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) Zeta potential Application examples Molecular weight Sizing Polydispersity

--> 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.

Işık kaynağı Örnek hücresi I 90 Foto çoğaltıcı Detektör I0I0 I0I0 I Saçılan ışık r (Rayleigh oranı )

Işık kaynağı Örnek hücresi I 90 Foto çoğaltıcı Detektör I0I0 I0I0 I Saçılan ışık r 90 o (1 + Cos 2  ) = 1

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:polymer physicspolymerchain 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:mean The theoretical hydrodynamic radius R hyd 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.solventradius of gyration

+ 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 TerminologyIUPAC Compendium of Chemical Terminology, 2nd Edition, 1997 The radius of gyration for this case is given by aN represents the contour length of the polymercontour length

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)) ( I ray.scatt.(90 o ) – I solvent (90 o )) *** R q = I x cal.cte. x N(q) R q sol’n = Isol’n x cal.cte. x N(q) R q solvent = Isolvent x cal.cte. x N(q) ΔR q = R q, sol’n – R q, solvent = ( Isol’n – Isolvent) x cal.cte. x N(q) *** scattering intensity of toluene at 90 o I toluene = *** q: scattering vector(angle) *** rayleigh ratio of 660nm = 1.183E-5 cm -1 *** cal. cte.= rayleigh ratio of toluene at 660nm I toluene (90 o ) *** web adress to find out (dn/dc) values for the polymers:

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 n toluen = (dn/dc) PS = ml/g K = (4π 2 n 0 2 (dn/dc) 2 ) / (N A λ 4 ) ( λ = 660nm) Cal Cte = x x (3.14) 2 (1.4903) 2 (0.1050) 2 ml 2 /g 2 K = x10 23 mol -1 x (660) 4 nm K = = x ml 2 mol /g 2 nm x K = 8.4 x cm 6 mol /g cm 4 K = 8.4 x cm 2 mol /g 2 Rθ = 1.183E -5 cm -1 Kc (cm 2 mol /g 2 ) g/cm 3 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 o C was determined in a light scattering photometer at various angles θ. The table shows values of C/ΔR θ for the various concentrations (c) and scattering angles (θ). ______________________________________________________________________ c ______________________________________________________________________ θ _____________________________________________________________________ Given n = 1.5, dn/dc = 0.11 cm 3 g -1, λ = 436 nm and Avagadro’s Number = 6.03 x 10 23, calculate M w and R g of PMMA.

AngleI (toluen) I(PS4.88) Normalizayonsolventi PS1,156 mg/ml PS2,03 mg/ml PS2,97 mg/ml PS3,99 mg/ml PS4,88 mg/ml ref Exercise 2

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.scattering SAS can refer to: Small angle neutron scattering (SANS) Small-angle X-ray scattering (SAXS)Small-angle X-ray scattering Biological small-angle scattering, SAXS or SANS applied to biological systemsBiological small-angle scatteringbiological

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.small angle X-ray scatteringlight 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]radius of gyrationGuinier[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.aqueouspowder crystalnuclei hydrogen 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.dynamical theory of diffractionrefractive indexscattering length density

Guinier law

Small Angle X-ray Scattering (SAXS)