained by making division of respective ΔFWN of two N-th waves obtained based on the half-value frequencies F1 and F2 obtained in the measuring step, the ΔFWN being a variation of a half value of a width between half-value frequencies F1 and F2 (=Δ(F1-F2)/2),Δ⁢⁢FwN=-f0π⁢⁢zq⁢1(1+C2⁢N2)⁢N2⁢ω2⁢ρ2⁢η2⁢h1μ1Equation⁢⁢1 the second calculating step is a step calculating a viscoelastic term (2) by substituting ΔFW obtained based on the half-value frequencies F1 and F2 obtained in the measuring step into Equation 2,Δ⁢⁢Fw=-f0π⁢⁢zq⁢G′G2⁢ω2⁢ρ2⁢η2⁢h1⁢⁢⁢Viscoelastic⁢⁢term⁢⁢(2)Equation⁢⁢2 the third calculating step is a step calculating a viscoelastic term (1) by substituting the viscoelastic term (2) obtained in the second calculating step into Equation 5 obtained by substituting Equation 4 into the viscoelastic term (1) in Equation 3,Δ⁢⁢F2=-f0π⁢⁢zq⁢ω⁢⁢ρ1⁢h1+f0π⁢⁢zq⁢(G′+G″)G2⁢ω2⁢ρ2⁢η2⁢h1⁢⁢⁢Mass⁢⁢load⁢⁢Viscoelastic⁢⁢term⁢⁢(1)Equation⁢⁢3 Equation 4
C=G″/G′ Equation 5
Viscoelastic term (1)=−(1+C)*Viscoelastic term (2) the fourth calculating step is a step calculating a mass load in the Equation 3 based on a variation ΔF2 of the half-value frequency F2 obtained in the measuring step and the viscoelastic term (1) obtained in the third calculating step, the fifth calculating step is a step calculating a viscoelastic term (3) in Equation 6 based on a variation ΔFs of the resonance frequency Fs obtained in the measuring step and the mass load obtained in the fourth calculating step,Δ⁢⁢Fs=-f0π⁢⁢zq⁢ωρ1⁢h1+f0π⁢⁢zq⁢G″G2⁢ω2⁢ρ2⁢η2⁢h1⁢⁢⁢Mass⁢⁢load⁢⁢Viscoelastic⁢⁢term⁢⁢(3)Equation⁢⁢6 the sixth calculating step is a step calculating the viscoelastic moduli G′ (storage elastic modulus) and G″ (loss elastic modulus) based on Equation 7 and Equation 4,G′=ω·[mass⁢⁢load][viscoelastic⁢⁢term⁢⁢(2)]·ρ2⁢η2(1+C2)·ρ1Equation⁢⁢7 wherein ΔFw =Δ(F1-F2)/2, G is a complex elastic modulus (MPa), G′ is a storage elastic modulus (dynamic elastic modulus) (MPa), G″ is a loss elastic modulus (dynamic loss) (MPa), ω is an angular frequency, ρ2 is the density (g/cm3) of the solution, η2 is the viscosity (Pa s) of the solution, h1 is the thickness (nm) of a film formed by the adsorbed substance, ρ1 is the density (g/cm3) of a film formed by the adsorbed substance, f0 is a fundamental frequency (Hz), Zq is the shear mode acoustic impedance (gm/sec/cm2) of crystal, and μ1 is the rigidity coefficient of the adsorbed substance.