Lecture : 2
Light scattering and determination
of the size of macromolecules
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)
Application examples
Molecular weight
Sizing
Polydispersity
Zeta potential
--> Fraunhofer Theory (diffraction)
--> 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.
Örnek hücresi
dI
 I
dl
I0
Işık kaynağı
I
r
I90
I
 e  l
Io
I0
Saçılan ışık
Foto çoğaltıcı
Detektör
I
84   2
 4 2 ( 1  Cos 2 )
Io
 r
Işığın boşluktaki (vakumdaki) hızı
no 
Işığın ortamdaki hızı

Io 2
(r )  R 
I

n o2 (n - n o )
2m
Io 2
(r ) 
I
m
Nc
M
2 2 n o2 (n
4
 no )
 m
2

2
(1  Cos )
(Rayleigh oranı)
16  R 
3 (1  Cos 2)
32 3 n o2 (n - n o ) 2
4
3 m
(1  Cos 2)
R   R 90 (1  Cos 2 )

16
R 90
3
Örnek hücresi
Io 2
2 2 n o2 (n  n o ) 2
2
(r ) 
(1

Cos
)
I
4 m
I0
I
Işık kaynağı
dn n - n o

dc
c
m
2


 2  n 2  dn  (1  Cos 2) 
o


 dc 
R  
Mc
4

N






R   K Mw c
  H Mw c
32 
H
3
n o2
2
 dn 
2
  (1  Cos )
 dc 
3 4 N
90o (1 + Cos2 ) = 1
r
Nc
M
I90
I0
Saçılan ışık
Foto çoğaltıcı
Detektör
 dn 
32 
 
 dc 
H
3 4 N
3
n o2
2
Hc Kc
1


 2 A2 c

R  Mw
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.
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-toend 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
Debye plots are most accurate when applied to any macromolecule with
Rg < 12 nm, including globular proteins and dendrimers. In addition, such
plots are generally accurate for random coil polymers with Mw < 100 kDa.
Static LS
Static LS & Dynamic LS
Dynamic LS
Particle Sizing in Concentrates by
Dynamic Light Scattering
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 sol’n = Isol’n x cal.cte. x N(q)
Rq solvent = Isolvent x cal.cte. x N(q)
ΔRq = Rq, sol’n – Rq, solvent
= ( Isol’n – 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 @ 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/dndc.htm
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 = (4π2 n02 (dn/dc)2) / (NA λ4)
Cal Cte = 1.2271 x 10 -5
( λ = 660nm)
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
Rθ = 1.183E-5 cm-1
Kc
(cm2 mol /g2) g/cm3
mol
___ = -------------------- =
------Rθ
cm-1
g
Experimental procedure
1) Preparation of Rayleigh scatter
2) 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
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 θ. The table shows values of C/ΔRθ for the various concentrations (c) and
scattering angles (θ).
______________________________________________________________________
c
______________________________________________________________________
θ
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 , λ = 436 nm and Avagadro’s Number = 6.03 x 1023,
calculate Mw and Rg of PMMA.
Exercise 2
I (toluen)
I(PS4.88)
Normalizayonsolventi
35
128623
325824.4
207813.7
247566
282419.2
306559.4
324676.6
50
46165
181010.2
100256.6
127548.4
151328
171045.8
1826687.6
75
36635
190970.2
96621.4
127821.2
156674.4
178220.2
191298
90
92441
473486.6
244018.4
322185.2
387445.6
441154.6
473517.7
105
53121
265265.9
135392.1
178984.4
216788.8
246891.4
266102.3
130
55953
264416.7
136747.4
178689.2
216152.8
247261.8
265326.7
145
66901
296682.8
155392.1
200970.8
242773.6
276153
295191.8
ref
181490
183074.8
183679.2
179994
182200
183381
183074.8
Angle
PS1,156
mg/ml
PS2,03
mg/ml
PS2,97
mg/ml
PS3,99
mg/ml
PS4,88
mg/ml
-6
9.0x10
-6
8.0x10
-6
7.0x10
-6
6.0x10
Kc/R
-6
5.0x10
-6
4.0x10
-6
3.0x10
-6
2.0x10
-6
1.0x10
0.0
0.0
0.2
0.4
0.6
2
Sin ()+24c
0.8
1.0
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
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]
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.
Guinier law
Guinier law
Small Angle X-ray Scattering (SAXS)