Dynamic Light Scattering Employing One- and Two-Dimensional Detectors and Different Time-Correlation Approaches

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1 Dynamic Light Scattering Employing One- and Two-Dimensional Detectors and Different Time-Correlation Approaches Ralf Klemt Summer Student Project FS-CXS September 10, 2015 Ralf Klemt Dynamic Light Scattering 1 / 17

2 Overview Coherent light scattered from disordered system Speckle patterns Dynamic light scattering (DLS) Time autocorrelation function of the intensity recorded with a point detector Additional information from multispeckle analysis 2D speckle patterns recorded Ralf Klemt Dynamic Light Scattering 2 / 17

3 Basic Theory (I) Basic theory for colloidal particles Nanoparticles in suspension Central object: Normalized intensity time autocorrelation function g 2 (q, τ) = I (q,t)i (q,t+τ) t I (q) 2 t Quasielastic light scattering q = k i k s = 4πn λ sin Θ 2 Ralf Klemt Dynamic Light Scattering 3 / 17

4 Basic Theory (II) For Gaussian fields: Siegert relation g 2 (q, τ) = 1 + β g 1 (q, τ) 2 where β [0, 1], g 1 (q, τ) = E s(q, 0)E s (q, τ) E s (q) 2 Assuming single scattering and free diffusion g 2 (q, τ) = 1 + βe 2Γτ where Γ = q 2 D = q 2 ( k BT 6πηR h ) Ralf Klemt Dynamic Light Scattering 4 / 17

5 Experimental Setup (I) Figure: Experimental Setup Ralf Klemt Dynamic Light Scattering 5 / 17

6 Experimental Setup (II) Laser: HeNe cw-laser, λ = nm Detector on a goniometer arm scan angles from 15 to 130 Samples: Polystyrene microspheres in water Sample 1: 2 µm spheres Sample 2: 4.5 µm spheres Ralf Klemt Dynamic Light Scattering 6 / 17

7 DLS Multispeckle Analysis DLS Analysis First measurement Dynamic light scattering with point detector Angles scanned from 30 to 130 in steps of 1 60 s measurement time per angle Recorded correlation data plotted and fitted relaxation rate Γ determined Ralf Klemt Dynamic Light Scattering 7 / 17

8 DLS Multispeckle Analysis Example g 2 -Functions (a) 2 µm spheres Figure: Example g 2 -functions at 40 (b) 4.5 µm spheres Γ = (18.6 ± 0.1) s 1 Γ = (7.3 ± 0.1) s 1 Ralf Klemt Dynamic Light Scattering 8 / 17

9 DLS Multispeckle Analysis 2 µm Spheres: Several g 2 -Functions Figure: 2 µm Spheres: Several g 2 -functions Ralf Klemt Dynamic Light Scattering 9 / 17

10 DLS Multispeckle Analysis Relaxation Rate (a) 2 µm spheres Figure: Relaxation rate Γ(q 2 ) (b) 4.5 µm spheres R h = (1.03 ± 0.03) µm R = (0.97 ± 0.03) µm R h = (2.53 ± 0.12) µm R = (2.26 ± 0.08) µm Ralf Klemt Dynamic Light Scattering 10 / 17

11 DLS Multispeckle Analysis Multispeckle Analysis Second Measurement Multispeckle analysis Speckle size Dynamics δx = λ L D Contrast Information on coherence C I (q, t, τ) = I px(q, t)i px (q, t + τ) px I px (q, t) px I px (q, t + τ) px. g 2 (q, t) = C I (q, t, τ) t. Ralf Klemt Dynamic Light Scattering 11 / 17

12 DLS Multispeckle Analysis Speckle Size (I) (a) 2 µm spheres at 15 (b) 2 µm spheres at 40 (c) 4.5 µm spheres at 15 (d) 4.5 µm spheres at 40 Figure: 400x400 pixels sections of the recorded speckle patters Ralf Klemt Dynamic Light Scattering 12 / 17

13 DLS Multispeckle Analysis Speckle Size (II) (a) Spatial autocorrelation function (b) Vertical speckle size Figure: Determination of the vertical speckle sizes Vertical speckle size constant for both samples No multiple scattering Ralf Klemt Dynamic Light Scattering 13 / 17

14 DLS Multispeckle Analysis Dynamics Better statistics, shorter measuring time 60 s vs 6 s per angle Limited frame rate of 120 fps Restricted to slower dynamics Two-times intensity correlation function can hint to further non-equilibrium processes before time averaging C I (q, t, τ) = I px(q, t)i px (q, t + τ) px I px (q, t) px I px (q, t + τ) px. Ralf Klemt Dynamic Light Scattering 14 / 17

15 DLS Multispeckle Analysis Two-Times Intensity Correlation Function (a) 2 µm spheres at 15 (b) 4.5 µm spheres at 15 Figure: Two-times correlation function for both samples Further processes Sedimentation? Vibrations? Ralf Klemt Dynamic Light Scattering 15 / 17

16 DLS Multispeckle Analysis Example g 2 -Functions (a) 2 µm spheres at 30 (b) 4.5 µm spheres at 30 Figure: g 2 -functions determined with point detector and CCD R h = (0.95 ± 0.05) µm R = (0.97 ± 0.03) µm R h = (1.94 ± 0.10) µm R = (2.26 ± 0.08) µm Ralf Klemt Dynamic Light Scattering 16 / 17

17 Summary DLS method a standard method to study properties of colloidal particles (nanoparticles in suspension) Particle size determination Applicability to microparticles possible with restrictions Extension of DLS setup with 2D detector Better statistics Characterisation of beam properties Identifying heterogeneous dynamics Limitation to lower time scales Ralf Klemt Dynamic Light Scattering 17 / 17

18 Backup: Very Low Concentration Reduce concentration: O(10 3 ) particles Figure: g 2 -function of 4.5 µm spheres at very low concentrations Ralf Klemt Dynamic Light Scattering 18 / 17

19 Backup: The Effect of Isopropane To avoid parasitic scattering from dust/dirt Cuvettes carefully cleaned Figure: Relaxation rate and median intensity for 2 µm spheres Ralf Klemt Dynamic Light Scattering 19 / 17

20 Backup: The RGD approximation Figure: Median of total scattered intensity Ralf Klemt Dynamic Light Scattering 20 / 17

21 Backup: Horizontal Speckle Size (a) Spatial autocorrelation function (b) Vertical speckle size Figure: Determination of the vertical speckle sizes Ralf Klemt Dynamic Light Scattering 21 / 17

22 Backup: Contrast (a) 2 µm spheres at 15 (b) 2 µm spheres at 40 Figure: Intensity distribution Shift of intensity from zero to one Otherwise: Contrast 1 Ralf Klemt Dynamic Light Scattering 22 / 17