How to Perform DLS Microrheology and Record Measurements

DLS Microrheology involves the extraction of linear rheological properties from the motion of colloidal probe (tracer) particles, of known size, that undergo thermal fluctuations (due to Brownian motion) in a system at thermodynamic equilibrium.

Relationships that allow quantitative rheological data to be obtained over a broad range of frequencies — and which have been demonstrated to be valid, in general, over a variety of complex fluid types — have been derived.

It is possible to obtain data for the frequency-dependent viscoelastic moduli — G′, elastic (storage) modulus and G′′, viscous (loss) modulus — using which it would be possible to calculate the frequency-dependent complex viscosity, η*.

Due to the fact that external forces are not applied on the probe (tracer) particles, DLS Microrheology is a passive microrheology method, and can also be called thermal diffusion microrheology.

DLS Microrheology measurements are specifically applicable for measuring low viscosity and weakly structured materials, such as biopolymer (such as protein) and polymer solutions. The method involves extending rheological data into the high-frequency range, which is a prerequisite for accessing the short-timescale dynamics of such systems (and goes further than the inertia-limited capabilities of mechanical rheometers in this regard).

Microrheology SOP

A Microrheology test necessitates the measurement of the correlation function of the probe (tracer) particles contained in the sample being tested. Then, the Mean Square Displacement (MSD) of probe particles is calculated. From this, the rheological properties of the sample are then evaluated, using the Generalized Stokes-Einstein Relation.

It should be noted that specific conditions for the tracer particle-sample matrix combination must be fulfilled to obtain reliable Microrheology data:

  • It is necessary for the probe particles to be well dispersed in the sample
  • Interactions between the sample matrix and the tracer particles should be minimal
  • The size of the probe particles should be larger than the relevant microstructural length scale, for example, mesh size in a polymer network, so that it probes the bulk material response, that is, the assumption of continuum viscoelasticity holds.
  • The probe particles’ concentration should be in such a way that the scattering signal is governed by the probe particle scattering, rather than the scattering from the sample matrix (while maintaining the single scattering condition)

It is advisable to use a defined experimental procedure to guarantee that a robust technique is generated for DLS Microrheology characterization of a specific complex fluid type. Hence, the Microrheology SOP in the Zetasizer software is designed with “pre-measurement” steps to enable evaluation of the aforementioned conditions.

Following are the “pre-measurement” steps included in the Microrheology SOP (illustrated in Figure 1):

  1. Measurement for evaluating tracer particle-sample matrix interactions (with the help of Zeta Potential test protocols)
  2. Measurement for evaluating tracer particle scattering in relation to sample matrix scattering (with the help size test protocols)

Microrheology SOP flowchart detailing two “pre-measurement” steps for development of robust experimental procedures

Figure 1. Microrheology SOP flowchart detailing two “pre-measurement” steps for development of robust experimental procedures

The aim of the methodology described in the Microrheology SOP (Figure 1) is to ensure the significant conditions for a specific tracer particle-sample matrix combination are fulfilled.

It should be noted that as soon as a specific sample type is evaluated for an appropriate probe particle size, type, and concentration, only an autocorrelation function (ACF) measurement has to be run for the extraction of Microrheology data.

User guidance is given in the software at each measurement step within the Microrheology SOP. After performing a Microrheology measurement, Expert Advice on data quality is also offered.

Microrheology SOP Step 1: Assess Tracer Particle-Sample Matrix Interactions Using Zeta Potential Test

In the Microrheology SOP, measurement step 1 is used to evaluate the appropriateness of probe particle chemistry to reduce particle-matrix interactions. This is performed by measuring:

  1. The zeta potential of the tracer particles in the dispersant (solvent) used for the Microrheology test
  2. The zeta potential of the tracer particles in the dispersant and the sample used for the Microrheology test

The concentration of probe particles used largely depends on the concentration of the sample in the dispersant (solvent). In the case of the initial measurement of the zeta potential (tracer/sample and tracer/buffer only), the following concentrations are recommended starting points:

  • Tracer particles in dispersant — 5 µl neat tracer particle suspension to 10 ml dispersant (solvent) (0.5 µl/ml)
  • Tracer particles in sample — add 0.5 µl neat tracer particle suspension to 1 ml of the sample being tested. It is recommended to start at low concentrations of tracer particles, and increase the concentration if necessary (see discussions below).

Note on filtering: While filtering tracer particle suspensions to be used in Microrheology testing, to ensure the most reproducible data, it is suggested to filter the tracer particle suspension using a suitably sized filter (i.e. filter size larger than the tracer size).

Microrheology SOP step 1 necessitates the use of a zeta potential capable cell — the software includes standard SOPs for:

  • DTS1061—Disposable folded capillary cell
  • ZEN1002—Universal dip cell

The Microrheology software performs a comparison of the two measured zeta potential results and investigates to see whether sample measurement falls within a predefined percentage of the tracer measurement (the “Acceptable Zeta Ratio”). The software default value for this difference is 25%, which can be varied on the “Advanced” SOP page, as illustrated in Figure 2.

Changing the Acceptable Zeta Ratio (%) in the software

Figure 2. Changing the Acceptable Zeta Ratio (%) in the software

The zeta potential of a colloidal particle will change if the surface properties of the particle change, for example, if components of the dispersant matrix, such as polymer or protein molecules, adsorb onto the particle surface.

In the case of a DLS Microrheology measurement, if the probes’ zeta potential in the presence of the sample is considerably different from the value acquired in the dispersant (solvent), this might suggest strong particle-matrix interactions. Such interactions will eventually have an impact on the obtained rheological data.

Malvern recommends the use of particles with distinct surface chemistries for tracer particles for Microrheology—for instance, sulfonated latex particles or carboxylated melamine particles. The availability of distinct surface chemistries allows the level of interaction between the tracer and the sample (with the help of aforementioned zeta potential measurements) to be tested, such that it is possible to select an optimum tracer particle surface chemistry for the specific sample type being tested.

It is vital to note that interactions between the tracer particles and the sample might not be immediately evident as they could take some time to manifest themselves. Similarly, in case the sample is not optimally dispersed before the measurement, then the measurement will not be actually representative of the sample. If necessary, the tracer particles can be dispersed by gentle mixing (for instance, with the help of a sample roller).

Guidelines if Zeta Potential Comparison is Outside the Acceptable Zeta Ratio (Default 25%)

The considerable differences between the sample/tracer and the dispersant/tracer systems in the measured zeta potential could be due to two probable causes:

  1. The concentration of tracer particles in the sample is not adequately high—in case the tracer concentration is very low, the sample, not the tracer, governs the zeta potential result. The addition of more tracer particles and re-testing can reveal whether this difference is because of concentration instead of interaction with the sample.
  2. Interaction between the sample and the tracer particles—when the sample and the tracer interact, the addition of more tracer particles will not enhance the difference in zeta potential (unless so much is added that it completely governs the zeta measurement). This outcome may suggest considerable tracer particle-sample matrix interactions, and it is necessary to analyze different probe chemistry.

Figure 3 illustrates the decision-making process for selecting a suitable tracer particle surface chemistry.

Decision-making process for probe surface chemistry

Figure 3. Decision-making process for probe surface chemistry

Measure Tracer Particle Size in Dispersant (Solvent)

Based on the zeta potential measurement sequence in the Microrheology SOP, the size of the tracer particles is measured in the dispersant (solvent). In order to obtain reliable sizing data, it is advisable to filter the tracer particle suspension sample using a suitable size filter (see “Note on filtering” above).

In case the SOPs are set up to use the folded capillary cell, the size measurement runs automatically. Upon using the dip cell, the user is prompted to load a disposable cuvette (DTS0012). To ensure accurate size measurements, it is necessary to rinse the disposable cuvette with clean dispersant (solvent) prior to the addition of the tracer particle suspension.

The tracer particle size reported as part of the test sequence is used at the time of the Microrheology step for the calculation. It is a noteworthy aspect that if the tracer particle size is not measured in dispersant, then the software uses the nominal particle size related to the specific tracer selected for the Microrheology calculations.

There are two significant points to be considered in this case:

  1. It is necessary to make sure that the tracer particle size is measured to make the Microrheology result as accurate as possible. There will be a slight change in the size of the tracer particle from the nominal size, based on the pH of the dispersant. This is caused due to the change in the electrical double layer (Debye layer) based on the ionic strength of the dispersant, thereby influencing the measured hydrodynamic size of the particle.
  2. The tracer size must be larger than the measured size of the sample. Under such conditions, the bulk material response is probed by the tracer particles, or in other words, the assumption of continuum viscoelasticity holds.

If the size of a tracer particle is small on the microstructural length scale of the sample matrix, then, it would not be possible to recover the bulk rheological properties from the Microrheology measurement.

Microrheology SOP Step 2: Assess Tracer Particle Scattering Relative to Sample Matrix Scattering Using Size Test

In the Microrheology SOP, measurement step 2 is employed to evaluate the level of tracer particle scattering against sample matrix scattering, and investigate the dispersion of the tracer particles. This is performed by measuring:

  1. The Intensity PSD peak from the sample
  2. The Intensity PSD peak following the addition of tracer particles

The guidance below is for the recommended concentration of tracer particles to be added to the sample:

  • Add a few µl (nearly 5 µl) of neat tracer particle suspension to 500 µl of sample

In case more tracer particles are necessitated to mask the sample scattering, a further 1 µl of neat tracer particle suspension should be added at a time.

Note on filtering: While filtering tracer particle suspensions to be used in Microrheology testing, to ensure the most reproducible data, it is suggested to filter the tracer particle suspension using a suitably sized filter (i.e. filter size larger than the tracer size).

Microrheology SOP step 2 is formulated to use either a disposable sizing cuvette or a disposable folded capillary cell.

The Microrheology software instructs the user to verify whether the following conditions for the Intensity PSD from the above two measurements are fulfilled:

  • It is necessary for the peak of the Intensity PSD for the tracer particle measurement to be at a larger size compared to the Intensity PSD for the sample only
  • The scattering signal (i.e. size of the Intensity PSD peak) for the tracer particle measurement should dominate over the scattering signal from the sample
  • It is necessary for the Intensity PSD for the tracer particles to be a single peak

The software asks the user to add additional tracer particles if the sample scattering is still observed. It should be made sure that the scattering from the tracer particles is equal to 90% or greater than the scattering signal from the sample matrix.

It should be noted that conditions of single scattering are necessitated for DLS Microrheology — in case the concentration of tracer particles in the sample is very high, the system will turn highly turbid. Hence, it is vital to use a concentration of tracer particles that is just enough to hide the sample scattering, and not added so much that the sample turns highly turbid (resulting in multiple scattering).

Microrheology SOP step 2 verifies whether the scattering signal is dominated by the tracer particles and whether they are dispersed well in the sample — conditions that are important for obtaining reliable Microrheology data.

Microrheology SOP Step 3: Microrheology Measurement

Upon satisfying the condition for tracer particle scattering, the software prompts the user to run the Microrheology measurement step.

A Microrheology measurement involves:

  • Recording the correlation function of the tracer particles in the sample
  • Evaluating the Mean Square Displacement (MSD) of the tracer particles
  • Calculating the rheological properties of the sample with the help of the Generalized Stokes-Einstein Relation

Microrheology Results

The charts shown in Figure 4 are included in the Microrheology workspace:

Correlogram

Figure 4. Correlogram

Correlogram

Correlogram is the measured correlation function of the tracer particles contained in the sample.

  • The Correlation Function describes the way the fluctuation in scattering intensity from the tracer particles changes with time.

Mean Square Displacement (MSD)

The Mean Square Displacement (MSD), which is deduced from the correlation function, is a representation of the movement of the tracer particles within the sample with time.

  • A linear response on log-log scale suggests a purely diffusive motion of the tracer particles — as would take place in a perfect Newtonian liquid
  • Deviations of the MSD of the tracer particles from linearity with time point toward sample viscoelasticity (and sub-diffusive motion of the tracer particles)

Mean Square Displacement (MSD) vs time

Figure 5. Mean Square Displacement (MSD) vs time

Rheological Parameters

Moduli (G Tab)

The Moduli tab displays the viscoelastic moduli versus frequency for the sample being tested — two sets of data are displayed on the chart:

  • G′, elastic (storage) modulus
  • G′′, viscous (loss) modulus

At lower frequencies (i.e. longer timescales), the viscous modulus (G′′) is dominant, and at higher frequencies (i.e. shorter timescales), the elastic modulus (G′) is dominant. If a cross-over occurs between the G′ and G′′, the frequency of the crossover relates to a significant relaxation time of the material. In the case of low-viscosity, non-Newtonian materials, the cross-over point is usually at a very high frequency, which cannot be accessed from inertia-limited mechanical rheometry techniques; however, these dynamics can be probed using the extended frequency range of DLS Microrheology.

For the sample types that can be used for DLS Microrheology — low-viscosity and weakly structured materials such as biopolymer (protein) and polymer solutions — it is reasonable to anticipate that the viscous (loss) modulus G′′ will dominate for at least a major part of the measured frequency range (and, in fact, for very weakly structured materials, the G′ component may be highly noisy).

Viscoelastic moduli (G′ and G′′) versus frequency. Viscoelastic data up to frequencies of ~105rads-1 is accessible using DLS Microrheology.

Figure 6. Viscoelastic moduli (G′ and G′′) versus frequency. Viscoelastic data up to frequencies of ~105rads-1 is accessible using DLS Microrheology.

Complex Viscosity (Eta Tab)

Complex viscosity (η*) versus frequency

Figure 7. Complex viscosity (η*) versus frequency

It is possible to derive the frequency-dependent complex viscosity, η*, from viscoelastic moduli. Then, this can be related to shear viscosity by applying the Cox-Merz rule.

This presumes that for a simple system such as a solution of linear polymers:

  • Angular frequency (ω) in rads-1 is equivalent to shear rate () in s-1
  • Complex viscosity (η*) in mPas (or cP) is equivalent to shear viscosity (η)

This rule is only actually applicable for simple systems. The differences between the shear viscosity and the complex viscosity increase as the sample structure turns highly complex.

Deriving complex viscosity could be highly useful for the sample types applicable to DLS Microrheology, and can highlight the following non-Newtonian material responses:

  • Zero shear viscosity
  • Infinite shear viscosity
  • Shear thinning index

Creep Compliance

MSD data is also associated with the creep compliance of the sample, which is an alternative representation of the viscoelasticity of the sample. Creep compliance data can be obtained from the results plotted against time (Figure 8).

Creep compliance

Figure 8. Creep compliance

Running only the Microrheology Measurement

It is possible to turn off the zeta potential measurement (step 1) and the Size measurement (step 2) within the Microrheology SOP such that the user can run the Microrheology measurement only.

After evaluating a specific sample type (using steps 1 and 2) for an appropriate probe particle size, type, and concentration, only a correlation function measurement has to be run to derive Microrheology data for subsequent tests.

For instance, in case a wide variety of concentrations of the same sample are under test, the zeta potential test must be run only once, on a single concentration. Moreover, in case the same tracer particle is used, the tracer size must be measured only once and it would be possible to set the same value in the SOP by verifying the edit box next to the Nominal Tracer Size (Figure 9) and varying the Nominal Tracer Size to the size that has been measured.

Changing the Nominal Tracer Size value

Figure 9. Changing the Nominal Tracer Size value

Microrheology Utilities

The Zetasizer software includes a utilities section for the Microrheology suite, which can be accessed using the Tools menu (Figure 10) or from the context menu (right click on a Microrheology measurement).

Accessing the Microrheology utilities panel

Figure 10. Accessing the Microrheology utilities panel

The Microrheology utilities panel displays three charts — the Viscoelastic moduli, the Mean Square Displacement, and the Complex viscosity.

On every page, there are rheological models that can be fitted to the data, for instance, Figure 11 illustrates complex viscosity data that has been analyzed with the help of a Cross model.

Model fitting using the Microrheology utilities

Figure 11. Model fitting using the Microrheology utilities

It is vital to note that it is not possible to apply all models to all datasets. To select suitable areas of data only for subsequent model fitting (i.e. to remove highly noisy data that can exist at the very shortest timescales), it is necessary to right click and drag the range pointers (the red triangles on the x-axis) to the suitable points on the chart.

Exporting Microrheology Data

It is possible to export the Microrheology results from the File menu (illustrated in Figure 12) or from the Microrheology utilities with the help of the save button.

Data Export from the file menu

Figure 12. Data Export from the file menu

The Microrheology utilities have two file options—save as .csv or save as .xml.

Following are the parameters that are exported:

Sample Name

Date

File Name

Lag times                              (µs)

Channel Values                     The Correlogram, plot against Lag times

Time                                      (µs)

Mean Square Displacement  Plot against Time

Creep Compliance                Plot against Time

Angular Frequency               (rad/s)

G Prime                                 (Pa) elastic component, plot against angular frequency

G Prime Prime                      (Pa) viscous component, plot against angular frequency

Complex Viscosity                (cP or mPas) plot against angular frequency

This information has been sourced, reviewed and adapted from materials provided by Micromeritics Instrument Corporation.

For more information on this source, please visit Micromeritics Instrument Corporation.

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