The hydrodynamic size is an indication of how the particle behaves in a fluid.  It is a particle size.... If, for example, it's a Au colloid coated with protective surfactant or stabilizer then the size measured will be a reflection of the center Au and the protective shell.  If you have a technique like electron microscopy or SAXS which probes the electron rich part of the particle then only the inner core will be seen and the result obtained will be smaller.  Both are correct but reflect different properties of the particulate system. DLS obtains a hydrodynamic diameter based on the diffusion of the particles.  The z-average is a harmonically weighted intensity mean.  You will get a handle on the differences by looking at the certificates for the NIST 8011 (especially) and other 801x standards. See (registration required):

May 26th, 2010 Gold nanoparticle verification standards https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W100319GoldNanoparticleVerificationStandards.html

September 22nd, 2011 The NIST Au colloid nanomaterial, RM 8011: a DLS and SAXS comparative study of the particle size distribution

https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W110922NISTGoldSolStandards.html

I also attach a 'Basic Principles'

Dear ALAN,

Thanks for your reply.

For one my studies of polymer grafted nanoparticle. The approximate size which I am getting from FESEM images and the  hydrodynamics size are very far different from each other.  What could be the reason behind it

You are measuring different things and both are useful.  A number distribution (from electron microscopy) will be much smaller than an intensity distribution (from DLS). Why do you expect them to be the same or even similar?  Ulf Nobbmann has answered many questions on this and similar topics on ResearchGate.  Try this:

http://www.materials-talks.com/blog/2014/01/23/intensity-volume-number-which-size-is-correct/

Dear ALAN,

Thanks for your reply.

Can you direct direct me towards any reported literature which I can cite for my current paper. 

Try T Allen Particle Size Measurement 5th Edition (or any of the preceding editions).  There are some references in the Basic Principles that I attached earlier and a bunch of stuff on the http://www.malvern.com website (use the search function in the top right) plus http://www,materialstalks.com  Look especially for the posts by Ulf Nobbmann.

Check this link, it gives precise and enough information about DLS-hydrodynamic diameter

https://www.fritsch-international.com/particle-sizing/fritsch-knowledge/hydrodynamic-diameter/

One question, dear colleagues. Hyndrodynamic size of particles in the suspension and the sliping plane, where zeta potential is measured -it is the same lines? Or the hydrodynamic size is a boundary of Stern layer (how we can see for example from the picture in this link... https://www.fritsch-international.com/particle-sizing/fritsch-knowledge/hydrodynamic-diameter/

@E. Yu. Pikalova The hydrodynamic size simply reflects how a particle moves in a fluid. The slipping plane indicates where particles interact with one another. In the case of steric stabilization where the particle may be covered with a layer of protective polymer, the hydrodynamic diameter takes into account the polymer layer whereas the slipping plane is located within this layer as the charge falls off from the surface. Very different in this case.

What is the role of Diffusion coefficient in DLS?

Samiksha Sikarwar The diffusion coefficient is inherent in the Stokes-Einstein equation linking it to hydrodynamic particle size. Small particles move (diffuse) quicker than large particles.

Thanks Alan F Rawle Sir.

@Alan F Rawle, Dear Sir, If particles have a range of few nm (for example 10nm to 100 nm); then do diffusion coefficient represent the average size of NPs?Thanks in advance.

Dharmendra Pratap Singh You should post a new question in order not the confuse the answers to this particular post and giving your own question priority.

The answer to your question is 'No'. There's a range/distribution of diffusion coefficients representing the different sizes in the distribution. Obviously with a distribution then averages can be calculated.

Thank you #Alan F Rawla.

As with any technique, it is useful to understand what the fundamental measurement is and the assumptions that lead to the number reported to the user.

DLS measures something very simple: how the intensity of light scattered by particles at a given moment in time depends on the intensity a certain amount of time earlier. That's it. Then the assumptions start: 1) the time dependency (correlation) is due to a purely random process; 2) that process is random diffusion; 3) the Stokes-Einstein relationship can be used to calculate an apparent spherical (hydrodynamic) diameter; 4) there are no other interactions affecting particle motion; 5) you can deconvolve the correlation data to obtain a distribution of diffusion coefficients.

The first 3 are standard. Number 4 can be readily addressed (e.g., measuring at different dilutions, adding small amounts of electrolyte). Number 5 is where the science of the technique becomes the art of the manufacturers. There are many algorithms. Today, we could call some "open source" and others proprietary.

Mohamadreza Youssefi Azarfam

Please post a separate question to avoid confusing this thread. Thank you.

Just did it. Thank you!

Firouz Aghazadeh

In this specific case, the question is about hydrodynamic size. That word doesn't even appear of the website you link to.

Sharing herewith one of our manuscripts explaining the differences of particle size distributions (intensity-weighted, volume-weighted, or number-weighted) obtained from DLS analysis. https://www.ingentaconnect.com/contentone/asp/jnn/2018/00000018/00000010/art00035?crawler=true&mimetype=application/pdf

Thank you #Swee Pin Yeap.