Hydrodynamic diameter and Particle Size

 

Hydrodynamic diameter and Particle Size

 by Dr. Mirza Salman Baig

The Hydrodynamic diameter (d_H) or the hydrodynamic particle size or is defined as the size of a hypothetical spherical particle that diffuse at the same speed as the actual particle being measured using dynamic light scattering (DLS) or Particle tracking analysis (PTA). The particle size is determined using Stokes-Einstein equation.

The nanoparticle consists of the particle core along with layer of ion or polymers bound to its surface. The d_H  is a very useful parameter for characterizing particles size when in solution and includes coatings or surface functionalization on the particle being investigated.

Figure depicting hydrodynamic diameter and core diameter of a particle

Diffusion rate of particles are measured using DLS or PTA method.  

In a DLS method the colloidal suspension of particles is bombarded with laser light (Gittings & Saville, 1998) (Gordillo-Galeano & Mora-Huertas, 2021). The fluctuations in the intensity of light occur over the time due to the Brownian motion (Kusaka & Adachi, 2007) of the particles which is observed by the detector (Hackley & Clogston, 2011). This signal depends on the particle diffusion rate. The diffusion rate of the particle is inversely proportional to its hydrodynamic size. The detected light from randomly diffusing particles integrated to create a fluctuating intensity signal. This data is then used to generate the autocorrelation function, with the decay in the curve being proportional to the particle diffusion coefficient. The diffusion coefficient is determined using the data obtained at the detector for light intensity fluctuation. Stokes-Einstein equation (Maguire et al., 2018) is used to obtain the d_H using diffusion coefficient.

 

Equation 1

Stokes-Einstein equation:  

dʜ = Hydrodynamic diameter

k= Boltzmann’s constant

T = Absolute Temperature

η = Viscosity

D = Diffusion coefficient

 

 

However according to Rayleigh theory, the intensity of scattered light is proportional to the sixth power of the particle diameter. Hence in DLS method the results are heavily weighted towards larger particle size or particle aggregate size.

In the case of PTA, the software video-records the individual particle movements frame-by-frame, to calculate the diffusion coefficient for each individual particle and distinguish the differences between two particles or populations based on diffusion (Maguire et al., 2018).

As Brownian motion occurs in three dimensions but PTA observes motion using image analysis software only in two dimensions the x and y directions. The mean squared displacement (x,y)² of a particle is determined using the equation 2. This value allows the particle diffusion coefficient (D) to be determined using the Stokes–Einstein equation.

Equation 2

It is noteworthy that the measurement of hydrodynamic diameter depends on certain crucial factors. Temperature and viscosity of the system has a direct effect on the measurement of dʜ. The measurement of dʜ also depends upon properties the solution and the Hydrogen bonds and van der Waals forces existing between solvent molecule and particles.

 

 

References:

 

Gittings, M. R., & Saville, D. A. (1998). The determination of hydrodynamic size and zeta potential from electrophoretic mobility and light scattering measurements. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 141(1), 111–117. https://doi.org/10.1016/S0927-7757(98)00207-6

Gordillo-Galeano, A., & Mora-Huertas, C. E. (2021). Hydrodynamic diameter and zeta potential of nanostructured lipid carriers: Emphasizing some parameters for correct measurements. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 620(January), 126610. https://doi.org/10.1016/j.colsurfa.2021.126610

Hackley, V. A., & Clogston, J. D. (2011). Measuring the Hydrodynamic Size of Nanoparticles in Aqueous Media Using Batch-Mode Dynamic Light Scattering. Methods in Molecular Biology, 697, 35–52. https://doi.org/10.1007/978-1-60327-198-1_4

Kusaka, Y., & Adachi, Y. (2007). Determination of hydrodynamic diameter of small flocs by means of direct movie analysis of Brownian motion. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 306(1-3 SPEC. ISS.), 166–170. https://doi.org/10.1016/j.colsurfa.2007.03.030

Maguire, C. M., Rösslein, M., Wick, P., & Prina-Mello, A. (2018). Characterisation of particles in solution–a perspective on light scattering and comparative technologies. Science and Technology of Advanced Materials, 19(1), 732–745. https://doi.org/10.1080/14686996.2018.1517587