# Calculating Molecular Weight with the Nicomp

The Nicomp can be used for estimating the average molecular weight, Mw, of particles or macromolecules suspended in solution. The word "estimate" is emphasized since the measurement of molecular weight using the technique of dynamic light scattering (DLS) is not as accurate as the determination of particle size, for which all DLS-based instruments are primarily designed.

## Introduction

The vital quantity measured in a DLS-based instrument refers to the particle diffusivity or diffusion coefficient, D. There is a simple empirical formula that can be employed for relating the molecular weight, Mw, of a suspended particle (or macromolecule) to its diffusivity, D:

 D = α Mw-β (1)

The pre-factor constant, α, is related to the particular composition of both the surrounding solvent and the diffusing particles. The pre-factor relies on the temperature T and solvent viscosity η, as well as the mass density of the particles. Constant β in the exponent is related to the configuration/shape of the particles and macromolecules (which may also be a function of particle and solvent composition, as in the case of polymers). Exponent β relies on the relationship between the molecular weight and the hydrodynamic radius; for simple spheres, β equals 1/3.

From Equation (1), a simple, general expression for the molecular weight, Mw, as a function of the diffusivity, D is shown in equation (2):

 Mw = (α/D)1/β (2)

In the Nicomp (Figure 1), Mw is computed from Equation (2) using the mean diffusivity D (intensity-weighted) attained from the simple Gaussian Analysis. Values for α and β are entered in the Control Menu shown in Figure 2.

Figure 1. Nicomp DLS system.

Reliable estimates of constants α and β must be available in order to obtain reliable estimates of the mean molecular weight of the particles. Table 1 lists values for a few representative polymer/solvent systems.

Table 1. α and β for the particle/solvent systems.

Polymer Solvent T(°C) α β
Polyacrylamide water 20 8.46 x 10-4 0.69
Polyacrylonitrile DMF 25 3.2 x 10-4 0.63
Polyacrylonitrile DMF 35 2.19 x 10-4 0.58
Polyvinyl acetate MEK 20 7.8 x 10-4 0.63
Polystyrene MEK 25 3.1 x 10-4 0.53
Polyisoprene chloroform MEK 20 3.5 x 10-4 0.42
Poly methyl methacrylate ethyl acetate 20 1.61 x 10-4 0.48
Polyvinyl alcohol water 20 5.5 x 10-10 0.68

## Sample Result

Immunoglobulin G (IgG) lyophilized powder (Athens Research) was produced at 1% weight percent by dissolving in PBS buffer, followed by then diluting to 10 mg/mL. The particle size and molecular weight estimate analysis was carried out using the conditions shown in Figure 3.

The sample was examined seven times and Control Menu settings and the final result showing both Mw and particle size results are shown in Figure 4.

Figure 4. Size and Mw results for IgG.

The expected Mw value for IgG is 145 kDa or 1.45e5 in Daltons, the units displayed in Figure 4. The value is somewhat higher than the reference value, perhaps due to aggregation and/or non-expert sample preparation.

## Conclusions

The Nicomp DLS system is mainly considered to be a particle size and zeta potential analyzer. Improved and more preferred techniques are available in order to determine the Mw of proteins and polymers, but an estimated value can be calculated by using the approach described in this article.

This information has been sourced, reviewed and adapted from materials provided by Entegris

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