The term "microrheology" is used to describe a range of techniques that extract local and bulk rheological properties of soft materials by measuring and analyzing the motion of colloidal tracer (or probe) particles of known size, dispersed in the sample. Microrheology is a relatively new analytical methodology that continues to be the subject of increasing academic study, and is of growing interest to those researchers working at the forefront of rheological characterization.
Dynamic Light Scattering (DLS) microrheology [1] is a passive microrheology technique. Linear rheological properties of a sample are determined from the average motion of an ensemble of dispersed tracer particles undergoing random thermal fluctuations in a system at thermodynamic equilibrium. Thermally-driven motion (or thermal diffusion) of the tracer particles is intimately linked to the rheological properties of the suspending fluid. The Mean Square Displacement (MSD) describes the tracer particle motion with time, and this is directly related to the correlation function of the tracer particles from a DLS measurement. From analysis of the MSD, the rheological properties of the sample are calculated using the Generalized Stokes-Einstein Relation. Results are obtained for viscoelastic moduli (elastic modulus, G' and viscous modulus, G'') of the sample.
In order to obtain reliable microrheology data, careful consideration must be given to the compatibility of a particular tracer particle and sample combination. The tracer particle surface chemistry, concentration and size are all factors to assess in order to be able to extract rheological responses that are truly representative of the underlying sample dynamics and microstructure.
One of the key requirements is to minimize tracer particle-sample interactions, since these will affect tracer particle diffusivity, and hence the Mean Square Displacement and therefore the extracted rheological data [2]. Consideration of the choice of tracer particle chemistry is crucial in this respect.
The zeta potential of a colloidal particle is the electrostatic potential between the dispersant matrix and the layer of fluid attached to the dispersed particle [3]. Zeta potential can be calculated by measuring the electrophoretic mobility of the colloidal particles.
The zeta potential of a colloidal particle will change if the surface properties of the particle change e.g. if components of the dispersant matrix, such as polymer or protein molecules, adsorb onto the particle surface.
A suggested measurement protocol for the use of zeta potential data as an indicator for tracer particle-sample interactions is as follows:
Note that if zeta potential data are to be used as an indicator of the presence of tracer particle-sample interactions, consideration must be given to the viscosity, and hence the concentration of the sample solution used in these measurements. Since zeta potential is related to electrophoretic mobility, UE, by the Henry equation [3]:
where Z is zeta potential and η is viscosity (and ε is dielectric constant, and f(κa) is Henry's function) - then the sample concentration used should be low such that any increase in viscosity of the solution is minimized compared to the base solvent, or a separate measurement should be undertaken for the solution viscosity that is then used in the zeta potential measurement. Note that if the solution is non-Newtonian, then an estimate of the zero shear viscosity would be an appropriate value to use.
The possible error in zeta potential measurement arising from the viscosity of the solution must be assessed and minimized, in order to use zeta potential as a reliable pre-measurement step to assess tracer particle-sample interactions for DLS microrheology measurements.
This study uses bovine serum albumin (BSA) solutions to investigate how zeta potential measurements can be used to assess tracer particle-sample interactions. BSA is known to coat polystyrene particles [4], and by undertaking DLS microrheology measurements using both polystyrene latex and melamine resin tracer particles, the impact on zeta potential data and the subsequent rheological response can be examined.
A sample of bovine serum albumin (BSA, purchased from Sigma Aldrich) was used without any further purification. Solutions were prepared for DLS microrheology by dissolving the BSA in phosphate buffered solution (PBS).
For the microrheology measurements, the following tracer particles were used:
Tracer particles were added to the BSA solutions and allowed to fully disperse for at least 12 hours prior to taking any measurements.
The tracer particle concentration was chosen such that the scattering intensity of the tracer particles dominates the scattering from the protein i.e. until the tracer particle peak of the particle size distribution (PSD) accounted for at least 90% of the total area. For each experiment, 10 µL of tracer particle suspension was added to 500 µL of sample. To verify that the tracer particles were fully dispersed, a stability check of the count rate with time was performed prior to each measurement.
Zeta potential and DLS measurements were performed with a Malvern Instruments Zetasizer Nano. Additional solution viscosity measurements were performed with a Malvern Instruments DSV (multi-capillary viscometer) system.
The change in zeta potential with tracer particle chemistry at 25°C for PBS buffer and BSA solution is shown in Table 1.
| BSA (10mg/ml) | Carboxylated melamine | Sulfonated PS latex | Carboxylated PS latex | |
|---|---|---|---|---|
| in PBS | -4.80 | -36.1 | -26.8 | -35.3 |
| in presence of BSA | - | -31.4 | -12.4 | -19.0 |
| DLS relative viscosity | - | 1.033 | 1.314 | 1.310 |
The change in zeta potential from measurements in PBS buffer, to measurements in 10 mg/mL BSA solution is much more significant for polystyrene (PS) latex tracer particles than it is with (carboxylated) melamine tracer particles. The implication from this is that there is a much lower level of interaction between melamine particles and BSA, compared to polystyrene particles and BSA.
To give further confidence in the above assessment, and as a check on the reliability of the zeta potential measurements to indicate tracer particle-sample interactions for the BSA solution, an assessment was made of solution viscosity.
The low concentration BSA solution at 10 mg/mL is expected to show Newtonian behavior [5]. Given tracer particles of a known size, the viscosity,η, of the suspending medium can be obtained using the Stokes-Einstein relation:
where D is the diffusion coefficient of the tracer particle as measured by DLS; a is the diameter of the tracer particle; kB is the Boltzmann constant and T is the temperature.
The relative viscosity is the ratio of the solution viscosity to the solvent (PBS buffer) viscosity, and this is also reported in Table 1 for the 10 mg/mL BSA solution with the different tracer particle types, as determined from DLS measurements.
The relative viscosity of a 10 mg/mL BSA solution (without probe particles) was also measured using a multi-capillary Dilute Solution Viscometer (DSV), and found to be 1.046 (i.e. only 4.6% higher viscosity than the PBS buffer). This is in very good agreement with the relative viscosity obtained from DLS measurements with the 0.615 µm melamine tracer particles (1.033), and gives further credence to melamine particles having low interaction with BSA. It would therefore be a suitable tracer for microrheology measurements. For the polystyrene tracer particles, where a relatively large change in zeta potential was obtained, there is also a larger estimate for the relative viscosity of the BSA solution (~1.31).
Proceeding with the microrheology analysis on the data obtained using both the melamine and the polystyrene tracer particles shows significant differences for the viscoelastic modulus data. Figure 1 shows the elastic modulus, G', for 10 mg/mL BSA solution at 70°C using the different tracer types. For PS tracers, G' data is significantly higher in magnitude than G' data from melamine tracer particles. As BSA denatures and starts to aggregate at elevated temperatures, G' will increase as the microstructure evolves. However the PS tracer particles show artificially high elasticity as a result of more pronounced sticking to the BSA, causing the particles to become associated with the forming aggregate structure, which gives rise to a higher G'. Analysis of the correlation function measured by DLS for the BSA solution at 70°C without tracer particles shows a relatively fast decay, which does not appear to be representative of the high G' obtained from the use of PS tracer particles. Melamine particles show weaker elasticity, and this appears more representative of the microstructure and dynamics of the BSA solution at 70°C [2]. The use of zeta potential pre-measurement steps, combined with subsequent analysis and verification of the solution viscosity data, are strong factors in backing up this assertion.
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A key requirement of a microrheology experiment is to minimize tracer particle-sample interactions, since the existence of significant physical (e.g. depletion or electrostatic) or chemical interactions of the dispersed probe particles with the surrounding material can alter the local material environment and affect diffusivity in a measureable way. Ensuring an appropriate choice of tracer particle type is an essential element of method development for DLS microrheology measurements for a particular complex fluid.
The use of zeta potential measurements appear to be a good indicator of any tracer particle-sample interaction effects, and therefore for checking the suitability of particles of various chemistries in correctly probing the underlying microstructure and dynamics and corresponding rheological response.
However, when comparing the zeta potential of the tracer particles in the solvent without the sample and with the sample, consideration must be given to minimizing the possible measurement error arising from a change in viscosity of the sample solution (as compared to that of the base solvent). Either the sample concentration used should be low such that any increase in viscosity of the solution is minimized compared to the base solvent, or a separate measurement should be undertaken for the solution viscosity that is then used in the zeta potential measurement.
Note also that zeta potential measurements may not be possible for all sample types e.g. where the solvent system has a very high conductivity, or is an organic liquid for example. In such cases, consideration should be given to possible alternative approaches to make an assessment of tracer particle-sample interactions. In fact, for any microrheology measurement, the use of independent techniques to verify the suitability of a particular tracer particle and sample combination, and to ensure that the reported rheological data is reliable in terms of describing the underlying microstructure and dynamics, are important experimental elements to consider.
Malvern Instruments, An Introduction to DLS Microrheology. MRK1836
Amin, S, Rega, C and Jankevics, H 'Detection of viscoelasticity in aggregating dilute protein solutions through dynamic light scattering-based optical microrheology' Rheologica Acta, 51, 1-14 (2012)
Malvern Instruments, Zeta Potential: An Introduction in 30 Minutes. MRK654
McGrath, JL, Hartwig, JH and Kuo, SC 'The mechanics of f-actin microenvironment depend on the chemistry of probing surfaces' Biophys J. 79, 3258-3266 (2000)
Malvern Instruments, Determination of Protein Solution Viscosity using DLS Microrheology. MRK1834
