Slayt 1

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Lecture 2 Light scattering and determination
of the size of macromolecules
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• Theory
• Static Light scattering(SLS) (static" or
  "Rayleigh" scattering or MALLS)
• (molecular weight, hydrodynamic size)
• Dynamic Light scattering(DLS) (photon
  correlation spectroscopy (PCS)
• or quasi-elastic light scattering (QELS))
  (polydispersity)
• Electrophoretic Light scattering(ELS)
  Zeta potential
• Application examples
• Molecular weight
• Sizing
• Polydispersity

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--gt Fraunhofer Theory (diffraction) 
--gt Mie Theory (diffraction - diffusion)
The Fraunhofer theory is applicable for large
particles compared to the wavelength l
(diffusion and absorption are not considered). 
For smaller particles, it is appropriate to use
Mie Theory.
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(Rayleigh orani)
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90o (1 Cos2 ?) 1
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In polymer physics, the radius of gyration is
used to describe the dimensions of a polymer
chain. The radius of gyration of a particular
molecule at a given time is defined as
                                   where
           is the mean position of the
monomers. As detailed below, the radius of
gyration is also proportional to the root mean
square distance between the monomers
                                                  
    
The theoretical hydrodynamic radius Rhyd arises
in the study of the dynamic properties of
polymers moving in a solvent. It is often similar
in magnitude to the radius of gyration.
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The radius of gyration for this case is given by
                      
aN represents the contour length of the polymer
contour length (in polymers) The maximum
end-to-end distance of a linear polymer chain.For
a single-strand polymer molecule, this usually
means the end-to-end distance of the chain
extended to the all-trans conformation. For
chains with complex structure, only an
approximate value of the contour lengthmay be
accessible. IUPAC Compendium of Chemical
Terminology, 2nd Edition, 1997
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Debye plots are most accurate when applied to any
macromolecule with Rg lt 12 nm, including globular
proteins and dendrimers. In addition, such plots
are generally accurate for random coil polymers
with Mw lt 100 kDa.
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Static LS
Dynamic LS
Particle Sizing in Concentrates by Dynamic Light
Scattering
Static LS Dynamic LS
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NORMALIZATION N(q)-1 ( I ray.scatt.(q) I
solvent(q)) ( Iray.scatt.(90o)
Isolvent(90o)) Rq I x cal.cte. x N(q)
Rq soln Isoln x cal.cte. x N(q)
Rq solvent Isolvent x cal.cte. x N(q)
?Rq Rq, soln Rq, solvent (
Isoln Isolvent) x cal.cte. x N(q)
scattering intensity of toluene at 90o
............................I toluene 0.964
q scattering vector(angle) rayleigh ratio of
toluene _at_ 660nm 1.183E-5 cm-1 cal. cte.
rayleigh ratio of toluene at 660nm I
toluene (90o) web adress to find out (dn/dc)
values for the polymers www.ampolymer.com/FRD/dn
dc.htm
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to find out the scattering intensities of the
samples at each angle, we have to divide the
intensity that is read by the instrument for that
angle by the referance intensity again read by
the instrument.
For PS ntoluen 1.4903 (dn/dc)PS 0.1050
ml/g K (4p2 n02 (dn/dc)2) / (NA ?4)
( ? 660nm) Cal Cte 1.2271 x 10 -5
4 x (3.14)2 (1.4903)2(0.1050)2 ml2/g2 K
----------------------------------------------
6.02 x10 23mol-1 x (660)4 nm4
0.965706797 K -----------------------------
8.454 x 10 -36 ml2 mol /g2 nm4 1.1422791 x
10 35 K 8.4 x 10 -36 cm6 mol /g2 10-28cm4 K
8.4 x 10 -8 cm2 mol /g2 R? 1.183E-5 cm-1 Kc
(cm2 mol /g2) g/cm3 mol ___
-------------------- ------- R?
cm-1 g
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• Experimental procedure
• Preparation of Rayleigh scatter
• Preparation of polymer/protein solutions

3) Determination of calibration constant of
Instrument (cal. Cte) 4) Measuring of scattering
intensity of normalization solution. 5)
Measuring of scattering intensity of solvent and
solutions
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Exercise 1

• The Rayleigh ratio for a series of dilute
  solutions of polymethyl methacrylate(PMMA) in
• ethylene dichloride at 25 oC was determined in a
  light scattering photometer at various
• angles ?. The table shows values of C/?R? for
  the various concentrations (c) and
• scattering angles (?).
• __________________________________________________
  ____________________
• c
• __________________________________________________
  ____________________
• ? 0.0096 0.0048 0.0024 0.0012
• 30 56.3 35.9 26.4 21.4
• 45 57.1 36.4 26.7 21.5
• 60 57.5 36.8 26.8 21.8
• 75 58.3 37.5 27.6 22.6
• 90 59.1 38.4 28.3
  23.6
• __________________________________________________
  ___________________
• Given n 1.5 , dn/dc 0.11 cm3 g-1 , ? 436
  nm and Avagadros Number 6.03 x 1023,
• calculate Mw and Rg of PMMA.

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Exercise 2
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Small-angle scattering

• Small-angle scattering (SAS) is a scattering
  technique based on the deflection of a beam of
  particles, or an electromagnetic or acoustic
  wave, away from the straight trajectory after it
  interacts with structures that are much larger
  than the wavelength of the radiation. The
  deflection is small (0.1-10) hence the name
  small-angle. SAS techniques can give information
  about the size, shape and orientation of
  structures in a sample.
• SAS can refer to
• Small angle neutron scattering (SANS)
• Small-angle X-ray scattering (SAXS)
• Biological small-angle scattering, SAXS or SANS
  applied to biological systems

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Small angle neutron scattering (SANS)

• Small angle neutron scattering (SANS) is a
  laboratory technique, similar to the often
  complementary techniques of small angle X-ray
  scattering (SAXS) and light scattering.
• While analysis of the data can give information
  on size, shape, etc., without making any model
  assumptions a preliminary analysis of the data
  can only give information on the radius of
  gyration for a particle using Guinier's
  equation.1

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Technique

• During a SANS experiment a beam of neutrons is
  directed at a sample, which can be an aqueous
  solution, a solid, a powder, or a crystal. The
  neutrons are elastically scattered by changes of
  refractive index on a nanometer scale inside the
  sample which is the interaction with the nuclei
  of the atoms present in the sample. Because the
  nuclei of all atoms are compact and of comparable
  size neutrons are capable of interacting strongly
  with all atoms. This is in contrast to X-ray
  techniques where the X-rays interact weakly with
  hydrogen, the most abundant element.
• In zero order dynamical theory of diffraction the
  refractive index is directly related to the
  scattering length density and is a measure of the
  strength of the interaction of a neutron wave
  with a given nucleus.

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Guinier law
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Guinier law

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Small Angle X-ray Scattering (SAXS)