Dynamic Light Scattering (DLS) Microrheology: Taking Rheological Characterization to Extremes

Microrheology is a relatively new and developing analytical methodology of growing interest to those working at the forefront of rheological characterization. The term “microrheology” is used to describe a range of techniques that enable the determination of local and bulk viscoelastic properties for a soft material by tracking how dispersed probe particles move within it. The motion of dispersed probe, or tracer, particles can be followed using either light scattering techniques or particle-tracking video microscopy.

In DLS Microrheology, the average movement of an ensemble of dispersed probe particles is tracked using dynamic light scattering (DLS). The technique has significant potential for measuring low-viscosity, weakly structured samples—for example, polymer and protein solutions—because it allows access to the very high frequencies needed to measure critical short timescale dynamics of these systems. An added benefit of DLS Microrheology is the ability to work with much smaller sample volumes than are typically needed for a mechanical rotational rheometer.

While microrheology methodology is currently being pursued in academic and industrial research laboratories, there is growing general interest in the technique and in its potential. Following an introduction to microrheology, this article discusses how the use of DLS Microrheology complements conventional rotational rheometry by extending rheological characterization into new areas, and presents data to demonstrate how this can be achieved.

Introducing Microrheology

Rheology is the study of the flow and deformation of materials under an applied force. Rheological testing yields parameters that directly quantify aspects of product performance and, as a result, it is applied across a number of industries. Properties such as viscosity and viscoelasticity play an important role in controlling the performance and in-process behavior of many products, ranging from paint, polymers, and adhesives to pharmaceuticals and foods.

Conventional rheological techniques use a mechanical system to impose a controlled force or displacement upon the sample. However, for some complex fluids, as exemplified by synthetic and biopolymer or protein solutions, and surfactant systems, there may be measurement limitations. Complex fluids have a liquid base, but also encompass supra-molecular structures formed by the constituent macromolecules or surfactant phase. These microstructures convey viscoelasticity, imparting rheological behavior that is somewhere between that of a liquid (viscous) and solid (elastic), but in some systems they are extremely weak and highly strain sensitive.

The characterization of such systems therefore demands application of very low stresses—typically a tiny fraction of the lowest torque range available from a standard laboratory rotational rheometer (which is typically optimized for measurements over multiple decades of stress). The limits of mechanical rheometry also become evident when studying behavior at very high frequencies (over very short timescales), where system inertia rapidly dominates measurement response, and/or when the amount of sample available is minimal, i.e., down to the microliter scale, as may be the case with high-value protein-based formulations.

Complex fluids often have a range of rich dynamics (over multiple length scales and timescales) that stimulate academic interest and inspire application in the formulation of everyday products such as foodstuffs, personal care and household items, and industrial chemicals. Microrheology techniques, which can move beyond the limitations of mechanical rheometry and extend rheological characterization to a wider range of material types, are therefore of growing interest to academics and to those working at the forefront of commercial product development.

Alternative approaches to microrheology measurements

Microrheology techniques can involve the application of passive or active measurement protocols. Passive or thermal diffusion microrheology measures the linear rheological properties of colloidal particles undergoing thermal fluctuations in a system at thermodynamic equilibrium. In other words, no external forces are exerted on the probe particles. DLS Microrheology is an example of a passive technique.

In contrast, active probe-based methods extract rheological properties from measurements of the forced motion of probe particles within a system, with the external force provided by, for example, laser or magnetic tweezers. Such techniques extend measurement capabilities and are undoubtedly beneficial for systems with significant elastic properties, but they are substantially more complex in terms of data interpretation.

Probe particle motion can be tracked either by light scattering techniques or particle-tracking video microscopy. Dynamic light scattering is an efficient solution for tracking the average motion of an ensemble of dispersed colloidal probe particles. It is a relatively straightforward technique that is used routinely to measure the size of particles suspended in a liquid, typically in the submicrometer region, and is applicable to a wide range of sample types, with optical characteristics ranging from transparent to slightly turbid.

Alternative techniques include the use of a video microscope to track the path of individual probe particles. Analyzing the resulting data using image processing software can be challenging. However, these methods can be extremely effective when only a single-probe particle needs to be imaged and tracked. In addition, they offer good spatial resolution.¹

Focus on DLS Microrheology

To develop a basic understanding of how DLS Microrheology works, consider the conventional application of DLS in particle size measurement.

DLS measurements quantify the Brownian motion of particles in a sample by correlating and relating a detected pattern of scattered light to that movement.² For a particle moving freely due to thermal fluctuations in a purely viscous (Newtonian) liquid, the mean square displacement (MSD) increases linearly with time. The slope of this increase is directly related to the diffusion coefficient, D, of the particle (Eq. [1]):

where {Δr² (t)} is the MSD of the particle.³

For a purely viscous (Newtonian) liquid, the Stokes-Einstein relation then gives the diffusion coefficient as a function of the particle size, viscosity of the continuous medium, and temperature (Eq. [2]):

where a is the hydrodynamic diameter of the particle, η is the viscosity of the fluid medium, T is the temperature, and k_B is the Boltzmann constant.

DLS is traditionally used to measure the size of particles in a suspension, especially when those particles are in the submicron region. The preceding correlations illustrate the principles that underpin this approach, which involves measuring particle movement and determining particle size from the resulting data using known values of temperature and viscosity. Conversely, with DLS Microrheology, the size of the (probe) particles is known, and the rheological properties need to be determined.

It is critical to reiterate that the preceding relations reliably hold only for Newtonian liquids, such as small molecule solvents, which exhibit constant viscosity regardless of the applied stress. However, the complex fluids of interest almost exclusively lie outside this classification, exhibiting non-Newtonian or viscoelastic behavior. As the elasticity of the suspending medium becomes significant, particle motion becomes subdiffusive, and behavior deviates markedly from the linearity exhibited in a purely viscous liquid.

The breakthrough that led to the development of microrheology was the extension of the generalized Stokes-Einstein relation linking MSD to the linear viscoelastic moduli of complex fluids,⁴ which enables application to these more rheologically interesting materials. Comprehensive details of the resulting mathematical models, which form the foundation of modern microrheology, can be found in Ref. 1.

Benefits of DLS Microrheology

The basic principles of DLS Microrheology and the fact that DLS technology is already established make the technology attractive. In addition to its being relatively accessible, other important benefits include:

• Wide frequency range: Laser-based DLS Microrheology probes a much wider frequency range than can be accessed via conventional mechanical rheometry because of its ability to capture dynamic behavior over very short timescales. This is a measurement area in which the inertia of mechanical instrumentation becomes severely limiting. Often low-viscosity complex fluids exhibit critical material dynamics that occur at these high frequencies.
• Small sample volumes: As with DLS particle size measurement, the sample volumes required for DLS Microrheology are typically on the microliter scale. This permits rheological characterization of material that is not available in larger volumes, e.g., protein-based formulations or those in the very earliest stages of development.
• Rapid measurement: By measuring ensemble statistics arising from the thermal (Brownian) motion of the probe particles, DLS Microrheology measurements effectively probe a complete range of measurement frequencies simultaneously. This makes the technique a relatively fast method of frequency-dependent rheological characterization.
• Measurement at very low applied stress: By utilizing the Brownian motion of tracer particles to determine the linear dynamics of a sample, results are gathered under conditions of very low applied stress, making the technique well suited to highly strain-sensitive systems.

These benefits stem directly from the technique itself; instrument/technology-specific features offer additional advantages. For example, use of a system with high single scattering detection capabilities⁵ makes microrheology measurements possible at lower added probe particle concentrations. This can be vital for some biological systems where minimizing probe–sample interactions—an essential precursor to reliable measurement—can be more difficult.

Practical aspects of DLS Microrheology measurements

Despite the availability of DLS technology for particle size measurement, few systems enable DLS Microrheology, one exception being the Zetasizer Nano ZSP (Malvern Instruments, Malvern, U.K.). The instrument incorporates the software required to access DLS Microrheology capabilities; however, measurement can be challenging. It is important to define a reliable method for any particular complex fluid type and avoid recognized measurement pitfalls.⁶ Method development should take into the account the need to:

• Assess the suitability of probe particle chemistry to minimize particle–sample interactions.
• Determine a suitable concentration of probe particles for measurement in the single scattering regime and ensure probe particles are dispersed properly
• Check that the microrheology data obtained are independent of probe particle concentration and probe particle size.

Key to the success of a microrheology experiment is the selection of an appropriate probe particle. Significant chemical or physical interactions between the embedded probe and the surrounding material can measurably alter the local material environment and affect diffusivity. Ensuring an appropriate choice of particle surface chemistry for the particular complex fluid solution is essential to probe particle selection.

The size of probe particle used can also significantly impact the extracted rheological parameters. Thus it is necessary to choose a probe particle size that permits the determination of bulk material properties. To achieve this, the probe size should be greater than the relevant microstructural length scale, e.g., mesh size in a polymer network. With a robust microrheology method, measurements should be independent of probe particle size and concentration.

A successfully validated method allows rapid, simple rheological characterization with just a small amount of sample (as little as 20 μL is possible). The following case studies provide a practical demonstration of what can be achieved and illustrate microrheology in practice.

Case study 1: Measuring the viscosity of water using DLS Microrheology

Water is a prime example of an ideal or Newtonian liquid, and is known to have a viscosity that is independent of applied shear stress. As such, it represents a class of materials in which the application of microrheology is potentially of less interest. However, by demonstrating the ability of microrheology to characterize a well-understood system, this experiment serves as a useful benchmarking exercise that illustrates the general approach.

Figure 1 – Plot of mean square displacement (MSD) {Δr² (t)} with time for two different latex probe sizes in water shows how the smaller particles (60 nm) move more quickly.

Since water is a Newtonian fluid, the Stokes-Einstein relation holds, and viscosity can be simply obtained from the diffusion coefficient of dispersed tracer particles of known size. The data in Figure  1 use the microrheology analysis (based on the generalized Stokes-Einstein Relation) to demonstrate that there is no frequency dependence of the viscosity. The figure shows measured MSD data for two different probe particles—60 nm and 200 nm latex—each dispersed in water. The linear nature of the log plots indicates purely diffusive motion, in both instances, confirming that the system is behaving as a Newtonian fluid.

Figure 2 – Complex viscosity, η*, for water measured at 25 ^oC, using DLS Microrheology with latex probes of 200 and 60 nm.

Figure 2 depicts the viscosity values for water, confirming that equivalent results are produced using either tracer, and that viscosity is independent of measurement frequency (as would be expected for a Newtonian fluid). The use of smaller particles can extend data to higher frequencies, whereas larger particles give access to lower frequencies. The viscosity obtained is consistent with published data for water, and shows that measurements can be made at frequencies in excess of 10⁵ rad^–1.

A frequency sweep on a rotational rheometer to characterize the viscoelastic spectrum of (relatively) low-viscosity polymer solutions is limited by inertia-dominated measurements, typically to below 100 rad/sec. However, characterizing the rheological response at short timescales (or higher frequencies) to extend the viscoelastic spectrum is necessary to reveal the dynamics of polymer solutions, from dilute through semidilute and into concentrated regimes. A polyethylene oxide (PEO) solution can be used as a “model system” to compare DLS Microrheology data and rotational rheology data, and to show extended viscoelastic data into high frequencies.

Measurement data were obtained using 700-nm latex tracer particles in a 2% by weight solution of PEO in water, with appropriate sample preparation protocols to ensure that the tracer particles were fully dispersed.

Figure 3 – Mean square displacement  {Δr² (t)} with time for 700-nm tracer probes.

Figure 3 shows the MSD of the tracer particles, which is nonlinear with time due to the viscoelasticity of the sample.

Figure 4 – Viscoelastic moduli (elastic [storage] modulus, G′, and viscous [loss] modulus, G′′) as a function of frequency for a 2wt% PEO solution in water.

Viscoelastic moduli (elastic [storage] modulus, G′, and viscous [loss] modulus, G′′) data are presented in Figure 4, both from a rotational rheometer and from DLS Microrheology. Good agreement is shown for data in the region of overlap for the two techniques. The extended frequency range available from DLS Microrheology data can reveal short timescale dynamics of polymer solutions, such as G′ and G′′ crossover (or characteristic relaxation time).

Case study 2: Investigating the rheological response of protein solutions  (bovine serum albumin [BSA])

Figure 5– Plots of complex viscosity against frequency for various concentrations of BSA in PBS solutions (from 10 mg/mL up to 666 mg/mL) derived from DLS Microrheology measurements (using 615-nm carboxylated melamine probe particles).

In this study, a series of investigations were carried out to examine the rheological response of a protein solution, BSA. Figure 5 shows plots of complex viscosity, as a function of frequency, for various concentrations of solutions of BSA in phosphate-buffered saline (PBS) derived from DLS Microrheology measurements. Carboxylated melamine probe particles, 615 nm in size, were used to produce these data.

These results show that at low concentrations the system behaves as a Newtonian fluid, but above 80 mg/mL, viscosity no longer remains constant with frequency. With more concentrated BSA solutions, viscosity decreases at higher frequencies, indicating non-Newtonian, shear thinning behavior.

Figure 6 – Plots of relative viscosity against concentration for BSA in PBS solutions measured using DLS Microrheology (ref. Figure 5) and dilute solution viscometry (DSV), at 25 °C, show close agreement.

From this plot it is possible to derive zero shear viscosity by extrapolating the complex viscosity data to zero frequency. Relative viscosity, the ratio of zero shear viscosity to PBS viscosity, can then be calculated at each BSA concentration. This enables a direct comparison of the results obtained with those produced by dilute solution viscometry, a capillary rheology technique (see Figure 6). This comparison demonstrates close agreement between the two sets of data, confirming the validity of the microrheology approach, which provides comparable data using a much smaller sample.

Protein solution studies using DLS Microrheology have also shown that, by studying the evolution of viscoelastic data (G′), it is possible to detect and investigate the mechanisms of protein denaturation and aggregation with temperature, to the point of gelation.⁶ Such studies point to the potential for wider application to efficiently gather information of industrial relevance.

Conclusion

DLS Microrheology is an emerging technology, and there is increasing evidence that it has interesting and valuable applicability; the above case studies help validate this. For complex fluids that cannot be characterized rheologically using conventional mechanical techniques (because they are so weakly structured and/or rheological behavior is only observable over very short timeframes) microrheology offers a possible solution. Although it is still a specialized tool, DLS Microrheology is of value both academically and commercially. New technology such as the Zetasizer Nano ZSP, which broadens access to microrheology, is therefore an important step in the assessment and exploitation of its full potential.

References

1. An Introduction to DLS Microrheology, MRK1836; www.malvern.com.
2. Dynamic Light Scattering: An Introduction in 30 Minutes, MRK656; www.malvern.com.
3. Chaikin, P.M.; Lubensky, T.C. Principles of Condensed Matter Physics; Cambridge University Press: Cambridge, U.K., 2000, p 371.
4. Mason, T.G.; Weitz, D.A. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. Phys. Rev. Lett.  1995, 74, 1250–3.
5. Peters, R. Fiber optic device for detecting the scattered light or fluorescent light from a suspension. US Patent No. 6,016,195 2000.
6. Amin, S.; Rega, C.A. et al. Detection of viscoelasticity in aggregating dilute protein solutions through dynamic light scattering-based optical microrheology. Rheol. Acta  2012, 51, 329–42.

Dr. Steve Carrington is Product Marketing Manager, Rheology, Malvern Instruments Ltd., Enigma Business Park, Grovewood Rd., Malvern, Worcestershire WR14 1XZ, U.K.; tel.: +44 (0) 1684 892456; fax: +44 (0) 1684 892789; e-mail: [email protected]; www.malvern.com.