1. Introduction

The surface charge or potential of nanoparticles or colloids is an important factor contributing to their colloidal stability in suspension. Surface charge arises from charged moieties or absorbates on the particle surface and leads to a surface potential. This potential is screened by counterions in solution, leading to a decline in the magnitude of the potential away from the surface. Counterions at higher concentrations or higher valences provide more effective charge screening, i.e., a more compressed electric double layer with a shorter Debye length (κ^–1). Charge screening results in diminished electrostatic repulsion forces and poorer colloidal stability for like-charged particles.

Electrophoretic light scattering (ELS) measurements are often used to evaluate the zeta potential (ζ) of the particles, i.e., the potential at the hydrodynamic shear plane. These measurements are based on the principle of the motion of charged particles in an electric field as evaluated through a force balance – particles with a higher magnitude of charge or potential will experience a stronger force in the electric field relative to the opposing drag or friction force and attain a higher steady-state velocity. For particles in motion, the frequency of their scattered light will change following the Doppler effect. ELS uses laser Doppler velocimetry measurements to determine the particle speed by evaluating the frequency shift between the scattered light and a reference beam of the incident light. The instrument utilized in this laboratory (Malvern Zetasizer Nano ZS) further implements mixed mode measurement – phase analysis light scattering (M3-PALS). PALS yields improved measurements of particles with lower velocities (or particles under a lower applied electric field), and the M3 (fast field reversal and slow field reversal) measurements yield higher quality measurements of zeta potential distributions by correcting for electro-osmotic effects.[1]

The ELS measurements of particle velocity are normalized by the applied electric field strength to determine the electrophoretic mobility (u_e) of the particles. Various model equations have been derived to convert u_e to ζ. The Hückel approximation, u_e = 2/3(εζ/η), applies for spherical particles with a very small radius (R_s) relative to the Debye length, i.e., R_s < 0.1κ^–1, whereas the Helmholtz-Smoluchowski approximation, u_e = εζ/η, applies for particles with a very large radius relative to the Debye length, i.e., R_s > 100κ^–1. For nanoparticles having diameters between 1 nm and 100 nm in monovalent electrolyte from 1 mM to 100 mM ionic strength, neither regime applies and the Henry equation should be used, in which the multiplicative factor is a function of kRs. Simplified expressions for f(κR_s) have been derived in various references, e.g., by Ohshima (1994),[2] where f(κR_s) ranges from 2/3 to 1 for u_e = f(κR_s)(εζ/η). (Note that many other references, including the Malvern Zetasizer software, write the Henry equation as u_e = f(κR_s)(2/3)(εζ/η), such that f(κR_s) ranges from 1 to 1.5.)

This laboratory will apply ELS measurements to determine zeta potentials for gold (Au) nanoparticles (nominally 60 nm diameter) in background electrolytes of varying concentration (1 mM, 20 mM, 50 mM, and 100 mM NaCl), valence (1 mM CaCl₂), and with a polymeric surface coating (polyvinylpyrrolidone coating, in 1 mM NaCl). The learning objectives of the laboratory include: (1) evaluating and explaining trends in the measured zeta potential; (2) identifying uncertainties in the measurement and data analysis; and (3) implementing best practices for ELS measurements.

The laboratory is paired with NCL Method PCC-2 — Measuring Zeta Potential of Nanoparticles to support the learning objectives.

2. Relevant Documentary Standards and Reading Exercises

3. Experimental Procedure

3.1 Chemical reagents

• Deionized (DI) water
• 60 nm Au nanoparticle stock suspension (BBI Solutions, EM.GC60)
• NaCl stock solutions (100 mM and 1 M)
• CaCl₂ stock solution (100 mM)
• Polyvinylpyrrolidone (PVP) stock solution (≈ 40 kDa molar mass, 10 g/L in DI water)

3.2 Equipment and supplies

• Malvern Zetasizer Nano ZSP instrument
• Malvern dip cell or disposable zeta cell
• Pipettors and pipet tips
• Polystyrene cuvettes (“macro” volume), 1 per sample, if using a dip cell

3.3 Procedures

Sample preparation

Confirm that all stock solutions are near pH 7 or otherwise adjust the pH to 7. (Note that you should separate an aliquot of Au nanoparticles prior to measuring pH, to avoid contaminating the purchased stock suspension).

Prepare the six samples below with the required volumes of deionized water, salt, and/or polymer stock solutions for 1 mL total of sample. The Au nanoparticles should be added immediately before the zeta potential measurement.

1. 1. 10X dilution of 60 nm citrate-Au nanoparticles in 1 mM NaCl background
   2. 10X dilution of 60 nm citrate-Au nanoparticles in 20 mM NaCl background
   3. 10X dilution of 60 nm citrate-Au nanoparticles in 50 mM NaCl background
   4. 10X dilution of 60 nm citrate-Au nanoparticles in 100 mM NaCl background
   5. 10X dilution of 60 nm citrate-Au nanoparticles in 1 mM CaCl₂ background
   6. 10X dilution of 60 nm citrate-Au nanoparticles with 1 g/L PVP in 1 mM NaCl background

Instrument setup

Turn on the Zetasizer instrument, and open the Manual measurement dialogue. Table L3.1 below specifies the instrument settings to apply for the measurements.

Table L3.1. Zetasizer Measurement Settings for Particle Zeta Potential Analysis by Electrophoretic Light Scattering

Sample analysis

1. As noted in the sample preparation instructions, the Au nanoparticles should not be added until immediately before each measurement. Add 0.1 mL of 60 nm Au nanoparticles to the first sample to be measured, and mix thoroughly.
2. Insert a Malvern zeta dip cell into the cuvette or load the sample into the disposable zeta cell, ensuring no bubbles have been trapped in the sample. Insert the dip cell assembly or disposable zeta cell into the Zetasizer sample compartment, ensuring that it is oriented in the correct direction and inserted all the way to the bottom such that the electrodes make secure contact with the instrument. Close the compartment.
3. In the Zetasizer software, open the Manual measurement dialogue. Input the sample name and verify the measurement settings listed in Table L3.1.
4. Click “Start measurement” to collect the measurements on your sample.
5. Record your observations on the measurements collected during the lab in the table below (one per sample).

Table L3.2. Observations Noted During Electrophoretic Light Scattering Analysis

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 3 Data Analysis Template) contains example data collected in the lab to be processed (sections in orange to be completed by the user following the steps below), along with figures showing the phase plots and zeta potential distributions.

1. Review the voltage settings that were applied to each of the six samples. Recommendations were discussed in the NCL PCC-2 Method regarding the voltage selection. Discuss the technical reasons for why the voltage selection can be important. Then, inspect your actual data collected in lab: Was there any trend in the applied voltage automatically determined by the instrument as ionic strength increased, and if so, does it match the recommendations?
2. Review the phase plots, zeta potential distribution plots, and other observations recorded in Table L3.2 for each of the six samples. Guidance related to data quality are noted in Table L3.2 and the NCL PCC-2 Method. Are there any samples where you might have data quality concerns? If so, indicate which sample and describe the issue of concern.
3. Complete Table L3.3 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 L3.3. Summary of Results
   

   Sample Background	Electrophoretic Mobility (μm cm V-1 s-1)	Zeta potential (mV)
   (i) 1 mM NaCl
   (ii) 20 mM NaCl
   (iii) 50 mM NaCl
   (iv) 100 mM NaCl
   (v) 1 mM CaCl2
   (vi) 1 g/L PVP, 1 mM NaCl

4. The Smoluchowski model was selected in the Zetasizer software to report the zeta potentials in Data Analysis Part 1 above. Compute the Debye parameter (κ) and the product (κR_s) for the seven samples. Does each sample fall within the Smoluchowski regime? Recompute the zeta potential using the Henry equation instead, using the approximation for f(κR_s) by Ohshima (1994), cited in the Introduction section above. Compute the % error of the Smoluchowski approximation compared to the Henry equation for each sample. Report all of the results in a table with four columns for κ, κR_s, ζ_Henry, and % error. Remember to include units if relevant.

5. Discussion Questions

1. Measurement settings
   For ELS measurements, the “Dispersant” tab requires one additional parameter, the dielectric constant or relative permittivity of the solvent, which was not required for the dynamic light scattering measurements in Laboratory 2. Discuss why this property is now required by identifying where (e.g. what model equation) an error in this parameter input would propagate to error in the zeta potential determination by ELS. 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. Sensitivity to electrolyte concentration and counterion valence
   For the citrate-stabilized Au nanoparticles in only NaCl (i.e., samples i-iv): Is there any trend in the zeta potential and the electrophoretic mobility with NaCl concentration? Also, compare the Au nanoparticles in 1 mM NaCl and 1 mM CaCl₂ (samples i and iv). Which sample has a lower magnitude (less negative) zeta potential? Discuss whether the trends observed with salt concentration and counterion valence meet the theoretical expectations. As part of your discussion, please note the relevant theory (equations) and how the salt concentration or valence impacts the result (e.g. which parameters are affected, and what is the impact in the model equations?).
   
3. Sensitivity to surface coatings
   Compare the uncoated (citrate-stabilized) and PVP-coated Au nanoparticles in 1 mM NaCl (samples i and vi). Which sample has a lower magnitude (less negative) electrophoretic mobility?  Is the ELS measurement sensitive to the presence of the coating? Explain theoretically why it would or would not be expected to be sensitive to an adsorbed coating layer.
4. Data analysis uncertainties
   The Smoluchowski approximation is often used as the default setting to convert electrophoretic mobility to zeta potential, regardless of the sample properties. Inspect your results from Data Analysis Step 4. Was there any trend in the % error with ionic strength (i.e., decreasing, increasing, or no trend in % error as ionic strength increases) when comparing the ζ values using the Smoluchowski model to the ζ_Henry values? Discuss whether the trend does or does not meet theoretical expectations, considering the assumptions of where the Smoluchowski model applies.
5. Sensitivity to pH
   Assuming the sample pH was approximately 7 for all of the citrate-stabilized Au nanoparticles measured in this laboratory, discuss how you might expect the zeta potential to change (or not) if the pH was decreased to pH 4 or increased to pH 10, and explain why. It is encouraged to review Activity 1 and Activity 2, which provide relevant information on citrate chemistry, to answer this question.

References