JP2003065930A - Method and apparatus for measuring local viscoelasticity of complex fluids - Google Patents

Abstract

(57) [Summary] To obtain knowledge about viscoelasticity of a micrometer-sized local region of a complex fluid having a complex internal structure and structure of a micrometer region of a complex fluid. SOLUTION: Probe particles having a nanometer size are mixed into a complex fluid 2 to be measured, and incident light 4 and reference light 5 are irradiated, and a sinusoidal electric field is applied to the probe particles, whereby the scattered light of the probe particles and the reference light are applied. A fundamental component (ω ₀ ) and a harmonic component (2ω ₀ ) relating to the frequency of the sinusoidal electric field are extracted from the heterodyne signal with the light 5, and the fundamental component and the harmonic component are subjected to analog squaring, and analog squaring is performed. The fundamental component (2ω ₀ ) and the harmonic component (4ω ₀ ) are detected by the lock-in amplifier 12 to determine the absolute value of the complex electrophoretic mobility and the delay phase, and the complex electrophoresis with respect to the frequency of the sinusoidal electric field is performed. The mobility spectrum is obtained, and the characteristic length based on the viscoelasticity of a local region of the complex fluid to be measured and the structure of the complex fluid to be measured is determined.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for obtaining knowledge about micrometer-scale local viscoelasticity of a complex fluid having a complicated internal structure and the structure of the micrometer region of the complex fluid.

[0002]

2. Description of the Related Art In recent years, there is an increasing need to measure the local viscoelasticity of a complex system such as a living cell or gel having a local nonuniformity of viscoelasticity. For example, the transport phenomenon of particles in a living body such as a tissue composed of lipids or a tissue composed of cytoskeletons is important from a biological point of view, and by knowing the local viscoelasticity of such a biological system, Can understand the transport phenomenon of. In addition, various proteins and secretions in the living body are considered to be transported in a potential formed by local interaction with a biological substance having a complicated internal structure in the surroundings, that is, a complex fluid, Obtaining dynamic knowledge of transport phenomena in the micrometer region in such complex fluids is indispensable for future advances in biotechnology and drug development. Also, in various industrial fields such as various pigments, paints, abrasives, liquid toners, ceramics, and fat emulsions that use colloidal particles such as emulsions, latexes and micelles, mass transport in the micrometer range in these complex fluids. Obtaining knowledge of phenomena has become indispensable for future technological development.

The mass transport phenomenon in a medium is called rheology, and the rheology in the micrometer range is called microrheology. For example, mobility is a physical property value that characterizes microrheology, and there are two systems in the conventional technique for measuring mobility in the micrometer range. One is to mix probe particles having a known particle size into a medium, observe Brownian motion of the probe particles by a light scattering method, etc., and determine the mobility of the medium around the probe particles from the Einstein-Stokes relationship. It is a statistical estimate. However, these methods only give average mobilities for the entire medium. The other is a method in which probe particles are excited thermally or by another excitation method and the response of the excited particles is observed to determine the mobility.
As one of such measuring methods, there is an electrophoretic mobility measuring method in which charged colloidal particles are used as probe particles and excited by applying an electric field to measure the mobility of the probe particles. Also, a method of applying a sinusoidal electric field as an applied electric field to obtain a mobility of a complex number is called a complex electrophoretic mobility measuring method.

DC electrophoretic mobility measuring devices have been commercialized by various companies. For example, ELS-800 (manufactured by Otsuka Electronics Co., Ltd.)
There is such a thing. In each of these devices, the DC mobility is obtained from the Doppler shift amount of the scattered light frequency associated with the electrophoresis of charged particles. However, the frequency shift amount has a distribution due to the Brownian motion and drift of the charged particles, and its measurement accuracy is greatly restricted. In recent years, a device has been put on the market that realizes accurate detection of DC electrophoretic mobility by solving this problem using Phase Analysis (ZetaPAL).
S, Brookhaven Instruments
Limited product).

In the conventional complex mobility measuring device, an ESA (Electrokiki) for measuring a sound wave electrically excited.
A method called "netic sonic amplitude" has been used and has already been commercialized (trade name: ES
A-9800, MATEC Instrument Co
companies, Inc). However, since the resonance of sound waves is used, the measurement frequency range is limited to around 1 MHz, and problems such as the fact that measurement can be performed only on a concentrated sample have become a bottleneck and have not yet spread.

By the way, conventionally, it has been impossible to obtain the knowledge about the viscoelasticity of the micrometer region and the structure of the micrometer region of the medium by measuring the complex electrophoretic mobility using the scattered light of the probe particles. . That is, in the signal contained in the scattered light of the probe particle, a component that changes irregularly in Brownian motion or drift motion is superimposed in addition to the response component due to the applied electric field of the probe particle, and the response component due to the applied electric field of the probe particle is superimposed. Cannot be separated. Further, the only method for analyzing the signal contained in the scattered light of the probe particles is the correlation function or the power spectrum, and only average information in a wide area can be obtained. Furthermore, if information is to be obtained from scattered light from probe particles in a medium with extremely high scattering power, it is necessary to use huge probe particles that scatter light so strongly that it surpasses unnecessary scattered light from surrounding media. However, it is impossible to obtain knowledge about the viscoelasticity of the micrometer region and the structure of the micrometer region of the medium, because large probe particles deform the structure of the medium because of large interaction with the medium. . For these reasons, conventionally viscoelasticity in the micrometer range,
It was not possible to obtain any knowledge about the structure of the micrometer region of the medium.

As described above, it has been impossible to obtain knowledge about the micrometer-scale local viscoelasticity of a complex fluid and the structure of the micrometer region of a complex fluid in the prior art.

[0008]

SUMMARY OF THE INVENTION In view of the above problems, the present invention obtains knowledge about the viscoelasticity of a micrometer-sized local region of a complex fluid having a complicated internal structure and the structure of the micrometer region of a complex fluid. It is an object to provide a method and a device.

[0009]

In order to solve the above-mentioned problems, the method for measuring the local viscoelasticity of a complex fluid according to the present invention comprises mixing probe particles of nanometer size into a complex fluid to be measured,
Applying a sinusoidal electric field to the probe particle while irradiating the probe particle with incident light and reference light, converting the optical heterodyne signal of the scattered light of the probe particle and the reference light into an electrical signal,
The fundamental wave component and the harmonic component related to the frequency of the sinusoidal electric field are extracted from the electric signal, and the analog square calculation of each of the fundamental wave component and the harmonic component is performed. Lock-in detection of the complex electrophoretic mobility to obtain the absolute value and the delay phase, and the complex electrophoretic mobility spectrum is obtained from the absolute value and the delay phase at each frequency of the sinusoidal electric field. It is characterized in that the viscoelasticity of the local region of the complex fluid to be measured and the characteristic length based on the structure of the complex fluid to be measured are obtained from the migration mobility spectrum. According to this configuration, since the nanometer-sized probe particles are used, the interaction with the complex fluid to be measured is small, and the structure of the complex fluid is not deformed. Since lock-in detection is performed, only the response component of the sinusoidal electric field from which the component based on Brownian motion is removed can be detected,
The relaxation property can be measured from the spectrum of complex electrophoretic mobility, and the relaxation property can provide the knowledge about the viscoelasticity and the structure depending on the frequency of the local region of the micrometer size of the complex fluid to be measured.

In the present invention, when the absolute value of the complex electrophoretic mobility and the delay phase are obtained, fluctuations due to Brownian motion of the analog squared fundamental wave component and the harmonic component are averaged to zero. In addition, the time constant of the lock-in amplifier is made large enough to detect the two-phase lock-in of the fundamental wave component and the harmonic component that have been analog-squared at the same time. The absolute value of the complex electrophoretic mobility can be obtained from and the delay phase can be obtained from the phase angle of the two-phase lock-in detection signal. According to this configuration, since the time constant is large, the randomly varying component based on the Brownian motion of the fundamental wave component and the harmonic component that have been analog-squared are eliminated by averaging, and the analog-squared basic component is eliminated. Only the response component of the applied electric field, which is the constant term of the wave component and the harmonic component, is detected. In addition, since each detected response component is represented by a Bessel function of different rank with a value proportional to the absolute value of the complex electrophoretic mobility as a variable, the complex electrophoretic mobility can be calculated from the ratio of these Bessel functions. The absolute value of the mobility can be calculated, and 2
The delay phase can be obtained from the phase angle of the phase lock-in detection signal.

In the above structure, when obtaining the absolute value of the complex electrophoretic mobility in the high frequency region, the sinusoidal electric field is set to a low frequency, and the complex electrophoretic mobility in the low frequency region is set by the method according to claim 2. The absolute value of the degree is calculated, and the applied electric field is composed of the sum of the low-frequency sinusoidal electric field and the high-frequency sinusoidal electric field, so that fluctuations due to Brownian motion of the fundamental wave component calculated by analog square are averaged. Make the time constant of the lock-in amplifier sufficiently large to detect the lock-in of the fundamental wave component that has been analog-squared at two frequencies, low frequency and high frequency, and calculate the ratio of the absolute value of each lock-in detection signal. It can be obtained from the ratio and the absolute value of the complex electrophoretic mobility in the low frequency region. According to this structure, since the fundamental wave component having a high intensity is used without using the harmonic component whose intensity decreases in the high frequency region, the absolute value of the complex electrophoretic mobility in the high frequency region can be accurately obtained.

A method for measuring local viscoelasticity of a complex fluid according to another aspect of the present invention is to mix nanometer-sized probe particles into a complex fluid to be measured, collect trapping laser light on the probe particles, and probe particles. Laser trap, apply a sinusoidal electric field to the complex fluid to be measured, collect the scattered light from the probe particles and the reference light at the confocal position,
Converts the optical heterodyne signal of scattered light and reference light into an electric signal at the confocal position, extracts the fundamental wave component and the harmonic component related to the frequency of the sinusoidal electric field from the electric signal, and extracts the fundamental wave component and the harmonic component, respectively. The complex electrophoretic mobility spectrum related to the frequency of the sinusoidal electric field is obtained by the lock-in detection to obtain the absolute value and the delay phase of the complex electrophoretic mobility, and the complex fluid locality of the measured complex fluid is calculated from the complex electrophoretic mobility spectrum. It is characterized by finding the characteristic length based on the viscoelasticity of the region and the structure of the complex fluid to be measured. According to this configuration,
Since the Brownian motion of the probe particles is suppressed by the laser trap, the complex electrophoretic mobility can be obtained without performing the analog square calculation, and as a result, 100 MH is obtained.
Ultra-wide band complex electrophoretic mobilities spanning z can be determined.

In the above structure, the application direction of the sinusoidal electric field is preferably the same as the optical path direction of the trapping laser light. The method of condensing the scattered light and the reference light at the confocal position is preferably a scattered light obtained by converting the scattered light into a parallel light flux with an optical member for converging the trapping laser light and making the light flux into a parallel light flux with an optical member for matching the optical paths. And the optical path of the reference light are made to coincide with each other, and the scattered light and the reference light having the coincident optical paths are condensed by a common optical member. The method of matching the optical paths can be performed by making the scattered light and the reference light respectively enter the incident surfaces of the beam splitter which are orthogonal to each other. According to these configurations, since the displacement direction of the probe particle is the same as the scattered light direction, the heterodyne signal can be generated with high efficiency. Moreover, the structure of the optical system is simplified, and the reliability and operability are high.

The method of converging the trapping laser light on the probe particles and making the scattered light into a parallel light beam is carried out by disposing an optical member having a variable focal length between the complex fluid to be measured and the beam splitter. obtain. In the method of collecting the trapping laser light on the probe particles and converting the scattered light into a parallel light flux, a movable convex lens may be arranged between the complex fluid to be measured and the beam splitter. According to these configurations, the position at which the trapping laser light is focused can be changed, so that the complex electrophoretic mobility at any position in the depth direction of the complex fluid to be measured can be measured.

Further, the complex fluid to be measured having electrodes is mounted on a movable table, and the movable platform controls the three-dimensional position of the complex fluid to be measured to perform the three-dimensional measurement of the complex fluid to be measured. And According to this configuration, the trapping laser light can be focused on the arbitrary three-dimensional position of the complex fluid to be measured, so that the three-dimensional local viscoelastic spectrum of the complex fluid to be measured and the characteristic length relating to the three-dimensional structure can be obtained. it can.

Further, preferably, a light source of the trapping laser light, a light source of the reference laser light, an optical member for condensing the trapping laser light and making the scattered light into a parallel light beam, the scattered light made into the parallel light beam and the reference light The optical member for aligning the optical path of the optical path, the optical member for converging the scattered light, which is formed into a parallel light beam and the reference light having the coincident optical paths at the confocal position, and the photodetector arranged at the confocal position are integrally configured. And make it a constituent unit, move the constituent unit parallel to the surface of the complex fluid to be measured,
In addition, the measurement is performed by changing the focal length of the optical member that collects the trapping laser light and changes the scattered light into a parallel light flux, or the position of the optical member. According to this configuration, the trapping laser light can be focused on the arbitrary three-dimensional position of the complex fluid to be measured, so that the three-dimensional local viscoelastic spectrum of the complex fluid to be measured and the characteristic length relating to the three-dimensional structure can be obtained. it can.

Further, when obtaining the absolute value of the complex electrophoretic mobility and the delay phase, the time constant of the lock-in amplifier is set so that fluctuations due to Brownian motion of the fundamental wave component and the harmonic wave component are averaged to zero. Make it sufficiently large to detect the two-phase lock-in of the fundamental wave component and the harmonic component, and obtain the absolute value of the complex electrophoretic mobility from the ratio of the absolute values of the two-phase lock-in detection signals. It is characterized in that the delay phase is obtained from the phase angle of the detection signal. According to this configuration, since the Brownian motion of the probe particles is suppressed, the fundamental wave component and the harmonic wave component of the heterodyne electric signal can be directly lock-in detected. Also, the absolute value of the detection signal is represented by a Bessel function of different rank with a value proportional to the absolute value of the complex electrophoretic mobility as a variable. Therefore, the complex electrophoretic mobility can be calculated from the ratio of these Bessel functions. The absolute value can be obtained, and the delay phase can be obtained from the phase angle of the two-phase lock-in amplifier.

When the absolute value of the complex electrophoretic mobility in the high frequency region is obtained, the sinusoidal electric field is set to a low frequency to obtain the absolute value of the complex electrophoretic mobility in the low frequency region and the applied electric field is set. It is composed of the sum of the low-frequency sinusoidal electric field and the high-frequency sinusoidal electric field, and the time constant of the lock-in amplifier is made sufficiently large so that the fluctuations due to the Brownian motion of the fundamental wave component are averaged to 0, The fundamental wave component is simultaneously lock-in detected at two frequencies, low frequency and high frequency, and the ratio of the absolute values of the lock-in detection signals of each is calculated. From the ratio and the absolute value of the complex electrophoretic mobility in the low frequency region, You can ask. According to this structure, since the fundamental wave component having a high intensity is used without using the harmonic component whose intensity decreases in the high frequency region, the absolute value of the complex electrophoretic mobility in the high frequency region can be accurately obtained.

The optical heterodyne signal of the scattered light of the probe particles and the reference light is preferably based on the displacement of the probe particles. It is preferable to extract the fundamental wave component and the harmonic component from the heterodyne electric signal with a bandpass filter. When obtaining the viscoelasticity of the local region of the complex fluid to be measured from the complex electrophoretic mobility spectrum, it is preferable to obtain it from the inverse proportional relationship between the complex electrophoretic mobility and the complex viscoelasticity. To obtain the characteristic length based on the structure of the complex fluid to be measured from the complex electrophoretic mobility spectrum, the absolute value of the complex electrophoretic mobility obtained from the real and imaginary components of the complex electrophoretic mobility spectrum and It is preferable to use the relaxation time as a basis.

The nanometer-sized probe particles are colloidal particles that are charged in the complex fluid to be measured.
The diffusion constant and the complex electrophoretic mobility of the probe particles in the fluid from which the structure of the measured complex fluid has been removed are measured in advance and are known. According to this configuration, the probe particles can be displaced by the sinusoidal electric field applied from the outside, and because the size is nanometer, it is smaller than the internal structure of the complex fluid and deforms the complex fluid to be measured. It is possible to measure at various spatial scales without doing this. In addition, since the diffusion constant and complex electrophoretic mobility of the probe particles in the liquid from which the structure of the complex fluid to be measured is removed are known, the known diffusion constant and complex electrophoretic mobility can be measured. It is possible to obtain the amplitude of the fluctuation based on the structure of the complex fluid to be measured from the relaxation time and the absolute value of the complex electrophoretic mobility in the complex fluid to be measured, which is obtained from the complex electrophoretic mobility spectrum. , The amplitude of fluctuation based on the structure of the measured complex fluid, that is, the characteristic length can be obtained.

When the characteristic length based on the structure of the complex fluid to be measured is obtained from the complex electrophoretic mobility spectrum, the relaxation time obtained from the real number component and the imaginary number component of the complex electrophoretic mobility spectrum and the autocorrelation are preferable. It is obtained from the diffusion constant obtained from the function. The diffusion coefficient obtained from the autocorrelation function is the time constant of the detection signal when the lock-in amplifier time constant is set to a value that is sufficiently small so that fluctuations due to Brownian motion of the fundamental wave component are not averaged to zero. It is calculated by integrating or integrating the autocorrelation function from the dependence, and by the relaxation time. According to this configuration, the diffusion constant can be directly obtained in the entire measured frequency range, and the diffusion constant of the probe particle and the complex electrophoretic mobility in the fluid without the structure of the complex fluid to be measured can be obtained. Instead, the characteristic length of the complex fluid to be measured can be obtained.

The complex fluid viscoelasticity measuring apparatus of the present invention is characterized by using the above method. According to this device, it is possible to obtain the knowledge regarding the viscoelasticity of a micrometer-sized local region of a complex fluid having a complicated internal structure and the structure of the micrometer region.

According to the method of the present invention and the measuring device of the present invention, it is possible to obtain the local viscoelasticity of the micrometer size of the complex fluid and the characteristic length based on the structure of the complex fluid.

[0024]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings. First, the first embodiment of the present invention will be described. First, the configuration of the apparatus used in the measuring method of the present invention will be described. FIG. 1 is a diagram showing the configuration of a measuring device for measuring complex electrophoretic mobility. The complex electrophoretic mobility measuring apparatus 1 includes a medium to be measured 2 in which probe particles are dispersed.
Container 3, an incident laser light source (not shown) that emits an optical heterodyne signal by irradiating the medium 2 to be measured in the container 3 with an incident laser beam 4, and a reference light laser light source (not shown) that generates a reference laser beam 5, and probe particles. Photodetector 6 for detecting an optical heterodyne signal generated by the interference between the scattered light of the laser beam and the reference laser beam 5, and the photodetector 6
Bandpass filter 9 for extracting only the fundamental wave and the harmonic component 8 from the detection signal 7 and the fundamental wave and the harmonic component 8
2 has an analog multiplier 10 and a lock-in amplifier 12 for detecting the intensity of a second harmonic component 11 obtained by squaring the fundamental wave and harmonic components 8. The container 3 is a cylindrical container 3 having transparent side walls, and an electrode 13 for applying an electric field to the medium 2 to be measured is provided in the container 3. The device 1 has a synthesizer 15 for generating an arbitrary frequency signal 14, and the signal 14 from the synthesizer 15
The high voltage amplifier 16 applies a predetermined voltage to the electrode 13 in synchronization with the frequency of. The signal 14 is also used as a reference signal for the lock-in amplifier 12. In the method of the present invention, the reference laser light 5 is used by distributing the laser light of the incident laser light 4.

Next, the measuring principle of the measuring method using the measuring apparatus of FIG. 1 will be described. The electric field vector E _s (t) (where t is time) of the scattered light by the probe particles in the medium to be measured 2 is given by the following equation as the position vector r _n of the probe particles.

[0026]

[Equation 1]

Here, I is E _s E _s ^* , and N is the number of probe particles in the region where the incident laser beam 4 and the reference laser beam 5 intersect, that is, in the scattering region. q is a scattered wave number vector and is determined by the scattering direction. From the refractive index n of the medium, the angle θ between the incident laser light 4 and the reference laser light 5 and the wavelength λ of the laser light, the absolute value of q is q
= 4πnsin (θ / 2) / λ. The scattered light and the reference laser light 5 are mixed to generate an optical heterodyne signal, which is converted into an electric signal by the photodetector 6. The detected heterodyne signal 7 is represented by the following equation.

[0028]

[Equation 2]

Here, E _R is the electric field vector of the reference laser beam 5, and the light intensity I ₀ is I ₀ = E _R E _R ^* . The position vector r _n (t) of the probe particle changes with time due to Brownian motion of the probe particle. When the external electric field E acts on the probe particles, a new displacement δr _En due to electrophoresis is added. The total displacement of the probe particle is r _n
= R _0n + δr _En . Here, r _0n is a particle position vector in the absence of an external electric field, which fluctuates due to Brownian motion of the probe particle. Therefore, the equation (2) can be rewritten as the following equation.

[0030]

[Equation 3]

Here, all probe particles have the same mobility.
Assuming that μ, the frequency ω from the synthesizer 15
₀In synchronization with the signal 14 of
Through a sinusoidal external electric field E = E₀cos (ω₀t) is measured
If applied to the constant medium 2, δr _EnIs

[0032]

[Equation 4]

It becomes Where δ is the delay phase with respect to the sinusoidal externally applied electric field. Therefore, the detection signal 7 is calculated from the equations (3) and (4),

[0034]

[Equation 5]

[0035] However, in the formula (5), c _n =
q · r _0n , z = μq · E ₀ / ω ₀ , and J _k is a Bessel function of the kth order. The detection signal represented by the equation (5) is composed of two components. One component is a component Σ _n cos (c _n ) and Σ _n sin (c _n ) that randomly fluctuate based on the Brownian motion of the probe particle.

The diffusion constant D is a randomly varying component Σ _n
It can be obtained from the autocorrelation function of cos (c _n ) or Σ _n sin (c _n ) shown below.

[0037]

[Equation 6]

The other signal component is a sinusoidal wave applied externally.
Component that follows the electric field ΣJ_2k(Z) cos (2k (ω₀t
+ Δ)), and ΣJ_2k-1(Z) sin ((2k-1).
(Ω ₀t + δ)). In principle from these ingredients
Complex electrophoretic mobility can be determined. But Naga
Based on the Brownian motion when trying to extract information,
The signal component that fluctuates randomly is sinusoidal.
Interferes with the component that follows the field, especially 1 / Dq²And 1 / ω₀
If the time determined by is almost equal, pull out the information.
I can't. For example, from the time domain signal,
1 / Dq by motion²Complex electrophoretic mobility in time
μ^*It is not possible to obtain information on the phase δ of. For this reason
Since then, the power of the scattered light has been used to obtain the complex electrophoretic mobility.
-I was measuring the spectrum. Apply a sinusoidal external electric field
The power spectrum P (ω) when applied is expressed by the equation (5).
And from the equation (6), it is given by the following equation.

[0039]

[Equation 7]

As is clear from the equation (7), P (ω)
Has a Lorentzian peak at a frequency that is an integer multiple of the frequency ω ₀ of the sinusoidal applied electric field, all peaks are spread by Brownian motion, and the half-value width of the peak is Dq ² . Therefore, the peak can be observed only when the condition of Dq ² <ω ₀ is satisfied, and the absolute value of μ ^* can be obtained as the ratio of these peaks, however, information on the delay phase δ cannot be obtained.

Recently, Ito et al. Proposed a new method for calculating a two-dimensional power spectrum (J. Chem. Ph.
ys. 1994, 100, 6098. J. Chem. P
hys. 1994, 101, 4463-4465). This method is to calculate a two-dimensional correlation function using the Wiener-Khinchin theorem. By this method, they simultaneously determined complex electrophoretic mobility μ ^* and diffusion constant in the frequency range up to 100 Hz. This method is to obtain the complex electrophoretic mobility μ ^* based on the fluctuation analysis method, and is based on the measured value of the power spectrum of scattered light.

Power spectrum of scattered light described above
How to measure is due to the critical issues described below.
Limited frequency range and limited measurable substance range
Is. First, the spectral density of noise is more or less
It has frequency dependence, so it is
The smaller peak is unobservable. Second, δ
Let ω be the bandwidth resolution determined from the observation time,
Wavenumber range ω₁<Ω <ω₁+ Δω signal strength P (ω₁)
To measure it, δω is defined as the peak half-width Dq. ²Than
Must also be kept much smaller. Therefore, the measurement
The signal strength exerted is significantly reduced. Third, the applied electric field
Phenomenon of probe particles observed when the size is large
Also makes measurement difficult. Drift velocity v_dBy Dori
Shift displacement δr_d(T) = v_dWhen there is t, from equation (7)
As you can see, every peak splits in two.
I, drift speed v_dUnless^*Ask for
Is impossible.

Therefore, the present inventors have already proposed a method for directly measuring the response to a sinusoidal applied electric field in the time domain, and solved the above problem (Langmuir 200).
0, 16, 9547-9554). A method of directly measuring the response to the sinusoidal applied electric field in the time domain will be described below. First of all, the fundamental wave (ω ₀ ) is detected from the detection signal 7 of the photodetector 6 by using the bandpass filter 9.
Only the component and the second harmonic (2ω ₀ ) component are extracted.
The fundamental wave (ω ₀ ) component of the equation (5) and the second harmonic (2
Assuming that the ω ₀ ) component is A ₁ and A ₂ , A ₁ and A ₂ are as follows.

[0044]

[Equation 8]

[0045]

[Equation 9]

These components of the detection signal 7 are averaged to 0 when lock-in is detected. This is because, cos by Brownian motion of probe particles (c _n), sin (c
_{This is because n} ) changes randomly. Therefore, the present inventors performed the square calculation of these components. The method of squared calculation is cos associated with Brownian motion of probe particles.
When the correlation time of fluctuation of (c _n ) is extremely long, the signal represented by the equation (8) is directly input to the two-phase lock-in amplifier, and its Y output Σsin (c _n (t)), and X
The output Σcos (c _n (t)) is taken in the computer in time series, and these are treated as complex numbers and squared on the computer. When the correlation time is short, the signal represented by the formula (8) is squared by the squaring unit composed of an analog multiplication amplifier. The squared components A ₁ ² and A ₂ ² are
The following expression is obtained from the expression (8) and the expression (9).

[0047]

[Equation 10]

[0048]

[Equation 11] However, it is assumed here that many particles do not correlate with each other regarding their position coordinates. That is, the following equation is assumed.

[0049]

[Equation 12]

The time constant of the LPF (low-pass filter) in the output stage of the lock-in amplifier is increased to detect each squared component in two phases of 2ω ₀ and 4ω ₀ . Since the time constant is large enough cos (c _n) and s
The in (c _n ) terms are averaged to be 0, and (Equation 10)
The constant term of the equation and the equation (11) is detected. The constant term is A
_{If 1} ', A ₂ ', then it is expressed by the following equation.

[0051]

[Equation 13]

[0052]

[Equation 14]

Therefore, the absolute value of the mobility of complex electrophoresis | μ
^* | Is -A ₂ '/ A ₁ ' = J ₂ ² (z) / J
It can be calculated from the relationship of ₁ ² (z),
If a 2-phase lock-in amplifier is used, the delay phase 2
δ and 4δ can also be obtained at the same time. According to the above method, by extracting only specific frequency components of the detected optical heterodyne signal, squaring those signals, and detecting the squared signal by adjusting the time constant of the lock-in amplifier. Since only the applied electric field response information from which the Brownian motion information has been removed can be directly measured in the time domain, as a result, the complex electrophoretic mobility μ ^* can be accurately and sensitively measured. In the above description, the fundamental wave and the second harmonic are combined for simplification of the description, but the fundamental wave and other higher-order harmonics, or harmonics having different orders may be combined. Is clear.

The present invention is based on the above-mentioned measurement method already proposed by the present inventors and uses nanometer-sized colloidal particles, and has a complex internal structure without deforming the internal structure of the complex fluid to be measured. The present invention enables a method and an apparatus for obtaining knowledge about the viscoelasticity of a micrometer region of a complex fluid and the structure of the micrometer region of a complex fluid.

The method of the present invention will be described below. In the present invention, since only the applied electric field response information from which the Brownian motion information has been removed can be directly measured in the time domain by using the device shown in FIG. Complex electrophoretic mobility can be measured even from weakly scattered light of nanometer-sized probe particles.
Also, because nanometer-sized probe particles are used,
It is possible to obtain the knowledge about the viscoelasticity of the local region of the micrometer size of the complex fluid having a complicated internal structure and the structure of the micrometer region of the complex fluid without deforming the internal structure of the complex fluid to be measured. Hereinafter, the method of the present invention for obtaining the knowledge about the viscoelasticity of the local region of the micrometer size and the structure of the micrometer region of the complex fluid from the measured complex electrophoretic mobility of the complex fluid will be described. Applied sinusoidal electric field E = E ₀ cos (ω
The frequency ω ₀ of ₀ t) is continuously increased from ₀ , and the frequency response characteristic of the complex electrophoretic mobility μ ^* is obtained by measuring at each frequency ω ₀ using the above measuring method.

FIG. 2 is a diagram showing an example of frequency response characteristics of the measured complex electrophoretic mobility. The present invention will be described based on the measurement example of FIG. The horizontal axis represents the frequency ω ₀ of the applied sinusoidal external electric field E = E ₀ cos (ω ₀ t) in logarithm, and the vertical axis represents the real and imaginary components of the complex electrophoretic mobility μ ^* . The solid line in the figure shows the frequency dependence of the imaginary component of the complex electrophoretic mobility μ ^* , and the dotted line shows the frequency dependence of the real component of the complex electrophoretic mobility μ ^* .
The relaxation times obtained from the peak position of the frequency-dependent curve of the imaginary number component in FIG. 2 are τ _H and τ _{L in} order from the highest frequency. Absolute value of the flat region of the frequency-dependent curve of the real component | μ
^* | In order of increasing frequency μ ₍₁₎ , μ ₍₂₎ , μ
₍₃₎ Using these parameters, the optimum fit equation of FIG. 2 is obtained as follows.

[0057]

[Equation 15]

As is clear from this equation, the complex electrophoretic mobility μ ^* of the complex fluid to be measured in the example of FIG. 2 is caused by the sum of two different viscoelasticities with different relaxation times or two different processes. It can be seen that there is two potentials due to the structure of the complex fluid to be measured. In this way, knowledge about the structure of the complex fluid to be measured can be obtained from the frequency response characteristics.

Next, a method for obtaining the amplitude of fluctuation of this potential, that is, the characteristic length based on the structure of the complex fluid to be measured, from the measured absolute values of τ and μ ^* will be described. The relaxation time τ is the time for the probe particles to diffuse over the fluctuation distance (<x ² >) ^1/2 , and the diffusion constant is D. From the molecular kinetic theory, the following relationship holds.

[0060]

[Equation 16]

Further, assuming that the elastic modulus is k and the friction coefficient is γ,
From the definition of viscoelasticity, there is the following relationship.

[0062]

[Equation 17]

In the measuring method of the present invention, the diffusion constants D ₀ and μ _{0 in the} state where the structure of the complex fluid to be measured does not exist.
^* For example, the diffusion constants D ₀ and μ ₀ ^* of the probe particles in the fluid from which the structure of the measured complex fluid is removed are measured in advance. From the Einstein relationship, D / μ = k _B T between the diffusion constant D and the electrophoretic mobility μ.
Since the relation of (k _B : Boltzmann's constant, T: absolute temperature) is established, the diffusion constant D of the complex fluid to be measured is obtained by removing the absolute value μ of the complex fluid to be measured and the structure of the complex fluid to be measured. Diffusion constant D previously measured in the fluid
It can be calculated from the following equation using ₀ and μ ₀ .

[0064]

[Equation 18]

Therefore, the measured μ is substituted into the equation (18) to obtain D, and this D and the measured τ are substituted into the equation (16) to obtain the fluctuation distance (<x ² >). ^1/2 can be calculated according to the following formula.

[0066]

[Formula 19]

For example, in the case of the measurement example of FIG. 2, the square of the fluctuation amplitude <x ₁ ² > at the relaxation time τ _H is <x ₁ ² >
= 2τ _H D ₀ μ ₁ / μ ₀ . Similarly, the square of the fluctuation amplitude at the relaxation time τ _L <x ₂ ² >
Can be obtained from <x ₂ ² > = 2τ ₂ D ₀ μ ₂ / μ ₀ . Or Einstein's relationship D ₀ / μ ₀ =
Substituting k _B T into the equation (19) gives the following equation,

[0068]

[Equation 20]

It can also be obtained from the relaxation time τ, the temperature T, and the absolute value μ of the complex electrophoretic mobility. Further, when the friction coefficient γ (= viscosity coefficient η) and the electrophoretic mobility μ have a simple inverse proportional relationship, it can be obtained from the following equation.

[0070]

[Equation 21]

The fluctuation distance thus obtained is a steric hindrance based on the structure of the medium to be measured, for example, based on the structure, and the fluctuation distance is a characteristic length characterizing the structure of the medium to be measured. That is, it is possible to obtain knowledge about the structure of the micrometer region of the medium to be measured.

In the above description, the diffusion constant D is obtained from the diffusion constant D _{0 in the} absence of the structure of the complex fluid to be measured, but it can be obtained directly from the measurement.
The method will be described below. The fundamental wave (ω ₀ ) component extracted by the bandpass filter, that is, the component represented by the equation (8) is directly lock-in detected. If the time constant of the lock-in amplifier is made sufficiently smaller than the correlation time of the Brownian motion of the probe particles, the signal Y (t) detected at the time t at the time t is, as is clear from the equation (8),

[0073]

[Equation 22]

Then, the function value of the displacement vector c _n (t) at the time t of Brownian motion of the probe particle is given. The diffusion coefficient D can be calculated from the relationship between the diffusion constant D and the autocorrelation function shown in the equation (6) by measuring the t dependence of Y (t), calculating the autocorrelation function of Y (t). . In addition, the method for obtaining the characteristic length based on the structure of the complex fluid to be measured from the complex electrophoretic mobility spectrum is performed by the relaxation time obtained from the real and imaginary components of the complex electrophoretic mobility spectrum and the autocorrelation function. It can be obtained from the diffusion constant. The diffusion coefficient obtained from the autocorrelation function is the time constant of this output when the lock-in amplifier's time constant is changed within the range where fluctuations due to Brownian motion of the fundamental wave component are not averaged, and the fundamental wave component is lock-in detected. Calculate the autocorrelation function from the dependence. According to this method
The diffusion constant can be directly obtained in the entire measured frequency range, and as is clear from the equation (16), the complex fluid to be measured can be calculated from the relaxation time τ obtained from the complex electrophoretic mobility spectrum and the diffusion constant D. The characteristic length <X ² > ^1/2 of can be obtained. It is not necessary to obtain the diffusion constant and complex electrophoretic mobility of the probe particles in the fluid from which the structure of the measured complex fluid has been removed.

Next, a method of accurately obtaining the complex electrophoretic mobility when the frequency of the sinusoidal applied electric field is high will be described. The method of obtaining the absolute value μ of the complex electrophoretic mobility described above is performed by using the bandpass filter 9 from the detection signal 7.
The fundamental wave component and the nth harmonic component extracted by using the above are squared, the time constant of the lock-in amplifier is increased, and these squared components are lock-in detected. there were. However, if the electric field strength of the sinusoidal applied electric field is the same, the displacement δr _{En of the} probe particle decreases in inverse proportion to the frequency ω ₀ of the sinusoidal applied electric field, as shown in equation (4). The intensities of the fundamental wave component and the nth harmonic component extracted from the detection signal 7 using the bandpass filter 9 are ω ₀ ,
It decreases in inverse proportion to (ω ₀ ) ⁿ . In particular, since the intensity of the nth harmonic component is significantly attenuated in the high frequency region, the method described above deteriorates the accuracy in the high frequency region.

Therefore, in the present invention, in the high frequency region, the complex electrophoretic mobility is obtained only from the fundamental wave component.
This method will be described below. First, the complex electrophoretic mobility μ (Ω) when the frequency of the sinusoidal applied electric field is low (the frequency is Ω) is measured from the simultaneous measurement of the fundamental wave and the harmonic wave by the method described above. I ask for it. Next, the sinusoidal applied electric field E _L cos (Ωt) of frequency Ω is applied to the sinusoidal applied electric field E _H cos of high frequency (the frequency is ω).
Applied electric field E _T with (ωt) added,

[0077]

[Equation 23]

The fundamental wave component is extracted from the detection signal 7 using the bandpass filter 9 and the fundamental wave component is squared to perform lock-in detection. The amplitude component corresponding to the equation (10) of the component obtained by squaring the fundamental wave component is 2Ω, 2ω
Against,

[0079]

[Equation 24]

[0080]

[Equation 25]

Therefore, the high frequency μ (ω) is calculated from the ratio of the lock-in detection signals of 2Ω and 2ω and the previously obtained μ (Ω) using the formulas (24) and (25). You can ask. According to this method, the complex electrophoretic mobility in the high frequency region can be accurately obtained.

Next, examples of the present invention will be described. A complex fluid having a lamellar structure formed by a dilute nonionic surfactant was used as the complex fluid to be measured. Complex fluid with lamellar structure is one of the simplest models of in vivo transport process. In this embodiment, n-dodecyl pentaethylene was used as the nonionic surfactant.
Glycol monodecylether (C
₁₂ E ₅ (CH ₃ (CH ₂ ) ₁₀ CH ₂ O (CH ₂ CH
₂ O) ₄ CH ₂ CH ₂ OH)) (hereinafter, C ₁₂ E
Called ₅ ). C ₁₂ E ₅ and hexanol (C ₆ H ₁₃ OH)
Was mixed with water to form a complex fluid to be measured.

Polystyrene latex (manufactured by Dow. Co. Ltd.) was used as the probe particles. The particle size (2a) is 42 nm. C ₁₂ E ₅ forms a bilayer membrane in which hydrophobic groups are bound to each other in a mixed solution of hexanol and water (lamellar structure). FIG. 3 shows a schematic diagram of the lamella structure.
As shown in FIG. 3A, in the complex fluid, the C ₁₂ E ₅ hydrophobic groups 31 are bonded to each other to form a bilayer film 33 having a film thickness β with the hydrophilic groups 32 as the upper surface and the lower surface. As shown in FIG. 3B, the bilayer films 33 adjacent to each other float with an average film distance d therebetween. Further, on the surface of the bilayer film 33, a protrusion 34 depending on the curvature elastic modulus κ of the bilayer film 33 and the temperature T is generated at an average distance ξ (this distance is referred to as a collision distance). As shown in FIG. 3C, the adjacent bimolecular films 33 face each other in parallel over an average distance L (this distance is referred to as a correlation length). Such a bilayer membrane is called a lamella structure, and a fluid having a lamella structure is called a lamella phase. The film spacing d of the bilayer film 33 is determined by the mixing ratio of C ₁₂ E ₅ , hexanol and water.

FIG. 4 is a diagram showing the relationship between the mixing ratio (mol%) of C ₁₂ E ₅ , hexanol and water and the inter-membrane distance d. Note that φ _m is called the volume fraction of the film, and the bimolecular film 33
The ratio of the thickness β of the bilayer membrane 33 to the inter-membrane distance d of is shown. As is clear from the figure, as the amounts of C ₁₂ E ₅ and hexanol are increased, φ _m , that is, the inter-film distance d of the bimolecular film 33 becomes smaller.

FIG. 5 shows the complex electrophoretic mobility of probe particles (polystyrene latex, 2a = 42 nm),
It is a diagram showing the results of measurement in an aqueous solution containing C ₁₂ E ₅ and the saturation concentration of hexanol critical micelle concentration. The aqueous solution having this composition has the same composition as that of the aqueous phase sandwiched between the lamellae phase films in an aqueous solution having a concentration that does not form structures or aggregates and forms a lamellar phase. The decrease in the apparent absolute value in the low frequency region is roughly in agreement with the behavior predicted from the correlation time associated with the Brownian motion estimated from the full width at half maximum of the bandpass filter and the grain size, and can be roughly corrected. As is clear from the figure, the measurement frequency range 0-10
Absolute value μ of complex electrophoretic mobility μ ^* over kHz
₀ was constant (= 5.7 × 10 ⁻⁸ Cm / Ns), and this value was in good agreement with the DC electrophoretic mobility measured by ELS-800 (manufactured by Otsuka Electronics Co., Ltd.). Moreover, since the apparent effect based on the characteristics of the bandpass filter does not affect the delay phase, there should be no change in the complex electric mobility in this frequency range.

Complex electrophoretic mobility μ ^* (ω) is a frequency-dependent response function defined by the ratio of the velocity of particles to the applied sinusoidal electric field. Smoluchowski equation (eg Colloidal Dispersi
ons Cambridge University Press D. A. Saville
e, W.E. R. (See Schowalter)), the mobility μ ^* (ω) is expressed by the complex viscoelasticity η ^* (ω) of the solvent and μ ^* (ω) = εζ / η ^* (ω). It is simply inversely proportional. Here, ζ is the zeta potential on the surface of the colloidal particles and ε is the dielectric constant of the surrounding solvent. Therefore, if charged particles whose electrophoretic mobility does not have frequency dependence are used, μ ^* ( ω)
Gives the local viscoelasticity of a complex fluid surrounding this particle. The probe particles used in this example satisfy this condition. In the lamellar phase, the hydrophilic group 3 of the amphipathic molecule
As shown in FIG. 3C, the fluid bilayer film 33 composed of 2 and the hydrophobic group 31 floats while facing each other at an average film distance d. This average film spacing d is a relationship between the volume fraction φ _m and the film thickness β of the bilayer film (about 3 nm in this embodiment), d≈β / φ _m It was calculated with logarithmic correction due to the thermal fluctuation of. In the present embodiment, in order to satisfy the relationship of d> 2a, the concentrations of the complex fluid component C ₁₂ E ₅ and hexanol are adjusted to obtain φ.
Lamellar phase samples were prepared in which _m was in the range of 2% <φ _m <6%. Very small amounts of probe particles (about 0.1 mol% or less) were added to the lamellar phase sample. This concentration c is c << 1
The concentration satisfies the relationship of / d ³ . This density is 1 side d
It means that the number of probe particles is 1 or less in a unit volume of, and that the interaction between probe particles is negligible in such a dilute solution. Since the displacement of particles by electrophoresis is 10 nm or less, the lamella structure is hardly affected by electrophoresis.

FIG. 6 shows φ_mIs 4.74% in lamella phase
Kick μ^*In the figure which shows the result of measuring the frequency spectrum of
is there. Area (1) divided in order from the highest frequency,
Defining (2) and (3), complex swimming in each area
Includes absolute mobility μ, diffusion constant D, and friction coefficient γ
The numbers (1), (2) and (3) are attached. Imaginary component of figure
The relaxation time calculated from the peak value of
To τ_H, Τ_LAnd Absolute value of flat area of real number component of figure
μ in order from the highest frequency₍₁₎, Μ₍₂₎Tosu
It From the figure, τ_H= 1.7 × 10^-Fours, τ_L= 6.6 ×
10 ^-2s, μ₍₁₎= 1.5 × 10^-8Cm / Ns, and μ
₍₂₎= 9.2 × 10^-9It can be seen that it is Cm / Ns.
The solid line and the dotted line in FIG._H, Τ_LAnd μ
₍₁₎, Μ₍₂₎The complex electrophoretic mobility index expressed using
It is an optimal fitting curve of a part and an imaginary part.

The absolute value of complex electrophoretic mobility μ ₍₁₎
And μ ₍₂₎ are much smaller than the mobility μ ₀ (= 5.7 × 10 ⁻⁸ Cm / Ns) measured in water without lamella structure. Assuming that the electrokinetic properties of the probe particles are not affected by the presence of the bilayer membrane 33, this change in mobility is due to an increase in the friction coefficient γ of the probe particles. The electrophoretic mobility μ is simply inversely proportional to the friction coefficient γ (= viscosity coefficient η) of the medium, and according to Stokes' law, the friction coefficients γ ₍₁₎ and γ ₍₂₎ are η ₀ . The viscosity coefficient in water can be obtained from γ ₍₁₎ = 6πη ₀ aμ ₀ / μ ₍₁₎ and γ ₍₂₎ = 6πη ₀ aμ ₀ / μ ₍₂₎ , and the measured values μ ₍₁₎ , μ By substituting ₍₂₎ , γ
₍₁₎ = 1.34 × 10 ⁻⁹ Ns / m and γ ₍₂₎ = 2.
18 × 10 ⁻⁹ Ns / m is obtained.

Assuming that the observed relaxation phenomenon is based on the confinement of the probe particles in some potential barrier, the fluctuation amplitude of the potential can be defined. The fluctuation amplitude <x ² > ^1/2 is the measured τ
It can be calculated from _H , τ _L , γ ₍₁₎ , and γ ₍₂₎ using the equation (21). <x ₁ ² > ^1/2 corresponding to τ _H is 33
<x ₂ ² > ^1/2 corresponding to nm and τ _L was 500 nm. The C ₁₂ E ₅ / hexanol / water lamellar phase is mainly stabilized by the three-dimensional structural interaction of the flexible bilayer membrane 33, and as shown in FIG.
It is known that there are two characteristic lengths. One is the average distance between to have protrusions 34 that occur between opposing bilayer membrane, i.e. a mutual distance xi] collide, kappa and (κ ≒ k _B T) as the average curvature modulus of bilayer 33, xi] ≒ (Κ / k _B
It is known that T) ^1/2 d≈d. The other is the correlation length L of the orientation showing the degree of orientation of the bilayer film, and L is L≈βex where β is the thickness of the bilayer film 33.
It is known to be calculated by p (2πκ / k _B T), and L is about 500 nm. These two of the lamella structure
The two characteristic lengths, ξ / 2 (32 nm at φ m = 4.74%) and L, are very small at <x ₁ ² > ^1/2 = 33 nm and <x ₂ ² > ^1/2 = 500 nm obtained from the experiment. It is a close value.

This indicates that the potential barrier is formed by the flexible bilayer film 33, and the probe particles are confined to some extent within these characteristic lengths. That is, in the highest frequency region (region (1)), the probe particles can freely diffuse within ξ.
In the region (2), the probe particles are weakly confined between the collision points of the bilayer membrane, and in order to diffuse further away from the trap site having the dimension of length ξ, it is possible to hop between the trap sites. is necessary. In the region of the lowest frequency (region (3)), μ ^* decreases to 0, which means that almost all particles are trapped in the region of length L. In an actual lamella structure, trap sites having a fast relaxation time dynamically fluctuate with time, and it is considered that the trap sites repeatedly disappear and rebuild. The shortest reconstruction time τ _m of the trap site is given by τ _m ≈ηξ ³ / κ. In this example, since d> 2a, τ _m > τ _H is always satisfied, so that the reconstruction of the trap site in the early relaxation phenomenon can be ignored.

In the region (1), although the probe particles are not directly trapped in the lamella structure, the friction coefficient γ ₍₁₎ is larger than γ ₀ estimated from the particle size by using Stokes' law. large. Figure 7 shows the friction coefficient γ
It is a diagram showing the results of measuring the C ₁₂ E ₅ Concentration dependence _(1). The vertical axis represents the reciprocal of the ratio of the friction coefficient γ _{(1) to} the friction coefficient γ ₀ , and the horizontal axis represents the reciprocal of the characteristic length of the bilayer membrane 33 obtained from the volume fraction φ _m 1 / ξ (= φ _m / β) is used instead of concentration. In the figure, ○ indicates the reciprocal of the ratio of the friction coefficient γ ₍₁₎ obtained from μ ₍₁₎ / μ ₀ to the friction coefficient γ ₀ . In FIG ● it was estimated from the relaxation time τ _H γ _(1), i.e., gamma the inverse of the ratio of the friction coefficient gamma ₀ of _{(1) = 2k B Tτ H} / ξ 2 Friction coefficient was estimated from gamma ₍₁₎ Shows. Γ ₀ / γ ₍₁₎ obtained by the two methods shows good agreement except for the sample with the highest concentration (φ _m = 5.9%).

The significant increase in γ _{(1) with} increasing φ _m is
It is thought to occur because particles are trapped between the walls of the bilayer. The solid line in the figure shows the value calculated by Stokes' law for the friction coefficient of spherical particles in the vicinity of two rigid boundary layers facing each other at a distance of 2ξ, under the condition of no slip.
Also, the calculated value of the friction coefficient of spherical particles in an infinite cylinder having a radius ξ ₀ is shown by the dotted line in the figure. In these calculations, particles are calculated as moving along the center line of each wall, but it is experimentally found that the moving position dependence of γ ₀ / γ _{(1) on} these walls is small. Known to. All measured values in this example are
It is between the solid and dotted lines. The difference in stress exerted on the moving probe particles can be explained by the spatial arrangement of the walls around the probe particles. That is, the probe particles between the walls of the flat plate have two-dimensional degrees of freedom as the degrees of freedom of movement, but the probe particles in the cylinder have only one-dimensional degree of freedom. As shown in FIG. 7, the fact that the measurement results of the present embodiment are all present between the solid line and the dotted line means that the degree of freedom of movement of the probe particle between the oscillating bilayer membranes 33 is less than 2. Is greater than.

The friction coefficient γ ₍₃₎ can be obtained from the diffusion constant D of the probe particles as γ ₍₃₎ = k _B T / D. In this embodiment, the scattering angle is set to 2π / q (≈3μ
Since m)> ξ is satisfied, it takes about 3 μm for the probe particle to hop trap sites of size ξ by hopping before the scattered light intensity loses memory of collision of probe particles. It is necessary and the measured diffusion constant D ₍₃₎ satisfies this condition.

FIG. 8 is a diagram showing the measurement results of the diffusion constant D ₍₃₎ . The diffusion constant D ₍₃₎ was measured using a sample with φ _m = 4.74% and was calculated using the equation (6). From D ₍₃₎ , the correlation time (= 1 / D ₍₃₎ q ² ) was about 230 s, and a very slow fluctuation was observed. Γ ₍₃₎ obtained from D ₍₃₎ is about 1.4 × 10 ⁴ times larger than γ ₀ . γ
_{The fact that (3)} shows such a large value indicates that the probe particles are almost completely trapped within the dimension L of the region (3). There are two possible processes for hopping probe particles in this region. one,
This is the process by which the probe particles jump the potential barrier, and the other is the dynamic reorganization process of the lamella structure.

In summary, the complex electrophoretic mobility μ ^* of nanometer-sized colloidal particles dispersed in a nonionic dilute lamella phase was measured, two characteristic lengths of the lamella structure were obtained, and the transport characteristics were clarified. did. INDUSTRIAL APPLICABILITY The method of the present invention is useful for elucidating the transport phenomenon of more complicated systems such as living cells.

Next, a second embodiment of the present invention will be described. FIG. 9 is a schematic diagram illustrating a method for measuring local viscosity of a complex fluid using laser trapping according to the present invention. In the figure, 72 is a beam splitter that is an optical member that matches the optical paths of the scattered light and the reference light, 74 is an optical member that converges the laser beam for laser trapping and makes the scattered light into a parallel light beam, and 79 is the same optical path. It is an optical member that collects the reference light and the scattered light at the same focal point. The laser trapping light 71 passes through the beam splitter 72,
An optical member 74 arranged between the medium to be measured 73 and the beam splitter 72 collects the probe particles 75.
Is irradiated. The scattered light 76 from the probe particle 75 traces the optical path in the opposite direction to become a parallel light flux by the optical member 74,
Change the optical path vertically with the reflective surface 77 of the beam splitter,
The reference laser light 78 incident on the beam splitter 72 from a direction orthogonal to the laser trapping light 71 is mixed with its optical path aligned. The mixed scattered light 76 and the reference laser light 78 are condensed by the optical member 79 at the same focal point, that is, the confocal point 80. The optical heterodyne signal is converted into the electrical signal 8 by the photodetector 81 arranged at the confocal point 80.
Converted to 2. Electrodes 83, 83 are provided on the upper and lower surfaces of the measured medium 73 perpendicular to the laser trapping light 71, and a predetermined sinusoidal voltage 84 is applied.

The method of obtaining the complex electrophoretic mobility from the electric signal 82 is simplified as compared with the case of the first embodiment described above. That is, since the probe particles 75 are laser-trapped by the laser trapping light 71 and the Brownian motion of the probe particles 75 is suppressed, sin (c _n ) and cos in the equation (5) are calculated.
(C _n ) becomes a constant, and the lock-in detection of the fundamental wave and the harmonic wave can be performed directly, and the absolute value of the complex electrophoretic mobility and the delay phase can be obtained from the equation (5). Therefore, the analog square calculation of the first embodiment is not necessary, and the delay time required for calculation is not limited.
Measurement can be performed in the 00 MHz band. Further, since the direction in which the probe particles 75 are displaced and the direction of the scattered light 76 coincide with each other, the optical path difference of the scattered light 76 with respect to the sinusoidal voltage 84 becomes large, and detection can be performed with high sensitivity. Further, as described in the first embodiment, particularly in the high frequency region of the sinusoidal electric field, the harmonic signal component becomes small,
The absolute value of the complex electrophoretic mobility obtained from the fundamental wave and the harmonic wave becomes inaccurate. In this case, as in the first embodiment, μ (Ω) is obtained in advance by the low frequency sinusoidal electric field (Ω), and the low frequency sinusoidal electric field (Ω) and the high frequency sinusoidal electric field are obtained. (Ω) is added to apply a sinusoidal electric field, the fundamental wave is directly lock-in detected with Ω and ω, and the complex electric field in the high frequency region is calculated from the ratio of these detection signals and μ (Ω) obtained in advance. The absolute value of migration mobility μ (ω) can be accurately obtained.

Further, by mounting the medium to be measured 73 on the piezo stage and precisely controlling the position of the medium to be measured 73 over three dimensions, the three-dimensional measurement of the medium to be measured becomes possible. Further, as the optical member 74, an optical member having a variable focal length or an optical member having a fixed focal length but capable of moving in the optical path direction of the laser beam 71 for laser trapping can be used to arbitrarily select the focusing position. It is possible to focus on the probe particles 75 existing at an arbitrary depth of the measured medium 73, and to measure a position of the measured medium 73 at an arbitrary depth. Further, the laser trapping laser light source, the reference laser light source, the optical member 74, the beam splitter 72, the optical member 79, and the photodetector 81 are integrally configured as a constituent unit, and the constituent unit is covered. By moving along the surface of the measurement medium 73, the focus position can be moved along the surface of the measurement medium 73. In this way, the light collection position can be moved in the depth direction of the medium-to-be-measured 73 and can be moved along the surface, so that three-dimensional measurement of the medium-to-be-measured is possible. The laser light source for laser trapping and the light source for reference laser light may be fixed, and the laser light from the laser light source for laser trapping and the light source for reference laser light may be guided to the beam splitter 72 by a flexible optical waveguide such as an optical fiber. .

Using the method of the present invention, the medium to be measured 73
The broadband three-dimensional complex electrophoretic mobility can be measured, and thus the broadband three-dimensional viscoelasticity can be measured. In addition, for example, it is possible to measure the displacement of the trap position due to the interaction of the probe particles 75 with the internal structure of the medium 73 to be measured. In particular, it is useful to apply a swollen gel as the medium 73 to be measured. The swollen gel is used as a carrier for chromatography or electrophoresis that separates substances according to the difference in transport rate in the network structure of the swollen gel, but by applying the method of the present invention, the dynamics of the transport phenomenon in the carrier gel. Can be traced back to the local interaction between the network structure and the substances dispersed in it.

[0100]

As can be understood from the above description, according to the present invention, the spectrum of local viscoelasticity in a complex fluid can be measured, and the characteristic length based on the structure of the complex fluid can be obtained. In addition, it is possible to obtain knowledge about the transport phenomenon in a complex fluid. The method of measuring local viscoelasticity using colloidal particles as a probe has recently attracted attention as a method of studying a macroscopic inhomogeneous structure, but the method of the present invention is different from these conventional methods. Since the probe particles can be made smaller than the internal structure of the complex fluid, it is possible to measure at various spatial scales. Further, the complex mobility measuring method of the present invention is characterized in that it enables high-accuracy and wide-band measurement by positively removing the influence of Brownian motion, and only the average response of the system is observed. This method enables single particle measurement, which cannot be realized in principle by the conventional electric relaxation spectroscopy method. Further, the measuring method of the present invention has a high noise removal performance and can be measured even in a medium having a strong scattering ability, and therefore, a measuring apparatus using the measuring method of the present invention, for example, a probe microscope, is not limited to a diluted sample, but a living body. It can also be applied to heterogeneous systems such as.
In recent years, various scanning probe microscopes that measure the shape and viscoelastic properties of solid surfaces with nanometer resolution far beyond the submicron range, which is the diffraction limit of visible light, have rapidly become widespread. It greatly contributes to the development of technology. In such a flow, the present invention enables a system for imaging a three-dimensional structure and a local viscoelastic spectrum in a complex fluid, for example, a probe microscope. This measuring device can be realized by the microscopic resolution and wide band measurement in the three-dimensional region enabled by the present invention, and various interactions or transport between constituent elements occurring in a complex fluid such as a living body. Information about the local dynamics of a phenomenon can be obtained.

[Brief description of drawings]

FIG. 1 is a schematic diagram showing the configuration of a measuring apparatus used in the method for measuring complex electrophoretic mobility of the present invention.

FIG. 2 is a graph showing an example of frequency characteristics of complex electrophoretic mobility measured by the method of the present invention.

FIG. 3 is a schematic diagram of a lamella structure.

FIG. 4 is a table showing the relationship between the mixing ratio (mol%) of C ₁₂ E ₅ , hexanol and water and the inter-membrane distance d.

FIG. 5: Probe particles (polystyrene latex, 2
a = 42 nm) of a graph showing C ₁₂ E ₅ and hexanol and fluid from the medium to be measured without the structure C ₁₂ E ₅ and hexanol comprising water, i.e., the result of measuring the complex electrophoretic mobility in water Is.

FIG. 6 is a graph showing the results of measuring the frequency spectrum of complex electrophoretic mobility in the lamella phase.

FIG. 7 is a graph showing the results of measuring the C ₁₂ E ₅ concentration dependence of the friction coefficient.

FIG. 8 is a graph showing measurement results of diffusion constant D ₍₃₎ .

FIG. 9 is a schematic diagram illustrating a method for measuring local viscosity of a complex fluid using laser trapping according to the present invention.

[Explanation of symbols]

1 Complex electrophoresis mobility measuring device 2 Medium to be measured 3 containers 4 incident laser beam 5 Reference laser beam 6 Photodetector 7 detection signal 8 Fundamental and harmonic components 9 band pass filter 10 analog multiplier 11 Second harmonic component 12 Lock-in amplifier 13 electrodes 14 signals 15 Synthesizer 16 High voltage amplifier 31 Hydrophobic group 32 hydrophilic group 33 bilayer membrane 34 Protrusion 71 laser trapping light 72 Beam splitter 73 Medium to be measured 74 Optical member 75 probe particles 76 scattered light 77 Reflective surface 78 Reference laser light 79 Optical member 80 confocal 81 Photodetector 82 Electric signal 83 electrodes 84 Sine voltage

Claims (21)

[Claims] 1. A probe particle having a size of nanometer is mixed in a complex fluid to be measured, the complex fluid to be measured is irradiated with incident light and reference light, and a sinusoidal electric field is applied to the probe particle to obtain the probe. The optical heterodyne signal of the scattered light of the particles and the reference light is converted into an electric signal, and the fundamental wave component and the harmonic component related to the frequency of the sinusoidal electric field are extracted from this electric signal, and the fundamental wave component and the harmonic component The analog square calculation is performed on each of them, and the fundamental wave component and the harmonic component obtained by the analog square calculation are respectively detected by lock-in to obtain the absolute value and the delay phase of the complex electrophoretic mobility.
Obtain the spectrum of the complex electrophoretic mobility from the absolute value and the delay phase at each frequency of the sinusoidal electric field, viscoelasticity of the local region of the complex fluid to be measured from the complex electrophoretic mobility spectrum, And a method for measuring local viscoelasticity of a complex fluid, characterized in that the characteristic length based on the structure of the complex fluid to be measured is obtained. 2. In the method of obtaining the absolute value of the complex electrophoretic mobility and the delay phase, fluctuations due to Brownian motion of the analog-squared fundamental wave component and the harmonic component are averaged to zero. As described above, the time constant of the lock-in amplifier is made sufficiently large to detect the two-phase lock-in of the fundamental wave component and the harmonic component, which have been analog-squared, at the same time. The local viscoelasticity of the complex fluid according to claim 1, wherein an absolute value of the complex electrophoretic mobility is obtained from a ratio of values, and a delay phase is obtained from a phase angle of the two-phase lock-in detection signal. Measurement method. 3. The method for obtaining the absolute value of the complex electrophoretic mobility in the high frequency region, the complex electrophoretic electrophoresis in the low frequency region according to claim 2, wherein the sinusoidal electric field is set to a low frequency. The absolute value of the mobility is calculated, and the applied electric field is composed of the sum of the low frequency sinusoidal electric field and the high frequency sinusoidal electric field, and the fluctuation due to the Brownian motion of the fundamental wave component calculated by the analog square operation is averaged. The time constant of the lock-in amplifier is set sufficiently large so that the fundamental wave component calculated by the analog square operation is divided into the low frequency and the high frequency.
Lock-in detection at one frequency at the same time, obtain a ratio of absolute values of respective lock-in detection signals, and obtain from the ratio and the absolute value of complex electrophoretic mobility in the low frequency region. Item 2. A method for measuring local viscoelasticity of a complex fluid according to Item 1. 4. A probe particle having a nanometer size is mixed into a complex fluid to be measured, a sinusoidal electric field is applied to the complex fluid to be measured, and trapping laser light is focused on the probe particle to laser the probe particle. Trap, collect the scattered light from the probe particles and the reference light at the confocal position, convert the optical heterodyne signal of the scattered light and the reference light at the confocal position into an electrical signal, and this electrical signal The fundamental wave component and the harmonic component related to the frequency of the sinusoidal electric field are extracted from, and the absolute value and the delay phase of the complex electrophoretic mobility are obtained by lock-in detection of the fundamental wave component and the harmonic component, respectively. The complex electrophoretic mobility spectrum for the frequency of the wavy electric field is obtained, and from this complex electrophoretic mobility spectrum, the viscoelasticity of the local region of the complex fluid to be measured and A method for measuring the local viscoelasticity of a complex fluid, characterized in that the characteristic length based on the structure of the complex fluid to be measured is obtained. 5. An electrode is provided on the upper and lower surfaces of the complex fluid perpendicular to the optical path of the trapping laser beam, and the sinusoidal electric field is applied to the electrode.
A method for measuring local viscoelasticity of a complex fluid described in 1. 6. An optical member for condensing the trapping laser light converts the scattered light into a parallel light flux, and an optical member for matching the optical paths matches the optical path of the scattered light converted into the parallel light flux with the optical path of the reference light, Characterized by condensing the scattered light and the reference light at a confocal position by condensing the scattered light and the reference light whose optical paths coincide with each other by a common optical member.
The method for measuring local viscoelasticity of a complex fluid according to claim 4. 7. The local viscoelasticity measurement of a complex fluid according to claim 6, wherein the scattered light and the reference light are respectively incident on incident surfaces of the beam splitter which are orthogonal to each other so that the optical paths coincide with each other. Law. 8. An optical member having a variable focal length is arranged between the complex fluid to be measured and the beam splitter, whereby trapping laser light is focused on the probe particles and the scattered light is collimated. The method for measuring local viscoelasticity of a complex fluid according to any one of claims 4 to 7, wherein the method is a method of converting light into a light flux. 9. A trapezoidal laser beam is focused on the probe particle and the scattered light is converted into a parallel beam by disposing a convex lens movable between the complex fluid to be measured and the beam splitter. The method for measuring local viscoelasticity of a complex fluid according to any one of claims 4 to 7, which is characterized. 10. A micrometer over a three-dimensional area of the complex fluid to be measured by mounting a complex fluid under measurement having the electrodes on a movable table, and controlling the three-dimensional position of the complex fluid under the measurement by the movable table. The method for measuring local viscoelasticity of a complex fluid according to claim 4, wherein the region is measured. 11. A light source for the trapping laser light, a light source for the reference laser light, an optical member for condensing the trapping laser light and making scattered light into a parallel light beam, and the scattered light made into a parallel light beam. An optical member that matches the optical path of the light, and an optical member that condenses the scattered light that has been made into a parallel light flux and the reference light that match the optical path at a confocal position,
A photodetector disposed at the confocal position is integrally configured as a structural unit, the structural unit is moved parallel to the surface of the complex fluid to be measured, and the trapping laser light is condensed and scattered. The method for measuring local viscoelasticity of a complex fluid according to any one of claims 4 to 9, wherein the focal length of an optical member for converting light into a parallel light flux or the position of the optical member is changed for measurement. 12. A method for obtaining an absolute value and a delay phase of the complex electrophoretic mobility, wherein the lock-in amplifier is such that fluctuations due to Brownian motion of the fundamental component and the harmonic component are averaged to zero. 2 time lock-in detection of the fundamental wave component and the harmonic wave component,
The absolute value of the complex electrophoretic mobility is obtained from the ratio of the absolute values of the respective two-phase lock-in detection signals, and the delay phase is obtained from the phase angle of the two-phase lock-in detection signal. 4. The method for measuring local viscoelasticity of complex fluid according to item 4. 13. The method for obtaining the absolute value of the complex electrophoretic mobility in the high frequency region is the complex electrophoretic electrophoresis in the low frequency region according to claim 12, wherein the sinusoidal electric field is set to a low frequency. The absolute value of the mobility is calculated, and the applied electric field is composed of the sum of the low-frequency sinusoidal electric field and the high-frequency sinusoidal electric field, and fluctuations due to Brownian motion of the fundamental wave component are averaged to zero. As described above, the time constant of the lock-in amplifier is made sufficiently large so that the fundamental wave component is simultaneously lock-in detected at the two frequencies of the low frequency and the high frequency, and the ratio of the absolute values of the lock-in detection signals is calculated. 5. The method for measuring local viscoelasticity of a complex fluid according to claim 4, wherein the ratio is obtained and the absolute value of the complex electrophoretic mobility in the low frequency region is obtained. 14. The method for measuring local viscoelasticity of a complex fluid according to claim 1, wherein the optical heterodyne signal of the scattered light of the probe particle and the reference light is based on the displacement of the probe particle. . 15. The method for measuring local viscoelasticity of a complex fluid according to claim 1, wherein a fundamental wave component and a harmonic component are extracted from the electric signal with a bandpass filter. 16. The complex electrophoretic mobility spectrum is used to determine the viscoelasticity of the local region of the complex fluid to be measured from the inverse proportional relationship between the complex electrophoretic mobility and the complex viscoelasticity. 1. The method for measuring local viscoelasticity of a complex fluid according to 1 or 4. 17. The nanometer-sized probe particles are colloidal particles that are charged in the complex fluid to be measured, and the diffusion constant of the probe particles in the fluid without the structure of the complex fluid to be measured, and The method for measuring local viscoelasticity of a complex fluid according to claim 1, wherein complex electrophoretic mobility is known in the measured frequency range. 18. A characteristic length based on the structure of a complex fluid to be measured from the complex electrophoretic mobility spectrum, a relaxation time and an absolute value obtained from a real number component and an imaginary number component of the complex electrophoretic mobility spectrum, 5. It is obtained from a known diffusion constant of the probe particles and a known complex electrophoretic mobility of the probe particles.
A method for measuring local viscoelasticity of a complex fluid described in 1. 19. The characteristic length based on the structure of a complex fluid to be measured from the complex electrophoretic mobility spectrum is a relaxation time obtained from a real number component and an imaginary number component of the complex electrophoretic mobility spectrum, and an autocorrelation function. The method for measuring local viscoelasticity of a complex fluid according to claim 1 or 4, wherein the diffusion coefficient is calculated from the diffusion constant. 20. The diffusion coefficient obtained from the autocorrelation function is locked in when the time constant of the lock-in amplifier is sufficiently small so that fluctuations due to Brownian motion of the fundamental wave component are not averaged to zero. 20. The method for measuring local viscoelasticity of a complex fluid according to claim 19, characterized in that it is detected and an autocorrelation function is calculated from the time dependence of the detected signal. 21. An apparatus for measuring local viscoelasticity of a complex fluid, which uses the method according to any one of claims 1 to 20.