1. Introduction

Nanoparticles and colloids in suspension scatter electromagnetic radiation (light) at various angles from the incident light direction. For particles that are small relative to the wavelength of the incident light, the intensity of the scattered light and its dependence on the particle properties (e.g., size and refractive index) and scattering angle can be modeled by Rayleigh-Gans scattering theory, while particles of any arbitrary size are modeled by Mie scattering theory.

In static or multi-angle light scattering (SLS or MALS), scattering intensities are averaged over the measurement duration. Measurements taken at multiple angles enable the determination of properties such as molecular weight and radius of gyration for polymers, or fractal dimension for particle aggregates. In contrast, dynamic light scattering (DLS) evaluates fluctuations of the scattering intensity over time, typically at a fixed scattering angle. The rate of the fluctuation in the scattered light intensity corresponds to the diffusion coefficient of the particles, with smaller (faster-diffusing) particles producing more rapid intensity fluctuations. Hence, DLS is utilized to determine particle size distributions based on their diffusion coefficient. The Stokes-Einstein equation is applied to convert diffusion coefficients to particles sizes for spherical particles.

In the DLS data processing, raw data on the light intensity measurements are first evaluated by computing an autocorrelation function representing the rate of decay (loss) of correlation between the intensity measured at each time point, t, and a delayed time point, t + 𝜏. Faster decay of the autocorrelation function vs. t corresponds to more rapid intensity fluctuations (smaller particle sizes). A broader or shallower decay of the autocorrelation function corresponds to a broader or more polydisperse size distribution. To quantitatively estimate diffusion coefficients or particle size distributions, two modeling approaches are commonly applied to fit the autocorrelation function: (1) cumulants analysis to fit the autocorrelation function with a single polynomial equation, yielding single values for the z-average size and polydispersity index; or (2) deconvolution/regularization analysis, such as a non-negative least squares (NNLS) analysis, to estimate a best-fit histogram for the intensity-weighted particle size distribution, from which other averaged size distributions (e.g., volume-average) can be computed using Mie theory when given the particle refractive index.

This laboratory will apply DLS measurements to determine particle sizes for a series of purchased gold (Au) nanoparticles (nominally 10 nm, 30 nm, 60 nm, and 100 nm), a mixture of the four sizes of Au nanoparticles, two unknown Au nanoparticle samples synthesized in class with different visible colors (pink and purple), the 60 nm Au nanoparticles with an adsorbed polymeric surface coating (polyvinylpyrrolidone), and titanium dioxide (TiO2) nanoparticles. The learning objectives of the laboratory include: (1) evaluating and explaining similarities or differences between the DLS sizes and the manufacturer’s reported sizes; (2) identifying uncertainties or errors in the measurement based on the results acquired; (3) interpreting and critically evaluating the quality of the raw data collected, the autocorrelation function, and the model fitting results; and (4) implementing best practices for sample preparation and handling for DLS measurements.

This laboratory is paired with ASTM E3247–20: Standard Test Method for Measuring the Size of Nanoparticles in Aqueous Media Using Dynamic Light Scattering, to support the learning objectives.

2. Relevant Documentary Standards and Reading Exercises

3. Experimental Procedure

3.1 Chemical reagents

• Deionized (DI) water
• 10 nm Au nanoparticle stock suspension (BBI Solutions, EM.GC10)
• 30 nm Au nanoparticle stock suspension (BBI Solutions, EM.GC30)
• 60 nm Au nanoparticle stock suspension (BBI Solutions, EM.GC60)
• 100 nm Au nanoparticle stock suspension (BBI Solutions, EM.GC100)
• Au nanoparticles synthesized in Activity 1 (pink color)
• Au nanoparticles synthesized in Activity 2 (purple color)
• TiO2 nanoparticle stock suspension (Evonik Aeroxide® P25, 2 g/L in DI water)
• Polyvinylpyrrolidone (PVP) stock solution (≈ 40 kDa molar mass, 10 g/L in DI water)

3.2 Equipment and supplies

• Malvern Zetasizer Nano ZS dynamic light scattering instrument
• Pipettors and pipet tips
• Polystyrene cuvettes (semi-micro volume), 1 cuvettte per sample

3.3 Procedures

Sample preparation

Rinse and inspect a polystyrene cuvette and cap for sample preparation following the guidelines from the ASTM E3247-20 standard. Prepare a total volume of 0.5 mL of each the following samples directly into the polystyrene cuvettes:

1. 1. 5X dilution of 10 nm Au nanoparticles in DI water (i.e., 0.1 mL of the purchased Au nanoparticles + 0.5 mL of DI water)
   2. 5X dilution of 30 nm Au nanoparticles in DI water
   3. 5X dilution of 60 nm Au nanoparticles in DI water
   4. 5X dilution of 100 nm Au nanoparticles in DI water
   5. Mixture of 10, 30, 60, and 100 nm Au nanoparticles in DI water, with each particle at 20X dilution in the final mixture (i.e., 0.025 mL of each size of purchased Au nanoparticles + 0.9 mL of DI water)
   6. Synthesized Au nanoparticles (pink) (undiluted from Activity 1)
   7. Synthesized Au nanoparticles (purple) (undiluted from Activity 1)
   8. 5X dilution of 60 nm Au nanoparticles with 1 g/L of PVP in DI water (i.e., 0.1 mL of purchased Au nanoparticles + 0.05 mL of PVP stock solution + 0.35 mL of DI water)
   9. 50X dilution of the TiO2 nanoparticle stock suspension in DI water (i.e., 0.01 mL of TiO2 stock suspension + 0.48 mL of DI water)

Instrument setup

Turn on the Zetasizer instrument, and open the Manual measurement dialogue. Table L2.1 below specifies the instrument settings to apply for the measurements.

Table L2.1. Zetasizer Measurement Settings for Particle Size Analysis by Dynamic Light Scattering

Sample analysis

1. Insert the cuvette for the first sample into the DLS sample compartment. Ensure the cuvette is oriented properly with respect to the laser and inserted all the way to the bottom of the cell holder. Close the compartment.
2. In the Zetasizer software, open the Manual measurement dialogue. Input the sample name and verify the measurement settings listed in Table L2.1.
3. Click “Start measurement” to collect the measurements on your sample.
4. Record your observations on the measurements collected during the lab in the table below (one per sample).

Table L2.2. Observations Noted During Dynamic Light Scattering Measurements

Shutdown procedure

Save and export all of your data. Discard all samples to the waste containers provided.

4. Data Analysis

The attached Excel file (UH – Exptl Methods Nano – Laboratory 2 Data Analysis Template) contains a set of example data to process, along with figures showing the autocorrelation functions and size distributions from the distribution fit.

1. Review all the observations noted in Table L2.2 during the lab. Report whether any of the samples may be too dilute or too concentrated for a reliable DLS analysis. Also, report whether there appeared to be any dust interference that could have influenced the results for any of the samples. Briefly explain the specific guidance from the ASTM E3247-20 standard that you are applying to evaluate the data, as well as which specific results or observations (from Table L2.2) you are evaluating to make each of these assessments.
2. Complete Table L2.3 with the results indicated. Report the mean +/- standard deviation of the triplicate measurements for each sample, and round the reported values to an appropriate number of significant figures based on the standard deviation.

Table L2.3. Summary of Results

5. Discussion Questions

1. Measurement settings
   Several pieces of information related to the sample and measurement properties were carefully inputted to set up the dynamic light scattering measurement (as shown in Table L2.2). Discuss why the temperature and solvent viscosity are important to input accurately by identifying where (i.e., in what model equation) errors in these parameter inputs would propagate to errors in the size determination by DLS. It is encouraged to refer to the introductory theory section of this laboratory and/or the ASTM E3247-20 standard for relevant discussion to answer this question.
   
2. Comparison of sizing methods
   
   1. The manufacturer of the purchased nanoparticles noted in the materials list provides certificates with each batch of nanoparticles that report the mean diameters, as determined by transmission electron microscopy (TEM). Examples are listed in Table L2.4 for some specific batches of nanoparticles:
      Table L2.4. Properties reported by BBI Solutions for purchased Au nanoparticles

      Sample Name	Batch Number	Mean Diameter, TEM (nm)	Gold chloride concentration in the synthesis	Estimated Number Concentration (particles/mL)
      Au 10 nm	22090119	9.5	0.01%	5.7 × 1012
      Au 30 nm	014022	29.6	0.01%	2.0 × 1011
      Au 60 nm	22050119	58.6	0.01%	2.6 × 1010
      Au 100 nm	22100048	103.7	0.01%	5.6 × 109

      You may retrieve the certificates for your specific batches of purchased Au nanoparticles, if available. Do you observe any systematic deviations (i.e., consistently higher or lower values) when comparing the z-average DLS size or intensity-averaged DLS size to the TEM sizes reported? Provide at least one theoretical reason why these DLS sizes would show the observed deviation from the TEM size. It is encouraged to refer to the introductory theory section of this laboratory and/or the ASTM E3247-20 standard for relevant discussion to answer this question.
      

   2. Compare the DLS cumulants analysis results for the pink and purple Au NPs (Samples vi and vii). Are the z-average size and PdI higher or lower for one of the samples? Compare to your interpretation of the results for these two unknown samples from Laboratory 1 (UV-Vis spectrophotometry) – do the results of your analyses from the two methods appear to agree or not?
3. Trends in scattering count rate vs. size
   According to the table above, the mass concentration of Au should be identical across all four purchased sizes (which were all diluted by the same factor for the measurements). The number concentration of particles decreases with increasing size, because the larger particles contain more mass per particle. Review your data for Samples i-iv. Is there any trend in the derived count rate versus particle size? Does it match your expectations from scattering theory? It is encouraged to refer to the introductory theory section of this laboratory and/or the ASTM E3247-20 standard for relevant discussion to answer this question.
    
4. Data analysis uncertainties
   The ASTM standards related to DLS provide guidance that the number-average size from the distribution fit analysis should not be reported. Based on your actual measured results on the samples with known particle sizes, do you observe substantial errors in any of the number-average results that would support the ASTM guidance?
5. Sensitivity/robustness to surface coatings
   Based on your actual measured results from Lab 1 (UV-Vis Spectrophometry) and this lab for the uncoated and PVP-coated 60 nm Au nanoparticles, which of the two measurements – UV-Vis or DLS – appears to be more sensitive to the presence of the PVP coating, i.e. which measurement shows a greater percent deviation between the results for the uncoated and PVP-coated particle? Explain theoretically why the DLS measurement would or would not be expected to be sensitive to an adsorbed coating layer. It is encouraged to refer to the introductory theory section of this laboratory and/or the ASTM E3247-20 standard for relevant discussion to answer this question.
   
6. Multimodal size distributions
   For Sample v (the mixture of four Au nanoparticle sizes), was the DLS measurement on the mixture able to resolve that there were four different sizes of nanoparticles mixed together – i.e., did four separate peaks appear in the intensity-weighted histogram? If not, which size particle most influenced the result? Explain whether the results match your expectations based on scattering theory and your observations in your table of results from the lab. It is encouraged to refer to the introductory theory section of this laboratory and/or the ASTM E3247-20 standard for relevant discussion to answer this question.
7. Challenges for nanomaterial characterization in products
   Recall the ASTM E3025-16 standard for characterization of silver nanomaterials in textiles from Chapter 8. In the summary list of analytical techniques for detection and characterization of silver in textiles (Table X2.1 in the standard), DLS is not listed as a suggested technique. Briefly explain a major reason why DLS would be highly challenging or unsuitable to apply in this scenario.