A method for determining the upper limit of the Guinier approximation analysis for polydisperse systems

Abstract

The present invention provides a method for determining the upper limit of the Ginyer approximate analysis of a polydisperse system, comprising: taking the logarithm of the scattering intensity I corresponding to different scattering vectors q of SAXS, and drawing a lnI~q curve; calculating the first-order derivative dlnI / dq according to the lnI~q curve, and reading out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region, marked as q1; drawing the Ginyer diagram lnI~q 2 , and the Guinier diagram lnI~q 2 The low q region is from the minimum q min 2 To q1 2 A linear fit is performed on the approximate straight line within the range of , and the average gyration radius R of the scatterer is calculated according to the slope after fitting g , R g =(‑3*slope) 1 / 2 The present invention is simple and convenient, can uniquely determine the upper limit of the Guinier approximation, effectively avoids the artificiality of the traditional operation method of directly drawing a straight line, and improves the accuracy of the analysis.

Description

Technical Field

[0001] The invention relates to the field of nanoscale scattering technology, and in particular to a method for determining the upper limit of Guinier approximate analysis of a polydisperse system. Background Art

[0002] Small-angle X-ray scattering (SAXS) is a physical characterization method for studying the structure of materials at the nanoscale. It is widely used in scientific fields such as nanomaterials, porous materials, polymers, and biomacromolecules. Since the scale of SAXS research is larger than the atomic distance, the scattering is considered to be caused by scatterers with a certain electron density, such as nanoscale particles in space, pores in continuous media, or other electron density fluctuations in the nanoscale of the sample. The scattering pattern reflects the spatial relationship of the scatterers and is the average result within a time range. The scattering intensity at each angle is related to the shape, size, and spatial distribution of the scatterers in the system, and is proportional to the difference in electron density between the scatterers and the medium.

[0003] At present, the systems suitable for SAXS research are mainly sparse systems. In this case, the total scattering intensity can be regarded as the superposition of the scattering intensities of each scatterer, so the analysis is relatively simple and mature. For dense systems, due to the concentration effect, interference phenomena will occur, and the corresponding analysis is still relatively difficult. In general, sparse systems can be divided into monodisperse systems and polydisperse systems. The former refers to a system in which the scatterers have the same shape and size; the latter refers to a system in which the scatterers have the same shape but different sizes.

[0004] The famous Guinier law in SAXS is based on a sparse monodisperse system and is widely used to approximate the radius of gyration of scatterers. It is also called the Guinier approximation. According to this method, the change of the scattering intensity I with the scattering vector q can be expressed as lnI~q 2 The core of Guinier's law is: when the scattering vector approaches zero, i.e., q→0, lnI~q 2 It will show an approximate linear relationship. By fitting the linear region, the gyration radius R of the scatterer can be calculated from the slope of the linear region. g , R g =(-3*slope) 1 / 2 , this method is often called the Guinier approximation. The radius of gyration is an important parameter that characterizes the size of the scatterer in the sample. For a scatterer of a specific shape, the characteristic size parameter of the scatterer can be calculated from the radius of gyration. For example, for a spherical scatterer, its radius R and the radius of gyration R g The relationship is: R g =(3 / 5) 1 / 2R. The calculation result of Guinier approximation method is an approximate value, but it is widely favored by researchers because of its simplicity and convenience.

[0005] With the development of SAXS, the application of the Guinier approximation has been extended to sparse polydisperse systems, which are also systems that researchers often encounter in practice. Similar to monodisperse systems, through the Guinier approximation analysis, the approximate mean radius of gyration of the polydisperse system, a basic and important parameter, can be calculated from the slope of the linear segment in the low q region on the Guinier plot. The lower limit of the linear region of the Guinier plot is easier to determine, because theoretically the lower limit is zero, and in practice the minimum measured q value can often be taken. The upper limit of the linear region of the Guinier plot is usually not easy to determine, because the curvature of the Guinier plot in the upper limit region often changes continuously. There are different views on the effective q range of the Guinier approximation. Some follow the view of monodisperse systems and believe that q<1 / R g ; Some believe that q < 1.3 / R g ; others believe that q<1.5 / R g , but there may be an error of 20-30%, and q>2 / R g The post-Guinier approximation is no longer applicable, which shows that there is no unified method to determine the upper limit of the Guinier linear region. In actual analysis, since the average radius of gyration of the system is usually not known in advance, it is somewhat artificial to directly select the linear region on the Guinier diagram. Summary of the invention

[0006] In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a method for determining the upper limit of the Guinier approximation analysis of a polydisperse system.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for determining the upper limit of the Guinier approximation analysis of a polydisperse system, comprising:

[0009] Take the logarithm of the scattering intensity I corresponding to different scattering vectors q of SAXS, and draw the lnI~q curve;

[0010] Calculate the first-order derivative dlnI / dq according to the lnI~q curve, and read out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region, marked as q1;

[0011] Draw the Guinier diagram lnI~q 2 , and the Guinier diagram lnI~q 2 The low q region is from the minimum q min 2 To q1 2 A linear fit is performed on the approximate straight line within the range of , and the average gyration radius R of the scatterer is calculated according to the slope after fitting g , Rg =(-3*slope) 1 / 2 .

[0012] Preferably, calculating the first-order derivative dlnI / dq according to the lnI~q curve comprises:

[0013] If the lnI~q curve is obtained from theoretical simulation, the first-order derivative dlnI / dq is directly calculated;

[0014] If the lnI~q curve is obtained from experimental testing, the lnI~q curve is fitted and then the first-order derivative dlnI / dq is calculated.

[0015] Preferably, the lnI~q curve is fitted by polynomial fitting.

[0016] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0017] The present invention provides a method for determining the upper limit of the Ginyer approximate analysis of a polydisperse system, comprising: taking the logarithm of the scattering intensity I corresponding to different scattering vectors q of SAXS, and drawing a lnI~q curve; calculating the first-order derivative dlnI / dq according to the lnI~q curve, and reading out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region, marked as q1; drawing the Ginyer diagram lnI~q 2 , and the Guinier diagram lnI~q 2 The low q region is from the minimum q min 2 To q1 2 A linear fit is performed on the approximate straight line within the range of , and the average gyration radius R of the scatterer is calculated according to the slope after fitting g , R g =(-3*slope) 1 / 2 The present invention is simple and convenient, can uniquely determine the upper limit of the Guinier approximation, effectively avoids the artificiality of the traditional operation method of directly drawing a straight line, and improves the accuracy of the analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0019] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0020] Figure 2A schematic diagram of the solution steps provided by an embodiment of the present invention;

[0021] Figure 3 A schematic diagram of the lnI~q curve provided in an embodiment of the present invention; wherein Figure 3 (a) is the theoretical scattering curve of the beta-type size distribution of spherical scatterers (shape parameters α = 5, β = 5); Figure 3 (b) is the experimental measurement scattering curve of colloidal solution of silica nanoparticles;

[0022] Figure 4 A schematic diagram of a dlnI / dq~q curve provided in an embodiment of the present invention; wherein Figure 4 (a) is the theoretical scattering curve of the beta-type size distribution of spherical scatterers (shape parameters α = 5, β = 5); Figure 4 (b) is the experimental measurement scattering curve of colloidal solution of silica nanoparticles;

[0023] Figure 5 lnI~q provided by the embodiment of the present invention 2 Curve diagram; Figure 5 (a) Theoretical scattering curve of beta-type size distribution of spherical scatterers (shape parameters α = 5, β = 5); Figure 5 (b) Experimental measurement scattering curve of colloidal solution of silica nanoparticles. DETAILED DESCRIPTION

[0024] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0026] The terms "first", "second", "third" and "fourth" in the specification and claims of the present application and the drawings are used to distinguish different objects rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a series of steps, processes, methods, etc. are not limited to the listed steps, but may optionally include steps that are not listed, or may optionally include other step elements inherent to these processes, methods, products or devices.

[0027] The purpose of the present invention is to provide a method for determining the upper limit of the Guinier approximation analysis of a polydisperse system, which is simple and convenient, can uniquely determine the upper limit of the Guinier approximation, effectively avoids the artificiality of the traditional direct straight line drawing operation method, and improves the accuracy of the analysis.

[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Figure 1 A flow chart of a method provided by an embodiment of the present invention, such as Figure 1 As shown, the present invention provides a method for determining the upper limit of the Gines approximate analysis of a polydisperse system, comprising:

[0030] Step 100: taking the logarithm of the scattering intensity I corresponding to different scattering vectors q of SAXS, and drawing a lnI~q curve;

[0031] Step 200: Calculate the first-order derivative dlnI / dq according to the lnI~q curve, and read out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region, marked as q1;

[0032] Step 300: Draw the Guinier diagram lnI~q 2 , and the Guinier diagram lnI~q 2 The low q region is from the minimum q min 2 To q1 2 A linear fit is performed on the approximate straight line within the range of , and the average gyration radius R of the scatterer is calculated according to the slope after fitting g , R g =(-3*slope) 1 / 2 .

[0033] Figure 2 A schematic diagram of the solution steps provided by an embodiment of the present invention, such as Figure 2 As shown, the solution steps provided in this embodiment are as follows:

[0034] 1. Coordinate transformation. Take the logarithm of the scattering intensity I corresponding to the theoretical simulation or measurement of SAXS at different scattering vectors q, and draw the lnI~q curve, such as Figure 3 As shown;

[0035] 2. Calculate the first-order differential (or derivative). If the I~q curve is obtained from theoretical simulation, the lnI~q curve is relatively smooth, and the first-order derivative dlnI / dq can be directly calculated; if the I~q curve is measured experimentally, the curve usually has certain fluctuations, so it is necessary to first perform appropriate fitting on the lnI~q curve, such as polynomial fitting, and then calculate the first-order derivative dlnI / dq. Then draw the first-order differential curve dlnI / dq~q as the scattering vector changes, such as Figure 4 Read out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region and mark it as q1.

[0036] 3. Draw the Guinier diagram lnI~q 2 ,like Figure 5 As shown. In the low q region, it generally starts from the minimum q min 2 To q1 2 The range is approximately a straight line. The linear fitting is performed on this straight line, and the average gyration radius R of the scatterer can be calculated from its slope. g , R g =(-3*slope) 1 / 2 .

[0037] from Figure 5 The calculated average gyration radii are 22.2nm (simulation) and 7.50nm (experimental), which are very close to the theoretical average gyration radius of 21.6nm and the diameter of 20nm provided by the manufacturer of the experimental sample, that is, the average gyration radius of 7.75nm, verifying the feasibility of the present invention.

[0038] The beneficial effects of the present invention are as follows:

[0039] In the existing Guinier approximation analysis, the important step, i.e., the determination of the linear fitting range, is determined by directly drawing a straight line on the Guinier diagram, which has certain artificiality, poor repeatability, and low accuracy. The first-order differential technique of the present invention is simple and convenient, can uniquely determine the linear range, effectively avoids the artificiality of the traditional operation method, and improves the accuracy of the analysis. In addition, the scope of application of the Guinier approximation determined by the first-order differential method is significantly wider than traditional cognition, which is more advantageous for data with a limited range of measurement data. The method is simple and convenient, can uniquely determine the upper limit of the Guinier approximation, effectively avoids the artificiality of the traditional direct straight line operation method, and improves the accuracy of the analysis.

[0040] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0041] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for determining the upper limit of the Gines approximate analysis of a polydisperse system, characterized in that: include: Take the logarithm of the scattering intensity I corresponding to different scattering vectors q of SAXS, and draw the lnI~q curve; Calculate the first-order derivative dlnI / dq according to the lnI~q curve, and read out the q value corresponding to the first valley of the dlnI / dq~q curve in the low q region, marked as q1; Draw the Guinier diagram lnI~q 2 , and the Guinier diagram lnI~q 2 The low q region is from the minimum q min 2 To q1 2 A linear fit is performed on the approximate straight line within the range of , and the average gyration radius R of the scatterer is calculated according to the slope after fitting g , R g =(-3*slope) 1 / 2 .

2. The method for determining the upper limit of the Gineser approximate analysis of a polydisperse system according to claim 1, characterized in that: Calculating the first-order derivative dlnI / dq according to the lnI~q curve includes: If the lnI~q curve is obtained from theoretical simulation, the first-order derivative dlnI / dq is directly calculated; If the lnI~q curve is obtained from experimental testing, the lnI~q curve is fitted and then the first-order derivative dlnI / dq is calculated.

3. The method for determining the upper limit of the Gineser approximate analysis of a polydisperse system according to claim 1, characterized in that: The fitting method for the lnI~q curve is polynomial fitting.

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