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Handbook of Size Exclusion Chromatography and Related ...

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is <strong>of</strong>ten found in the literature when referring to the square root <strong>of</strong> the mean square<br />

radius (r.m.s. radius).<br />

From the theoretical summaries above, we see that light scattering<br />

measurements <strong>and</strong> their interpretation depend simply on two fundamental<br />

principles: 1) the intensity <strong>of</strong> light scattered by a sample is directly proportional to<br />

the product <strong>of</strong> the molar mass <strong>and</strong> concentration (that is, measure the<br />

concentration <strong>and</strong> then read <strong>of</strong>f the molar mass!), <strong>and</strong> 2) the variation <strong>of</strong> the<br />

scattered light intensity with angle is proportional to the molecules’ average size.<br />

These are somewhat simplified versions <strong>of</strong> the following more exact statements.<br />

1) The scattered light flux per unit solid angle about a direction u, in excess<br />

<strong>of</strong> that scattered by the solvent, divided by the incident light intensity is directly<br />

proportional to the product <strong>of</strong> the weight-average molar mass <strong>and</strong> the molecular<br />

concentration. This means that R(u, c) / Mwc in the limit as c <strong>and</strong> u ! 0. 2) The<br />

variation <strong>of</strong> scattered light flux with respect to sin 2 u=2 is directly proportional to<br />

the average molecular mean-square radius in the limit as c <strong>and</strong> u ! 0.<br />

Equivalently, dR(u, c)=d( sin 2 u=2) / kr2 gl in the limit as c <strong>and</strong> u ! 0.<br />

A more detailed review <strong>of</strong> the theory <strong>and</strong> its interpretation may be found<br />

in Ref. 14.<br />

4 INSTRUMENTATION<br />

Figure 1 is a schematic <strong>of</strong> the MALS measurement showing a light source<br />

(generally a laser) producing a fine beam incident on the sample. The sample may<br />

be contained in a cuvette <strong>of</strong> a flow cell. The scattered light from the sample is<br />

collected over a range <strong>of</strong> angles with respect to the forward direction. Most MALS<br />

measurements are made with light polarized perpendicular to the plane <strong>of</strong><br />

measurement. In recent years, solid-state lasers have replaced the formerly used<br />

© 2004 by Marcel Dekker, Inc.<br />

Figure 1 Schematic <strong>of</strong> an MALS measurement.

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