UGC-DAE Consortium for Scientific Research, Mumbai

1. UGC-DAE Consortium for Scientific Research, Mumbai Light Scattering studies on Colloids & Gels Goutam Ghosh

2. UGC-DAE Consortium for Scientific Research, Mumbai q scattering angle q = Iks – kiI = scattering vector IksI = IkiI = 2p / l q = ks q q ki - + Case 2 I ~ I(t) ~ n(t) ~ f(t) Elastic Light Scattering ks q ki ki Brownian motion Count scattered intensity as a function of q or time (t) Case 1 I ~ <n> (mp – ms) V2 P(q) I ~ <n> (mp – ms) V2 P(q) S(q) d = p / q Static Light Scattering (SLS) D t ~ 50 nSec Dynamic Light Scattering (DLS)

3. UGC-DAE Consortium for Scientific Research, Mumbai z x • Angle between direction • of polarization and • scattering plane,y • Scattering angle ,q Basic scattering geometry ki Y y q Incident Scattering vector, q ks Scattered • Scattering vector, q = ki - ks Source: Vertically polarized, monochromatic (l = 532 nm) laser light. Classical theory of Scattering

4. UGC-DAE Consortium for Scientific Research, Mumbai - + Oscillating electric field Induced dipole moment Scattered Electric field Scattered intensity Rayleigh law True for particles whose size less than l /20 Classical theory of Scattering

5. UGC-DAE Consortium for Scientific Research, Mumbai Polarization dependence I For perpendicular polarization, y = 90, for all q II For parallel polarization, y = 0 when q = 90 and y = 90 when q = 0 and 180 III For unpolarized light Rayleigh ratio Angular distribution independent of size Classical theory of Scattering

6. UGC-DAE Consortium for Scientific Research, Mumbai q Light Scattering Set up LS P1 L S PD PM P2 VH VV LS → Laser source (100 mW, He-Ne, 532 nm vertically polarized) P1 and P2 → Linear Polarizers L → Lens used to focus the incident beam at the sample PD → Photo-Diode PM → Power meter PMT → Photo-multiplier Tube detector C → Computer for data collection q → Scattering angle C PMT

7. UGC-DAE Consortium for Scientific Research, Mumbai Light Scattering method • Average structure • Interactions • Liquid phase • Fast and wide range (DLS) • Non-destructive • Indirect (reciprocal space) • Low resolution (DLS) • Interference (dust)

8. UGC-DAE Consortium for Scientific Research, Mumbai Light, neutron and X-ray scattering Size range of different scattering methods 1 10 100 1000 10000 Dimension (nm) SANS, SAXS USANS Comparison (Static scattering) - Different length scales - scattering power light (refractive index) x-rays (electron density) neutrons (scattering length density) SLS RGD MIE DLS Works in a range where optical microscopy fails!

9. UGC-DAE Consortium for Scientific Research, Mumbai Systems studied using Light Scattering method • Colloidal solutions - Surfactants - Polymers - Drugs - Nanoparticles • Gels In a colloidal solution particles execute Brownian motion in the entire volume. In a gel a macroscopic network is formed and noBrownian motion exist.

10. UGC-DAE Consortium for Scientific Research, Mumbai Form factor for non-interacting particles, S(q) = 1 P(q) = F(q) 2 = , I(q)= I(0) exp(-q2Rg2/3) Guinier law Small limit,qr <<1, 50 nm For sphere where Static Light Scattering I ~ <n> (mp – ms) V2 P(q) S(q) • For non-interacting particles, S(q) = 1 • Non-aqueous solution • Infinitely dilute solution in water • Moderate concentration (vol. frac. < 10-2) in water with • salt concentration > 10 mM

11. UGC-DAE Consortium for Scientific Research, Mumbai P(q) for a large sphere & S(q) = 1 220 nm 450 nm Static Light Scattering

12. UGC-DAE Consortium for Scientific Research, Mumbai When the positions are correlated I(q) ~ <n> (mp – ms) V2 P(q) S(q) Small particle limit g(r) represents the probability of finding another particle at a distance r and r+dr S(q), Concentration dependence • Vol. Fraction • Charge • Ionic strength As concentration increases, peak develops at q ~ p/d Interparticle Structure factor, S(q) Static Light Scattering

13. UGC-DAE Consortium for Scientific Research, Mumbai Dynamic Light Scattering (DLS) Also known as Photon Correlation Spectroscopy (PCS) and Quasi-Elastic Light Scattering (QELS)

14. UGC-DAE Consortium for Scientific Research, Mumbai q r(t) Auto-correlation function 1 2 3 4 “large” slow moving particles I(t) g(2)(t) “small” fast moving particles t (mS) t (mS) Dynamic Light Scattering (colloidal system) I ~ I(t) ~ n(t) ~ f(t) Time Resolved Experiment • Number density changes with time • Net intensity changes with time • Diffusion rate depends on particle size, • medium viscosity, temperature

15. UGC-DAE Consortium for Scientific Research, Mumbai Polydispersity index = CONTIN NNLS Siegart’s relation: g2(t) = 1 + |bg1(t)|2 , 0 < b ≤ 1 I ~ < E >2 G =1/TR= q2 D = Exponential fit Relaxation time dist. Method of Cumulant DLS on colloids

16. UGC-DAE Consortium for Scientific Research, Mumbai g1(t) = A exp (- Dq2t) translational Stokes-Einstein relation 1 2 3 4 Do = kT / (6phRh) Do - diffusion coefficient, T - temperature h - viscosity, Rh - hydrodynamic radius • Monodisperse spheres (single exponential decay) 2.5 nm (1) 54 nm (2) 214 nm (3) 422 nm (4) DLS on colloids

17. UGC-DAE Consortium for Scientific Research, Mumbai Da (slope) For translational diffusion, G = Dq2 SDS micelles in presence of additive DLS on colloids

18. UGC-DAE Consortium for Scientific Research, Mumbai qL > 3 kT G Isotropic Anisotropic DR A1 q2 F(p) – shape factor F(p) D = 3phL translational A D G rotational A2 t q2 Non- Spherical particles (rotational diffusion) VH VV DLS on colloids

19. UGC-DAE Consortium for Scientific Research, Mumbai Sphere-to-Rod transition of SDS micelles with addition of TBABr DLS on colloids

20. UGC-DAE Consortium for Scientific Research, Mumbai Stokes-Einstein relation D = kBT / f DLS on colloids

21. UGC-DAE Consortium for Scientific Research, Mumbai Semi-dilute regime Number density > 4Rg3 Fast mode – Diffusion Slow mode – stress relaxation Polymer solutions DLS on colloids

22. UGC-DAE Consortium for Scientific Research, Mumbai x Colloidal solution Polymer gel DLS on Gel What is a gel ? A gel is a physically or chemically cross-linked three dimensional network which can hold liquid; therefore, visco-elastic in nature.

23. UGC-DAE Consortium for Scientific Research, Mumbai • Characterization of the Sol-gel transition : •  Gelation kinetics • Gelation mechanism • Characterization of the gel phase : • Morphology • Dynamics What is measured on gel using DLS ? DLS on Gel

24. UGC-DAE Consortium for Scientific Research, Mumbai Scattered counts Measured time Gelation kinetics :-The time taken by the polymer solution to transform to a macroscopic gel phase is called the gelation time (tgel). The inverse of tgel is the gelation rate (tgel-1), or the gelation kinetics. Measurement methods (gelation kinetics): ● Test tube tilt (TT) ● Light Scattering (LS) NO FLOW DLS on Gel

25. UGC-DAE Consortium for Scientific Research, Mumbai Method 1 (Pusey): <I (q )>T = <I (q )>E [S (q,t ) – S (q, ∞)] Non-ergodic ratio: Y  <I (q )>E / <I (q )>T <I (q )>T <I (q )>E where A gel is anon-ergodicsystem, as its dynamics are restricted by bonds. Therefore, a time-averaged measurement does not represent the complete structural and dynamical aspects of a gel system. So, how to measure a Gel using DLS ? DLS on Gel

26. UGC-DAE Consortium for Scientific Research, Mumbai Method 2 (Xue):In this method, the detection area has to be such that multiple speckles can be seen at a time. The sample (gel) is either rotated or translated to average over multiple orientation of the sample. Therefore, directly measures g1(t) or S(q,t) DLS on Gel

27. UGC-DAE Consortium for Scientific Research, Mumbai Dynamic structure factor, S(q,t ) of a gel phase has two modes, namely, fast mode and slow mode, i.e., S(q,t ) = Sf(q,t ) + Ss(q,t ) Fast mode : The fast mode relaxation which gives rise to the initial exponential decay of S(q,t ) arises due to the diffusive mode of segmental dynamics in polymer chains between two cross-link points. Df = E /f Stokes-Einstein’s equation : Df = E /f = kBT / 6ph DLS on Gel

28. UGC-DAE Consortium for Scientific Research, Mumbai • Slow mode : The origin of the slow mode is not very clear. Two models are reported. • Gel mode plus inhomogeneity (GMPI) – gel is viewed as an elastic medium with overdamped modes describing the density fluctuations. Coupled with some static inhomogeneities this picture can qualitatively describe the initial decay of the correlation function (fast mode) and its saturation at long time (slow mode). • Harmonically bound Brownian particle (HBBP) – at short time the particles (chain segments) undergo simple diffusion, but at longer time they find that they are restricted to a maximum displacement when the elastic energy equals the thermal energy, i.e., • kx 2/ 2 = kBT/ 2 DLS on Gel

29. UGC-DAE Consortium for Scientific Research, Mumbai How to determine to dynamics of the slow mode ? The two models can be distinguished by studying S(q,t) at different wavevector (q). For example, (1) in GMPI model, the fast mode of S(q,t) is q dependent, but the slow mode is independent of q, and (2) in HBBP model, both modes are q dependent. DLS on Gel

30. UGC-DAE Consortium for Scientific Research, Mumbai Reference: Dynamic Light Scattering: Application of Photon Correlation Spectroscopy, Ed. Robert Pecora, Plenum Press, New York and London, 1985. Goutam Ghosh ghoshg@barc.gov.in ghoshg@csr.ernet.in Ph: 2550 5327 UGC-DAE Consortium for Scientific Research http://www.csr.ernet.in Thank you