CILAS laser- increase your activity
HOMEPRODUCTSSALES NETWORKSUPPORTABOUT CILASCONTACT USLINKS
CILAS laser - the automated auto sampler

 

Key Features

 

 

 

 

 

 

 

Click an icon for more information

NANO DS PARTICLE SIZE ANALYZER THEORY

Introduction

The Cilas Nano DS instrument combines static and dynamic light scattering for improving the reliability of results for bigger particles and polydisperse samples.  The static light scattering is based on a spatial dependence of the scattered light.  In DLS mode, the scattered light is time-dependent.  These different approaches of the scattered light are based on two theoretical aspects which we develop in this document. 

Brownian Motion Origin

The motion of the molecules of the fluid, due to the fact that the fluid contains heat, causes the molecules to strike the suspended particles at random.  The impact makes the particles move. The molecules of the liquid will move faster when the liquid is heated, causing more agitated Brownian movement of the big particles.  Similarly, if you make the liquid less viscous, the molecules can move more easily, also resulting in more particle motion.  If the particle is too big, the random bumps by molecules won't be noticed at all.

Speckle pattern

Particles illuminate by a laser source scatter light.  This scattered light then undergoes either constructive or destructive interference by the surrounding particles and within this intensity fluctuation.  The sum of these constructive and destructive interferences generates a speckle pattern.  The rate of intensity fluctuation occurs depends on the particle size.

 

      Cilas Nano DS Theory - Speckle patternConstructive and Destructive Interference  Nano DS constructive and destructive interference

                   Figure 1:  Constructive and destructive interferences and speckle pattern

Correlation funtion

The dynamic information of the particles is derived from the autocorrelation of the intensity trace recorded during the experiment.

                    Time-dependence of scattered intensity

                 Figure 2:  Time-dependence of the scattered intensity for large and small particles

At short time delays,  the correlation is high because the particles do not have a chance to move to a great extent from the initial state they were in.  The two signals are thus essentially unchanged when compared after only a short time interval.  

As the time delays become longer, the correlation decays exponentially, meaning that after a long time period has elapsed, there is no correlation between the scattered intensity of the initial and final states.

The second order autocorrelation curve is generated from the intensity trace as follows:

   Intensity equations for Nano DS

where g2(q, t) is the autocorrelation function at a particular wave vector, q, and time delay,  t,  and I is the intensity.

  

where the parameter b is a correction factor that depends on the geometry and alignment of the laser beam in the light scattering setup.

  

  

where Dt is the translational diffusion coefficient

where no is the refractive index of the sample, l is the incedent laser wavelength, and q is the angle at which the detector is located.

g2(q, t) is the auto-correlation function, an exponential decaying function of the correlator time delay, t.

The correlogram can give a lot of information about the sample.  The time at which the correlation starts to significantly decay is an indication of the mean size of the sample.  The steeper the line, the more mondisperse the sample is.

            Correlogram sample curve

Figure 3 : Normalized auto-correlation function, from 22412 ISO Standard

Stockes Einstein equation

                            Stockes Einstein equation

The determination of the translation diffusion coefficient thanks to the auto-correlation function allows to determine the particle size.

Algorithms used for particle size analysis in DLS

Cumulant

One of the most common methods is the cumulant method, from which in addition to the sum of the exponentials above, more information can be derived about the variance of the system as follows:

                  Equation for Cumulant Method

Where t is the average decay rate and 2 is the second order polydispersity index (or an indication of the variance).  A third order polydispersity index may also be derived but this is only necessary if the particles of the sstem are highly polydisperse.

One must note that the cumulant method is valid for small t and sufficiently narrow G(t).  The cumulant method is far less affected by experimental noise than other methods.

Laplace inversion
A method for analyzing the autocorrelation function can be achieved through an inverse Laplace transform known as CONTIN developed by Steven Provencher.
The particle size distribution is obtained thanks to fit a multiple exponential to the correlation function.

The CONTIN analysis is ideal for heterodisperse, polydisperse and multimodal systems which cannot be resolved with the cumulant method.

The resolution for separating two different particle populations is approximately a factor of five or higher and the difference in relative intensities between two different populations should be less than 1 : The resolution for separating two different particle populations.
 


Come and see our solutions at the following trade shows:

 

Pittcon 2016

Atlanta, GA

March 6 - 10, 2016

 

ACeRS Regional Refractories Show

St. Louis, MO

March 29 - 31, 2016

 

Ceramics Expo

Cleveland, OH

April 26 - 28, 2016

 

Powder & Bulk Solids International

Chicago, IL

May 3 - 5, 2016

 

NanoTech Conference and Expo

Washington, DC

May 22 - 25, 2016

 

Southeast Catalyst Show

Asheville, NC

September 2016

 

WI-MN SWE Annual Conference

Eau Claire, WI

October 2016

 

American Association of Pharmaceutical Scientists Show

Denver, CO

November 13 - 17, 2016

 

MRS Fall Meeting

Boston, MA

Nov 27 - Dec 2, 2016

 

setstats 111 11