Combining Light Scattering with Chromatography for Full Characterization
Figure 2: A typical SEC arrangement combining UV, MALS, and RI detection in series.
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Although light-scattering measurements performed on unfractionated samples will yield average values for both mass and size,
following Zimm's method (discussed briefly in the previous section), the true characterization of any nonmonodisperse sample
requires that the differential and cumulative distributions be measured. To achieve this, the sample must first be fractionated,
for instance by SEC or GPC. Figure 2 shows a typical SEC arrangement combined with a light-scattering detector.
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The light-scattering detector is usually placed between the concentration detector (a DRI or UV detector) and the SEC columns
(31). Samples separated by the columns are generally diluted between 10 and 100 times from the injected concentration (which,
in itself, can often lead to varying degrees of disaggregation, if aggregates were first present in the injected sample),
so the second virial coefficient term in equation 2 may generally be neglected. Therefore, for GPC or SEC, equations 1 and
2 both reduce to the form
It is important to note that the baseline adjusted light-scattering signal (excess Rayleigh ratio) is proportional to the
product of the molecular weight times c. Because c is proportional to the number density multiplied by the molecular weight, the excess Rayleigh ratio is proportional to the
number of molecules per unit volume multiplied by the square of the molecular weight. Thus, the excess Rayleigh ratio, which
is measured at each eluted fraction (slice), may be extrapolated to zero scattering angle to determine the molecular weight
for that fraction from the intercept with the ordinate axis.
Because the fractionation process itself is assumed to yield monodisperse fractions at each collection, the weight-, number-,
and z-average molecular weights should be the same at each such slice. The concentration (UV or RI) detector measures a concentration
at each slice; therefore, one can calculate the differential and cumulative-weight fraction molecular weight for each sample
injected. The mean square radius may be calculated at each slice from the slope of the excess Rayleigh ratio as a function
of sin2θ/2 extrapolated to zero scattering angle, and thus the distributions of the mean square radius may also be calculated. Note
that the mean square radius may be calculated without any knowledge of the sample concentration, provided that the result
of equation 8 holds.
From a measurement of the root mean square radius and the corresponding mass at each slice, the conformation of the molecules
making up the distribution present in the sample ensemble may be determined, as well. There are two requirements for this
to be possible: First, the molecules must be large enough to permit a meaningful measurement of the mean square radius and,
second, the distribution present must be polydisperse and span a reasonable range of molecular weights. Finally, it should
be noted that for certain types of copolymers, the mean square radius cannot be calculated immediately from the variation
of the excess Rayleigh ratio with sin2θ/2.
Conclusion
Here in part I of this two-part column, we have discussed the history of light-scattering detection in tandem with chromatography
for biopolymer separations and characterizations, and briefly discussed current applications. We have also provided a summary
of the theory of light scattering and how it is combined with chromatography. In part II, we will provide a more in-depth
discussion of several applications of light scattering in biotechnology: measuring protein stability, measuring aggregates
in formulation studies, and characterizing low-molecular-weight heparin. We also compare the performance of light-scattering
methods with MS detection and other methods.
Acknowledgments
This column has been a group effort, involving several unsung contributors, as well as those whose names appear on the first
page. More specifically, we are indebted to several colleagues at Wyatt Technology in Santa Barbara, California, who read
various sections, always making constructive and useful, suggested revisions. (Often, we actually listened to such suggestions.)
In particular, our acknowledgement and appreciation goes to Phil Wyatt for the description of the fundamentals of light-scattering
theory and equations and to John Champagne for the section on using light scattering without chromatography in free solution.
Other people we wish to ackowledge at Wyatt include Cliff Wyatt, Geof Wyatt, Michelle Chen, and Sigrid Kuebler. Any errors
of omission or commission are clearly those of the editors and co-author (S.K.) alone.
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