WO2018086168A1 - 一种基于分形维数的碳纳米管分散状态的数值化表征方法 - Google Patents

一种基于分形维数的碳纳米管分散状态的数值化表征方法 Download PDF

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WO2018086168A1
WO2018086168A1 PCT/CN2016/108061 CN2016108061W WO2018086168A1 WO 2018086168 A1 WO2018086168 A1 WO 2018086168A1 CN 2016108061 W CN2016108061 W CN 2016108061W WO 2018086168 A1 WO2018086168 A1 WO 2018086168A1
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carbon nanotubes
carbon nanotube
dispersion
fractal dimension
image
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徐鸣
张蒙蒙
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Huazhong University of Science and Technology
Shenzhen Huazhong University of Science and Technology Research Institute
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    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
    • G01N2021/4106—Atmospheric distortion; Turbulence
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    • G—PHYSICS
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    • G06T2207/10—Image acquisition modality
    • G06T2207/10056—Microscopic image
    • G06T2207/10061—Microscopic image from scanning electron microscope

Definitions

  • the invention belongs to the field of preparation and application of nano composite materials, and more particularly to a numerical characterization method for the dispersion state of carbon nanotubes based on fractal dimension, which can utilize fractal dimension to carry out the dispersion state of carbon nanotubes. Accurate, quantitative assessment.
  • Carbon nanotubes have excellent electrical and mechanical properties, so they are often used as filler materials in the field of composite materials to enhance the electrical and mechanical properties of materials.
  • the dispersion state of carbon nanotubes as a key factor directly affects the final properties of the material. Since Ajayan first prepared carbon nanotube composites by ultrasonic method in 1993, researchers have been searching for various methods to characterize the dispersion state of carbon nanotubes in dispersion systems. At present, the main characterization methods can be divided into topography and spectroscopy depending on the mechanism. The morphology method is to directly characterize the structure of carbon nanotubes in the dispersion system by optical microscope, scanning electron microscope and transmission electron microscope, and then evaluate the dispersion state of carbon nanotubes.
  • the spectroscopy method is through ultraviolet-visible spectroscopy.
  • the number of carbon nanotubes in the suspension of the dispersion was evaluated, and then the evaluation of the dispersion state of the carbon nanotubes was achieved by comparison between the samples. Comparing the above two methods, the spectroscopy can only evaluate the number of carbon nanotubes in the suspension of the dispersion system, but can not explain the size and morphology information of the agglomerates of carbon nanotubes. Therefore, this method evaluates carbon nanotubes.
  • the morphology method can reflect the unwrapping and size change of carbon nanotube aggregates in the dispersion system, so it can comprehensively characterize and evaluate the dispersion state of carbon nanotubes. However, the limitation of this method is that it can only be qualitative. Describe the dispersion state of carbon nanotubes, which makes the morphology method also have certain deficiencies in evaluating the dispersion state of carbon nanotubes.
  • the characterization method of characterizing the dispersion state of carbon nanotubes by the topography method and then numerically processing the acquired images has been paid more and more attention by researchers.
  • Value the image The treatment can express the rich information (such as concentration, carbon nanotube diameter, carbon nanotube length, dispersion condition) contained in the dispersed state of the carbon nanotubes by a numerical value, thereby realizing the quantification of the dispersed state of the carbon nanotubes.
  • Evaluation. Literature Carbon, 2011, 49(4): 1473-1478 published a method for characterizing the dispersion state of carbon nanotubes in SEM images using the positional randomness index. The smaller the positional randomness index, the probability of adjacent carbon nanotubes agglomerating together.
  • the present invention provides a method for numerically characterizing the dispersion state of carbon nanotubes based on fractal dimension, and aims to accurately use the fractal dimension to accurately disperse the carbon nanotubes. Quantitative evaluation to achieve regulation and prediction of its performance during the preparation of composite materials.
  • a method for calculating a fractal dimension in a SEM image which is characterized in that it adopts a box algorithm, and the algorithm formula of the box is as follows:
  • ⁇ i is the side dimension of the box
  • N i is the total number of boxes covering the area occupied by the carbon nanotube or agglomerate boundary contour in the processed image with the side dimension ⁇ i
  • D is the fractal dimension
  • the minimum size of the ⁇ i in one picture is the length represented by one pixel, and the maximum size is the length represented by the total number of horizontal or vertical pixels of the picture.
  • a pixel represents a length between 0.34 nm and 100 nm, so that the smallest size box can reflect the nanometer size effect of the carbon nanotube when covering the boundary contour, and As for the internal tube wall structure reflecting the carbon nanotubes.
  • the SEM image is a picture at a two-dimensional scale, so the calculated fractal dimension value is between 1.0 and 2.0.
  • a numerical characterization method for a dispersion state of a carbon nanotube based on a fractal dimension comprising the steps of:
  • the steps of dispersing the carbon nanotubes by using different dispersion conditions are as follows. First, different amounts of carbon nanotubes are weighed and added to a certain volume of the organic solvent to prepare different ones. The concentration of the precursor liquid, and then using a dispersion method having a different dispersion mechanism, by adjusting the dispersion time and dispersing the power, a diverse dispersion state of the carbon nanotubes is obtained.
  • the dilution ratio of the carbon nanotube dispersion in the step (1) is 100 times.
  • the solvent volatilization in the step (2) is carried out at room temperature.
  • the sample is subjected to gold spraying, and the gold spraying time is 80 seconds.
  • the picture in the step (3) is to remove noise in the picture during processing.
  • the different dispersion conditions in the step (1) should involve different dispersion methods (or different dispersion mechanisms), different dispersion times, different dispersion powers, different dispersion concentrations and the like. And the dilution ratio of the carbon nanotube dispersion is 100 times.
  • the different diluted carbon nanotube dispersions in step (2) should ensure that the amount of the extracted dispersion is the same when taking a certain amount on the silicon wafer. And when performing SEM testing, the acquired carbon nanotube scanning electron microscope images should have the same magnification and the same scale.
  • the boundary contour extraction of single carbon nanotubes or carbon nanotube aggregates in step (3) should be accurate, and the interference of the inner boundary contour of carbon nanotube aggregates should be excluded.
  • the fractal dimension thus calculated is a quantitative description of the rich information in the dispersed state of the carbon nanotubes.
  • the image can be processed and calculated directly by ImageJ software. In this process, no additional experimental processing and characterization methods are needed, so the operation process is simple and quick.
  • Example 2 is a schematic diagram showing a comparison of a scanning electron microscope image and a box algorithm of the dispersed state of the carbon nanotubes obtained in Example 1-3;
  • Fig. 3(a) is a transmission electron micrograph, a scanning electron microscope image, and an optical microscope image of the dispersed state of the carbon nanotube obtained in Example 4.
  • 3(b) is a fractal dimension diagram calculated from the actual size of the box in the picture in the dispersed state of the carbon nanotube obtained in Example 4;
  • Example 4 is a standard deviation diagram of a fractal dimension of a carbon nanotube dispersed state in Example 5;
  • Example 5 is a fitting curve of the dispersion state of the carbon nanotubes in Example 6 and Example 7 and the electrical conductivity of the composite material.
  • the invention provides a calculation method of fractal dimension in a SEM image, which is characterized in that it adopts a box algorithm, and the algorithm formula of the box is as follows:
  • ⁇ i is the side dimension of the box
  • N i is the total number of boxes covering the area occupied by the carbon nanotube or agglomerate boundary contour in the processed image with the side dimension ⁇ i
  • D is the fractal dimension
  • the minimum size of the ⁇ i in one picture is the length represented by one pixel, and the maximum size is the length represented by the total number of horizontal or vertical pixels of the picture.
  • a pixel is replaced by a pixel
  • the length of the watch is between 0.34 nm and 100 nm, so that the smallest size of the box can not only reflect the nano-size effect of the carbon nanotubes, but also reflect the internal wall structure of the carbon nanotubes when covering the boundary contour.
  • the SEM image is a picture at a two-dimensional scale, so the calculated fractal dimension value is between 1.0 and 2.0.
  • a numerical characterization method for a dispersion state of a carbon nanotube based on a fractal dimension comprising the steps of:
  • the steps of dispersing the carbon nanotubes by using different dispersion conditions are as follows. First, different amounts of carbon nanotubes are weighed and added to a certain volume of the organic solvent. , formulated into different concentrations of the precursor liquid, and then using a dispersion method with different dispersion mechanisms, by adjusting the dispersion time, dispersion power, to obtain a variety of carbon nanotube dispersion state.
  • the dilution ratio of the carbon nanotube dispersion in step (1) is 100 times.
  • the solvent volatilization in step (2) is volatilized at room temperature.
  • step (2) before the image is acquired by scanning electron microscopy, the sample was subjected to gold spray treatment and the gold injection time was 80 seconds.
  • the picture in step (3) is to remove noise from the picture during processing.
  • the invention discloses a method for numerically characterizing the dispersion state of carbon nanotubes based on fractal dimension, which can express the rich information contained in the dispersed state of the carbon nanotubes by a numerical value, thereby making it applicable to the electrical properties of the composite material. Regulation and prediction.
  • Example 1 was repeated in the same manner as above except that 0.5 g was weighed in the step (1).
  • the carbon nanotubes were subjected to a conical grinding method (shear-emulsification mechanism) to disperse the carbon nanotube/methyl isobutyl ketone mixture, the grinding time was 75 min, and the grinding speed was 180 r/min.
  • Example 1 was repeated in the same manner as above except that the mass of the carbon nanotubes in the step (1) was 1.0 g, and the carbon nanotube/methyl isobutyl ketone was dispersed by an ultrasonic method (cavitation mechanism). The mixture was sonicated for 120 min and the ultrasonic power was 480 W.
  • Example 3 is repeated in the same manner as described above, with the difference that:
  • the amount of carbon nanotubes weighed in the step (1) was 0.5 g, and the carbon nanotube/methyl isobutyl ketone mixed solution was also dispersed by an ultrasonic method (cavitation mechanism).
  • the carbon nanotube dispersion liquid was dropped on the silicon wafer, and the scanning electron microscope image at 20,000 times and 80,000 times was taken.
  • the carbon nanotube dispersion liquid is dropped on the slide glass and the copper mesh respectively, and the two samples to be tested need not be subjected to gold spray treatment.
  • the sample to be tested on the slide was observed by an optical microscope at a magnification of 100 times.
  • the sample to be tested on the copper mesh was observed by a transmission electron microscope, and the magnification was 160,000 times.
  • Example 1 is repeated in the same manner as described above, with the difference that:
  • step (1) a series of masses of carbon nanotubes are weighed in an organic solvent, methyl isobutyl ketone, respectively, using different dispersion mechanisms (eg, vortex-jet mechanism, cavitation mechanism, impact grinding mechanism) And a dispersion method of the carbon nanotube/methyl isobutyl ketone mixture by a dispersion method of shear emulsification mechanism.
  • dispersion mechanisms eg, vortex-jet mechanism, cavitation mechanism, impact grinding mechanism
  • a dispersion method of the carbon nanotube/methyl isobutyl ketone mixture by a dispersion method of shear emulsification mechanism.
  • each sample when taking a SEM image, each sample should select a different area to take a picture with the same magnification (40000 times), and the number of pictures is 3-5 sheets.
  • the fractal dimension of the same sample in the step (4) is composed of 3-5 images in the fractal The dimensions are averaged and the corresponding standard deviation is calculated.
  • Example 5 was repeated in the same manner as above except that in the step (1), carbon nanotubes of different masses were weighed in an organic solvent, methyl isobutyl ketone, and then the above mixture was dispersed by an ultrasonic method (cavitation mechanism). liquid.
  • the ultrasonic time such as 10 min, 30 min, 60 min, 90 min, 120 min
  • the ultrasonic power such as 320 W, 400 W, 480 W, 560 W
  • the fractal dimension of the sample calculated in Example 6 is fitted to the conductivity of the sample to establish the relationship between the dispersion state of the carbon nanotubes and the electrical conductivity of the composite material.
  • the fractal dimension is used to control the electrical properties of the composite material. And forecasting.
  • the SEM image obtained in Example 1 is as shown in the lower right illustration of Fig. 1, and the magnification is 40,000 times.
  • the image processing software ImageJ is used to binarize the image in black and white, and then extract the boundary contour of a single carbon nanotube or carbon nanotube agglomerate, as shown in Fig. 1.
  • the calculation principle of the box algorithm is shown in Fig. 1.
  • the processed picture is divided into square grids (boxes) of a certain size, and then the total number of boxes covering the area occupied by the boundary contour of the carbon nanotubes or agglomerates can be obtained.
  • the difference between the dispersed states of the carbon nanotubes can be clearly distinguished according to the difference between the fractal dimensions.
  • the fractal dimension When the carbon nanotubes are in agglomerated state, the fractal dimension is small; when the carbon nanotubes are unwrapped, the fractal dimension is large.
  • the fractal dimension In an ideal state, when the carbon nanotubes are completely covered in a agglomerated state, the fractal dimension is 1.0; when the carbon nanotubes are covered with a perfect single unwrapped state, the fractal dimension is 2.0.
  • Example 4 a picture of the dispersed state of the same sample in a transmission electron microscope (160,000 times), a scanning electron microscope (20000 times, 40,000 times and 80,000 times), and an optical microscope (100 times) was obtained. According to the actual scale in the picture, calculate the actual length represented by one pixel in each picture, as shown in Figure 3a). For optical microscopy images (100x) and transmission electron microscopy images (160,000x), the actual length of a pixel (the smallest box size) is 234nm and 0.30nm, respectively, the former far exceeds the upper limit of the nanoscale.
  • the calculated fractal dimension does not reflect the nano-size effect of carbon nanotubes; the latter is smaller than the tube spacing of carbon nanotubes by 0.34nm, so the calculated fractal dimension reflects the inner wall of the carbon nanotube Structural information.
  • the length represented by one pixel should be between 0.34 nm and 100 nm.
  • the number of boxes corresponding to the different sizes is taken as a logarithm, as shown in Figure 3b). It can be seen from the figure that the fractal dimension of the SEM image at the three magnifications can be used to quantitatively describe the dispersion state of the carbon nanotubes.
  • Example 5 the fractal dimension of a series of diversified carbon nanotube dispersion states was obtained, and the uniformity of the distribution of carbon nanotubes in the dispersion system was described by calculating the standard deviation, as shown in FIG. 4 . It can be seen from the figure that as the fractal dimension increases, the standard deviation gradually decreases, reflecting the more uniform distribution of carbon nanotubes in the dispersion system.
  • Example 6 Combining Example 6 with Example 7, the relationship between the dispersed state of the carbon nanotubes and the electrical properties of the composite was established, as shown in FIG.
  • the carbon nanotubes dispersed by a single dispersion mechanism are dispersed.
  • the electrical conductivity of the composite material is basically consistent with the electrical conductivity of the matrix; when the fractal dimension exceeds a certain value, the electrical conductivity of the composite material begins to increase rapidly, indicating that the composite material The inside begins to form a conductive path.
  • the electrical conductivity of the composite material is proportional to the fractal dimension of the dispersed state. It can be seen that the fractal dimension of the dispersed state of the carbon nanotube can be used to judge whether the conductive path inside the composite material is formed or not, and can be applied to the prediction of the electrical conductivity of the composite material.

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Abstract

一种基于分形维数的碳纳米管分散状态的数值化表征方法。该方法首先通过获取分散体系中碳纳米管分散状态的扫描电镜图片，然后采用图像处理软件(ImageJ)将所得扫描电镜图片进行二值化处理，再提取出图片中单根碳纳米管或者碳纳米管团聚体的边界轮廓，最后利用盒子算法计算处理后图片的分形维数，所得的分形维数值即是对碳纳米管分散状态中丰富信息的定量化描述，从而实现分散体系中碳纳米管分散状态的数值化表征。量化了碳纳米管的分散状态，为碳纳米管复合材料宏观性能的调控，对比及预测提供了有力的依据。

Description

一种基于分形维数的碳纳米管分散状态的数值化表征方法 【技术领域】
本发明属于纳米复合材料制备及应用领域，更具体地说，涉及一种基于分形维数的碳纳米管分散状态的数值化表征方法，其能够利用分形维数来对碳纳米管的分散状态进行准确、定量的评估。
【背景技术】
碳纳米管具有优异的电学，力学性能，因此其常用作填充材料被广泛应用于复合材料领域，用于增强材料的电学，力学性能等。在复合材料的制备过程中，碳纳米管的分散状态作为一个关键因素，直接影响了材料的最终性能。自从1993年Ajayan利用超声法第一次制备出碳纳米管复合材料以来，研究者们不断地寻找各种方法对分散体系中碳纳米管的分散状态进行表征。目前，主要的表征方法依据机理不同可分为形貌法和光谱法。形貌法是通过光学显微镜、扫描电子显微镜、透射电子显微镜直接对分散体系中碳纳米管的结构形貌进行表征，进而对碳纳米管的分散状态进行评估；光谱法是通过紫外-可见光谱对分散体系悬浮液中碳纳米管数量进行评价，然后通过样品间的对比实现对碳纳米管分散状态的评估。对比上述两种方法，光谱法由于只能对分散体系悬浮液中碳纳米管的数量进行评估，而不能说明碳纳米管团聚体的尺寸和形貌信息，因此，这种方法在评估碳纳米管的分散状态时存在很大的不足。形貌法能够反映分散体系中碳纳米管团聚体的解缠情况和尺寸变化情况，因此能够对碳纳米管的分散状态进行比较全面的表征和评价，但这种方法的局限性在于只能定性的描述碳纳米管的分散状态，这使得形貌法在评估碳纳米管分散状态时也存在一定的不足。
近年来，利用形貌法对碳纳米管的分散状态进行表征，然后将获取的图片进行数值化处理的表征手段越来越受到研究者重视。对图片进行数值 化处理，能够将碳纳米管分散状态中所包含的丰富信息(如浓度，碳纳米管直径，碳纳米管长度，分散条件)用一个数值来表达，从而实现对碳纳米管分散状态的定量化评价。文献Carbon,2011,49(4):1473-1478发表了利用位置随机性指数来表征扫描电镜图片中碳纳米管分散状态的方法，位置随机性指数越小，相邻碳纳米管团聚在一起几率越小，碳纳米管分散状态越好。但此种方法的计算思想是基于纳米颗粒分散体系，没有考虑碳纳米管的纳米纤维特征，因此用该方法计算得到的数值来评估碳纳米管的分散状态具有很大的局限性。
针对上述技术问题，目前还没有看到一套精确、有效、方便的碳纳米管的分散状态数值化表征方法，如何解决上述技术难点，设计一套行而有效的表征方法，实现数值表征结果与实际分散状态的无限接近，是本发明要解决的问题。
【发明内容】
针对现有技术的以上缺陷或改进需求，本发明提供了一种基于分形维数的碳纳米管分散状态数值化表征方法，其目的在于利用分形维数来对碳纳米管的分散状态进行准确的，定量的评估，从而在复合材料的制备过程中，实现对其性能的调控和预测。
为实现上述目的，按照本发明的一个方面，提供了一种扫描电镜图片中分形维数的计算方法，其特征在于，其采用盒子算法，该盒子算法公式如下：
Figure PCTCN2016108061-appb-000001
其中，δi为盒子的侧边尺寸，Ni为用侧边尺寸是δi的盒子覆盖处理后图片中碳纳米管或者团聚体边界轮廓所占据区域的盒子总数，D为分形维数。
优选地，所述δi的尺寸在一张图片中的最小尺寸为一个像素点所代表的长度，最大尺寸为图片的横向或纵向像素点总数所代表的长度。
优选地，对于一张图片来讲，一个像素点所代表的长度在0.34nm至100nm之间，以使最小尺寸的盒子在覆盖边界轮廓时，既能够体现碳纳米管的纳米尺寸效应，又不至于反映出碳纳米管的内部管壁结构。
优选地，扫描电镜图片为二维尺度下的图片，因此计算获得的分形维数值在1.0-2.0之间。
按照本发明的另一方面，提供了一种基于分形维数的碳纳米管分散状态的数值化表征方法，包括以下步骤：
(1)采用不同的分散条件分散碳纳米管，获得多样的碳纳米管分散状态，然后将其稀释处理得到样品液；
(2)取一定量上述稀释过的样品液于干净的硅片上，待溶剂完全挥发后，利用扫描电镜采集硅片上碳纳米管的图像；
(3)将扫描电镜获取的图像进行二值化黑白处理，然后提取图像中单根碳纳米管或者碳纳米管团聚体的边界轮廓；
(4)通过不断改变图片中覆盖碳纳米管边界轮廓的盒子的尺寸δi，获取一系列相应的盒子数Ni，采用上述计算方法，计算经过处理后图像的分形维数，实现对碳纳米管分散状态的定量化表征。
进一步优选地，所述步骤(1)中，采用不同的分散条件分散碳纳米管的步骤如下，首先称取不同量的碳纳米管，分别将其加入到一定体积的有机溶剂中，配制成不同浓度的前驱液，然后采用具有不同分散机理的分散方法，通过调节分散时间，分散功率，获得多样化的碳纳米管分散状态。
优选地，所述步骤(1)中碳纳米管分散液的稀释倍数为100倍。
优选地，所述步骤(2)中溶剂挥发采用室温挥发。
优选地，所述步骤(2)中在用扫描电镜采集图像前，样品要经过喷金处理，喷金时间为80秒。
优选地，所述步骤(3)中图片在处理过程中要除去图片中的噪声。
具体地，步骤(1)中不同的分散条件应涉及到不同的分散方法(或不同的分散机理)，不同的分散时间，不同的分散功率，不同的分散浓度等变量因素。并且碳纳米管分散液的稀释倍数为100倍。
步骤(2)中不同的稀释过的碳纳米管分散液在取一定量于硅片上时，应保证所提取的分散液量是相同的。并且在进行扫描电镜测试时，获取的碳纳米管扫描电镜图片应当具有相同的放大倍数，相同的标尺。
步骤(3)图片中单根碳纳米管或者碳纳米管团聚体的边界轮廓提取应当准确，排除碳纳米管团聚体内部边界轮廓的干扰。由此计算得到的分形维数，是对碳纳米管分散状态中丰富信息的定量化描述。
按照本发明的另一方面，提供了一种碳纳米管分散状态数值化表征方法在复合材料电学性能调控和预测中的应用。
总体而言，通过本发明所构思的以上技术方案与现有技术相比，由于定量化的表征了碳纳米管的分散状态，能够取得以下有益成果：
(1)利用分形维数实现了对扫描电镜图片中碳纳米管分散状态的数值化表征，能够将碳纳米管分散状态中所包含的丰富信息用一个数值来描述。
(2)在获取扫描电镜图片后，能够直接通过ImageJ软件对图片进行处理和计算，此过程中不需要额外的实验处理和表征手段，因此操作过程简便快捷。
(3)通过对碳纳米管分散状态进行定量化表征，一些肉眼不能区分出来的碳纳米管分散状态，能够依据分形维数值的差异被简单直观地区别开来。
(4)借助于碳纳米管分散状态的数值化表征，能够建立碳纳米管的分散状态与复合材料性能之间的联系，从而为碳纳米管复合材料性能的预测和调控提供指导。
【附图说明】
图1为实施例1中得到的碳纳米管分散状态的扫描电镜图片及盒子算 法示意图；
图2为实施例1-3中得到的碳纳米管分散状态的扫描电镜图片及盒子算法对比示意图；
图3(a)为实施例4中得到的碳纳米管分散状态的透射电镜图片、扫描电镜图片和光学显微镜图片。
图3(b)为实施例4中得到的碳纳米管分散状态的由图片中盒子的实际尺寸计算而得的分形维数图；
图4为实施例5中碳纳米管分散状态的.分形维数的标准偏差图；
图5为实施例6和实施例7中碳纳米管的分散状态与复合材料的电导率的拟合曲线。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。
本发明提供一种扫描电镜图片中分形维数的计算方法，其特征在于，其采用盒子算法，该盒子算法公式如下：
Figure PCTCN2016108061-appb-000002
其中，δi为盒子的侧边尺寸，Ni为用侧边尺寸是δi的盒子覆盖处理后图片中碳纳米管或者团聚体边界轮廓所占据区域的盒子总数，D为分形维数。
在本发明的一个优选实施例中，所述δi的尺寸在一张图片中的最小尺寸为一个像素点所代表的长度，最大尺寸为图片的横向或纵向像素点总数所代表的长度。
在本发明的一个优选实施例中，对于一张图片来讲，一个像素点所代 表的长度在0.34nm至100nm之间，以使最小尺寸的盒子在覆盖边界轮廓时，既能够体现碳纳米管的纳米尺寸效应，又不至于反映出碳纳米管的内部管壁结构。
在本发明的一个优选实施例中，扫描电镜图片为二维尺度下的图片，因此计算获得的分形维数值在1.0-2.0之间。
按照本发明的另一方面，提供了一种基于分形维数的碳纳米管分散状态的数值化表征方法，包括以下步骤：
(1)采用不同的分散条件分散碳纳米管，获得多样的碳纳米管分散状态，然后将其稀释处理得到样品液；
(2)取一定量上述稀释过的样品液于干净的硅片上，待溶剂完全挥发后，利用扫描电镜采集硅片上碳纳米管的图像；
(3)将扫描电镜获取的图像进行二值化黑白处理，然后提取图像中单根碳纳米管或者碳纳米管团聚体的边界轮廓；
(4)通过不断改变图片中覆盖碳纳米管边界轮廓的盒子的尺寸δi，获取一系列相应的盒子数Ni，采用上述计算方法，计算经过处理后图像的分形维数，实现对碳纳米管分散状态的定量化表征。
在本发明的一个优选实施例中，步骤(1)中，采用不同的分散条件分散碳纳米管的步骤如下，首先称取不同量的碳纳米管，分别将其加入到一定体积的有机溶剂中，配制成不同浓度的前驱液，然后采用具有不同分散机理的分散方法，通过调节分散时间，分散功率，获得多样化的碳纳米管分散状态。
在本发明的一个优选实施例中，步骤(1)中碳纳米管分散液的稀释倍数为100倍。
在本发明的一个优选实施例中，步骤(2)中溶剂挥发采用室温挥发。
在本发明的一个优选实施例中，步骤(2)中在用扫描电镜采集图像前， 样品要经过喷金处理，喷金时间为80秒。
在本发明的一个优选实施例中，步骤(3)中图片在处理过程中要除去图片中的噪声。
本发明的一种基于分形维数的碳纳米管分散状态数值化表征方法，该方法能够将碳纳米管分散状态中包含的丰富信息用一个数值来表达，从而使其可应用于复合材料电学性能的调控和预测中。
为了进一步具体解释本发明，以下给出了七个具体实施例。
实施例1
(1)称量0.1g的碳纳米管于一定体积的有机溶剂甲基异丁基甲酮中，浸没5min，然后采用球磨法(冲击-研磨机理)研磨上述混合液，研磨时间为30min，研磨转速为200r/min。随后用移液枪定量取出50微升研磨后的碳纳米管分散液于25ml的血清瓶中，用甲基异丁基甲酮溶剂将其稀释100倍，然后用超声清洗机超声振荡2min。
(2)清洗一定数量的硅片，保持硅片亮光面清洁。然后用移液枪量取一定量稀释过的碳纳米管分散液，滴在干净的硅片上。等待5-10min至溶剂挥发完全。随后将制备好的待测样品喷金处理80s，开始拍摄扫描电镜图片，拍摄时图片的放大倍数为40000倍。
(3)将所拍摄的扫描电镜图片用图像处理软件ImageJ转化为二值黑白图片，然后去除图片中存在的噪声，再利用软件中的边界提取功能提取出单根碳纳米管或者碳纳米管团聚体的边界轮廓。
(4)利用盒子算法，计算出上述图片的分形维数。在计算过程中，通过不断改变盒子的尺寸δi，获取一系列相应的盒子数Ni，依据公式即可得到图片的分形维数。
实施例2
以上述的相同步骤重复实施例1，区别在于，所述步骤(1)中称取0.5g 的碳纳米管，采用锥形磨法(剪切-乳化机理)来分散碳纳米管/甲基异丁基甲酮混合液，研磨时间为75min，研磨转速为180r/min。
实施例3
以上述的相同步骤重复实施例1，区别在于，所述步骤(1)中称取碳纳米管的质量为1.0g，采用超声法(空化机理)来分散碳纳米管/甲基异丁基甲酮混合液，超声时间为120min，超声功率为480W。
实施例4
以上述的相同步骤重复实施例3，区别在于：
(1)所述步骤(1)中称取碳纳米管量为0.5g，同样采用超声法(空化机理)来分散碳纳米管/甲基异丁基甲酮混合液。
(2)所述步骤(2)中除了在硅片上滴加碳纳米管分散液拍摄40000倍的扫描电镜图片外，还拍摄20000倍下和80000倍下的扫描电镜图片。此外分别在载玻片上和铜网上滴加碳纳米管分散液，这两个待测样品无需经过喷金处理。载玻片待测样品采用光学显微镜观察，放大倍数为100倍。铜网待测样品采用透射电子显微镜观察，放大倍数为160000倍。
实施例5
以上述的相同步骤重复实施例1，区别在于：
(1)所述步骤(1)中称量一系列质量的碳纳米管于有机溶剂甲基异丁基甲酮中，分别采用具有不同分散机理(如涡旋-喷射机理，空化机理，冲击研磨机理和剪切乳化机理)的分散方法分散碳纳米管/甲基异丁基甲酮混合液。通过改变碳纳米管浓度，分散时间，分散功率，获得多样化的碳纳米管分散状态。
(2)所述步骤(2)中在拍摄扫描电镜图片时，每一个样品都要选择不同的区域来拍摄具有相同放大倍数(40000倍)的图片，图片数量为3-5张。
(3)所述步骤(4)中同一样品的分形维数要由3-5张图片中的分形 维数取平均数得到，同时计算出相应的标准偏差。
实施例6
以上述的相同步骤重复实施例5，区别在于，所述步骤(1)中称取不同质量的碳纳米管于有机溶剂甲基异丁基甲酮中，然后采用超声法(空化机理)分散上述混合液。在此过程中，改变超声时间(如10min，30min，60min，90min，120min)，超声功率(如320W，400W，480W，560W)，获取不同的碳纳米管分散状态。
实施例7
将实施例6中计算得到的样品分形维数与样品的电导率相拟合，建立碳纳米管分散状态与复合材料电导率之间的关系，借助于分形维数，实现复合材料电学性能的调控和预测。
实验结果分析
实施例1中获取的扫描电镜图片如图1中的右下插图所示，放大倍数为40000倍。利用图像处理软件ImageJ将图片二值化黑白处理，再提取出单根碳纳米管或者碳纳米管团聚体的边界轮廓，如图1所示。在图1中显示了盒子算法的计算原理，将处理后的图片划分成一定尺寸的方格子(盒子)，然后即可得出覆盖碳纳米管或者团聚体边界轮廓所占据区域的盒子总数。随后改变所划分的方格子尺寸，便可得到另外一组盒子总数，以此类推，即可得到一系列对应一定盒子尺寸的盒子总数，从而依据分形维数计算公式实现对碳纳米管分散状态的定量化表征。
将实施例1-3中获取的扫描电镜图片做对比，如图2所示。很明显，相互间的碳纳米管分散状态具有很大的差异。将图片进行边界轮廓提取后，采用相同尺寸的盒子来覆盖碳纳米管或者团聚体边界轮廓所占据的区域，可以得到数值不同的盒子数。然后依据盒子算法，将盒子数和盒子尺寸分别取对数做曲线，由斜率即可得出图片的分形维数。从拟合曲线来看，实施例1中曲线的斜率(1.1526)小于实施例2中曲线的斜率(1.4659)， 实施例2中曲线的斜率小于实施例3中曲线的斜率(1.8051)。由此可见，碳纳米管分散状态间的差异能够依据分形维数间的差异被很明显的区分开来。并且碳纳米管呈团聚状态时，分形维数小；碳纳米管呈解缠状态时，分形维数大。在理想状态下，碳纳米管完全以团聚状态存在铺满图片时，分形维数为1.0；碳纳米管以完美单根解缠状态铺满图片时，分形维数为2.0。
实施例4中获取了同一样品在透射电子显微镜(160000倍)，扫描电子显微镜(20000倍，40000倍和80000倍)，光学显微镜(100倍)下的碳纳米管分散状态图片。依据图片中的实际标尺，计算出每张图片中一个像素点所代表的实际长度，如图3a)所示。对于光学显微镜图片(100倍)和透射电子显微镜图片(160000倍)来讲，一个像素点(最小的盒子尺寸)代表的实际长度分别为234nm和0.30nm，前者远远超过了纳米尺度的上限尺寸100nm，因此计算获得的分形维数并不能体现碳纳米管的纳米尺寸效应；后者小于了碳纳米管的管间距0.34nm，因此计算获得的分形维数反映出了碳纳米管的内部管壁结构信息。对于一张图片来讲，一个像素点所代表的长度应该在0.34nm至100nm之间。对于以上图片，根据盒子的具体实际尺寸，将其与不同尺寸下所对应的盒子数分别取对数做曲线，如图3b)所示。由图看出，3种放大倍数下扫描电镜图片的分形维数均可用来定量化描述碳纳米管的分散状态。
实施例5中获取了一系列多样化碳纳米管分散状态的分形维数，通过对其标准偏差进行计算，描述了碳纳米管在分散体系中分布的均匀性，如图4所示。由图可以看出，随着分形维数的增大，标准偏差逐渐减小，反映了碳纳米管在分散体系中分布的越来越均匀。
将实施例6和实施例7相结合，建立了碳纳米管分散状态与复合材料电学性能之间的联系，如图5所示。鉴于实施例6中采用了超声法(空化机理)来分散碳纳米管，因此对于采用单一分散机理获取的碳纳米管分散 状态，其分形维数在小于一定值时，复合材料的电导率基本上与基体的电导率一致；当其分形维数超过一定值后，复合材料的电导率开始快速增大，这表明复合材料内部开始形成导电通路。并且在分形维数超过一定值后，复合材料的电导率与分散状态的分形维数成正比关系。由此可见，碳纳米管分散状态的分形维数既可以用来判断复合材料内部导电通路是否形成，又可以应用于复合材料电导率的预测中。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

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  1. 一种扫描电镜图片中分形维数的计算方法，其特征在于，其采用盒子算法，该盒子算法公式如下：
    Figure PCTCN2016108061-appb-100001
    其中，δi为盒子的侧边尺寸，Ni为用侧边尺寸是δi的盒子覆盖处理后图片中碳纳米管或者团聚体边界轮廓所占据区域的盒子总数，D为分形维数。
  2. 如权利要求1所述的计算方法，其特征在于，所述δi的尺寸在一张图片中的最小尺寸为一个像素点所代表的长度，最大尺寸为图片的横向或纵向像素点总数所代表的长度。
  3. 如权利要求2所述的计算方法，其特征在于，在一张图片来中，一个像素点所代表的长度在0.34nm至100nm之间。
  4. 如权利要求3所述的计算方法，其特征在于，计算获得的分形维数值在1.0-2.0之间。
  5. 一种基于分形维数的碳纳米管分散状态的数值化表征方法，包括以下步骤：
    (1)采用不同的分散条件分散碳纳米管，获得多样的碳纳米管分散状态，然后将其稀释处理得到样品液；
    (2)取一定量上述稀释过的样品液于干净的硅片上，待溶剂完全挥发后，利用扫描电镜采集硅片上碳纳米管的图像；
    (3)将扫描电镜获取的图像进行二值化黑白处理，然后提取图像中单根碳纳米管或者碳纳米管团聚体的边界轮廓；
    (4)通过不断改变图片中覆盖碳纳米管边界轮廓的盒子的尺寸δi，获取一系列相应的盒子数Ni，采用权利要求1-4中任一项所述的计算方法，计算经过处理后图像的分形维数，实现对碳纳米管分散状态的定量化表征。
  6. 如权利要求5所述的数值化表征方法，其特征在于，所述步骤(1)中，采用不同的分散条件分散碳纳米管的步骤如下，首先称取不同量的碳纳米管，分别将其加入到一定体积的有机溶剂中，配制成不同浓度的前驱液，然后采用具有不同分散机理的分散方法，调节分散时间和分散功率，获得多样化的碳纳米管分散状态。
  7. 如权利要求6所述的数值化表征方法，其特征在于，所述步骤(1)中碳纳米管分散液的稀释倍数为100倍。
  8. 如权利要求7所述的数值化表征方法，其特征在于，所述步骤(2)中溶剂挥发采用室温挥发。
  9. 如权利要求8所述的数值化表征方法，所述步骤(2)中在用扫描电镜采集图像前，样品要经过喷金处理，喷金时间为80秒。
  10. 如权利要求9所述的数值化表征方法，其特征在于，所述步骤(3)中图片在处理过程中要除去图片中的噪声。
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