Introduction
An atomic force microscope is an excellent for visualizing particles with sizes ranging from 1nm to 10 micron. Another advantage of the AFM is its simplicity of operation and that the AFM requires minimal sample preparation. Additionally, the AFM can operate in air, liquid or a vacuum. In comparison to traditional techniques for single particle analysis of sub micron particles, the AFM gives three dimensional profiles. It is possible to make quantitative measurements of particle sizes with an AFM. Measuring particle sizes with all microscopy techniques, such as SEM, is relatively straightforward as long the particles are large in comparison to the size of the probe. An AFM can easily measure particle sizing parameters as long as the particle is > 100 nm. If the particle size is less than 100 nm special considerations must be taken into account.
Single Particles
Single Particle Software Analysis
Images created by an AFM are stored in a computer as a three dimensional array of numbers and can be displayed and analyzed in many formats. When doing the quantitative analysis of nanoparticles with an AFM, the two modalities of measurements are the two dimensional analysis and three dimensional analysis.
In a two dimensional analysis, a single line, or slice is made across an image. From the profile, the relative spacing between two points on the line may be calculated. This is typically achieved by placing a cursor at two points on the profile. The profiles may be made horizontally, vertically or at any angle across an image. Figure 1 shows an example of a line profile.
Three-dimensional analysis is made using the X, Y and Z data in an image. Typically the image is displayed in a color scale format, such that the height of features in the image is related to the color scale of the image. Then, using specialized thresh-holding software, the particles are identified. From such an image, the particle height, diameter, volume, etc. may be calculated, Figure2.
Single Particle Sizing Limitations
All microscopy methodologies have measurement limitations associated with the physical limitations of the measurement. As an example, an optical microscope with a resolution of 1 micron typically cannot be used to make particle size measurements on 1 micron diameter particles. However, it is possible to measure sizes of particles that are substantially greater than the resolution of an optical microscope. Similarly for SEM, several factors make it difficult to measure particle sizes. Factors include; coatings on non-conductive particles, width of the electron beam, astigmatism, aberration and the penetration depth6 (volume of interaction), Figure 3.
In an AFM there are similar limitations as the image is a combination of the probe geometry and the sample geometry. However, with the AFM it is possible to remove the effects of the probe diameter. The ability to do particle size measurements with the AFM is limited primarily by the probe geometry.
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In all microscopy techniques, distributions can be measured, that is to say that the measurements are precise and not accurate.
Single Particle Size
Particle size is typically defined by one parameter, assuming the particles are isotropic. Using traditional techniques such as the TEM/SEM, particle size is defined as the diameter of the particle in the XY plane. With the AFM, the particle size is defined as the maximum height of the particle, Figure4.
This parameter is also constant and is independent of tip diameter. This is a major advantage over other techniques because the measurement does not depend on the quality of the probe (or beam), Figure5.
The particle size distribution of an ensemble of particles may be calculated using three- dimensional analysis software. This assumes that the particles are separated and not in a cluster. The particle sizes measured this way will be accurate as long as the thresh-holding identifies correctly. The particle size using the heights will be correct.
Single Particle Volume, Surface Area, Perimeter:
Because an AFM image has three dimensions of data, X,Y and Z, it is possible to calculate many parameters such as the diameter, volume and surface area of a particle. These measurements are affected by the probe geometry. Figure 6 shows three separate cases of probe diameter and particle size. Because of this, calculations of particle volume, area, and circumference do not give accurate values. In particular, particle diameter and particle area will depend on the thresh-holding used for calculating the parameters.
It is clear that the probe geometry as well as the thresh-holding technique plays a large role in the calculations of particle parameters such as volume, area, and perimeter. The distribution curves are accurate. Thus, it is possible to tell if the particles have a large distribution or a narrow distribution from such an analysis.
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Particle Clusters
Often it is not possible to disperse nanoparticles on a surface such that they are supported as single particles. In fact, often the particles form clusters of two or more nanoparticles. It is also possible to get nanoparticle sizes from AFM images of particle clusters.
To measure particles sizes of particles in clusters, it is ideal if the nanoparticles are dispersed in a monolayer or in monolayer patches. Also, it is critical that the probe be less than half the diameter of the nanoparticles being imaged.
Line Profiles
Line profiles are helpful for measuring nanoparticle sizes of nanoparticles in monolayers. Measuring the “pitch” of the nanoparticles is very accurate because it does not depend on the specific probe geometry, Figure10.
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Spectral Analysis
Particle sizes of cluster with long-range correlation can be discerned from FFT analysis of topographical data. The primary advantage of this technique is that it takes into account a large number of nanoparticles, Figure11.
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Errors
Errors in nanoparticle size measurement with an AFM depend on the noise floor of the AFM instrument and on the relative size of the probe relative to the particle. The noise floor of an AFM is typically less than 0.1 nm so it is theoretically possible to measure nanoparticle sizes with an error of much less than a nanometer. However, because there are not atomic scale standards for an AFM with heights less than 10 nm, the measurements are not as accurate as may first appear.
Conclusion
The atomic force microscope is ideal for measuring images of nanoparticles adhered to surfaces. It is relatively easy to measure distribution curves for nanoparticles. Also, provided the AFM is calibrated in the Z dimension, it is possible to measure the particle sizes. Other parameters such as the particle volume and circumference depend critically on the geometry of the probe.
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