<< Chapter < Page Chapter >> Page >

Then, for the measurement itself, one has to select the appropriate stabilization time and the duration time. Normally, longer striation/duration time can results in more stable signal with less noises, but the time cost should also be considered. Another important parameter is the temperature of the sample, as many DLS instruments are equipped with the temperature-controllable sample holders, one can actually measure the size distribution of the data at different temperature, and get extra information about the thermal stability of the sample analyzed.

Next, as is used in the calculation of particle size from the light scattering data, the viscosity and refraction index of the solution are also needed. Normally, for solutions with low concentration, the viscosity and refraction index of the solvent/water could be used as an approximation.

Finally, to get data with better reliability, the DLS measurement on the same sample will normally be conducted multiple times, which can help eliminate unexpected results and also provide additional error bar of the size distribution data.

Data analysis

Although size distribution data could be readily acquired from the software of the DLS instrument, it is still worthwhile to know about the details about the data analysis process.

Cumulant method

As is mentioned in [link] , the decay rate Γ is mathematically determined from the g 1 ( τ ) curve; if the sample solution is monodispersed, g 1 ( τ ) could be regard as a single exponential decay function e τ , and the decay rate Γ can be in turn easily calculated. However, in most of the practical cases, the sample solution is always polydispersed, g 1 ( τ ) will be the sum of many single exponential decay functions with different decay rates, and then it becomes significantly difficult to conduct the fitting process.

There are however, a few methods developed to meet this mathematic challenge: linear fit and cumulant expansion for mono-modal distribution, exponential sampling and CONTIN regularization for non-monomodal distribution. Among all these approaches, cumulant expansion is most common method and will be illustrated in detail in this section.

Generally, the cumulant expansion method is based on two relations: one between g 1 ( τ ) and the moment-generating function of the distribution, and one between the logarithm of g 1 ( τ ) and the cumulant-generating function of the distribution.

To start with, the form of g 1 ( τ ) is equivalent to the definition of the moment-generating function M (- τ , Γ) of the distribution G (Γ), [link] .

g 1 ( τ ) = 0 G ( Γ ) e Γτ = M ( τ , Γ ) size 12{g rSub { size 8{1} } \( τ \) = Int rSub { size 8{0} } rSup { size 8{ infinity } } {G \( Γ \) e rSup { size 8{ - Γτ} } dΓ} =M \( - τ,Γ \) } {}

The m th moment of the distribution m m (Γ) is given by the m th derivative of M (- τ , Γ) with respect to τ , [link] .

m m ( Γ ) = 0 G ( Γ ) Γ m e Γτ τ = 0 size 12{m rSub { size 8{m} } \( Γ \) = Int rSub { size 8{0} } rSup { size 8{ infinity } } {G \( Γ \) Γ rSup { size 8{m} } e rSup { size 8{ - Γτ} } dΓ} \lline rSub { size 8{ - τ=0} } } {}

Similarly, the logarithm of g 1 ( τ ) is equivalent to the definition of the cumulant-generating function K (- τ , Γ), EQ, and the m th cumulant of the distribution k m (Γ) is given by the m th derivative of K (- τ , Γ) with respect to τ , [link] and [link] .

ln g 1 ( τ ) = ln M ( τ , Γ ) = K ( τ , Γ ) size 12{"ln"g rSub { size 8{1} } \( τ \) ="ln"M \( - τ,Γ \) =K \( - τ,Γ \) } {}
k m ( Γ ) = d m K ( τ , Γ ) d ( τ ) m τ = 0 size 12{k rSub { size 8{m} } \( Γ \) = { {d rSup { size 8{m} } K \( - τ,Γ \) } over {d \( - τ \) rSup { size 8{m} } } } \lline rSub { size 8{ - τ=0} } } {}

By making use of that the cumulants, except for the first, are invariant under a change of origin, the k m (Γ) could be rewritten in terms of the moments about the mean as [link] , [link] , [link] , and [link] , where μ m are the moments about the mean, defined as given in [link] .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play

Source:  OpenStax, Nanomaterials and nanotechnology. OpenStax CNX. May 07, 2014 Download for free at http://legacy.cnx.org/content/col10700/1.13
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Nanomaterials and nanotechnology' conversation and receive update notifications?