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Introduction to DYNAMIC LIGHT SCATTERING (DLS) Christer Svanberg or PHOTON CORRELATION SPECTROSCOPY (PCS)

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Outline Basic of DLS –Experimental set-up –Accessible time- and length-scales Applications –Size and shape of sub-micron objects Research –Glass transition –Polymer dynamics

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Experimental set-up correlation

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DLS probes density fluctuations concentration fluctuations Scattered Electric Field

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LOG(TIME (s)) -14 -10-6-2 2 QENS Raman Brillouin DLS Dielectric NMR Time range of DLS DLS covers a very large time range! Typically: 10 -7 - 10 3 s! => 10 decades in time!

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Experimentally accessible wave vectors Q-range:typically 0.6 – 2×10 -3 Å -1 DLS is therefore suitable for diffusional studies of macromolecules, such as polymers and large biomolecules!

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Advantages and Disadvantages Wide time range Cheap Simple experimental set-up Only transparent samples Very clean samples needed Sensitive for mechanical disturbances

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Commerically avaliable products

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Scientific instruments More laser power! Specially designed cryo-furnaces Polarization options Vibration isolation table

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Scotland, 1827

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Brownian Motion First observed in 1827 by the botanist Robert Brown. He was looking at pollen grains under a microscope. The force of life? Desaulx in 1877: "In my way of thinking the phenomenon is a result of thermal molecular motion in the liquid environment (of the particles).” The mathematical theory of Brownian motion was developed by Einstein in 1905. Jean-Baptiste Perrin verified Einstein's analysis (Nobel Prize 1926).

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Brownian Motion Explanation: A suspended particle is constantly and randomly bombarded from all sides by molecules of the liquid. If the particle is very small, the number of hits it takes from one side at a given time will be stronger than the bumps from other side. This make the particle jump. These small random jumps are what make up Brownian motion. Stoke-Einstein relation:

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Applications of DLS Size: Using Stoke-Einstein equation DLS can be used to easy, fast and accurate determination of the hydrodynamic radius of particles. Typically range: 1 nm – 1μm. Shape: Ellipsodial particles results in a small fraction depolarized scattered light. Can be used for estimation of ellipticity of the particles. Difficult!

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Examples Some examples of sub-micron systems: –Micro-emulsions –peptides –micelles –macromolecules –polymers –paint pigments –bacteria, viruses

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The influence of pH on silica nanoparticles Distribution of sizesExp Data

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Estimation of Ellipsodial objects Lysozome Hydrodynamic size Calculated hard sphere Calculated ellipitic shape

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Size Distribution of Insulin Diameter (nm) Intensity

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The influence of pH on Insulin Diameter (nm) Amplitude

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Research using DLS Determination of size on complex systems: –“water-in-oil” –bio-molecules –cellulose Glass transition dynamics Polymer dynamics

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-relaxation –cooperative intermolecular motion –stretched exponential decay –non-Arrhenius temp. dep. –freezes at T g -relaxation –local motion –broad response –Arrhenius temp. dep. Glass transition dynamics log 1/T 1/T g liquid glass fast 1.0 0.8 0.6 0.4 0.2 0.0 correlation -2012 log[t/ (s)]

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Poly(propylene glycol) 0 0,2 0,4 0,6 0,8 1 10 -6 10 -4 10 -2 10 0 2 4 Time (s) 221 K 192 K Temp.

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-12 -8 -4 0 4 22.533.544.555.56 Arrhenius Plot log[ Relaxation time (s)] 1000/T (1/K) Monomer (n=1) Dimer (n=2) Polymer (n=69) Oligomer (n=7) Arrhenius Plot Conclusion: Shorter polymer chains relax faster than long chains.

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Glass Transition dynamics in Free-standing Polymer Films Polystyrene 200 - 500 Å DLS can be used to probe the dynamics of thin free-standing polymer films T g =369 K

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Glass-to-glass transitions copolymer micellar system SCIENCE 300, 619 (2003)

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Multiple Glassy States in a Simple Model System SCIENCE 296 104 ( 2002) Sterically stabilized PMMA-particles in cis-decalin.

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Polymer Dynamics h 2R g ** Brownian motion Entangled dynamics Semi-dilute solutionsDilute solutions

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Dynamic Correlation Length ξ h

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Polymer Gel Electrolytes Poly(methyl methacrylate) + Propylene Carbonate / Ethylene Carbonate + Lithium Perchlorate (LiClO 4 )

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Dynamics in a Polymer Gel Electrolyte

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Relaxations and Conductivity in Polymer Gel Electrolytes Nernst-Einstein equation …there is a close connection between the fast diffusive process and the ionic conductivity!

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Outlook: X-ray PCS Exemplary correlation functions of colloidal silica suspension measured at q ~ 7.6 × 10 -4 Å -1 using three different X-ray energies as indicated.

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Summary: DLS technique Probes density and/or concentration fluctuations. Time scales:~10 -6 - 10 3 s Wave vectors:~10 -3 Å -1 Standard characterisation techniques for particles –Determination of size1 nm - 1 m –Estimation of ellipticity and/or swelling Research –Polymer dynamics –Glass transition dynamics

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