by Paul West and Natasha Starostina
Pacific Nanotechnology, http://nanoparticles.pacificnano.com/

Introduction

An atomic force microscope is an excellent for visualising particles with sizes ranging from 1 nm to 10 μm. 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-μm 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 analysed 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.

Figure 1. Horizontal, vertical and angled line profiles are shown across an 1.6 ×1.6 µm AFM image of nanoparticles.

Three-dimensional analysis is made using the X, Y and Z data in an image. Typically the image is displayed in a colour scale format, such that the height of features in the image is related to the colour scale of the image. Then, using specialised threshholding software, the particles are identified. From such an image, the particle height, diameter, volume etc. may be calculated, Figure 2.

Figure 2. Threshholding algorithms applied to the images of nanoparticles shown in Figure 1. Each of the particles is automatically identified with threshholding.

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 μm typically cannot be used to make particle size measurements on 1 μm 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 depth (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.

Figure 3. Factors that affect magnified images created with electron beams (left) include the beam width, a conductive coating and beam penetration/scattering. The primary factor that affects AFM images is the probe geometry.

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, Figure 4.

Figure 4. At the top-left is a TEM image showing nanoparticles. The dimension that best characterises the nanoparticle is the width in the horizontal plane. At the top-right is an AFM image of a nanoparticle. The dimension that best characterises the nanoparticle in AFM images is the height.

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), Figure 5.

Figure 5. The AFM line profile of a nanoparticle shows that the width (w) of the nanoparticle depends on probe shape; however, the nanoparticle height (h) is independent of the probe shape.

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 threshholding used for calculating the parameters.

It is clear that the probe geometry as well as the threshholding 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.

Figure 6: There are three cases (shown left, centre and right) of probe geometry relative to the size of the particle being imaged. Left: the probe tip diameter is much smaller than the diameter of the particle and measurements are governed by the shaft angle. Centre: the probe tip is the same size as the diameter and calculations such as the particle volume are governed by the probe tip diameter. Right: the probe tip is much larger than the particle, and the particle parameters calculated are governed by the very end of the probe.

Figure 7. Several graphs may be generated for the analysis of AFM nanoparticle images. Shown here are the particle versus volume, height versus volume and number versus radius.

Figure 8. Smallest particles, 1µm diameter, Left: AFM image of 8µm particles of tin supported on a gold surface. Right: line profile of showing a width (2) and height (1) of the 8µm nanoparticles.

Figure 9. Largest particles (~10µm), >1µm diameter, Left: AFM image of 8µm particles of tin supported on a gold surface. Right: line profile of showing a width (2) and height (1) of the 8µm nanoparticles.

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, Figure 10.

Figure 10. Line profiles of a cluster of particles. From the line profile it is possible to measure the size of the nanoparticles in the image. The diameter of the particles measured from the blue line profile is 100 nm.

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, Figure 11.

Figure 11. Fourier analysis of an AFM image of a monolayer of nanospheres establishes the size of the spheres. Because the spheres are “close packed”, the probe diameter is not critical as long as individual spheres can be distinguished.

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 nanometre. 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.

Conclusions

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.

References

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