**What is the hydrodynamic diameter (D _{H}) defined as?**

The hydrodynamic diameter (D_{H}) is defined as the diameter of a hard sphere that diffuses at the same speed as the particle being measured. Only for a *perfectly* spherical particle, the particle size can be accurately defined as a linearly measured length. For all other shapes, particle sizes have to be measured via equivalent diameter techniques and the D_{H} is one of these.

**How is the hydrodynamic diameter (D _{H}) calculated? What physical parameters can affect it?**

The hydrodynamic diameter is measured using the Stokes-Einstein equation:

The physical parameters that affect the diameter measured by DLS are:

- Sample viscosity
- Temperature
- Refractive index of the dispersant

**Is the hydrodynamic diameter (D _{H}) equal to the diameter measured via TEM?**

The D_{H} is typically larger than the diameter measured via TEM. In addition to the core of the particle, the D_{H} takes surface structure and ions into account. The D_{H} also includes waters of hydration. Several studies have also shown a gel layer consisting of silica chains to protrude from the surface of a silica nanoparticle when it is in contact with water which results in a higher size being reported.

**Then, what is the comparison between the hydrodynamic diameter (D _{H}) and the physical diameter (D) of a silica particle?**

In our experience, the D_{H} is approximately 5% larger than the physical diameter.

**What does Polydispersity mean?**

The term ‘polydispersity’ as per IUPAC defines the non-uniformity of a specific distribution.

In Dynamic Light Scattering, the *mean* size and the *standard deviation* from the mean can be obtained directly from the statistics of the distribution. Here, the absolute width of the distribution can be compared to the mean to calculate a relative polydispersity. For a theoretical Gaussian distribution, the overall polydispersity is equal to the relative polydispersity and measured as [width/mean]^{2}.

**How do you define a distribution as monodisperse vs polydisperse quantitatively?**

A monodisperse distribution has a polydispersity index between 0.0 to 0.1. This is classified as a “narrow” distribution. A polydisperse sample has a PDI between 0.1 to 0.4 and is classified as a “broad” distribution.

**What is the contact angle with water for hydrophobic and superhydrophobic silica?**

The contact angle for superhydrophobic silica is approximately 150^{o} whereas that for hydrophobic silica is approximately 100^{o}.