Method and apparatus for obtaining nanoscale chemical heterogeneity of a solid surface

Abstract

The application provides a method and device for obtaining nanometer chemical heterogeneity of a solid surface, and relates to the technical field of solid surface chemistry. The method comprises the following steps: correcting the total interaction force between a colloid and a solid surface based on a coincidence area fraction to obtain a corrected total interaction force; determining a primary minimum value according to the corrected total interaction force; determining a chemical heterogeneity distribution function according to the corrected total interaction force, the primary minimum value and a measured value of an actual adhesion force between the colloid and the solid surface; and inversely obtaining the chemical heterogeneity of the solid surface according to the chemical heterogeneity distribution function. The device executes the above method. The method and device for obtaining nanometer chemical heterogeneity of a solid surface provided in the embodiments of the application can further determine the variation trend of the chemical heterogeneity of the solid surface with the salinity and temperature through the chemical heterogeneity of the solid surface, and help to improve the accuracy of information prediction.

Description

Technical Field

[0001] This invention relates to the field of solid surface chemistry, and more specifically to a method and apparatus for obtaining nano-chemical heterogeneity of solid surfaces. Background Technology

[0002] The DLVO theory provides a theoretical tool for predicting interactions between solid surfaces, but many experimental results contradict its predictions when qualitatively explaining the adhesion and desorption of colloids on solid surfaces. An energy barrier arises when the electric double-layer repulsive interaction between the colloid and the surface dominates (the so-called "unfavorable condition"), hindering colloid adhesion. However, reports frequently exist of colloids adhering to solid surfaces even under unfavorable conditions. This discrepancy is attributed to the oversimplified assumptions of the DLVO theory, namely, the assumption of perfectly smooth and uniformly charged solid surfaces.

[0003] In fact, natural surfaces exhibit a certain degree of roughness at the nanoscale, and the surface charge of solids also exhibits chemical heterogeneity. The physical heterogeneity of solid surfaces can be directly measured using atomic force microscopy. When the roughness is less than 1 nm, its influence can be ignored, and it is unaffected by temperature and salinity. With certain techniques, the influence of physical heterogeneity can be eliminated. However, the chemical heterogeneity of solid surface charge is affected by changes in temperature and salinity, and its impact on the interactions between solid surfaces is more complex and significant. Furthermore, quantitative characterization methods for the chemical heterogeneity of solid surfaces have been lacking. Summary of the Invention

[0004] To address the problems in the prior art, embodiments of the present invention provide a method and apparatus for obtaining nano-chemical heterogeneity of solid surfaces, which can at least partially solve the problems existing in the prior art.

[0005] On one hand, this invention proposes a method for obtaining nano-chemical heterogeneity of solid surfaces, comprising:

[0006] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0007] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0008] The primary minimum is determined based on the corrected total interaction force;

[0009] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0010] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0011] Determining the overlapping area fraction includes:

[0012] Identify chemically heterogeneous regions in the interaction region between colloids and solid surfaces;

[0013] The ratio of the area of ​​the chemically heterogeneous region to the area of ​​the interacting region is taken as the overlapping area fraction.

[0014] The total interaction force includes the electrostatic interaction force of the electric double layer; correspondingly, the correction of the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain the corrected total interaction force includes:

[0015] The difference between 1 and the overlapping area fraction is used as the first correction term for the electrostatic interaction force of the double layer, and the overlapping area fraction is used as the second correction term for the electrostatic interaction force of the double layer between the heterogeneous regions of the colloid and the solid surface.

[0016] The total interaction force between the colloid and the solid surface is corrected based on the first correction term and the second correction term to obtain the corrected total interaction force.

[0017] The step of determining the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface includes:

[0018] The primary minimum value is substituted into the calculation expression corresponding to the corrected total interaction force for calculation, and the actual adhesion force measurement value is used as a known quantity to obtain the chemical heterogeneity distribution function.

[0019] The step of obtaining the chemical heterogeneity of the solid surface by inversion based on the chemical heterogeneity distribution function includes:

[0020] The Zeta potential and area of ​​the fixed surface chemical heterogeneity region are obtained by inversion based on the chemical heterogeneity distribution function, and the chemical heterogeneity of the solid surface is determined based on the Zeta potential and the area.

[0021] The method for obtaining nano-chemical heterogeneity of solid surfaces further includes:

[0022] The trend of the chemical heterogeneity of the solid surface with salinity and temperature is determined based on the chemical heterogeneity of the solid surface.

[0023] The method for obtaining nano-chemical heterogeneity of solid surfaces further includes:

[0024] Based on the trend of the chemical heterogeneity of the solid surface changing with salinity and temperature, the transport information of bacteria and colloids in the groundwater environment is predicted.

[0025] On one hand, the present invention proposes an apparatus for obtaining nano-chemical heterogeneity of solid surfaces, comprising:

[0026] The correction unit is used to correct the total interaction force between the colloid and the solid surface based on the overlapping area fraction, so as to obtain the corrected total interaction force.

[0027] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0028] A computational unit is used to determine the primary minimum based on the corrected total interaction force;

[0029] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0030] The acquisition unit is used to determine the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value, and the measured value of the actual adhesion force between the colloid and the solid surface, and to invert the chemical heterogeneity of the solid surface based on the chemical heterogeneity distribution function.

[0031] In another aspect, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the following method:

[0032] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0033] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0034] The primary minimum is determined based on the corrected total interaction force;

[0035] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0036] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0037] This invention provides a computer-readable storage medium, comprising:

[0038] The computer-readable storage medium stores a computer program that, when executed by a processor, implements the following method:

[0039] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0040] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0041] The primary minimum is determined based on the corrected total interaction force;

[0042] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0043] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0044] The method and apparatus for obtaining nanoscale chemical heterogeneity of solid surfaces provided in this invention corrects the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain a corrected total interaction force. The total interaction force between the colloid and the solid surface reflects changes in salinity and temperature. A primary minimum is determined based on the corrected total interaction force, where the primary minimum is the primary minimum of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity. A chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion using the chemical heterogeneity distribution function. The chemical heterogeneity of the solid surface can be further used to determine the trend of its chemical heterogeneity with salinity and temperature, which helps improve the accuracy of information prediction. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0046] Figure 1This is a schematic flowchart of a method for obtaining nano-chemical heterogeneity of solid surfaces according to an embodiment of the present invention.

[0047] Figure 2 This is a flowchart illustrating a method for obtaining nano-chemical heterogeneity of solid surfaces according to another embodiment of the present invention.

[0048] Figure 3 This is a flowchart illustrating a method for obtaining nano-chemical heterogeneity of solid surfaces according to another embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of the Zeta potential and area effect of a fixed surface chemical heterogeneity region provided in an embodiment of the present invention.

[0050] Figure 5 This is a schematic diagram of the Zeta potential and area effect of a fixed surface chemical heterogeneity region provided in another embodiment of the present invention.

[0051] Figure 6 This is a schematic diagram of the device for obtaining nano-chemical heterogeneity of solid surfaces provided in an embodiment of the present invention.

[0052] Figure 7 This is a schematic diagram of the physical structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0054] Figure 1 This is a schematic flowchart of a method for obtaining nano-chemical heterogeneity of solid surfaces according to an embodiment of the present invention, as shown below. Figure 1 As shown in the embodiments of the present invention, the method for obtaining nano-chemical heterogeneity of a solid surface includes:

[0055] Step S1: Correct the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain the corrected total interaction force;

[0056] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0057] Step S2: Determine the primary minimum based on the corrected total interaction force;

[0058] The primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface, taking into account chemical heterogeneity.

[0059] Step S3: Determine the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value, and the measured value of the actual adhesion force between the colloid and the solid surface. Obtain the chemical heterogeneity of the solid surface by inversion based on the chemical heterogeneity distribution function.

[0060] In step S1 above, the device corrects the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain the corrected total interaction force.

[0061] The total interaction force between the colloid and the solid surface reflects changes in salinity and temperature. The apparatus can be a computer device, such as a server, that performs the method. The acquisition, storage, use, and processing of data in this application all comply with relevant regulations.

[0062] Before step S1, the total interaction force between the colloid and the solid surface can be obtained first, such as... Figure 2 As shown, the specific explanation is as follows:

[0063] Establish the relationship between van der Waals potential energy and temperature; van der Waals potential energy V LW The calculation formula is:

[0064]

[0065] Where, r s λ is the colloidal radius; λ = 100 nm is the interaction characteristic length; h is the separation distance between the colloid and the solid surface; A 132 This is the Hamaker constant.

[0066] The relationship between van der Waals potential energy and temperature is characterized by establishing the relationships between Hamaker constant, dielectric constant, and refractive index and temperature.

[0067] Hamaker constant A 132 The Hamaker constant A is established due to the influence of temperature. 132 The relationship with temperature T is as follows:

[0068]

[0069] Where ε is the static dielectric constant; n is the refractive index; subscripts 1, 2, and 3 represent colloid, solid surface, and NaCl solution, respectively; h w h is Planck's constant. w =6.62607015×10 -34 J·s;v e It is a constant adsorption frequency, ve =3.0×10 15 s -1 k B It is the Boltzmann constant.

[0070] Furthermore, the dielectric constant and refractive index are affected by temperature, and the relationships between the dielectric constant and refractive index and temperature T are established respectively: ε1(T), ε2(T), ε3(T), n1(T), n2(T) and n3(T).

[0071] In summary, the van der Waals potential V is established. LW Formulas related to temperature T:

[0072]

[0073] in:

[0074]

[0075] Establish the relationship between the electrostatic interaction potential energy of the electric double layer and temperature; electrostatic interaction potential energy of the electric double layer V EDL The calculation formula is:

[0076]

[0077] Where κ is the inverse Debye length, γ is the approximate Zeta potential, and subscripts 1 and 2 represent the colloid and solid surfaces, respectively; n ∞ It refers to the bulk ion concentration.

[0078] The calculation formula shows that the electrostatic interaction potential energy V of the double electric layer is... EDL The electrostatic interaction of the double layer is affected by temperature. Further characterization of this interaction with temperature is achieved by establishing relationships between the inverse Debye length κ, the approximate Zeta potential γ, and the Zeta potential ζ with temperature and salinity. The inverse Debye length κ is determined by both temperature and salinity. The relationship between κ and temperature T and salinity is established as follows:

[0079]

[0080] Where q is the elementary charge, C is the salinity, and N is the salinity. A ε is Avogadro's constant, ε0 is the vacuum medium constant, ε3 is as explained above, and k B Here, T is the Boltzmann constant, and T is the temperature.

[0081] The approximate Zeta potential γ is determined by both temperature T and Zeta potential ζ. The relationship between γ and temperature T and Zeta potential ζ is established as follows:

[0082]

[0083] Where z is the valence of the electrolyte solution and q is the elementary charge.

[0084] Furthermore, since ζ is affected by temperature and salinity, we establish the relationship between ζ and temperature T and salinity C: ζ1(T,C) and ζ2(T,C), where the meanings of 1 and 2 can be found in the above explanation.

[0085] In summary, the electrostatic interaction potential energy V of the double electric layer is established. EDL The formulas for calculating temperature T and salinity C are as follows:

[0086]

[0087] in

[0088] Establish the relationship between Born potential energy and temperature; Born potential energy V B The calculation formula is:

[0089]

[0090] Where, σ c =0.5nm is the collision diameter. A 132 Let A be the Hamaker constant. From the above, we know that the Hamaker constant A... 132 The relationship between temperature T and temperature.

[0091] In summary, the Born potential V is established. B The formula for calculating temperature T is as follows:

[0092]

[0093] in:

[0094]

[0095] Establish the relationship between hydration potential energy and salinity C; hydration potential energy V H The calculation formula is:

[0096]

[0097] Where, E0 = N A C h Cλ h , which is the maximum hydration repulsion energy per unit area, J / m 2 It is related to salinity (C); N A C is Avogadro's constant; h It is a proportionality constant, defined as the "hydration constant", 1.6 × 10⁻⁶. -20 J;λ h 0.6 nm represents the characteristic decay length, and h is the separation distance between the colloid and the solid surface.

[0098] In summary, the hydration potential V is established. H The formula for calculating salinity C is:

[0099]

[0100] In summary, the calculation model for the total interaction potential energy between colloids and solid surfaces, which is related to temperature and salinity, is as follows:

[0101] V XDLVO (T,C)=V LW (T)+V EDL (T,C)+V B (T)+V H (C)

[0102] The model for calculating the total interaction potential energy between colloids and solid surfaces, which is related to temperature and salinity, is differentiated with respect to h. The total interaction force F between the colloid and the solid surface is obtained. XDLVO Calculation models related to temperature and salinity:

[0103]

[0104] Determining the overlapping area fraction includes:

[0105] Identify chemically heterogeneous regions in the interaction region between colloids and solid surfaces;

[0106] The ratio of the area of ​​the chemically heterogeneous region to the area of ​​the interacting region is taken as the overlapping area fraction.

[0107] in, The area of ​​the chemically heterogeneous region. The area of ​​the interaction region.

[0108] The total interaction force includes the electrostatic interaction force of the electric double layer; correspondingly, the correction of the total interaction force between the colloid and the solid surface based on the overlap area fraction to obtain the corrected total interaction force includes:

[0109] The difference between 1 and the overlapping area fraction is used as the first correction term for the electrostatic interaction force of the double layer, and the overlapping area fraction is used as the second correction term for the electrostatic interaction force of the double layer between the heterogeneous regions of the colloid and the solid surface.

[0110] The total interaction force between the colloid and the solid surface is corrected based on the first correction term and the second correction term to obtain the corrected total interaction force.

[0111] like Figure 3 As shown, a corrected calculation model for the total interaction force considering the chemical heterogeneity of the solid surface is established. The basic assumption of this corrected calculation model is that the solid surface contains chemically heterogeneous regions. When the interaction region (R) between the colloid and the solid surface... ZOI When a region coincides with a chemically heterogeneous region, let the fraction of the overlapping area be f. i There is an electrostatic interaction force between the colloid and the heterogeneous regions of the solid surface.

[0112] Considering the chemical heterogeneity of the solid surface, a modified calculation model for the interaction forces considering the chemical heterogeneity of the solid surface is established:

[0113]

[0114] Further results were obtained:

[0115]

[0116] Further results were obtained:

[0117] F HXDLVO (T,C)=F XDLVO (T,C)-f i F EDL (T,C)+F EDL (T,C)

[0118] In step S2 above, the device determines the primary minimum based on the corrected total interaction force;

[0119] The primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface, taking into account chemical heterogeneity.

[0120] The external force applied by the cantilever of the atomic force microscope (AFM) pushes the colloids on the probe through the energy barrier, enabling them to reach the vicinity of the primary minimum h1.

[0121] In step S3 above, the device determines the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value, and the measured value of the actual adhesion force between the colloid and the solid surface, and obtains the chemical heterogeneity of the solid surface by inversion based on the chemical heterogeneity distribution function.

[0122] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface, including:

[0123] The primary minimum value is substituted into the calculation expression corresponding to the corrected total interaction force for calculation, and the actual adhesion force measurement value is used as a known quantity to obtain the chemical heterogeneity distribution function.

[0124] The interaction force profile (F) between the colloid and the solid surface (considering chemical heterogeneity) HXDLVO Substitute the primary minimum value of -h) into the calculation expression corresponding to the corrected total interaction force, and set the calculation result of the expression to be equal to the actual measured value of adhesion force F. ad (T,C), that is:

[0125]

[0126] Further results were obtained:

[0127]

[0128] in

[0129]

[0130] The determination of the chemical heterogeneity distribution function is explained below:

[0131] Referring to the steps above, the explanation is as follows:

[0132]

[0133] Multiply both sides simultaneously get:

[0134]

[0135] Depend on and Further results were obtained:

[0136]

[0137] in,

[0138] Furthermore, the distribution function J(S,ζ) of solid surface chemical heterogeneity related to temperature and salinity is obtained:

[0139]

[0140] Further results were obtained:

[0141]

[0142] in,

[0143] The process of inverting the chemical heterogeneity of a solid surface based on the chemical heterogeneity distribution function includes:

[0144] The Zeta potential and area of ​​the fixed surface chemical heterogeneity region are obtained by inversion based on the chemical heterogeneity distribution function, and the chemical heterogeneity of the solid surface is determined based on the Zeta potential and the area.

[0145] The method for obtaining nano-chemical heterogeneity of solid surfaces further includes:

[0146] The trend of the chemical heterogeneity of the solid surface with salinity and temperature is determined based on the chemical heterogeneity of the solid surface.

[0147] The measured value of the actual adhesion force F between a known colloid and a solid surface under conditions of temperature T and salinity C. ad (T,C), based on the solid surface chemical heterogeneity distribution function J(S,ζ), the solid surface chemical heterogeneity, i.e. the Zeta potential ζ and area S of the surface chemical heterogeneity region, are obtained.

[0148] Furthermore, given a series of actual adhesion force measurements under temperature T and salinity C conditions, the trend of solid surface chemical heterogeneity with salinity and temperature can be obtained.

[0149] The method for obtaining nano-chemical heterogeneity of solid surfaces further includes:

[0150] Based on the trend of solid surface chemical heterogeneity with salinity and temperature, the migration information of bacteria and colloids in groundwater environments is predicted. That is, this method can be applied to scenarios involving the prediction of bacterial and colloid migration. The method for obtaining nanoscale chemical heterogeneity of solid surfaces provided in this embodiment of the invention is further described below:

[0151] Example 1:

[0152] Taking 10μm polystyrene colloidal microspheres, silica surface, and NaCl salt solution as examples, this paper illustrates how to obtain the chemical heterogeneity of silica solid surface and its trend with salinity and temperature by inverting the adhesion force values ​​between colloidal microspheres and silica surface under different salinities and temperatures.

[0153] The first step is to establish a calculation model for the total interaction force between polystyrene colloidal microspheres and the silica solid surface, which is related to salinity and temperature. This specifically includes:

[0154] I. Establishing the van der Waals potential energy V LW The formula for calculating temperature T is as follows:

[0155]

[0156] Where A 132 (T):

[0157]

[0158] Establish the dielectric constant ε1 and refractive index n1 of polystyrene colloid, and the dielectric constant ε2 and refractive index n1 of silicon dioxide, respectively.

[0159] The relationships between the dielectric constant ε3 and refractive index n3 of n2 and NaCl solutions and temperature T are as follows:

[0160] ε1=0.0004533T 2 -0.0268T+2.8567

[0161] ε2 = 3.8

[0162] ε3=4288T -0.5403 -119.1

[0163] n1 = 1.5523 - 1.7336 × 10 -4 T

[0164] n² = 1.382 × 10 -8 T 2 +8.253×10 -7 T+1.456

[0165] n3 = -2.64 × 10 -12 T 3.851 +1.341

[0166] II. Establishing the electrostatic interaction potential energy V of the double electric layer EDL The formulas for calculating temperature T and salinity C are as follows:

[0167]

[0168] in

[0169] The relationships between the Zeta potential ζ1 of polystyrene colloidal microspheres and the Zeta potential ζ2 of silica and temperature T were established respectively:

[0170] ζ1(T)=[0.01712(T-298.15)+1][4.1692log(C)-23.233] / 1000

[0171] ζ2(T)=[0.01712(T-298.15)+1][9.5842log(C)-1.9142] / 1000

[0172] III. Establishing the Born potential V B The formula for calculating temperature T is as follows:

[0173]

[0174] IV. Establishing the hydration potential energy V H The formula for calculating salinity C is:

[0175]

[0176] Where E0(C) = N A C h Cλ h .

[0177] In summary, a calculation model is established for the interaction potential energy between the colloid and the silica solid surface, which is related to temperature and salinity:

[0178] V XDLVO (T,C)=V LW (T)+V EDL (T,C)+V B (T)+V H (C)

[0179] The interaction potential energy between the colloid and the solid surface is calculated using a model that relates to temperature and salinity, and the separation distance is differentiated to obtain the interaction force F between the colloid and the solid surface. XDLVO Calculation models related to temperature and salinity:

[0180]

[0181] The second step is to establish a corrected calculation model for the total interaction force considering the chemical heterogeneity of the solid surface. The basic assumption of this corrected calculation model is that the solid surface contains chemically heterogeneous regions. When the interaction region (R) between the colloid and the solid surface... ZOI When a region coincides with a chemically heterogeneous region, let the fraction of the overlapping area be f. i There is an electrostatic interaction force between the colloid and the heterogeneous regions of the solid surface.

[0182] Considering the chemical heterogeneity of the solid surface, a modified calculation model for the interaction forces considering the chemical heterogeneity of the solid surface is established:

[0183]

[0184] Among them, f i The interaction region between the colloid and the solid surface Chemical heterogeneity region Area fraction occupied:

[0185] Further results were obtained:

[0186]

[0187] Further results were obtained:

[0188] F HXDLVO (T,C)=F XDLVO (T,C)-f i F EDL (T,C)+F HEDL (T,C)

[0189] Thirdly, the external force applied by the AFM cantilever pushes the colloids on the probe through the energy barrier, allowing them to reach near the primary minimum. The force profile (F) between the colloid and the solid surface (considering chemical heterogeneity) is then calculated. HXDLVO The primary minimum value of -h) is used as the predicted measurement value of the actual adhesion force between the colloid and the solid surface, F. ad (T,C), that is:

[0190]

[0191] Further results were obtained:

[0192]

[0193] in

[0194]

[0195] Further results were obtained:

[0196]

[0197] Multiply both sides simultaneously get:

[0198]

[0199] Depend on and Further results were obtained:

[0200]

[0201] in,

[0202] The solid surface chemical heterogeneity distribution function J(S,ζ) in relation to temperature T and salinity C is obtained:

[0203]

[0204] Further results were obtained:

[0205]

[0206] in,

[0207] The fourth step involves measuring the adhesion force F between the colloid and the solid surface under known conditions of temperature T and salinity C. ad (T,C), based on the solid surface chemical heterogeneity distribution function J(S,ζ), the solid surface chemical heterogeneity, i.e. the Zeta potential ζ and area S of the surface chemical heterogeneity region, are obtained.

[0208] (1) Under the experimental conditions of temperature T = 298.15 K and C = 0.001 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (298.15, 0.001) = 40.12nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0209]

[0210] (2) Under the experimental conditions of temperature T = 298.15 K and C = 0.005 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (298.15, 0.005) = 34.40nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0211]

[0212] (3) Under the experimental conditions of temperature T = 298.15 K and C = 0.01 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (298.15, 0.01) = 31.00nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0213]

[0214] (4) Under the experimental conditions of temperature T = 298.15 K and C = 0.05 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (298.15, 0.05) = 24.50nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0215]

[0216] (5) Under the experimental conditions of temperature T = 298.15 K and C = 0.1 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (318.15,0.1)=20.8nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0217]

[0218] Example 2:

[0219] The steps are the same as above. The adhesion force between polystyrene colloidal microspheres and silica solid surface at different temperatures is measured using AFM. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), the solid surface chemical heterogeneity at different temperatures is obtained, that is, the Zeta potential ζ and area S of the surface chemical heterogeneity region.

[0220] (1) Under the experimental conditions of temperature T = 303.15 K and C = 0.01 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (303.15, 0.01) = 28.1nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0221]

[0222] (2) Under the experimental conditions of temperature T = 308.15 K and C = 0.01 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad(308.15, 0.01) = 24.6nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f... i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0223]

[0224] (3) Under the experimental conditions of temperature T = 313.15 K and C = 0.01 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (313.15,0.01)=21.2nN. Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0225]

[0226] (4) Under the experimental conditions of temperature T = 318.15 K and C = 0.01 M, the adhesion force between polystyrene colloidal microspheres and the silica solid surface was measured by AFM. ad (318.15,0.01)=18nN.

[0227] Based on the solid surface chemical heterogeneity distribution function J(S,ζ), let f i When = 0.1, the chemical heterogeneity of the silica solid surface can be obtained, that is, the Zeta potential and area of ​​the chemically heterogeneous region of the surface:

[0228]

[0229] Example 3:

[0230] Based on the adhesion force measurement data under a series of temperature T and salinity C conditions in Examples 1 and 2, the variation trend of solid surface chemical heterogeneity with salinity and temperature can be obtained. The variation trend of silica solid surface chemical heterogeneity with salinity and temperature is shown in Table 1 (trend of solid surface chemical heterogeneity with salinity at 298.15 K) and Table 2 (trend of solid surface chemical heterogeneity with temperature at 0.01 M). Figure 4 and Figure 5 As shown. Among them, Figure 4 and Figure 5 The orange curve in the image represents ζ. Figure 4 and Figure 5 The blue curve in the diagram represents S.

[0231] From Table 1, Table 2, Figure 4 and Figure 5 It can be seen that the Zeta potential of the chemically heterogeneous region on the surface of silica solid is highly sensitive to temperature and salinity, and the Zeta potential decreases significantly with increasing salinity and temperature; the area of ​​the chemically heterogeneous region is highly sensitive to changes in salinity, and decreases significantly with increasing salinity; the sensitivity to temperature changes is weak, and decreases slightly with increasing temperature.

[0232] Table 1

[0233]

[0234] Table 2

[0235]

[0236] The method for obtaining nanoscale chemical heterogeneity of solid surfaces provided in this invention corrects the total interaction force between the colloid and the solid surface based on the overlapping area fraction, obtaining a corrected total interaction force. The total interaction force between the colloid and the solid surface reflects changes in salinity and temperature. A primary minimum is determined based on the corrected total interaction force, where the primary minimum is the primary minimum of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity. A chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then inverted based on the chemical heterogeneity distribution function. The chemical heterogeneity of the solid surface can be further used to determine the trend of its chemical heterogeneity with salinity and temperature, which helps improve the accuracy of information prediction.

[0237] Further, determining the overlapping area fraction includes:

[0238] Determine the chemically heterogeneous region in the interaction region between the colloid and the solid surface; the above examples can be referred to for illustration, and will not be repeated here.

[0239] The ratio of the area of ​​the chemically heterogeneous region to the area of ​​the interacting region is taken as the overlapping area fraction. This can be referred to the above embodiments for explanation, and will not be repeated here.

[0240] Furthermore, the total interaction force includes the electrostatic interaction force of the electric double layer; correspondingly, the correction of the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain the corrected total interaction force includes:

[0241] The difference between 1 and the overlapping area fraction is used as the first correction term for the electrostatic interaction force of the electric double layer, and the overlapping area fraction is used as the second correction term for the electrostatic interaction force of the electric double layer between the heterogeneous regions of the colloid and the solid surface; the above embodiments can be referred to for explanation, and will not be repeated here.

[0242] The total interaction force between the colloid and the solid surface is corrected based on the first and second correction terms to obtain the corrected total interaction force. This can be referred to the above embodiments for further explanation, and will not be repeated here.

[0243] Further, determining the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface includes:

[0244] The primary minimum value is substituted into the calculation expression corresponding to the corrected total interaction force for calculation, and the actual adhesion force measurement value is used as a known quantity to obtain the chemical heterogeneity distribution function. This can be referred to the above embodiments for explanation, and will not be repeated here.

[0245] Further, the step of inverting the chemical heterogeneity of the solid surface based on the chemical heterogeneity distribution function includes:

[0246] The Zeta potential and area of ​​the fixed surface chemical heterogeneity region are obtained by inversion based on the chemical heterogeneity distribution function, and the chemical heterogeneity of the solid surface is determined based on the Zeta potential and the area. This can be referred to the above embodiments for explanation, and will not be repeated here.

[0247] Furthermore, the method for obtaining nano-chemical heterogeneity of solid surfaces also includes:

[0248] The trend of the chemical heterogeneity of the solid surface with salinity and temperature is determined based on the aforementioned chemical heterogeneity. This can be referred to the above embodiments for explanation, and will not be repeated here.

[0249] Furthermore, the method for obtaining nano-chemical heterogeneity of solid surfaces also includes:

[0250] Based on the trend of the chemical heterogeneity of the solid surface changing with salinity and temperature, the transport information of bacteria and colloids in the groundwater environment is predicted. This can be referred to the above embodiments for explanation, and will not be repeated here.

[0251] Figure 6 This is a schematic diagram of the device for obtaining nano-chemical heterogeneity of solid surfaces according to an embodiment of the present invention, as shown below. Figure 6 As shown, the apparatus for obtaining nano-chemical heterogeneity of solid surfaces provided in this embodiment of the invention includes a correction unit 601, a calculation unit 602, and an acquisition unit 603, wherein:

[0252] The correction unit 601 is used to correct the total interaction force between the colloid and the solid surface based on the overlapping area fraction to obtain the corrected total interaction force; wherein, the total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature; the calculation unit 602 is used to determine the primary minimum value based on the corrected total interaction force; wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity; the acquisition unit 603 is used to determine the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value and the measured value of the actual adhesion force between the colloid and the solid surface, and to invert the chemical heterogeneity of the solid surface based on the chemical heterogeneity distribution function.

[0253] Specifically, the correction unit 601 in the device is used to correct the total interaction force between the colloid and the solid surface based on the overlapping area fraction, to obtain the corrected total interaction force; wherein, the total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature; the calculation unit 602 is used to determine the primary minimum value based on the corrected total interaction force; wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity; the acquisition unit 603 is used to determine the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value and the measured value of the actual adhesion force between the colloid and the solid surface, and to invert the chemical heterogeneity of the solid surface based on the chemical heterogeneity distribution function.

[0254] The apparatus for obtaining nanoscale chemical heterogeneity of solid surfaces provided in this invention corrects the total interaction force between the colloid and the solid surface based on the overlapping area fraction, obtaining a corrected total interaction force. The total interaction force between the colloid and the solid surface reflects changes in salinity and temperature. A primary minimum is determined based on the corrected total interaction force, where the primary minimum is the primary minimum of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity. A chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then inverted based on the chemical heterogeneity distribution function. The chemical heterogeneity of the solid surface can be further determined by analyzing the chemical heterogeneity of the solid surface, which changes with salinity and temperature, thus improving the accuracy of information prediction.

[0255] The embodiments of the present invention provide an apparatus for obtaining nano-chemical heterogeneity of solid surfaces, which can be used to execute the processing flow of the above-described method embodiments. Its function will not be repeated here, but can be referred to the detailed description of the above-described method embodiments.

[0256] Figure 7This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention, such as... Figure 7 As shown, the electronic device includes: a processor 701, a memory 702, and a bus 703;

[0257] The processor 701 and the memory 702 communicate with each other via the bus 703.

[0258] The processor 701 is used to call program instructions in the memory 702:

[0259] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0260] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0261] The primary minimum is determined based on the corrected total interaction force;

[0262] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0263] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0264] This embodiment discloses a computer program product, which includes a computer program that, when executed by a processor, implements the following method:

[0265] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0266] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0267] The primary minimum is determined based on the corrected total interaction force;

[0268] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0269] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0270] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the following method:

[0271] The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force.

[0272] The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature.

[0273] The primary minimum is determined based on the corrected total interaction force;

[0274] Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity;

[0275] The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function.

[0276] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0277] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0278] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0279] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0280] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0281] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for obtaining nanoscale chemical heterogeneity of solid surfaces, characterized in that, include: The total interaction force between the colloid and the solid surface is corrected based on the overlapping area fraction to obtain the corrected total interaction force. The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature. The primary minimum is determined based on the corrected total interaction force; Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity; The chemical heterogeneity distribution function is determined based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface. The chemical heterogeneity of the solid surface is then obtained by inversion based on the chemical heterogeneity distribution function. Determining the overlapping area fraction includes: Identify chemically heterogeneous regions in the interaction region between colloids and solid surfaces; The ratio of the area of ​​the chemically heterogeneous region to the area of ​​the interacting region is taken as the overlapping area fraction. The total interaction force includes the electrostatic interaction force of the electric double layer; correspondingly, the correction of the total interaction force between the colloid and the solid surface based on the overlap area fraction to obtain the corrected total interaction force includes: The difference between 1 and the overlapping area fraction is used as the first correction term for the electrostatic interaction force of the double layer, and the overlapping area fraction is used as the second correction term for the electrostatic interaction force of the double layer between the heterogeneous regions of the colloid and the solid surface. The total interaction force between the colloid and the solid surface is corrected according to the first correction term and the second correction term to obtain the corrected total interaction force. The determination of the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface includes: The primary minimum value is substituted into the calculation expression corresponding to the corrected total interaction force for calculation, and the actual adhesion force measurement value is used as a known quantity to obtain the chemical heterogeneity distribution function; The process of inverting the chemical heterogeneity of a solid surface based on the chemical heterogeneity distribution function includes: The Zeta potential and area of ​​the fixed surface chemical heterogeneity region are obtained by inversion based on the chemical heterogeneity distribution function, and the chemical heterogeneity of the solid surface is determined based on the Zeta potential and the area. The chemical heterogeneity distribution function J(S, )for: in, Let be the area of ​​the chemically heterogeneous region, T be the temperature, C be the salinity, and z be the valence of the electrolyte solution. The zeta potential represents the region of surface chemical heterogeneity. For Boltzmann constant, The zeta potential represents the chemically heterogeneous region of a solid surface. This is the actual measured adhesion force value. This represents the total interaction force between the colloid and the solid surface. This refers to the bulk ion concentration. The colloidal surface has an approximate Zeta potential. It is the reverse Debye length. This represents the separation distance between the colloid and the solid surface corresponding to the primary minimum value.

2. The method for obtaining nano-chemical heterogeneity of solid surfaces according to claim 1, characterized in that, The method for obtaining nano-chemical heterogeneity of solid surfaces further includes: The trend of the chemical heterogeneity of the solid surface with salinity and temperature is determined based on the chemical heterogeneity of the solid surface.

3. The method for obtaining nano-chemical heterogeneity of solid surfaces according to claim 2, characterized in that, The method for obtaining nano-chemical heterogeneity of solid surfaces further includes: Based on the trend of the chemical heterogeneity of the solid surface changing with salinity and temperature, the transport information of bacteria and colloids in the groundwater environment is predicted.

4. A device for obtaining nanoscale chemical heterogeneity of solid surfaces, characterized in that, include: The correction unit is used to correct the total interaction force between the colloid and the solid surface based on the overlapping area fraction, so as to obtain the corrected total interaction force. The total interaction force between the colloid and the solid surface can reflect changes in salinity and temperature. A computational unit is used to determine the primary minimum based on the corrected total interaction force; Wherein, the primary minimum value is the primary minimum value of the interaction force profile between the colloid and the solid surface considering chemical heterogeneity; The acquisition unit is used to determine the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum value, and the measured value of the actual adhesion force between the colloid and the solid surface, and to obtain the chemical heterogeneity of the solid surface by inversion based on the chemical heterogeneity distribution function. Determining the overlapping area fraction includes: Identify chemically heterogeneous regions in the interaction region between colloids and solid surfaces; The ratio of the area of ​​the chemically heterogeneous region to the area of ​​the interacting region is taken as the overlapping area fraction. The total interaction force includes the electrostatic interaction force of the electric double layer; correspondingly, the correction of the total interaction force between the colloid and the solid surface based on the overlap area fraction to obtain the corrected total interaction force includes: The difference between 1 and the overlapping area fraction is used as the first correction term for the electrostatic interaction force of the double layer, and the overlapping area fraction is used as the second correction term for the electrostatic interaction force of the double layer between the heterogeneous regions of the colloid and the solid surface. The total interaction force between the colloid and the solid surface is corrected according to the first correction term and the second correction term to obtain the corrected total interaction force. The determination of the chemical heterogeneity distribution function based on the corrected total interaction force, the primary minimum, and the measured actual adhesion force between the colloid and the solid surface includes: The primary minimum value is substituted into the calculation expression corresponding to the corrected total interaction force for calculation, and the actual adhesion force measurement value is used as a known quantity to obtain the chemical heterogeneity distribution function; The process of inverting the chemical heterogeneity of a solid surface based on the chemical heterogeneity distribution function includes: The Zeta potential and area of ​​the fixed surface chemical heterogeneity region are obtained by inversion based on the chemical heterogeneity distribution function, and the chemical heterogeneity of the solid surface is determined based on the Zeta potential and the area. The chemical heterogeneity distribution function J(S, )for: in, Let be the area of ​​the chemically heterogeneous region, T be the temperature, C be the salinity, and z be the valence of the electrolyte solution. The zeta potential represents the region of surface chemical heterogeneity. For Boltzmann constant, The zeta potential represents the chemically heterogeneous region of a solid surface. This is the actual measured adhesion force value. This represents the total interaction force between the colloid and the solid surface. This refers to the bulk ion concentration. The colloidal surface has an approximate Zeta potential. It is the reverse Debye length. This represents the separation distance between the colloid and the solid surface corresponding to the primary minimum value.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 3.

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