## Does Shape of Microparticles Matter?

Particle shape plays a critical role in how the particles travel, behave, interact with each other and their environment. It also influences particle flow characteristics.

### Flow characteristics (ball-bearing effect) of spherical particles:

Spherical shape of microparticles is often desirable because spheres and microspheres are well-known for their ball-bearing effect. They roll and spread out. If you spill spheres on the ground, the floor will turn into a skating rink. Unlike the non-round granular or flake particles with uneven and sharp edges, spherical particles glide past each other and surfaces they contact with minimal effort and friction. This can be part of the reason that coronavirus spreads so easily compared to other viruses that do not have spherical shape.

Non-spherical (irregular) shape particles maybe desired for applications where rough, high-friction, non-slippery surface area is required. It is not uncommon for low-cost low-quality microparticles to contain a significant amount of crushed, oblong and non-spherical particles, which could negatively impact the texture, appearance and feel of finished products and/or performance in an application.

### Packing properties of spherical particles:

Both shape and size distribution influence the packing density of materials. Particle shape has a significant effect on packing structure. The packing of non-spherical particles is considerably different from that of spherical particles. Typically the packing density increases with improved sphericity of the particles. ^{1} The data also shows that increasing particle irregularity causes a decrease in stiffness and heightened sensitivity to the state of stress.

### Optical properties of spherical particles:

Spherical shape is critical for optical properties of the particles, especially when particles are used as miniature lenses, such as in retroreflectivity applications. In this situation it is desired that the spherical surface of each particle behaves as a concave mirror with the required curvature for retroreflection. Even though the shape is not the only parameter to achieve optimum optical effect, it is one of the critical components.

### Controlled surface area of spherical particles:

In biotechnology and biomedical applications, there are numerous benefits of using microspheres in drug delivery due to their precise uniform dimensions, larger surface area per unit volume, as well as the ability to be surface-functionalized or loaded with active compounds and other additives. Due to small size and spherical shape, microspheres can be delivered via oral, parentral, nasal, ophthalmic, transdermal, colonal delivery methods.

### Mathematical models of microparticle behavior – test particles:

Most mathematical models (e.g. models based on Stoke’s law) are founded on the assumption of a *perfectly spherical particle shape*. The spherical particle shape of the test material is critical for successful validation of mathematical models.

## How Do We Characterize (Measure) the Shape of Microparticles?

Characterizing shape of a population of microparticles is challenging because we are looking for statistically significant value that is measured in three dimensions with a large number of unique variations.

Currently there is no golden standard in the industry that successfully meets this goal. Instead, we look at a combination for several measurements to get a general idea of the shape of the particles we are working with.

These parameters are *Roundness* and *Sphericity*. Often these terms are used interchangeably but they are not synonymous. It is critical for scientists and engineers who work with microparticles to understand that these concepts are quite different and each carries important and unique information about the behavior and properties of the microparticles individually and as a population.

### What is Roundness of Microparticles?

The best definition of roundness comes from geology and was described by Krumbein in 1941 in his work on shape and roundness of sedimentary particles. ^{2}.

*Roundness of Microparticles* is the smoothness of the edges. Are the edges sharp? An object with very sharp edges has low roundness, an object with no sharp edges (a smooth object) has high roundness.

When measuring roundness we are looking at the curvature of the corners of the particle and determining the size of a sphere that would fit into that corner. Roundness is usually measured using a visual method by comparing the images of the particle to a chart as shown. Even when this process is automated, there is some algorithmic version of the same process of grouping particles into categories based on the sharpness of the edges.

### What is Sphericity of Microparticles?

Sphericity of microparticles is a measure purely of the form of the particle and how closely all the cross-sections of the particle are to resembling a perfect circle. This measure does not provide any information on the sharpness of the edges.

“Fundamentally, the shape is the measure of the ratio of the surface area of the particle to its volume. For a sphere this ratio is a minimum, for other shapes it is larger. Hence, the ratio of surface are to volume indicates how closely or remotely a particle resembles a sphere in form.”

^{2}.

Mathematically, we are looking at the ratio of the actual volume of the particle to the maximum volume of the sphere that can be embedded inside this particle. The cubic root of this ratio is defined as *sphericity* of the particle.

*Sphericity of the particle* is often estimated by calculating the ratio of the smallest diameter of the particle to the largest diameter of the particle. The closer this ratio is to the value of one, the closer the particle shape is to that of a sphere.

### Understanding Roundness and Sphericity of a Powder (a large population of particles):

We are typically working with large populations of microparticles (powders). This means that we are usually looking at a distribution of shapes in a population. Knowing an average number for sphericity and roundness of the particles does not provide enough information when looking at billions of particles.

For this reason at Cospheric, we typically specify our quality criteria for sphericity and roundness of the particles. For example, most of the grades of Cospheric Microspheres specify that greater than 90% of the particles are spherical and greater than 90% of the particles are round. Higher precision grades have higher standards of greater than 95% of the particles are spherical and greater than 95% of particles are round. For our most precise grades of microspheres we specify that greater than 99% of particles are spherical.

### In a Nutshell: We need to know both Roundness and Sphericity

A particle may be mostly spherical but not round (e.g. some pinecones), or it may be round but not spherical (e.g. form may be elliptical). Information about both of these parameters is critical when sourcing microparticles for a specific application where the true shape (form) of the particles as well as its roundness (smoothness of the edges) play a critical role.

## Technical Support

As always, *Cospheric technical support staff is available* via email to answer any questions, offer product recommendations, provide quotes, or address custom manufacturing inquiries. We have over 2000 products in stock. If you are not finding what you are looking for on Cospheric website, let us know! We most likely will be able to recommend an alternative product to meet your needs.

### Sources:

- Zhao, Shiwei & Zhou, Xiaowen & Liu, Wenhui & Lai, Chengguang. (2015). Random packing of tetrahedral particles using the polyhedral discrete element method. Particuology. 23. 10.1016/j.partic.2015.02.007. [↩]
- William Christian Krumbein; Measurement and geological significance of shape and roundness of sedimentary particles.
*Journal of Sedimentary Research*1941; 11 (2): 64–72. doi: https://doi.org/10.1306/D42690F3-2B26-11D7-8648000102C1865D[↩][↩]

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