Lecture : 2 Light scattering and determination of the size of macromolecules

1. Lecture : 2 Light scattering and determination of the size of macromolecules

2. 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

6. --> 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.

8. Örnek hücresi I0 I I0 Işık kaynağı r I90 Saçılan ışık Foto çoğaltıcı Detektör (Rayleigh oranı)

9. Örnek hücresi I0 I I0 Işık kaynağı r I90 Saçılan ışık Foto çoğaltıcı Detektör 90o (1 + Cos2) = 1

13. In polymer physics, the radius of gyration is used to describe the dimensions of a polymerchain. 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 radiusRhyd 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.

14. 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

19. 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.

36. Static LS Dynamic LS Particle Sizing in Concentrates by Dynamic Light Scattering Static LS & Dynamic LS

41. 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

42. 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) ( λ = 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 Rθ = 1.183E-5 cm-1 Kc (cm2 mol /g2) g/cm3 mol ___ = -------------------- = ------- Rθ cm-1g

43. Experimental procedure • Preparation of Rayleigh scatter • Preparation of polymer/protein solutions 3) Determination of calibration constant of Instrument (cal. Cte) 4) Measuring of scatteringintensity of normalization solution. 5) Measuring of scattering intensity of solvent and solutions

44. 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.

45. Exercise 2

47. 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

48. 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]

49. 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.

50. Guinier law