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"Discover the insights revealed by static light scattering in characterizing particle structures, dimensions, and properties such as molar mass and diffusion coefficients. Explore fractal dimensions and real-world examples showcasing its applications."
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786 Static Light Scattering Part 1: Aggregate Structure & Internal Dynamics
Understanding SLS static data I(q): control parameter q [units 1/Length] Large q probes small length scales Small q probes large length scales Shape of I vs q reveals particle structure
What can light scattering measure? For a solute in solution, light scattering can determine: Molar mass, M Size, rg Second virial coefficient, A2 Translational diffusion coefficient, DT - Can be used to calculate rh
Understanding SLS static data Very small particles scatter isotropically I(q) ~ constant Larger aggregates can be assessed for their fractal dimension Df, in region where I ~ q-Df rusnauka.com
Dimensionality From linear dimension to areal dimension, non- fractal linear objects are squared to give area From linear dimension to volume dimension, non- fractal linear objects are cubed to give volume Fractal objects: can t obtain area simply by squaring linear portion, nor volume simply by cubing linear segment
Fractal Dimensions 1 dimensional object Df > 1 Df approaching 2 2 dimensional object Df > 1 Df approaching 2 3 dimensional object
Example: CNT dispersions CNT dispersions reveal fractal aggregates Fractal region may not extend over entire q range Remember: Large q probes small length scales; Small q probes large length scales
Example: Fullerene NP aggregation Aggregate growth extends range of q in the power law region
Df~ 1? Correction to Stokes for Rods DLS measures Diffusion constant D k 6 T = B D Spheres: a Rods with length L diameter d: 2 +0.316+0.5825d +0.050d D=kBT 3pmL lnL d L L van Bruggen, Lekkerkerker, Dhont, Physical Review E (1997) 56 4394. Brancaa, Magazu, Mangione. Diamond & Related Materials (2005) 14 846.
Dependence on Aspect Ratio 3 p L 1 k T = + + + 2 ln . 0 316 . 0 5825 . 0 050 B D p p p = D/L; 5x 104 100 250 500 750 1000 2500 5000 4 Legend indicates values of L (nm) 3 t (ms) 2 1 0 0 0.2 0.4 0.6 0.8 1 p Both bundling & length increase diffusion time as a function of aspect ratio p
Also: dynamics as a function of angle SLS can simultaneously measure angular dependence of dynamics in the system Diffusive dynamics are defined by 2 quantities: control parameter wave vector q [units 1/Length] measured time scale Diffusion has units [L2/T] D = 1/q2 We can measure vs q. If D is constant, we expect
Fluctuation time-scale vs. q 1 10 G390, 150mM Combo Day 1 Combo Day 15 If D is a constant, then D = 1/q2 and so = (1/D) q-2 -2 t (s) 100 Typical diffusive behavior should exhibit a power law with slope -2 10 1 106 107 108 q (1/nm)
Fluctuation time-scale vs. q 1 10 G390, 150mM Combo Day 1 Combo Day 15 -2 t (s) 100 Typical diffusive behavior should exhibit a power law with slope -2 10 1 106 107 108 q (1/nm) Dynamics in Combo evolve over time. The kinks in the dynamics at higher q, beginning at 1/q ~ 75 nm, are robust!
Investigating Morphology 2 1 10 10 DYNAMICS STRUCTURE 10 3 t (s) 100 I/I0 10 4 Power law region indicates fractal structure, Df < 3. 10 1 10 5 106 107 108 106 107 108 q (1/nm) q (1/nm) Transition at 1/q ~ 75 nm in both structure and dynamics may suggests spherical primary particles at sizes <75 nm.
Lab tasks SLS on CNT samples SLS on protein/polymer/gel samples More to come on SLS
