# 1.5 Dynamic light scattering  (Page 5/7)

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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] .

${g}_{1}\left(\tau \right)={\int }_{0}^{\infty }G\left(\Gamma \right){e}^{-\mathrm{\Gamma \tau }}\mathrm{d\Gamma }=M\left(-\tau ,\Gamma \right)$

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] .

${m}_{m}\left(\Gamma \right)={\int }_{0}^{\infty }G\left(\Gamma \right){\Gamma }^{m}{e}^{-\mathrm{\Gamma \tau }}\mathrm{d\Gamma }{\mid }_{-\tau =0}$

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] .

$\text{ln}{g}_{1}\left(\tau \right)=\text{ln}M\left(-\tau ,\Gamma \right)=K\left(-\tau ,\Gamma \right)$
${k}_{m}\left(\Gamma \right)=\frac{{d}^{m}K\left(-\tau ,\Gamma \right)}{d\left(-\tau {\right)}^{m}}{\mid }_{-\tau =0}$

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

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles