NANOPARTICLE SIZE AND ZETA POTENTIAL ANALYZERS

 

 

 

 

 

 

 

 

 

 

BeNano Series Nanoparticle Size and Zeta Potential Analyzer

The BeNano Series, developed by Bettersize Instruments, represents the most recent iteration of nanoparticle size and zeta potential analyzers. It incorporates dynamic light scattering (DLS), electrophoretic light scattering (ELS), and static light scattering (SLS) to deliver precise measurements of particle size, zeta potential, and molecular weight.

The BeNano Series finds extensive use in academic and manufacturing applications across a range of industries, including but not limited to chemical engineering, pharmaceuticals, food and beverage, inks and pigments, and life science.

Dynamic light scattering (DLS)

In the field of nanoparticle characterization, dynamic light scattering (DLS) or photon correlation spectroscopy (PCS) is a widely utilized method. The DLS particle size analyzer provides accurate, rapid, and highly repeatable measurements for nanoparticles, emulsions, and suspensions. The BeNano 180 Zeta Pro nanoparticle analyzer utilizes dynamic light scattering and can accurately measure nanomaterials as small as 0.3 nanometers. This capability makes it an indispensable tool for analyzing the size distribution of nanoparticles and researching nano-powdered materials.

Theoretical Background

Light scattering refers to the dispersion of light in all directions from an oscillating dipole formed when a monochromatic and coherent light source interacts with the charges in atoms that make up a particle.

The intensity of the scattered light is influenced by the particle's intrinsic physical properties, such as its size and molecular weight. This intensity fluctuates over time due to the random movement of particles undergoing Brownian motion, which occurs when particles move spontaneously and continuously in a medium as a result of collisions with molecules in the medium.

The fluctuations in scattered light intensity with time enable the determination of the diffusion coefficient through analysis of the auto-correlation function. The translational diffusion coefficient, specifying only the translational movement of the particle and not its rotational movement, is used to quantify the speed of Brownian motion. This coefficient is measured in units of area per unit of time to account for the possibility of the particle moving away from its starting point.

The particle size distribution can then be calculated from the diffusion coefficient using the Stokes-Einstein equation. This analytical method is known as dynamic light scattering, often abbreviated as DLS.

The Stokes-Einstein equation is expressed as follows:

Equation 1: The Stokes-Einstein equation

The hydrodynamic radius is the effective size of a particle that diffuses at the same rate as a perfectly spherical particle of that size. In Figure 1, the actual size of the particle is the distance between its center and outer edge, whereas the hydrodynamic radius takes into account the length of attached segments because they diffuse as a single entity. The hydrodynamic radius varies inversely with the translational diffusion coefficient.

Figure 1: Illustration of hydrodynamic radius.

Optical Setup

Figure 2 displays the complete arrangement of the DLS instrument.

Figure 2 illustrates the optical set-up of BeNano 90, Bettersize Instruments, for dynamic light scattering.

• Laser

The majority of laser devices used in DLS instruments consist of gas lasers and solid-state lasers. An example of a gas laser commonly found in DLS setups is the helium-neon laser, which emits light with a wavelength of 632.8 nm. A solid-state laser utilizes a solid material as the means for producing light. In these lasers, small amounts of impurities called "dopants" are added to the solid material to alter its optical properties. These dopants are often rare-earth minerals such as neodymium, chromium, and ytterbium. The most frequently employed solid-state laser is the neodymium-doped yttrium aluminum garnet, which is abbreviated as Nd: YAG. Gas lasers have the advantage of emitting light with a stable wavelength at a relatively low cost. However, gas lasers are typically bulky due to their large volume. Conversely, solid-state lasers are compact and lighter, making them more manageable to work with.

• Detector

The sample cell is irradiated by a laser beam, causing the particle to scatter light, which is then fluctuated due to Brownian motion. A detector with high sensitivity captures these fluctuations in scattered light signals, even at low intensities, and converts them into electrical signals for analysis in the correlator. Photomultiplier tubes and avalanche photodiodes are commonly used as detectors in the optical setup of DLS. According to Lawrence W.G. et al., PMT and APD exhibit similar noise to signal performance at most signal levels, with APD outperforming PMT in the red and near-infrared spectral regions. APD also demonstrates higher absolute quantum efficiency compared to PMT. Due to these reasons, APD is increasingly being used in DLS devices.

• Correlator

Once the optical setup is completed, the correlator analyzes the signals detected by the detectors to calculate the distribution of hydrodynamic radius. By multiplying the scattering intensity collected from the detector with a time-shifted version of itself, the correlator generates the auto-correlation function G1(q, τ) using a mathematical algorithm. The function G1(q, τ) exhibits a single-exponential decay from 1 to 0, signifying the correlation between signals at time t and time t plus τ. The obtained correlation function information is then used to compute the hydrodynamic radius using the Stokes-Einstein equation.

Monodisperse vs. Polydisperse

Monodisperse particles exhibit uniformity in size, shape, and mass, leading to a single narrow peak in the particle size distribution curve. In contrast, polydisperse particles display variability in these characteristics. It's crucial to acknowledge the polydispersity of the samples as the algorithms for calculating the hydrodynamic radius distribution in the correlator differ based on whether the samples are monodisperse or polydisperse.

Two primary mathematical algorithms are employed to address the auto-correlation function of polydisperse samples. The most common method is the Cumulants method, which entails solving the Taylor expansion of the auto-correlation function. However, the Cumulants method is applicable only to samples with minimal size polydispersity. One way to validate the calculation is by computing and checking the polydispersity index (PDI); Cumulants analysis is valid only if the PDI value is relatively small. On the other hand, the CONTIN algorithm can directly compute the hydrodynamic radius distribution for samples with broad dispersion. It involves a rather complex mathematical technique incorporating regularization.

Data Interpretation

When evaluating the particle size test results, interpreting the data can provide insights into the quality and distribution of particle sizes. It is important to assess the correlation function's quality before moving on to the particle size analysis, as it directly impacts the accuracy of the particle size results. The overall quality of the correlation function can be inferred from its shape. In figure 6, a smooth, exponentially decaying correlation curve from 1 to 0 without noise indicates a well-performed correlation, signaling readiness to proceed with the particle size distribution analysis.

Figure 6 illustrates a well-defined correlation function curve.

If the curve remains generally smooth with some noise, depicted in figure 7, it could be attributed to impurities present in the samples affecting the consistency of the results. In this case, the operator has the option to filter the sample solution once more using the suitable syringe pore size to eliminate impurities like large dust particles in the solution.

Figure 7 displays a correlation function curve with noise as an example.

The correlation function curve in figure 8 would resemble the curve when there is inadequate scattering during a test.

Figure 8 displays an illustration of a correlation function curve that indicates a lack of strong correlation.

The function's maximum value in this scenario is significantly lower than 1, and it does not display exponential decay characteristics. To address this, the operator might consider increasing the sample concentration or the number of sub-runs to enhance the scattering.

Dynamic Light Scattering (DLS) provides data on z-average particle size, which represents a size weighted by scattered intensity. This is due to the computation of the correlation function integral using the Cumulants and CONTIN method, producing an average translational diffusion coefficient and thereby yielding the average hydrodynamic radius from the Stokes-Einstein equation. The validity of the z-average particle size should be verified using the polydispersity index (PDI). When examining the results table, a DLS particle size report includes the z-average particle size with its corresponding uncertainty, as well as the PDI value.

It is important to note that a large PDI value suggests potential polydispersity in the samples, making the z-average particle size an incomplete representation of the sample.

According to the ISO 22412:2017 Particle Size analysis of dynamic light scattering, the particle size measurements should be accompanied by uncertainties and repeatability. The measurement uncertainty is denoted by the standard deviation, while repeatability is represented by the relative standard deviation that indicates the closeness of results obtained from multiple measurements within each test run. As per ISO 22412:2017 standards, monodisperse materials with diameters between 50nm and 200nm should exhibit a z-average particle size repeatability of less than 2%.

Technology for Detecting Backscattering

Utilizing Intelligent Search to Find the Best Detection Position

Static Light Scattering (SLS)

In SLS technology, the weight-average molecular weight of macromolecules like polymers and proteins dissolved in solutions is measured. When conducting an SLS measurement, the instrument identifies scattering intensities of particles in solutions at varying concentrations. The Rayleigh ratios of samples at different concentrations are computed and then plotted against concentrations to create a Debye plot. Subsequently, the molecular weight Mw and the second virial coefficient A2 are derived from the intercept and slope of the linear fit of the Debye plot, respectively.

Electrophoretic Light Scattering (ELS)

In the realm of light scattering technology, ELS is used for measuring the zeta potential of particles that are suspended in a solution. This is achieved by observing Doppler shifts in the scattered light. When an electric field is applied to the sample, the charged particles dispersed in the suspension undergo electrophoretic movement. The Doppler effect causes a frequency shift in the scattered light compared to the incident light, and the magnitude of this shift is dependent on the particles’ electrophoretic velocity. A detector positioned in the forward direction captures the scattering signal, from which the frequency shift Δf and the electrophoretic mobility can be determined. Henry's equation is then used to derive the zeta potential and its distribution based on the obtained electrophoretic mobility.