Nanometer bubble optical coefficient measuring method based on multilayer spherical shell Mie theory

Abstract

The invention discloses a nano-bubble optical coefficient measurement method based on a multilayer spherical shell Mie theory, relates to the technical field of nano-bubble and nano-particle optical property measurement, and aims to solve the problem that an existing method cannot measure the optical property of a nano-bubble, the energy of laser absorbed by nano-particles is obtained according to the change of the transmission light intensity of the nano-particles, and the optical coefficient of the nano-bubble is measured according to the change of the transmission light intensity of the nano-particles. And substituting the refractive index field into an energy equation, obtaining the temperature and density in the nano-bubble forming process through a lattice Boltzmann method, and further obtaining the optical coefficient of the nano-particles wrapped by the nano-bubbles based on the multilayer spherical shell Mie theory according to the change condition of the refractive index field along with the degree.

Description

Technical Field

[0001] This application relates to the field of optical property measurement technology for nanobubbles and nanoparticles, specifically a method for measuring the optical coefficients of nanobubbles based on the Mie theory of multilayer spherical shells. Background Technology

[0002] The photoexcitation-generated plasma nanobubbles based on precious metal nanoparticles have attracted widespread research attention due to their unique photothermal conversion efficiency and tunable optical properties. This technology has been widely applied in fields such as biosensing, tissue imaging, targeted gene and drug delivery, disease treatment, and materials synthesis. Notably, when nanostructures are irradiated with lasers at their local surface plasmon resonance wavelength, the fluid medium undergoes a phase transition due to local overheating, thus forming nanobubbles. These nanobubbles, with their controllable nonlinear optical properties, excellent photothermal performance, and significant mechanical effects, show important application potential in multiple disciplines. For example, in the biomedical field, their light scattering properties make them particularly suitable for disease imaging and diagnostic applications. Therefore, researchers have devoted considerable effort to elucidating the fundamental mechanisms of plasma nanobubble formation and exploring the transient optical properties of nanoparticles encapsulated within nanobubbles. However, current nanobubble detection methods, such as dark-field microscopy, acoustic detection, and optical transmission measurement, can only obtain the size of the nanobubbles and cannot measure their optical properties. Summary of the Invention

[0003] The purpose of this invention is to address the problem that existing methods cannot measure the optical properties of nanobubbles, and to provide a method for measuring the optical coefficients of nanobubbles based on the Mie theory of multilayer spherical shells.

[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0005] A method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells is disclosed. The method is implemented using a measuring device comprising a pulsed laser, a probe laser, an objective lens, a first photodetector, and a second photodetector. The high-energy pulsed laser emitted by the pulsed laser is focused by the objective lens and then irradiates the nanoparticles in an aqueous solution. Simultaneously, the low-energy continuous laser emitted by the probe laser also irradiates the nanoparticles. The first and second photodetectors are used to acquire the laser intensity of the nanoparticles after irradiation by the pulsed laser and the probe laser, respectively.

[0006] The measurement method is specifically as follows:

[0007] Step 1: Turn on the probe laser to allow the continuous laser emitted by the probe laser to irradiate the nanoparticles. At the same time, obtain the laser power of the probe laser after irradiating the nanoparticles through the second photodetector.

[0008] Step 2: Turn on the pulsed laser and preheat it thoroughly. Then, adjust the output power and position of the pulsed laser until the signal of the second photodetector changes. At this point, the laser emitted by the pulsed laser will irradiate the nanoparticles.

[0009] Step 3: Record the output power of the pulsed laser, i.e. the incident laser power, and turn on the first photodetector to record the transmitted laser power after the laser irradiates the nanoparticles;

[0010] Step 4: Subtract the transmitted laser power from the incident laser power to obtain the laser power absorbed by the nanoparticles from the incident laser. ;

[0011] Step 5: Obtain the volume of the nanoparticles and use laser power. Divide by the volume of the nanoparticles to obtain the volumetric heat source density of the nanoparticles. ;

[0012] Step Six: Calculate the volumetric heat source density of the nanoparticles. Substituting into the energy equation, we obtain the spatial distribution of temperature. Based on the spatial distribution of nanoparticles and temperature The fluid density was obtained using the lattice Boltzmann method.

[0013] Step 7: Based on the spatial distribution of fluid density, the spatial distribution of fluid refractive index is obtained by interpolation. Then, based on the spatial distribution of fluid refractive index, the transient optical coefficients of nanoparticles during the formation of nanobubbles are obtained using the multilayer spherical shell Mie theory.

[0014] Furthermore, the optical coefficient in step seven includes absorption. ,scattering and extinction coefficient , is represented as:

[0015] ;

[0016] ;

[0017] ;

[0018] in, , , Let be the refractive index at the outermost cutoff point of the spherical shell. The radius of the outermost spherical shell, The wavelength of the incident wave in a vacuum. and The scattering coefficient is... As an intermediate variable, It is a constant.

[0019] Furthermore, the scattering coefficient Represented as:

[0020] ;

[0021] Scattering coefficient Represented as:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] in, To handle intermediate quantities in TM wave recursion, To handle intermediate quantities in the recursion of TE waves, The relative refractive index is used to divide the total number of spherical shells. , , and For Riccati-Bessel functions, , To divide the spherical shell into a total number of parts, and The logarithmic derivative of the Riccati-Bessel function. For the first The relative refractive index of a spherical shell, For the first The relative refractive index of a spherical shell, For the first The dimensional parameters of the spherical shell, For the first The dimensional parameters of the spherical shell, , , and It is an intermediate variable.

[0031] Furthermore, step six specifically involves:

[0032] Step 61: Calculate the volumetric heat source density of the nanoparticles. Substituting the values ​​into the energy equation and solving it using the finite difference method, the temperature of the nanoparticles is obtained. and fluid temperature And utilize the temperature of nanoparticles and fluid temperature Constructing temperature spatial distribution ;

[0033] Step 62: Obtain the fluid velocity and fluid density based on the intermolecular forces and the distribution function in the lattice Boltzmann method;

[0034] Step 63: Determine if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, proceed to Step 64. If the maximum number of iterations has not been reached, proceed to Step 65.

[0035] Step 64: Output the obtained fluid density;

[0036] Step 65: Based on temperature spatial distribution The fluid pressure is obtained using the PR equation of state, and the fluid pressure and fluid velocity are used as the fluid pressure and fluid velocity in the energy equation and distribution function, respectively. Steps 61 to 63 are repeated.

[0037] Furthermore, the energy equation is expressed as:

[0038] ;

[0039] ;

[0040] in, , , These are fluid density, thermal conductivity, and specific heat capacity, respectively. For time, subscript Precious metal material, subscript It is an aqueous solution. For fluid pressure, The fluid velocity.

[0041] Furthermore, the distribution function is expressed as:

[0042] ;

[0043] ;

[0044] in, For position vectors, For time step, It is the identity matrix. For discrete force terms, For source terms, It is a diagonal matrix composed of relaxation parameters. , , , Both are distribution functions. Let be the equilibrium state distribution function. For discrete velocities.

[0045] Furthermore, the source item Represented as:

[0046] ;

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] in, , , , , , for The amount, For the speed of sound in a grid, and For coefficients, The coefficient of intermolecular forces. It is a pseudopotential function. The forces between fluid molecules. , , They are respectively Along , , The components in the three directions of the axis.

[0054] Furthermore, the discrete force term Represented as:

[0055] ;

[0056] in, , , For fluid velocity along , , The components in the three directions of the axis.

[0057] Furthermore, the intermolecular forces of the fluid molecules Represented as:

[0058] ;

[0059] ;

[0060] ;

[0061] in, These are the weighting coefficients. It is an intermediate variable.

[0062] Furthermore, the fluid velocity Represented as:

[0063] ;

[0064] ;

[0065] in, It is the distribution function;

[0066] The fluid pressure Represented as:

[0067] ;

[0068] in, This is the universal gas constant. and It is a constant.

[0069] The beneficial effects of this invention are:

[0070] This application obtains the energy of laser absorbed by nanoparticles based on the change in the intensity of transmitted light, incorporates it into the energy equation, obtains the temperature and density of the nanobubble formation process through the lattice Boltzmann method, and then obtains the optical coefficients of the nanoparticles encased in the nanobubble based on the change of the refractive index field with temperature and the multilayer spherical shell Mie theory.

[0071] This application can accurately measure the spectral characteristics of nanobubbles, enabling indirect and non-contact measurement, reducing computational costs while improving computational efficiency. It is applicable to particles of different materials and sizes. This application completes the measurement of optical properties during the formation of nanobubbles by measuring the optical absorption of nanoparticles, the lattice Boltzmann method, and the multilayer spherical shell Mie theory. This provides a new technical means for the photo-optical detection of nanobubbles and the application of nanobubbles in photothermal diagnostic and therapeutic integration. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the measuring device used in this application;

[0073] Figure 2 This is a flowchart of the overall measurement method of this application. Detailed Implementation

[0074] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0075] Specific Implementation Method 1: This implementation method describes a method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells. The method is implemented using a measuring device, which includes a pulsed laser, a probe laser, an objective lens, a photodetector, and a data acquisition and processing computer. The high-energy pulsed laser emitted by the pulsed laser is focused by the objective lens and irradiates gold nanoparticles in water. Simultaneously, the probe laser emits a low-energy continuous laser that also irradiates the nanoparticles. Photodetectors 1 and 2 respectively acquire the laser intensity after the pulsed laser and probe laser irradiate the nanoparticles. The probe laser is used to determine whether the laser emitted by the pulsed laser heats the surrounding water and generates bubbles. Specifically, a change in the probe laser signal received by photodetector 2 indicates the generation of nanobubbles. Photodetector 1 receives the laser power after the pulsed laser irradiates the nanoparticles. Finally, the data acquisition and processing computer records the intensity of the incident and transmitted lasers from the pulsed laser and probe laser.

[0076] The method for measuring the absorption, extinction, and scattering coefficients of plasma nanobubbles based on the multilayer spherical shell Mie theory is implemented using a device based on the multilayer spherical shell Mie theory for measuring the absorption, extinction, and scattering coefficients of plasma nanobubbles. The method includes the following steps:

[0077] Step 1: Turn on the probe laser and let the continuous laser emitted by the probe laser irradiate the gold nanoparticles. Adjust the power of the probe laser to keep it at a very small value, so that the nanoparticles can absorb enough energy from the probe laser to prevent the formation of nanobubbles. At the same time, the laser power after the probe laser irradiates the nanoparticles is obtained through photodetector 2.

[0078] Step 2: Turn on the pulsed laser and preheat it thoroughly. Then, adjust the output power of the laser so that the nanoparticles can heat the surrounding water to produce nanobubbles. Adjust the position of the laser. When the signal in the photodetector 2 changes, it is assumed that the pulsed laser is irradiating the gold nanoparticles, and the nanoparticles are heating the surrounding water to produce nanobubbles.

[0079] Step 3: Record the incident laser power using an integrated data acquisition and processing computer. Turn on photodetector 1 to record the transmission signal after the laser irradiates the nanoparticles, and record the transmitted laser power.

[0080] Step 4: Based on the incident laser power and transmitted laser power from Step 3, subtract the transmitted laser power from the incident laser power to obtain the laser power absorbed by the nanoparticles from the incident laser. This portion of the energy is converted into heat by the gold nanoparticles, heating the surrounding water to produce nanobubbles.

[0081] Step 5; Based on the laser power absorbed by the nanoparticles in Step 4 , laser power Dividing by the particle's volume gives the particle's volumetric heat source density. The energy equations are then substituted into the energy equations, and the temperature during the formation of nanobubbles is solved using the finite difference method. The energy equations for the water surrounding the nanoparticles and the interior of the nanoparticles are as follows:

[0082] ;

[0083] ;

[0084] in , , These are density, thermal conductivity, and specific heat capacity, respectively, indicated by subscripts. and These represent water and gold, respectively. The spatial temperature distribution across the entire geometric domain can be obtained based on the temperature of the nanostructure and the fluid temperature. , Represents time, Represents pressure, Represents fluid velocity.

[0085] Step Six: Using the temperatures of the nanoparticles and fluid obtained in Step Five, the density and pressure of the fluid during the formation of nanobubbles are obtained using the lattice Boltzmann method, thereby determining the size of the nanobubbles. The specific process of Step Six includes:

[0086] The distribution function is used to simulate the interactions between fluid molecules. The macroscopic motion state of the fluid is obtained through the "collision" and "diffusion" steps of the distribution function, that is, through its iterative update. The update equation of the distribution function is as follows:

[0087] ;

[0088] ;

[0089] in For position vectors, For time step. It is the identity matrix. For discrete force terms, For source terms, It is a diagonal matrix composed of relaxation parameters. , , , Both are distribution functions, and they are connected by a transformation matrix. accomplish, = , = , It is by The matrix formed It is by The matrix formed This is the equilibrium state distribution function.

[0090] Furthermore, the intermolecular forces of fluid molecules can be obtained from the distribution function. Fluid molecules move under this force, and its specific expression is as follows:

[0091] ;

[0092] in The coefficient of intermolecular forces. These are weighting coefficients. It is a discrete velocity. It is a pseudopotential function, which is obtained by the following formula:

[0093] ;

[0094] in For the speed of sound in a grid, .

[0095] The velocity and density of a fluid can be obtained based on intermolecular forces and distribution functions, as shown in the following equation:

[0096] ;

[0097] ;

[0098] in For fluid density, The fluid velocity.

[0099] The fluid pressure is obtained using the PR equation of state, which is shown below:

[0100] ;

[0101] in This is the universal gas constant. and It is a constant. The expression is as follows:

[0102] ;

[0103] in It is the critical temperature.

[0104] Step Seven: Based on Step Six, the temperature, pressure, and density at each moment during the formation of nanobubbles can be updated in real time. The refractive index of water changes drastically with the density of the fluid; therefore, the refractive index of water can be obtained based on the density distribution of the fluid.

[0105] Step 8: Based on the spatial distribution of water refractive index obtained in Step 7, the transient optical properties of gold nanoparticles during the formation of nanobubbles, such as absorption, scattering and extinction coefficients, are obtained using the multilayer spherical shell Mie theory.

[0106] Furthermore, absorption ,scattering and extinction coefficient The solution method is as follows:

[0107] ;

[0108] ;

[0109] ;

[0110] in , , The refractive index at the outermost cutoff point of the spherical shell, The radius of the outermost spherical shell, It is the wavelength of the incident wave in a vacuum.

[0111] Scattering coefficient and It can be represented as:

[0112] ;

[0113] ;

[0114] in and It can be represented as:

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] in, It is the relative refractive index. These are dimensional parameters. It represents the total number of divisions of the spherical shell. and It is the Riccati-Bessel function. and It is the logarithmic derivative of the Riccati-Bessel function.

[0123] In this embodiment, the pulse width of the pulsed laser is between 100 fs and 100 ns, the pulsed laser power is between 3 mW and 200 mW, the diameter of the nanoparticles is between 10 nm and 100 nm, and the material is a precious metal.

[0124] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells, characterized in that... The measurement method is based on a measurement device, which includes a pulsed laser, a probe laser, an objective lens, a first photodetector, and a second photodetector. The high-energy pulsed laser emitted by the pulsed laser is focused by the objective lens and then irradiates the nanoparticles in the aqueous solution. At the same time, the low-energy continuous laser emitted by the probe laser also irradiates the nanoparticles. The first and second photodetectors are used to obtain the laser intensity of the nanoparticles after the pulsed laser and the probe laser irradiate them, respectively. The measurement method is specifically as follows: Step 1: Turn on the probe laser to allow the continuous laser emitted by the probe laser to irradiate the nanoparticles. At the same time, obtain the laser power of the probe laser after irradiating the nanoparticles through the second photodetector. Step 2: Turn on the pulsed laser and preheat it thoroughly. Then, adjust the output power and position of the pulsed laser until the signal of the second photodetector changes. At this point, the laser emitted by the pulsed laser will irradiate the nanoparticles. Step 3: Record the output power of the pulsed laser, i.e. the incident laser power, and turn on the first photodetector to record the transmitted laser power after the laser irradiates the nanoparticles; Step 4: Subtract the transmitted laser power from the incident laser power to obtain the laser power absorbed by the nanoparticles from the incident laser. ; Step 5: Obtain the volume of the nanoparticles and use laser power. Divide by the volume of the nanoparticles to obtain the volumetric heat source density of the nanoparticles. ; Step Six: Calculate the volumetric heat source density of the nanoparticles. Substituting into the energy equation, we obtain the spatial distribution of temperature. Based on the spatial distribution of nanoparticles and temperature The fluid density was obtained using the lattice Boltzmann method. Step 7: Based on the spatial distribution of fluid density, the spatial distribution of fluid refractive index is obtained by interpolation. Then, based on the spatial distribution of fluid refractive index, the transient optical coefficients of nanoparticles during the formation of nanobubbles are obtained using the multilayer spherical shell Mie theory.

2. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 1, characterized in that... The optical coefficients in step seven include absorption. ,scattering and extinction coefficient , is represented as: ； ； ； in, , , Let be the refractive index at the outermost cutoff point of the spherical shell. The radius of the outermost spherical shell, The wavelength of the incident wave in a vacuum. and The scattering coefficient is... As an intermediate variable, It is a constant.

3. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 2, characterized in that... The scattering coefficient Represented as: ； Scattering coefficient Represented as: ； ； ； ； ； ； ； ； in, To handle intermediate quantities in TM wave recursion, To handle intermediate quantities in the recursion of TE waves, The relative refractive index is used to divide the total number of spherical shells. , , and For Riccati-Bessel functions, , To divide the spherical shell into a total number of parts, and The logarithmic derivative of the Riccati-Bessel function. For the first The relative refractive index of a spherical shell, For the first The relative refractive index of a spherical shell, For the first The dimensional parameters of the spherical shell, For the first The dimensional parameters of the spherical shell, , , and It is an intermediate variable.

4. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 3, characterized in that... Step six specifically involves: Step 61: Calculate the volumetric heat source density of the nanoparticles. Substituting the values ​​into the energy equation and solving it using the finite difference method, the temperature of the nanoparticles is obtained. and fluid temperature And utilize the temperature of nanoparticles and fluid temperature Constructing temperature spatial distribution ; Step 62: Obtain the fluid velocity and fluid density based on the intermolecular forces and the distribution function in the lattice Boltzmann method; Step 63: Determine if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, proceed to Step 64. If the maximum number of iterations has not been reached, proceed to Step 65. Step 64: Output the obtained fluid density; Step 65: Based on temperature spatial distribution The fluid pressure is obtained using the PR equation of state, and the fluid pressure and fluid velocity are used as the fluid pressure and fluid velocity in the energy equation and distribution function, respectively. Steps 61 to 63 are repeated.

5. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 4, characterized in that... The energy equation is expressed as: ； ； in, , , These are fluid density, thermal conductivity, and specific heat capacity, respectively. For time, subscript Precious metal material, subscript It is an aqueous solution. For fluid pressure, The fluid velocity.

6. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 5, characterized in that... The distribution function is expressed as: ； ； in, For position vectors, For time step, It is the identity matrix. For discrete force terms, For source terms, It is a diagonal matrix composed of relaxation parameters. , , , Both are distribution functions. Let be the equilibrium state distribution function. For discrete velocities.

7. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 6, characterized in that... The source item Represented as: ； ； ； ； ； ； ； in, , , , , , for The amount, For the speed of sound in a grid, and For coefficients, The coefficient of intermolecular forces. It is a pseudopotential function. The forces between fluid molecules. , , They are respectively Along , , The components in the three directions of the axis.

8. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 7, characterized in that... The discrete force term Represented as: ； in, , , For fluid velocity along , , The components in the three directions of the axis.

9. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 8, characterized in that... The intermolecular forces of the fluid Represented as: ； ； ； in, These are the weighting coefficients. It is an intermediate variable.

10. The method for measuring the optical coefficient of nanobubbles based on the Mie theory of multilayer spherical shells according to claim 9, characterized in that... The fluid velocity Represented as: ； ； in, It is the distribution function; The fluid pressure Represented as: ； in, This is the universal gas constant. and It is a constant.

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