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An alternative way to analyze quasi-elastic light scattering data for broadly distributed samples


In Quasi-Elastic Light Scattering (QELS), an apparent average hydrodynamic radius\(R_{h, app} \left( { \equiv [\left\langle {1/R_h } \right\rangle _z ]^{ - 1} } \right)\) can be calculated from the measuredz-average translational diffusion coefficient 〈D z by using the Stokes-Einstein equation:\(R_{h, app} = \frac{{k_B T}}{{6\pi \eta \left\langle D \right\rangle _z }}\) withk B,T and η being the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. It is known thatR h, app is not the same as 〈R h z because\(\frac{1}{{\left\langle D \right\rangle _z }} \ne \left\langle {\frac{1}{D}} \right\rangle _z\), especially when a sample is broadly distributed. In order to obtain 〈R h z instead ofR h, app, an alternative way to analyze QELS data is proposed: at first, we manipulate the measured correlation functionb 1/2|g (1)(t)| into a new function\(\int_t^\infty {b^{1/2} } \left| g \right.^{(1)} (t)\left| {dt} \right.\); and then, we can analyze this new function to obtain an apparent parameter 〈Dapp and an apparent distribution width\(\mu _{2, app} (D)/\left\langle D \right\rangle _{app}^2\). We have shown that no matter how broadly a sample is distributed, 〈Dapp can be easily reduced to 〈R h z , and\(\mu _{2, app} (D)/\left\langle D \right\rangle _{app}^2\) is directly related to the distribution width. In this report, besides using a simulated time correlation function, we also used two measured correlation functions of a latex dispersion with a broad particle size distibution and a polystyrene standard with a broad molecular weight distribution to demonstrate this alternative way.

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Wu, C. An alternative way to analyze quasi-elastic light scattering data for broadly distributed samples. Colloid Polym Sci 271, 947–951 (1993).

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Key words

  • QELS
  • DLS
  • hydrodynamic size
  • polydispersity
  • data analysis