A microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles

Abstract

The present invention belongs to the technical field of microrheological characterization methods, and discloses a microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles. The microrheological characterization method is as follows: anisotropic tracer particles are dispersed in a sample or sample solution, and depolarized dynamic light scattering is used to detect the sample at two different scattering angles, i.e., a microrheological test is performed, and the light intensity autocorrelation equation is obtained and converted into an electric field autocorrelation equation, thereby obtaining a microrheological rheological curve. The method of the present invention is simple, and the obtained rheological curve has high accuracy in an ultra-wide frequency range, especially for the high-frequency region, it has excellent characterization capabilities, effectively filling the frequency gap of traditional mechanical rheology; at the same time, due to its specific detection of the depolarization signal of the tracer particles, it also has high detection accuracy for turbid systems. The characterization method of the present invention is applied to wide-band microrheological testing of clear or turbid systems.

Description

Technical Field

[0001] The present invention relates to the technical field of rheological characterization methods, and in particular to a microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles. Background Art

[0002] Rheological methods are often used to characterize the viscoelastic properties of materials. The most common of these are the storage modulus G' and the loss modulus G", which represent the storage of elastic energy and the viscous loss of energy, respectively. These parameters are related to the basic structure of the material. Traditional mechanical rheological methods are currently commonly used for such characterization, but they suffer from long measurement times, a limited test frequency range, and low characterization accuracy for low-modulus samples. To expand the frequency range of rheological characterization methods and improve their accuracy for low-modulus samples, microrheological methods can be used to achieve high-precision rheological characterization over a wide frequency range.

[0003] However, existing microrheological characterization methods based on conventional light scattering and imaging methods have low accuracy, cumbersome testing and data processing, and are only applicable to transparent samples. This greatly limits the application of microrheological methods. Summary of the Invention

[0004] To address the shortcomings of existing rheological techniques, such as the long mechanical rheological time required, narrow frequency range, low accuracy for low-modulus samples, and the high sample limitations of existing microrheological techniques, this present invention provides a microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles. Because this method detects the specific depolarized scattered light from anisotropic tracer particles, it is applicable to both clear and turbid samples, has a wide test frequency range, and is simple to test.

[0005] In order to achieve the above invention objectives, the technical solution adopted is:

[0006] A microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles comprises the following steps: dispersing anisotropic tracer particles in a sample or sample solution, detecting the sample at two different scattering angles using depolarized dynamic light scattering, i.e., performing a microrheological test, obtaining a light intensity autocorrelation equation and converting it into an electric field autocorrelation equation, thereby obtaining a microrheological curve;

[0007] The anisotropic tracer particles are gold nanorods, etc.

[0008] The sample is a soft substance or a polymer solution, such as a gel, an emulsion, a mucus, a biomolecule condensate, a suspension, or a polymer solution.

[0009] For example, the sample is a hydrogel, a four-arm-polyethylene glycol hydrogel, and the concentration of the polymer solution is above 5%, that is, the polymer solution includes a semi-concentrated solution and a concentrated polymer solution.

[0010] The diameter and length of the gold nanorods are larger than the characteristic dimensions of the sample.

[0011] In the depolarized dynamic light scattering, a polarizer with an extinction ratio of at least 100,000:1 is selected, and the extinction ratio is ≥100,000:1.

[0012] The depolarized dynamic light scattering is performed by placing a polarizer in front of a dynamic light scattering instrument and adjusting the polarization direction so that the polarization direction is perpendicular to the incident direction of the laser.

[0013] When performing depolarized dynamic light scattering detection, the light intensity is 100-1000 kcp.

[0014] Different scattering angles refer to two scattering angles that differ by 20-100 degrees, for example, one scattering angle is 20-80 degrees (preferably 55-65 degrees), and the other scattering angle is 90-160 degrees (preferably 125-135 degrees).

[0015] The concentration of the tracer particles in the sample or sample solution can be fine-tuned according to the actual laser power used. Taking into account the power differences of the lasers used, different lasers may require different concentrations of tracer particles. According to the detector count rate, the depolarized scattered light intensity needs to be above 100 kcp, or based on a correlation equation that can be measured smoothly.

[0016] The light intensity autocorrelation equation and the electric field autocorrelation equation are:

[0017] g2(q,t)=1+β|g1(q,t)| 2

[0018] Where β is the coherence coefficient of the instrument, q is the spatial scale in the reciprocal space, which is directly related to the scattering angle θ, n is the refractive index of the sample, λ is the laser wavelength, t is the lag time, g1(q,t) is the electric field autocorrelation equation, and g2(q,t) is the light intensity autocorrelation equation obtained by the test.

[0019] The specific equation of the light intensity autocorrelation equation g2(q,t) is:

[0020]

[0021] I(τ), I(τ+t) are the light intensities at time τ and τ+t.

[0022] Extracting the mean square rotation angle <δθ from the light intensity autocorrelation equation 2(t)>; where q1 and q2 are the inverse space scales corresponding to scattering angle 1 and scattering angle 2, i.e., the two different scattering angles mentioned above;

[0023]

[0024] The obtained mean square rotation angle can be related to the complex modulus G*, storage modulus and loss modulus through the following equations:

[0025]

[0026] in:

[0027]

[0028] in is the aspect ratio of the tracer particles.

[0029] k B is the Boltzmann constant, and Γ(1+α(ω)) is the gamma function.

[0030] Principle of the present invention: The present invention loads anisotropic tracer particles into the sample, obtains the light intensity autocorrelation equation at two different scattering angles through depolarized dynamic light scattering detection, extracts the mean square rotation angle from the correlation equation, calculates through the generalized Stokes-Einstein equation based on anisotropic particles, and obtains the rheological master curve of the sample from the mean square rotation angle data. The present invention also discloses a practical method and a data processing method of microrheology technology. The characterization method of the present invention is simple, and the technical equipment used can be simply modified based on the existing light scattering instrument. The obtained rheological master curve has high accuracy in an ultra-wide frequency range, especially for the high-frequency region. It has excellent characterization capabilities and effectively fills the frequency gap of traditional mechanical rheology; at the same time, due to its specific detection of the depolarization signal of the tracer particles, compared with traditional light scattering microrheology, it also has high detection accuracy for turbid systems. The characterization method of the present invention is applied to wide-band microrheological testing of clear or turbid systems.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1) Compared with traditional mechanical rheology (1Hz-100Hz), the frequency range of modulus testing has been greatly broadened.

[0033] 2) Compared to other microrheological techniques based on light scattering, this method offers fewer sample limitations. By detecting only the depolarized scattered light from anisotropic tracer particles, the present invention can independently detect the motion of the tracer particles and calculate the corresponding rheological curve, regardless of the sample's turbidity or concentration.

[0034] 3) The data processing of the present invention is simple, and data in a wide frequency range can be obtained through a single test without the need for time-temperature equivalence. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The microrheological characterization results of the four-arm-polyethylene glycol hydrogel in Example 1 are as follows;

[0036] Figure 2 Optical photographs of the hydrogels of Example 2; left: four-arm polyethylene glycol hydrogel without PS microspheres, right: four-arm polyethylene glycol hydrogel with PS microspheres;

[0037] Figure 3 is the microrheological curve of the hydrogel of Example 2;

[0038] Figure 4 is the microrheological curve of the polymer solution of Example 3;

[0039] Figure 5 This is the rheological curve of Comparative Example 1. DETAILED DESCRIPTION

[0040] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0041] The present invention discloses a rheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles, comprising the following steps: dispersing anisotropic tracer particles in a sample, detecting the sample at two different scattering angles using depolarized dynamic light scattering, i.e., performing a microrheological test, obtaining a light intensity autocorrelation equation and converting it into an electric field autocorrelation equation, thereby obtaining a microrheological curve.

[0042] The anisotropic tracer particles are rod-shaped particles, such as gold nanorods; the diameter and length of the gold nanorods are larger than the characteristic dimensions of the sample. The concentration of the tracer particles in the sample (or sample solution) is approximately 0.5 mg / mL, and the specific concentration can be fine-tuned based on the actual laser power used.

[0043] The sample is a soft substance or a polymer solution, such as a gel, an emulsion, a mucus, a biomolecule condensate, a suspension, or a polymer solution.

[0044] For example, the sample is a hydrogel, a four-arm-polyethylene glycol hydrogel, and the concentration of the polymer solution is above 5%, that is, the polymer solution includes a semi-concentrated solution and a concentrated polymer solution.

[0045] In the depolarized dynamic light scattering, a polarizer with an extinction ratio of at least 100,000:1 is selected, and the extinction ratio is ≥100,000:1.

[0046] The depolarized dynamic light scattering is performed by placing a polarizer in front of a dynamic light scattering instrument and adjusting the polarization direction so that the polarization direction is perpendicular to the incident direction of the laser.

[0047] When performing depolarized dynamic light scattering detection, the light intensity is 100-1000 kcp.

[0048] Depolarized dynamic light scattering (DLS) testing is used to obtain the light intensity autocorrelation equations at two different scattering angles and convert them into electric field autocorrelation equations. The specific detection method is the same as that of conventional dynamic light scattering testing, except that an additional polarizer is placed in front of the detector and adjusted to a horizontal polarization direction (perpendicular to the polarization direction of the incident laser). For common detectors, the test conditions require optimizing the light intensity to 100-1000 kcp to facilitate normal testing. The different scattering angles can be any scattering angle without restrictions, but for most light scattering instruments, 60 degrees and 130 degrees are recommended.

[0049] g2(q,t)=1+β|g1(q,t)| 2

[0050] Where β is the coherence coefficient of the instrument (in the present invention, this parameter is about 0.8. It should be noted that this parameter does not affect the presentation of the final results). q is the spatial scale in the reciprocal space, which is directly related to the scattering angle θ, n is the refractive index of the sample, λ is the laser wavelength, t is the lag time, g1(q,t) is the electric field autocorrelation equation, and g2(q,t) is the light intensity autocorrelation equation obtained by the test.

[0051] Extracting the mean square rotation angle <δθ from the light intensity autocorrelation equation 2 (t)>; (where q1 and q2 are the inverse space scales corresponding to angles 1 and 2, respectively, i.e., the two different scattering angles mentioned above)

[0052]

[0053] The obtained mean square rotation angle can be related to the complex modulus G*, storage modulus and loss modulus through the following equations:

[0054]

[0055]

[0056] in:

[0057]

[0058] in is the aspect ratio of the tracer particles.

[0059] kB is the Boltzmann constant, and Γ(1+α(ω)) is the gamma function.

[0060] Example 1

[0061] A rheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles comprises the following steps:

[0062] 1) A polyethylene glycol with an amino terminal group and a molecular weight of 40k was dissolved in a buffer solution at a concentration of 40 mg / mL, the buffer solution was pH = 7.4, and the ionic strength was 50 mM to obtain a polyethylene glycol solution with an amino terminal group; a polyethylene glycol with a molecular weight of 40k and a succinimide glutaric acid terminal group was dissolved in a buffer solution at a concentration of 40 mg / mL, the buffer solution was pH = 5.8, and the ionic strength was 50 mM to obtain a polyethylene glycol solution with a succinimide glutaric acid terminal group; the two solutions were mixed in equal volumes, and gold nanorod tracer particles (controlled concentration of 0.5 mg / mL) were added, mixed evenly, and allowed to stand for 12 hours to obtain a four-arm-polyethylene glycol hydrogel sample; wherein the aspect ratio of the gold nanorods was 50*20 nm (i.e. ).

[0063] 2) Place the polarizer in front of the dynamic light scattering detector and adjust it to the horizontal polarization direction (perpendicular to the polarization direction of the incident laser); use depolarized dynamic light scattering to detect the sample at scattering angles of 60 degrees and 130 degrees, that is, perform microrheological testing, and perform ensemble averaging on the gel sample to obtain the light intensity autocorrelation equation and convert it into the electric field autocorrelation equation to obtain the microrheological curve. Light intensity autocorrelation equation and electric field autocorrelation equation:

[0064] g2(q,t)=1+β|g1(q,t)| 2

[0065] Where β is the coherence coefficient of the instrument (in the present invention, this parameter is about 0.8), q is the spatial scale in reciprocal space, which is directly related to the scattering angle θ, n is the refractive index of the sample, λ is the laser wavelength, t is the lag time, g1(q,t) is the electric field autocorrelation equation, and g2(q,t) is the light intensity autocorrelation equation obtained by the test;

[0066] Extracting the mean square rotation angle <δθ from the light intensity autocorrelation equation 2 (t)>; (where q1 and q2 are the inverse space scales corresponding to angle 1 (i.e., 60-degree scattering angle) and 2 (i.e., 130-degree scattering angle), respectively)

[0067]

[0068] The obtained mean square rotation angle can be related to the complex modulus G*, storage modulus and loss modulus through the following equations:

[0069]

[0070] in:

[0071]

[0072] in is the aspect ratio of the tracer particle, k B is the Boltzmann constant, and Γ(1+α(ω)) is the gamma function.

[0073] The q values ​​corresponding to 60 degrees and 130 degrees are 0.01266nm respectively -1 , 0.02295nm -1 Refractive index n = 1.33, temperature T = 298K, laser wavelength λ = 660nm. B is the Boltzmann constant.

[0074] Calculate the obtained data to get Figure 1 Rheological curve shown.

[0075] Compared with traditional mechanical rheology (1Hz-100Hz), the frequency range of the modulus test obtained based on this method has been greatly broadened. For example, the frequency range of the modulus test of four-arm-polyethylene glycol hydrogel is 1-100000Hz.

[0076] The four-arm polyethylene glycol hydrogel of this example is a typical representative of low modulus samples (plateau modulus of about 300 Pa) due to its high molecular weight and low concentration. The data show that the method provided by the present invention can obtain accurate rheological curves for such low modulus samples.

[0077] Example 2

[0078] Unlike Example 1, polystyrene (PS) microspheres with a diameter of 90 nm (at a concentration of 2 mg / mL) were added to the blended solution to adjust the multiple scattering of the sample. It should be noted that since the amounts of PS microspheres and gold nanorods added were very small, they did not affect the rheological properties of the sample itself.

[0079] Optical images of four-arm polyethylene glycol hydrogel without PS microspheres and four-arm polyethylene glycol hydrogel with PS microspheres are shown in Figure 2. Figure 2 As shown; the left picture is a clear sample without adding PS microspheres (TPEG), and the right picture is a turbid sample with adding PS microspheres (TPEG-c).

[0080] The rheological curve of this embodiment is as follows Figure 3 As shown, TPEG-c is a turbid sample with PS microspheres added, while TPEG is a clear sample without PS microspheres. The rheological curves of the two are almost identical, demonstrating the reliability of this method for rheological testing of turbid samples.

[0081] Example 3

[0082] A rheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles comprises the following steps:

[0083] 1) preparing a PEG-20k solution to obtain a PEG-20k aqueous solution with a concentration of 100 mg / mL;

[0084] 2) Add gold nanorod tracer particles (control concentration is 0.5 mg / mL), mix well, and obtain a polymer solution sample; wherein the aspect ratio of the gold nanorods is 50*20 nm (i.e. );

[0085] 3) Depolarized dynamic light scattering was used to detect the sample at scattering angles of 60 degrees and 130 degrees, that is, microrheological testing was performed, and ensemble averaging was performed on the sample to obtain the light intensity autocorrelation equation and convert it into the electric field autocorrelation equation, thereby obtaining the microrheological rheological curve.

[0086] This method is also applicable to polymer solutions, rheological curves such as Figure 4 As shown, the frequency range is 2000Hz-2000000Hz. It should be noted that the frequency range covered by the microrheological test provided by the present invention is not fixed, and the specific range is related to the size of the tracer particles and the characteristics of the sample.

[0087] Comparative Example 1

[0088] This comparative example is different from Example 1 in that the test is performed using incompletely depolarized dynamic light scattering, where incomplete depolarization means that no polarizing plate is placed in front of the dynamic light scattering detection instrument.

[0089] Rheological curves such as Figure 5 The rheological curve obtained in this comparative example has serious fluctuations, and a crossover between the storage modulus and the loss modulus occurs at about 10,000 Hz, which seriously deviates from the rheological characteristics of the hydrogel.

Claims

1. A microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles, characterized by: The following steps are involved: Anisotropic tracer particles are dispersed in the sample or sample solution, and the sample is tested at two different scattering angles using depolarized dynamic light scattering, i.e., a microrheological test is performed. The light intensity autocorrelation equation is obtained and converted into an electric field autocorrelation equation, thereby obtaining the microrheological curve; The anisotropic tracer particles are gold nanorods; The sample is a soft substance, a polymer solution; In the depolarized dynamic light scattering, a polarizer with an extinction ratio of at least 100,000:1 is selected, and the extinction ratio is ≥100,000:1; The depolarized dynamic light scattering method is to place a polarizer in front of the dynamic light scattering instrument and adjust it so that the polarization direction is perpendicular to the incident direction of the laser. The light intensity autocorrelation equation and the electric field autocorrelation equation are: g2(q,t)=1+β|g1(q,t)| 2 Where β is the coherence coefficient of the instrument, q is the spatial scale in reciprocal space, which is directly related to the scattering angle θ, n is the refractive index of the sample, λ is the laser wavelength, t is the lag time, g1(q,t) is the electric field autocorrelation equation, and g2(q,t) is the light intensity autocorrelation equation obtained by the test; Extracting the mean square rotation angle <δθ from the light intensity autocorrelation equation 2 (t)>; where q1 and q2 are the inverse space scales corresponding to scattering angle 1 and scattering angle 2, i.e., the two different scattering angles mentioned above; The obtained mean square rotation angle can be related to the complex modulus G*, storage modulus G' and loss modulus G" by the following equations; in: in is the aspect ratio of the tracer particle, L is the length of the tracer particle, d is the diameter of the tracer particle, T is the temperature, k B is the Boltzmann constant, Γ(1+α(ω)) is the gamma function, The light intensity autocorrelation equation g2(q,t) is: I(τ), I(τ+t) are the light intensities at time τ and τ+t.

2. The microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles according to claim 1, characterized in that: The sample is a gel, emulsion, mucus, biomolecule aggregate, suspension, or polymer solution; When performing depolarized dynamic light scattering detection, the light intensity is 100-1000 kcp.

3. The microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles according to claim 1, characterized in that: The diameter and length of the gold nanorods are greater than the characteristic dimensions of the sample; Different scattering angles refer to two scattering angles that differ by 20-100 degrees.

4. The microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles according to claim 3, characterized in that: Different scattering angles refer to a scattering angle of 20-80 degrees and another scattering angle of 90-160 degrees.

5. The microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles according to claim 1, characterized in that: The concentration of the tracer particles in the sample or sample solution is determined by the following method: in terms of the detector count rate, the depolarized scattered light intensity needs to be above 100 kcp, or a smooth correlation equation is measured as a benchmark.

6. The microrheological characterization method based on depolarized dynamic light scattering and anisotropic tracer particles according to any one of claims 1 to 5, characterized in that: The sample is a clear or turbid system, or a sample with a modulus lower than 500 Pa; The method is used for broadband microrheological testing.

Images