With the rapid development of nanotechnology, nanomaterials have shown great potential for applications in various fields such as biomedicine, catalysis, electronic devices, and environmental protection, and are gradually penetrating into our daily lives. nanoparticleUsually between 10-1000 nm, they exhibit distinct physical, chemical, and biological properties compared to traditional macroscopic materials. These characteristics make nanoparticles highly valuable in biomedical fields such as drug delivery, diagnosis, and treatment. Therefore, the characterization of nanoparticles has become an important link in the research of nanomaterials. Accurate analysis of particle size, quantity, concentration, morphology, surface properties, and electrical properties not only helps to deepen the understanding of their structure-activity relationship, but also provides scientific basis for the development of new nanotechnology and optimization of existing applications. According to different principles and algorithms, different methods for characterizing nanoparticle size will provide users with various data results. This article will provide a detailed introduction to the important data and parameter meanings in nanoparticle characterization experiments.

01

Key factors related to particle sizeparameter

average particle size(Mean Size) ：

The average particle size refers to the average size distribution of all particles in a sample, representing the general size of the sample. Usually, the arithmetic mean is used for calculation, which is the sum of the particle sizes of all detected particles divided by the total number of particles. It is an important characteristic parameter of particle distribution, but in polydisperse systems, it is susceptible to the influence of particles and detection method range (LOD), so it can only be used as a rough estimate for reference.

Formula:

among which,For each particle size,nNumber of particles.

Standard deviation of particle size (StdDev Size):

The standard deviation (STD) of particle size is an indicator that quantifies the degree of dispersion of particle size distribution, indicating the degree to which the particle size deviates from its average value. The larger the standard deviation, the greater the variation in particle size and the stronger the polydispersity of the sample. The standard deviation is usually calculated based on the particle size distribution and can reflect the uniformity of the particle size distribution.

Formula:

among which,Is the particle size of a single particle,The average particle size of the particles.

Concentrated particle size(Mode Size) ：

The concentrated particle size is the most frequently occurring particle size value in the sample's particle size distribution. It represents the most common particle size in particle distribution. Compared with the average particle size, the concentrated particle size can better reflect the most dominant particle population in the sample. In highly monodisperse samples, the concentrated particle size is usually very close to the average particle size.

Median particle size(Median Size) ：

Median particle size（D₅₀The median particle size refers to the particle size distribution where exactly half of the particles have a diameter larger than this value and the other half have a diameter smaller than this value. It is the central value of particle size distribution, which can better reflect the typical characteristics of particle size distribution, especially suitable for samples with asymmetric or multimodal distribution.

D₅₀ofphysical meaningThe volume (number) of particles larger or smaller than this diameter each accounts for 50% of the total volume (total number) of the particles.

D₉₀ ：

D₉₀In the particle size distribution, 90% of the particle volume (quantity) is smaller than this particle size. Especially in polydisperse systems,D₉₀andD₁₀Relative values represent a larger portion of the particle distribution, usually related to the maximum size of the particles. Also often writtenD_v0.9orD_v09.

D₁₀ ：

D₁₀In the particle size distribution, 10% of the particles have a volume (quantity) smaller than this particle size. andD₉₀Relative values,D₁₀The smaller part representing the particle distribution is usually related to the minimum size (Min Size) of the particles. Also often writtenD_v0.1orD_v01.

In addition, it can also be usedD₀₃andD₉₇Wait to indicate the distribution of particles.D₀₃orD_v03Particles smaller than this diameter account for 3% of the total volume (quantity) of particles, and so on.

Span（Span) ：

Span is a parameter used to quantify the width of particle size distribution, reflecting the degree of dispersion of particle size.It is achieved throughD₉₀TheD₅₀andD₁₀To calculate, it is usually used when describing uneven particle size distribution.The larger the span value, the wider the particle size distribution and the more uneven the sample.

Formula:

among which,D₉₀TheD₁₀andD₅₀90%, 10%, and 50% of the particles are smaller than this particle size, respectively.

Dispersion coefficient（Dispersion Coefficient) ：

The dispersion coefficient is used to quantitatively describe the degree of dispersion of each component in a multi dispersed or unevenly distributed particle sample, and is more suitable for representing the distribution of each component in a multi distributed sample. The dispersion coefficient is often used together with the standard deviation of particle size to better characterize the dispersion effect of particles.

Algorithm description: After obtaining the actual distribution of the sample; If the sample is a mixture of multiple peaks, analyze multiple sets of distributions. Calculate the ratio of STD value (standard deviation of particle size) to the average particle size of each distribution group, and take the maximum ratio in each group as the value of dispersion coefficient.

The dispersion coefficient can also be used in conjunction with the parameter span, which provides a more precise analysis of sample dispersion. Especially in the case of multiple distributions, the dispersion coefficient can more accurately characterize the dispersion of the sample and is not affected by multiple distributions; When using, both dispersion coefficient and span value can be selected for comprehensive evaluation of sample situation. In the case of a single distribution, the dispersion coefficient and span are only different forms of representation, and one of them can be used as a reference.

02

Regarding particlesnumber concentrationKey parameters of

Dilution factor:

The dilution factor refers to the proportional relationship between the volume of the original sample and the diluted solution when the sample is diluted before testing. It is used to ensure that the testing instrument operates within its appropriate detection range, while avoiding interference caused by particle overlap or multiple effects due to high concentration. In nanoparticle characterization, dilution factor is one of the key parameters for calculating the concentration of the original sample.

It should be noted that errors may be introduced during the dilution process, so precise pipetting tools should be used and the sample should be thoroughly mixed to ensure the uniformity of dilution.

Test particle number:

The particle count here specifically refers to the total number of nanoparticles detected in a single test, usually recorded directly by an instrument and used for statistical analysis of the sample size. This parameter reflects the number of particles involved in the actual measured sample during the testing process and is an important basis for calculating particle concentration. The high or low particle count is crucial for downstream data analysis: for low concentration samples, insufficient particle count may lead to statistical errors; High concentration samples: Excessive particle count may result in particle overlap or reduced detection efficiency.

In practical applications, the number of particles is usually calculated or measured by the following methods:

• Resistance Pulse Induction Method (RPS)Single particles are detected and counted one by one, so the number of particles directly comes from the test records;
• Dynamic Light Scattering (DLS) method: indirect estimation of particle concentration;
• Microscopic imaging method: counting the number of particles through image analysis;
• In other testing methods, the number of particles can also be calculated by instruments, and the concentration can be determined by combining it with the sample volume.
  
  

Concentration test:

The test concentration (i.e. loading concentration) refers to the actual concentration of the diluted sample during testing. It is the concentration measured directly in experiments by dispersing nanoparticles in a solvent and diluting them appropriately for instrument detection. It is usually expressed in units of particle quantity (such as particle/mL) or mass (such as mg/mL).The range of test concentration reflects the sensitivity and accuracy of the instrument measurement. Excessive concentration may lead to particle overlap or blockage, while insufficient concentration may result in insufficient signal-to-noise ratio.

Formula:

among which,C_testRepresents the test concentration,N_particlesIt is the number of test particles,V_sampleIt is the volume of the actual test sample.

Considerations for concentration detection:

• The concentration detection range of testing equipment (such as resistance pulse induction method, optical particle tracking method).

• Uniformity and dispersion of sample particles.

• Ultimately, it is necessary to reverse calculate the original concentration.

  
  

Original Concentration:

The original concentration refers to the initial concentration of nanoparticles in the undiluted sample after preparation or purification, which is usually the target value for final analysis. It is the benchmark concentration of the sample in practical applications or research, reflecting the total amount and distribution of nanoparticles during the preparation process. It can help researchers understand the preparation process, yield, and concentration range of nanoparticles in practical applications. The accurate determination of raw concentration is of great significance in many fields, such as dose control in drug delivery systems and sensitivity evaluation of diagnostic reagents. By combining dilution factors and test concentrations, the number and concentration of nanoparticles in the original sample can be accurately calculated.

Formula:

among which,C_originalRepresents the original concentration,C_testRepresents the test concentration,nIndicates the dilution factor.

03

Regarding particlessurface chargeKey parameters of

Zeta electricityPosition（Zeta Potential)：

Zeta potential refers to the potential difference at the slip shear layer of the double layer on the surface of nanoparticles, and is an important parameter for characterizing the surface charge characteristics of particles. It reflects the charge state of particles in liquid media, directly affecting the stability, dispersion, and interaction behavior of particles. Zeta potential is usually expressed in millivolts (mV), and the higher its absolute value, the stronger the electrostatic repulsion of particles and the higher the stability of the suspension. The change in Zeta potential may be attributed to environmental conditions such as chemical modifications on the particle surface, pH value of the solution, and ionic strength, making it a key indicator for studying the functionalization and environmental responsiveness of nanoparticles.

The traditional Zeta potential testing method is usually based on optical or electrophoretic measurements, providing the average Zeta potential of the entire sample. However, these methods are difficult to reflect the individual characteristics of different particles in the sample, especially in mixed samples with high heterogeneity. Single particle Zeta potential detection can provide more key information by measuring the surface charge characteristics of each particle one by one:

• The difference in charge between particles: Revealing the heterogeneity of charge distribution in the sample, providing more accurate data for studying particle modification, surface modification, etc. Single particle potential analysis based on RPS technology can also provide the relationship between particle potential and particle size.
• Sample charge uniformity: helps evaluate the stability and consistency of the sample preparation process.
• Resolution of heterogeneous particle mixtures: In complex systems, such as biological samples, it is possible to distinguish the surface charge characteristics of different particles, which helps to study the interactions between particles.

Single particle Zeta potential detection has significant advantages in the field of biomedicine, such as quality control of drug delivery particles and accurate characterization of surface charges of extracellular vesicles (EVs).

Average Zeta electricityPosition（Mean Zeta Potential) ：

The average Zeta potential refers to the arithmetic mean of the Zeta potential values of all (or all detected) particles in a sample, and is one of the commonly used parameters to describe the overall surface charge characteristics of the sample. The average Zeta potential can quickly provide the overall charge state of the sample for evaluating its stability and dispersibility.

Formula:

among which,For the Zeta potential of each particle,nNumber of particles.

It should be noted that the average Zeta potential may mask the distribution characteristics of surface charges on particles in the sample. Therefore, in samples with poor uniformity, comprehensive analysis should be conducted in conjunction with other parameters such as median Zeta potential and Zeta potential distribution.

Median Zeta Potential:

Median Zeta potential（Z₅₀）, refers to the situation where 50% of the particles in the sample have a Zeta potential value lower than this value, while the other 50% have a Zeta potential value higher than this value, similar to the median particle size in particle size characterization（D₅₀）The median Zeta potential is a statistical parameter that reflects the center of charge distribution in a sample, and can to some extent reduce the impact of a few outliers on the overall description of the data.

Compared with the average Zeta potential, the median Zeta potential is more representative of samples with asymmetric surface charge distribution, especially suitable for describing complex or highly heterogeneous samples.

Z₉₀andZ₁₀：

Z₉₀The Zeta potential of 90% of the particles in the sample is lower than this value, which is used to characterize the upper limit distribution of surface charge of the particles.Z₁₀The Zeta potential of 10% of the particles in the sample is lower than this value, which is used to characterize the lower limit distribution of surface charge of the particles.

Z₉₀andZ₁₀The combination can be used to describe the range and uniformity of Zeta potential distribution of the sample. Similarly to particle size distribution analysis, the dispersion of particle surface charge distribution can be further quantified by calculating the span of Zeta potential.

04

summary

The characterization of nanoparticles is a core link in the research and application of nanomaterials. By accurately measuring and analyzing key parameters such as particle size, concentration, and surface charge, the physical and chemical properties of nanoparticles and their interactions with the external environment can be comprehensively revealed. These parameters are not only experimental data, but also a window for deconstructing the structure-activity relationship of nanomedicine and nanomaterials.

Through continuous innovation and standardization of characterization techniques, nanoscience is bringing more breakthrough discoveries and practical applications in fields such as biomedicine, catalysis, and electronic devices. The core of all of this is to use scientifically rigorous methods to transform nanoparticles from the invisible microscopic world into measurable, understandable, and controllable macroscopic data, thereby promoting the seamless connection between nanotechnology and practical needs, advancing the industrialization process of nanotechnology, and opening up broader innovation prospects.