Molecular weight using static light scattering

Measurement devices

BeNano series Molecular weight determination

Knowledge of the molecular weight (alternatively molecular mass) of a substance is important in order to better understand its structure and chemical properties: For example, in pharmacy, the molecular weight parameter is crucial for the dosage and efficacy of a drug.

Static light scattering (SLS) is a suitable method for determining the molecular weight of colloidal particles of different sizes, structures and materials. The basic set-up of an SLS experiment is shown in the following figure:

In this method, the particles in the measuring cuvette interact with a monochromatic light source (laser). The light is elastically scattered by the particles and the time-averaged value of the light scattering intensity I_s(θ) is detected at a specific angle. The temporal fluctuations of the scattering intensity, which are investigated in dynamic light scattering, therefore play no role due to the temporal averaging! The molecular weight M_w (as a weight average) can then be determined from the light scattering intensity I_s(θ).

Depending on the type of sample to be examined and the evaluation model, the angular arrangement of the detector (scattering angle θ) plays an important role, and several detectors can also be used. The reason for these different setups is in particular the angular dependence of the scattered light intensity for particles with a diameter greater than about 1/20th of the light wavelength used.

With the measuring devices of the BeNano series, the light scattering intensity I_s is measured at one scattering angle (90° or 173°). The simplified Rayleigh equation [1] for small particles (d<λ/20, Is independent of the detector angle) is used to determine the molecular mass M_w from the measured light scattering intensity I_s:

Here K is the so-called contrast factor, c the mass concentration, R_θ the so-called Rayleigh ratio, M_w the average molecular weight of the particles and A₂ the 2nd virial coefficient. Due to the assumption of angle-independent light scattering of the particles, the measuring range for the molecular mass is limited (342 Da – 2×10⁷ Da, depending on the sample properties).

The contrast factor K reflects the scattering power of a single dispersed particle and is calculated from

Here, λ₀ is the wavelength of the incident laser, N_A is the Avogadro constant, n_D,0 is the refractive index of the solvent and (∂n_d/∂c) is the refractive index increment of the “solution” in relation to the concentration. The optical constant K thus summarizes the optical parameters of the system and reflects the difference between the refractive index of the solvent and the dispersed particle.

The Rayleigh ratio R_θ indicates the ratio between the intensity of the input radiation (I₀) and scattered radiation (I(θ)) as determined by the experimental setup:

The distance r between the detector and the scattering volume is just as influential here as the scattering volume v detected by the detector. R_θ therefore makes the measured values independent of the experimental setup.

The virial coefficient A₂ comes from the derivation of the Rayleigh equation through the series development of osmotic compressibility, which will not be discussed further here. A₂ is the 2nd virial coefficient, which indicates the deviation from the ideal behavior of the osmotic pressure due to interparticle interactions.

In practice, the molecular weight of a sample is determined with the devices of the BeNano series using the so-called Debye plot of the simplified Rayleigh equation: First, the scattering intensity I_Std of a standard material (usually toluene) with a known Rayleigh ratio R_Std is determined experimentally. Then the scattering intensity of the pure sample solvent (I_LM) and a series (normally 3-5) of the sample (I_LSG) are measured at different concentrations c.

A modification of the Rayleigh ratio equation above gives the relationship:

The Rayleigh ratio R_θ is calculated from this equation at different concentrations and Kc/R_θ is plotted against the concentration c (Debye plot). The intersection of this line with the Y-axis then gives the reciprocal molecular weight, the slope of the line gives the 2nd virial coefficient (multiplied by 2).

Literature and Norms

/1/ Debye,P.; “Molecular-weight determination by light scattering”; The Journal of Physical Chemistry 51.1 (1947): 18-32