786 Data Analysis Options.

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Presentation transcript:

786 Data Analysis Options

Fluctuations in scattered light arise from diffusive motion Recall: DLS Basics Fluctuations in scattered light arise from diffusive motion Correlation Intensity Exponential decay Hardware correlators measure fluctuations in the scattered light signal at very short time scales (~100 nanoseconds) Time τ at which G(τ) decays shows the diffusive timescale of particles moving in and out of the incident laser, causing fluctuations in I(t).

Size Measurement Equations Measured diffusion constant: τ = timescale obtained from exponential fit q = scattering vector, with units 1/length Use Stokes Einstein to obtain size

Fitting options Exponentials Cumulant Analysis CONTIN/NNLS/Regularized Single, double, stretched Cumulant Analysis CONTIN/NNLS/Regularized

Fitting Exponentials Single Exponential fit: Double Exponential fit:

Cumulant Analysis Obtain 1, 2, or 3 parameters to generate size distribution First order (single exponential) One parameter (average time) Second order Two parameters (average time and u2 related to width) Third order Three parameters (average time, u2 related to width, u3 to skew) Assumptions Gaussian distribution Polydispersity Index Alternative to 2nd moment NOT PDI of polymer MWs http://www.people.vcu.edu/~ecarpenter2/DigitalCorrelator.htm

CONTIN/NNLS/Regularized Variations on a theme: fit using sum of many exponential decays Extract time scale distribution directly: Data with fits Results http://www.people.vcu.edu/~ecarpenter2/DigitalCorrelator.htm

CONTIN/NNLS/Regularized Pros & Cons Result of fits are complete size distribution Methods are fairly sensitive to noise in G: Inverse Laplace transform is ill-posed problem References, from s-provencher.com, include CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations. Comput. Phys. Commun. 27, 229 (1982).

How Small Can DLS Measure? Limited mainly by the shortest measurable timescale In water; 532 nm; 900 10-2 ms  ~2 nm Particle size measurement : spherical approximation