A method for determining the surface charge density of micro- and nanoparticles

Abstract

This invention discloses a method for determining the surface charge density of micro / nano particles. The method first uses light scattering technology to determine the critical agglomeration concentration of micro / nano particles at a given electrolyte type and temperature. Then, under this concentration condition, the resultant force of electrostatic repulsion and long-range molecular attraction between particles is calculated, and the particle surface potential under this condition is determined. Finally, the surface charge density of the particles is obtained based on the obtained surface potential. This invention can accurately calculate the surface charge density of micro / nano particles by determining the critical agglomeration concentration using a laser scattering instrument, eliminating the need to separately measure the outer surface area of ​​the particles in a gaseous medium and the number of surface charges in a liquid medium before calculating the surface charge density.

Description

Technical Field

[0001] This invention belongs to the technical field of methods for measuring the surface charge density of micro and nanoparticles, and particularly relates to the technical field of measuring the surface charge density of micro and nanoparticles using dynamic light scattering technology. Background Technology

[0002] Surface charge density is a very important parameter in the interfacial properties of nanoparticles and microparticles. It determines the electric field strength on the surface of nanoparticles and thus affects the interaction between nanoparticles and microparticles.

[0003] However, to date, no existing technology has an instrument that can directly measure this important parameter. Current technologies obtain the surface charge density of nano- and micro-sized particles by estimating the surface area measured in a gaseous medium and the amount of surface charge measured in a liquid medium. Due to inconsistent measurement environments, this estimation method yields surface charge density with poor accuracy.

[0004] Therefore, there is an urgent need for a method that can accurately measure the surface charge density of nano- and micro-sized particles in order to overcome the shortcomings of existing evaluation methods and achieve a breakthrough in the study of material interface properties. Summary of the Invention

[0005] The purpose of this invention is to provide a method for accurately measuring the surface charge density of nano- and micro-sized particles directly in a liquid medium using a laser scattering instrument.

[0006] The present invention first provides the following technical solution:

[0007] A method for determining the surface charge density of micro / nano particles, comprising:

[0008] S1 uses dynamic light scattering technology to determine the critical aggregation concentration of micro / nano particles in electrolyte solution;

[0009] S2 is based on the condensation energy barrier equation of micro-nano particles at the critical flocculation concentration. According to the obtained critical flocculation concentration value, the surface potential of micro-nano particles is obtained by approximation method. The surface charge density of the micro-nano particles is calculated based on the obtained surface potential.

[0010] in,

[0011] The condensation energy barrier equation for the micro / nano particles is as follows:

[0012]

[0013]

[0014] Where Δw represents the condensation energy barrier of micro / nano particles; x represents the distance between particles; h represents the effective head thickness of the particle, i.e., the effective thickness when nano / micro particles condense, which can be determined empirically; P net (x) represents the resultant force of long-range molecular attraction; A eff denoted as Hamaker constant for nano- and micro-sized particles; a and b represent P net The two values ​​of x when (x) = 0; k represents the Boltzmann constant; T represents the absolute temperature; P EDL (x) represents the electrostatic repulsion between micro-nano particles at the critical flocculation concentration, which is related to the surface potential of micro-nano particles and the critical flocculation concentration.

[0015] The surface charge density of the micro / nanoparticles is calculated as follows:

[0016]

[0017] Wherein, σ0 represents the surface charge density of the micro / nano particles; ε represents the surface potential of the micro / nano particles; v represents the vacuum permittivity; D represents the relative permittivity of the medium (e.g., if the medium is water, then D = 80); c i Z represents the concentration of ion i in the system; i The valence of ion i is represented by ; R is the gas constant; β is the effective charge coefficient of the counterion (if ion i is of the same charge, then β = 1); e is the natural index; e0 is the elementary charge.

[0018] According to some specific embodiments of the present invention, the electrostatic repulsion between the micro / nanoparticles is obtained through the following calculation model:

[0019] When the charge ratio of the cations and anions in the electrolyte used is 1:1:

[0020]

[0021] when

[0022]

[0023] when

[0024] Wherein, CCC represents the critical coagulation concentration; The thickness of the diffusion layer is represented at the critical coagulation concentration, F represents the Faraday constant, and ε represents the dielectric constant of the medium.

[0025] When the charge ratio of the cations and anions in the electrolyte used is 1:2:

[0026]

[0027] when

[0028]

[0029] when

[0030] Among them, the calculation parameters

[0031] Calculation parameters

[0032] The thickness of the diffusion layer at the critical agglomeration concentration.

[0033] According to some specific embodiments of the present invention, obtaining the critical coagulation concentration includes:

[0034] (1) Using dynamic light scattering technology, observe the change in the effective diameter of micro-nano particles during the aggregation process in an electrolyte solution with a known electrolyte concentration c0, obtain the change in effective diameter over time D(t), and obtain the instantaneous aggregation rate v(t, c0) of micro-nano particles based on the change in effective diameter over time D(t).

[0035] (2) The average condensation rate of micro- and nanoparticles from time t = 0 to any time t = t is obtained by using the instantaneous condensation rate v(t, c0).

[0036] (3) Based on the average aggregation rate of the obtained micro- and nano-particles Obtain the total average condensation rate of micro / nanoparticles from time t=0 to time t=t0.

[0037] Under different electrolyte concentrations c0, the total average aggregation rate of micro and nanoparticles was determined according to the process (1)-(3) above. Plotting electrolyte concentration c0 on the x-axis, the resulting total average coagulation rate Plotting the vertical axis The concentration at the inflection point between the two sloping segments of the curve is the critical flocculation concentration.

[0038] According to some specific embodiments of the present invention, the instantaneous condensation rate v(t, c0) of the micro / nanoparticles is obtained by the following formula:

[0039]

[0040] Where t represents time.

[0041] According to some specific embodiments of the present invention, the average aggregation rate of the micro / nanoparticles We obtain it from the following formula:

[0042]

[0043] According to some specific embodiments of the present invention, the overall average aggregation rate of the micro / nanoparticles We obtain it from the following formula:

[0044]

[0045] Where D(t) and D(0) are the effective diameters of the condensed micro / nanoparticles at time t and the initial time, respectively.

[0046] According to some specific embodiments of the present invention, the assignment approximation method includes:

[0047] A surface potential set under the critical coagulation concentration condition Based on the critical agglomeration concentration and the surface potential, calculate P when the interparticle distance is x. EDL (x) value; according to P EDL The value of (x) is obtained, and P is further obtained. net The values ​​of (x) and Δw are used to calculate the value of Δw. The calculated value of Δw is compared with the value of 0.2kT. If Δw > 0.2kT, the surface potential is reduced. The absolute value of the surface potential is used to recalculate the reduction. The absolute value of Δw is obtained and compared with the value of 0.2kT. The process stops when Δw < 0.2kT. The surface potential in the above process is... Plot the value of t as the x-axis and the obtained Δw as the y-axis, and plot the curve when Δw = 0.2kT. The value is taken as the value of the surface potential to be determined.

[0048] According to some specific embodiments of the present invention, when the charge ratio of the anions and cations in the electrolyte used is 1:1: the surface charge density σ0 of the micro / nanoparticles is obtained by the following formula:

[0049]

[0050] Wherein, CCC represents the critical coagulation concentration, ε v denoted by ; D represents the vacuum permittivity; D represents the relative permittivity of the medium (e.g., D = 80 for water); R is the gas constant; β represents the effective charge coefficient of the counterion; e represents the natural index; e0 represents the elementary charge.

[0051] According to some specific embodiments of the present invention, when the charge ratio of the anions and cations in the electrolyte used is 1:2: the surface charge density σ0 of the micro / nanoparticles is obtained by the following formula:

[0052]

[0053] Wherein, CCC represents the critical coagulation concentration, ε v denoted by ; D represents the vacuum permittivity; D represents the relative permittivity of the medium (e.g., D = 80 for water); R is the gas constant; β represents the effective charge coefficient of the counterion; e represents the natural index; e0 represents the elementary charge.

[0054] The surface charge density of micro- and nano-particles measured by this invention is the true value in the liquid phase medium, which does not require estimation using the specific surface area measured under gas phase conditions. The result is more accurate and is expected to enable automatic measurement by instruments. Attached Figure Description

[0055] Figure 1 As described in the specific implementation method curve.

[0056] Figure 2 P as described in the specific implementation method net (x)-x curve.

[0057] Figure 3 The surface potential described in the specific implementation embodiment A schematic diagram for determining the [specific element].

[0058] Figure 4 This is a graph showing the change in the effective diameter of the colloidal particles obtained in Example 1 during the coagulation process.

[0059] Figure 5 The result obtained in Example 1 Line graph.

[0060] Figure 6 P obtained in Example 1 net (x)-x curve.

[0061] Figure 7 The result obtained in Example 1 Line graph.

[0062] Figure 8 The graph shows the relationship between surface charge density and critical condensation concentration obtained in Example 2. Detailed Implementation

[0063] The present invention will now be described in detail with reference to embodiments and accompanying drawings. However, it should be understood that the embodiments and drawings are for illustrative purposes only and do not constitute any limitation on the scope of protection of the present invention. All reasonable modifications and combinations included within the inventive spirit of the present invention fall within the scope of protection of the present invention.

[0064] According to the technical solution of the present invention, some specific embodiments of the method for determining the surface charge density of micro / nano particles include the following steps:

[0065] S1 uses a laser scattering instrument to determine the critical aggregation concentration (CCC) of micro / nanoparticles in an electrolyte solution.

[0066] Furthermore, in some specific embodiments, the determination of the critical flocculation concentration includes:

[0067] Dynamic light scattering technique was used to observe the change in the effective diameter of micro / nano particles during the aggregation process in an electrolyte solution with a known electrolyte concentration c0. The change in effective diameter over time, D(t), was obtained. Based on the obtained change in effective diameter over time, D(t), the aggregation rate v(t, c0) of the micro / nano particles was obtained as follows:

[0068]

[0069] Then the average condensation rate of micro / nanoparticles from t=0 to any t=t during the condensation process. for:

[0070]

[0071] The total average condensation rate of micro / nanoparticles from t=0 to any t=t0 The definition is as follows:

[0072]

[0073] Where D(t) and D(0) are the effective diameters of the condensed micro / nanoparticles at time t (t>0) and the initial time (t=0), respectively.

[0074] Based on the above calculation model, the total average aggregation rate of micro and nanoparticles was determined under different electrolyte concentrations. Plotting electrolyte concentration c0 on the x-axis, the resulting total average coagulation rate Plotting the vertical axis Curve, as attached Figure 1 As shown, the concentration at the inflection point between the two sloping segments of the curve is the CCC value.

[0075] S2 obtains the electrostatic repulsion P between micro / nanoparticles at the critical coagulation concentration (CCC) based on the measured critical coagulation concentration. EDL (x) The resultant force P of long-range molecular attraction net (x) The energy barrier of particle aggregation and the surface potential of the particles are used to solve for the surface charge density of micro and nano particles.

[0076] Furthermore, in some specific embodiments, S2 further includes:

[0077] S21 obtained the electrostatic repulsion P between micro and nanoparticles at the critical flocculant concentration. EDL (x), as follows:

[0078] When the charge ratio of the cations and anions in the electrolyte used is 1:1, such as when the electrolyte used is NaCl:

[0079]

[0080] when

[0081]

[0082] when

[0083] in, The value represents the thickness of the diffusion layer at the critical flocculation concentration, where k is the Boltzmann constant, F is the Faraday constant, ε is the dielectric constant of the medium, R is the gas constant, T is the absolute temperature, and π is pi. Let β be the surface potential, β be the effective charge coefficient of the counterion, and e0 be the elementary charge, i.e., e0 = 1.6 × 10⁻⁶. -19 C, x is the distance between particles.

[0084] The effective charge coefficients of common counterions are: Na ion 1.21, K ion 2.18, Ca ion 2.60, and Mg ion 1.34, which can be determined by ion exchange adsorption methods, etc.

[0085] When the charge ratio of the cations and anions in the electrolyte used is 1:2, such as when the electrolyte used is CaCl2:

[0086] when

[0087]

[0088]

[0089] when

[0090] Among them, the calculation parameters

[0091] Calculation parameters

[0092] This indicates the thickness of the diffusion layer at the critical agglomeration concentration.

[0093] S22 is based on the obtained electrostatic repulsion P EDL (x), to obtain the resultant force P between micro and nanoparticles at the critical flocculation concentration. net (x), as follows:

[0094]

[0095] Among them, A eff is the Hamaker constant for nano- and micro-sized particles.

[0096] S23 is based on the resultant force P between the particles. net (x), the energy barrier for the condensation of micro- and nano-particles is obtained as follows:

[0097]

[0098] Under CCC conditions, the energy barrier for the condensation of micro / nano particles is:

[0099]

[0100] Where h is the effective head thickness of the particle, which can be taken as 1 nm for the aggregation of nano- and micro-sized particles; the values ​​of a and b depend on the surface potential, and are P net The value of x when (x) = 0, i.e., P net The coordinates of the intersection points of the (x)-x curve and the x-axis are shown in the attached figure. Figure 2 As shown.

[0101] S24 solves for the surface potential based on the energy barrier of micro / nanoparticle condensation under the obtained CCC by an approximation method. include:

[0102] See attached document Figure 3 First, assume the surface potential under CCC conditions is... Calculate P under the corresponding electrolyte system. EDL The value of (x) is calculated, where the 1:1 electrolyte is calculated using equation (5) and the 1:2 electrolyte using equation (7), and P is further calculated sequentially. net The values ​​of (x) and Δw are used to compare the calculated Δw value with 0.2kT. If Δw > 0.2kT, then the value is increased. The value is recalculated and compared until Δw < 0.2kT, at which point the process stops. Plotting the curve with Δw as the x-axis and Δw as the y-axis, and taking the curve where Δw = 0.2kT... The value is taken as the value of the surface potential to be determined.

[0103] S25 obtains the surface charge density σ0 of the micro / nano particles based on the surface potential obtained from the solution, as follows:

[0104]

[0105] Where, ε v The value of C represents the vacuum permittivity, D represents the relative permittivity of water (D = 80), and c represents the relative permittivity of water. i Z represents the concentration of ion i. i This indicates the valence of ion i.

[0106] In a 1:1 electrolyte system, the surface charge density σ0 of the micro / nano particles is:

[0107]

[0108] In a 1:2 electrolyte system, the surface charge density σ0 of the micro / nanoparticles is:

[0109]

[0110] Therefore, based on the obtained particle surface potential The effective charge coefficient of the counterion in the system can be used to calculate the surface charge density of the substance under the corresponding conditions.

[0111] Example 1

[0112] The surface charge density of montmorillonite particles was measured as follows:

[0113] (1) The change in the diameter of montmorillonite colloidal particles with time was determined using a light scattering instrument, as shown in the attached figure. Figure 4 As shown.

[0114] (2) According to the appendix Figure 4 Based on the experimental data and combined with equations (1) and (3), the total average coagulation rate of montmorillonite colloidal particles was calculated. Based on the calculated total condensation rate The results of plotting the electrolyte concentrations are shown in the attached figure. Figure 5 shown Line graph.

[0115] from Figure 5It can be seen that two line segments are obtained. One line segment corresponds to the rapid coagulation stage. The total coagulation rate increases linearly with the increase of electrolyte concentration. When the particle coagulation reaches equilibrium, the coagulation rate no longer increases significantly with the increase of concentration. That is, the slope of the former is much greater than that of the latter. The intersection of the two lines is the critical coagulation concentration CCC of montmorillonite particles in NaCl solution. The result is CCC = 0.1328 mol / L.

[0116] (3) Based on the obtained CCC value, the average kinetic energy Δw of particle aggregation is further calculated. The process is as follows: first, assume a series of surface potentials. The electrostatic repulsion pressure P is calculated from equations (4) and (5). EDL , calculate P EDL Substitute into equation (8) to calculate the net repulsive pressure P net The obtained P net The -x curve is attached. Figure 6 As shown, the area between the curve and the x-axis in the Pnet-x plot is calculated using equation (9), thus obtaining the average kinetic energy Δw under CCC conditions. The obtained average kinetic energy Δw is then used to calculate the surface potential. Plot the graph, assuming the surface potential When the absolute value of is too high, the calculated average kinetic energy Δw will be higher than 0.2kT, so it needs to be reduced. Continue calculating Δw until Δw < 0.2kT, as shown in the attached figure. Figure 7 The Δw- shown The graph shows that when the average kinetic energy of montmorillonite particles at the critical condensation concentration is 0.2 kT, the particle surface potential is -0.08236 V.

[0117] (4) Based on the measured particle surface potential of -0.08236V, the effective charge coefficient β of Na ions is known. Na =1.1, and the surface charge density of montmorillonite is calculated to be 0.1180 C / m² using equation (12). 2 .

[0118] Montmorillonite has a specific surface area of ​​716 m² in the liquid phase. 2 / g, surface charge quantity is 84.8cmol (-) Based on a surface charge density of montmorillonite per kg, the surface charge density is 0.1143 C / m³. 2 The theoretical value and the measured value are in good agreement.

[0119] Example 2

[0120] The surface charge density of different types of nano / micro particles was measured according to the process in Example 1, and the correlation diagram between the density and the critical condensation concentration was obtained, as shown in the attached figure. Figure 8As shown, there is a significant positive correlation between surface charge density and critical condensation concentration. The larger the CCC value of particle condensation, the higher its surface charge density and the greater its charge.

[0121] In practice, the CCC value reflects the ease or difficulty of particle aggregation; a higher CCC value indicates that particles require a very high concentration to aggregate. This aligns with the fact that the greater the surface charge of particles, the stronger the electrostatic repulsion between particles, making aggregation more difficult. Therefore, the surface charge density of nano- and micro-sized particles calculated using this invention's method shows a consistent trend with experimentally observed particle aggregation.

[0122] The above embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the surface charge density of a micro- or nano-particle, characterized in that, It comprises: S1 determines the critical coagulation concentration of the micro-nanoparticles in the electrolyte solution by dynamic light scattering technology; S2 obtains the surface potential of the micro-nanoparticles by the method of assignment approximation based on the coagulation energy barrier equation of the micro-nanoparticles at the critical coagulation concentration, according to the value of the obtained critical coagulation concentration, and calculates the surface charge density of the micro-nanoparticles according to the obtained surface potential; Wherein, The coagulation energy barrier equation of the micro-nanoparticles is as follows: wherein, Aw represents the agglomeration energy barrier of the micro-nanoparticles; x represents the distance between the particles; h represents the effective head thickness of the particles, i.e. the effective thickness when the micro-nanoparticles agglomerate, which can be valued according to experience; P net (x) represents the resultant force of long-range molecular attraction; A eff is the Hamaker constant of the micro-nanoparticles; a and b represent the P net (x) represents the resultant force of long-range molecular attraction; A EDL (x) represents the resultant force of long-range molecular attraction; A (x) represents the electrostatic repulsion between the micro-nanoparticles at the critical coagulation concentration related to the surface potential and the critical coagulation concentration of the micro-nanoparticles; The calculation of the surface charge density of the micro-nanoparticles is as follows: wherein σ0represents the surface charge density of the micro- or nanoparticles; is the surface potential of the micro- or nanoparticles; ε v represents the vacuum permittivity; D represents the relative permittivity of the medium; c i represents the concentration of the i ions; Z i represents the valence of the i ions; R is the gas constant; β represents the effective charge coefficient of the counter ions; e represents the natural exponential; e0is the elementary charge.

2. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 1, wherein: The electrostatic repulsion between the micro-nanoparticles is obtained by the following calculation model: In the case of the charge ratio of the anion and the cation of the used electrolyte being 1:1: When time; When time; CCC represents the critical coagulation concentration; CCC represents the critical coagulation concentration; F represents the Faraday constant; and ε represents the dielectric constant of the medium. In the case of the charge ratio of the anion and the cation of the used electrolyte being 1:2: When When time; wherein the calculation parameters Computing parameters represents the thickness of the diffusion layer at the critical flocculation concentration.

3. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 1, wherein, The obtaining of the critical coagulation concentration comprises: (1) using dynamic light scattering technology to observe the change of the effective diameter of the micro-nanoparticles in the electrolyte solution with a known electrolyte concentration c0 during the coagulation process, obtaining the change amount D(t) of the effective diameter with time, and obtaining the instantaneous coagulation rate v(t, c0) of the micro-nanoparticles according to the change amount D(t) of the effective diameter with time; (2) The average coagulation rate of the micro- or nanoparticles from the time t = 0 to any time t = t is obtained by the resulting instantaneous coagulation rate v(t, c0) (3) according to the average coagulation rate of the resulting micro- and nanoparticles obtaining the total average coagulation rate of the micro- and nanoparticles from the moment t = 0 to the moment t = t0 The total average coagulation rate of the micro-nanoparticles was determined according to the above (1)-(3) at different electrolyte concentrations c0 The total average coagulation rate of the micro-nanoparticles was determined according to the above (1)-(3) at different electrolyte concentrations c0 The total average coagulation rate of the micro-nanoparticles was determined according to the above (1)-(3) at different electrolyte concentrations c0 -c0 curve, the concentration corresponding to the inflection point between the two inclined sections of the curve is the critical coagulation concentration.

4. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 3, wherein, The instantaneous coagulation rate v(t, c0) of the micro-nanoparticles is obtained by the following formula: Wherein, t represents time.

5. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 4, wherein, Average coagulation rate of micro- and nanoparticles By the following formula:

6. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 5, wherein, The total average coagulation rate of the microparticles By the following formula: Wherein, D(t) and D(0) are the effective diameters of the coagulated micro-nanoparticles at time t and the initial time, respectively.

7. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 1, wherein, The assignment approximation method comprises: A surface potential set under the critical coagulation concentration condition Based on the critical agglomeration concentration and the surface potential, calculate P when the interparticle distance is x. EDL (x) value; according to P EDL The value of (x) is obtained, and P is further obtained. net The values ​​of (x) and Δw are used to calculate the value of Δw. The calculated value of Δw is compared with the value of 0.2kT. If Δw > 0.2kT, the surface potential is reduced. The absolute value of the surface potential is used to recalculate the reduction. The absolute value of Δw is obtained and compared with the value of 0.2kT. The process stops when Δw < 0.2kT. The surface potential in the above process is... Plot the value of t as the x-axis and the obtained Δw as the y-axis, and plot the curve when Δw = 0.2kT. The value is taken as the value of the surface potential to be determined.

8. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 1, wherein, In the case of the charge ratio of the anion and the cation of the used electrolyte being 1:1: the surface charge density σ0 of the micro-nanoparticles is obtained by the following formula: where CCC represents the critical coagulation concentration, ε v represents the vacuum permittivity; D represents the relative permittivity of the medium; R is the gas constant; β represents the effective charge coefficient of the counter-ion; e represents the natural exponential; and e0 represents the elementary charge.

9. The method of determining the surface charge density of a microparticle or nanoparticle according to claim 1, wherein, In the case of the charge ratio of the anion and the cation of the used electrolyte being 1:2: the surface charge density σ0 of the micro-nanoparticles is obtained by the following formula: where CCC represents the critical coagulation concentration, ε v wherein ε represents the vacuum permittivity; D represents the relative permittivity of the medium; R is the gas constant; β represents the effective charge coefficient of the counter-ion; e represents the natural exponential; and e0 represents the elementary charge.

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