5. Characterization methods
5.2. Dynamic light scattering
36
performance due to a small aperture. The instrument is equipped with a single cell Peltier thermostat for the temperature control.
5.2. Dynamic light scattering
Dynamic light scattering (DLS) is an important and one of the most popular experimental techniques, which is used to determine the size distribution profile of small particles in suspension of colloidal particles in solution, it allows particle sizing down to 1 nm diameter.184-186 DLS is often used to monitor aggregation in polymer solutions. In this method, the sample in the cell is illuminated with monochromatic coherent laser light, and the light is scattered by fluctuations of the concentration of molecules, particles, or aggregates suspended in a sample solution and undergoing Brownian motion (Figure 5.1). The intensity fluctuations of the scattered light are recorded as a function of time and converted into electrical pulses, which are fed into a digital correlator. The rate of decay of the fluctuations of scattered light is indicative of the diffusion coefficient of the scattering species in the sample, which is lower for large particles and higher for small particles.
Figure 5.1: Schematic representation of: conventional, 90° dynamic light scattering instrument (a); and backscattering, 173° DLS instrument (b). Measurement volume at 90º and 173º.
37 In most instruments, a monochromatic coherent He-Ne, Ar or Kr ion lasers with a fixed wavelength are used as the light source, which converges to a waist of focus in the sample, by use of a focusing lens. Particles of different sizes scatter with different intensities in dependence of the scattering angle and photon detection at several scattering angles (multiangle DLS), for instance wide-angle light scattering setups covering approximately the range 20° - 180°, may provide a high quality analysis for polydisperse samples. In contrast, a conventional DLS instrument only detects the scattered light at one angle. For highly dilute solutions, almost transparent, the DLS instrument with detection of the scattered light signal at 90° (right angle, Figure 5.1a) is used, while for more concentrated solutions, and aggregated particles, the instrument with detector at 173° (backscattering angle, Figure 5.1b) is more applicable.187 The DLS measurements with the right angle detection is successfully applied for analysis of sample solutions with concentration that gives the highest scattering light intensity, but below the concentration where multiple scattering effect starts to occur.
Backscattering geometry of the DLS measurement with non-invasive backscatter (NIBS) system allows to reduce the multiple scattering effect, due to the minimization of the distance through the cuvette that light must travel from the scattering volume. Moreover, the measurement volume is increased by about 8-fold compared with a 90º instrument, with a corresponding increase in sensitivity (Figure 5.1c). In addition, by moving a focusing lens, through which pass both the incident and the scattered beams, between the laser and the sample, it is possible to shorten or to enlarge the measurement position within the cell. The shorter distance from the cell allows to reduce the distance that the light must travel through the sample within the cell and hence to minimize multiple scattering. The larger distance allows to minimize the effect of laser flare to increase the signal to noise ratio and to improve sensitivity, particularly to weakly scattering and dilute samples.
5.2.1. Data processing
Dynamic light scattering outputs the normalized time autocorrelation function, G(2)(τ), of the scattered light intensity fluctuations, which directly related to the motion of particles in solution; it is generated from the intensity trace as follow:
2
5.2. Dynamic light scattering
38
where I(t) is the initial intensity for all starting times t and I(t
) is the intensity after a delayed time τ.188 After only a very short time interval, the correlation of the scattering intensity is high and the intensity is essentially unchanged. At longer time delays, the correlation between the scattered intensity of the initial and final states is decreases and the correlation function decays exponentially. When the intensity correlation is lost, the correlation functions reaches zero.The intensity fluctuations are correlated with fluctuations in the electric field. The correlation function of the scattered electric field,
G
(1)( )
, can be obtained using the Siegert relation:
1
22 ( ) 1 G ( )
G( )
( )
, (5.3)where β is the coherence factor, which represents the degree of spatial coherence of the scattered light over the detector and is determined by the geometry of the instrument.
The correlation function for dilute suspensions of identical species in Brownian motion decays exponentially with decay rate Γ:
) e
(
G
(1) . (5.4)The decay rate Γ is the inverse of the correlation time τ and related to the transitional diffusion coefficient of the particle
D
t as follow:q
2where 𝜆0 is the incident laser light wavelength, 𝑛0 the refractive index of the sample solution and θ is the scattering angle at which the detector is located with respect to the sample cell.
The size of non-interacting diffusing particles can be determined using the Stokes-Einstein relation, which links the diffusion coefficient of a molecule or particle with its radius:
39
where 𝑘𝐵 is Boltzmann’s constant, T is the absolute temperature and 𝜂0 is the viscosity of the solution and RH is the particles hydrodynamic radius.
In the case of polydisperse sample with two different particle sizes, the autocorrelation corresponding stretching exponents which are characteristic of the breadth of the distribution of the relaxation times and assumes values in the interval [0, 1].189
For data evaluation, the DTS (Nano) software (Malvern) was used, which provides the hydrodynamic radius, Rh, and the fraction of each measured species.
5.2.2. Instrument
DLS measurements were carried out using a Zetasizer Nano ZS (Malvern) laser particle size analyzer, which is a high performance two angle size analyzer of particles and molecules in solution.190 The laser particle size analyzer equipped with a 633 nm laser at an angle of 173°
(backscattering detection). Non-invasive backscatter (NIB) system is used in Zetasizer Nano ZS, which provide the highest sensitivity simultaneously with the highest size and concentration range: a size measurement from 1 nm (hydrodynamic radius, Rh) to 1000 nm. It allows to measure small samples, minimum sample volume is 12 μL, and samples concentration from very low to high, i.e. from 0.1 ppm to 40% w/v. The instrument temperature range extends from 0 °C to 90 °C, with an additional option of measurements at 120 ºC. The Zetasizer software controls the optical unit as well as processing and presenting the measured data to give the size, fraction, molecular weight or zeta potential for the sample measured.