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Published byEdgar Legard Modified over 2 years ago

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Introduction to Light Scattering A bulk analytical technique

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What is light scattering? In nature… blue sky and clouds red sunsets

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What is light scattering? In the lab…

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What can light scattering measure? Molar mass, M Size, r g Second virial coefficient, A 2 Translational diffusion coefficient, D T - Can be used to calculate r h For a solute in solution, light scattering can determine:

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Light and its properties Light is an oscillating wave of electric and magnetic fields Polarization: direction of electric field oscillation Intensity:

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How does light scatter? When light interacts with matter, it causes charges to polarize. The oscillating charges radiate light. How much the charges move, and hence how much light radiates, depends upon the matter’s polarizability.

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Index of refraction n The polarizability of a material is directly related to its index of refraction n. The index of refraction is a measure of the velocity of light in a material. e.g., speed of light For solutes, the polarizability is expressed as the specific refractive index increment, dn/dc.

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Adding light Interference: Incoherent sum Coherent sum

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How light scattering measures M coherent: incoherent:

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Isotropic scattering For particles much smaller than the wavelength of the incident light ( <10 nm for = 690 nm), the amount of radiation scattered into each angle is the same in the plane perpendicular to the polarization.

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Angular dependence of light scattering detector at 0° scattered light in phase detector at scattered light out-of-phase Intramolecular interference leads to a reduction in scattering intensity as the scattering angle increases.

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Definitions

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How light scattering measures r g To calculate the angular distribution of scattered light, integrate over phase shifts from extended particle. Integrating over extended particle involves integrating over mass distribution.

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Conformation: r h vs. r g 3-arm star polymer solid sphere

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Molar mass and radius r g < 10 nm isotropic scatterer r g > 10 nm Why isotropic if radius of gyration < 10 nm?

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Basic light scattering principles Principle 1 The amount of light scattered is directly proportional to the product of the polymer molar mass and concentration. Principle 2 The angular variation of the scattered light is directly related to the size of the molecule.

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Basic light scattering equation In the Rayleigh-Gans-Debye limit, the two light scattering principles are embodied in the equation: This equation also contains a correction due to concentration c. The correction is due to coherent intermolecular scattering, and contains information on the second virial coefficient.

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Definition of terms 1 K*. n 0 – solvent refractive index N A – Avogadro’s number 0 – vacuum wavelength of incident light dn/dc - spec. refractive index increment M – molar mass R( ) – excess (i.e., from the solute alone) Rayleigh ratio. The ratio of the scattered andincident light intensity, corrected for size of scattering volume and distance from scattering volume.

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Definition of terms 2 c – solute concentration (g/ml) P( ) –form factor or “scattering function”. P( ) relates the angular variation in scattering intensity to the mean square radius r g of the particle. The larger r g, the larger the angular variation. Note that P(0°) = 1. A 2 – second virial coefficient, a measure of solute-solvent interaction. Positive for a “good” solvent.

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Running an experiment 1: Calibration Why? The detectors output voltages proportional to the light scattering intensities. The voltages must be converted to meaningful units. How? 1. Flow pure, filtered (0.02 m) toluene through the flow cell. 2.ASTRA software measures the voltages from the 90° and laser monitor photodiodes with the laser on and off (dark voltages). 3.ASTRA then computes the calibration constant.

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Running an experiment 2: Normalization Why? detector sensitivities vary. each detector views a different scattering volume. scattered light is refracted. only the 90° detector is calibrated. How? 1.Fill flow cell with isotropic scatterer in actual solvent to be used. 2.ASTRA software measures voltages for each angle and: a.Determines refraction angle from solvent index of refraction. b.Determines angle and scattering volume corrections. c.Normalizes each corrected detector voltage signal to the 90° detector.

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Online Data Collection Record Rayleigh ratio varying angle (3 or 18 angles for miniDAWN or DAWN) but measuring concentration.

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Online Data Analysis 1.Perform fit of angular data to retrieve M and r g. 2.Assess quality of fit using a Debye plot.

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Batch Data Collection Record Rayleigh ratio varying - angle (3 or 18 angles for miniDAWN or DAWN) - concentration (multiple injections of known c). excess scattering solvent scattering + detector offset

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Batch Data Analysis 1.Perform global fit of data to light scattering equation to retrieve M, r g, and A 2. 2.Assess quality of fit using a Zimm plot.

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Zimm Plot of a Protein Molar Mass (MM): (7.714±0.01)e+4 g/mol(0.16%) RMS Radius (Rz): 2.6±2.2 nm(84%) 2nd virial coefficient: (1.413±0.06)e-4 mol mL/g 2 (3%) Aqueous microbatch Zimm Plot of BSA monomer

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27 Radius Results: Light Scattering &Viscometry Rg or RMS radius – mass average (root mean square) distance of each point in a molecule from the molecule’s center of gravity. *lower limit 10nm Rh or Hydrodynamic radius – radius of a sphere with the same diffusion coefficient or viscosity as “our” sample. *lower limit 1nm

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28 Hydrodynamic Radius Theoretical Examples Rh H2OH2O H2OH2O H2OH2O H2OH2O H2OH2O + + + _

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29 What can QELS Measure? Diffusion constant, D T Size, r h Polydispersity Conformation, r h vs. r g

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30 What is a QELS Experiment? Scattered light intensity is measured through time

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31 How QELS Works: Interference of Light Constructive interference Particles diffuse due to Brownian motion, resulting in light intensities which fluctuate with time. Destructive interference Diffusion!

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32 What is translational diffusion ? Translational diffusions: signal change Rotational diffusions: no signal change Diffusion of molecules ---- Brownian Motion

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33 Timescale of Motion k B – Boltzmann’s constant T – temperature (Kelvin) – viscosity of solvent r h – hydrodynamic radius

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34 D T T High temperature speeds it up D T 1/R Small particles move faster D T 1/f s Asphericity slows it down What affects translational diffusion? D T 1/f h Attached solvent and/or interparticle interactions create drag D T 1/ Viscous solvent slows it down. …and if concentration too high, ‘viscosity effects’

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