An electrophoretic light scattering run returns a zeta potential with a standard deviation attached, and neither of those two numbers is the quantity the instrument actually measured. Laser Doppler electrophoresis measures the electrophoretic mobility of the dispersed material; the zeta potential follows from that mobility only once an electrokinetic model has been chosen [1]. For peptide nanofibres, hydrogel precursors and peptide-based particles, that model is often left at an instrument default rather than chosen against the particle size and the ionic strength actually in the cell.
The observable and the inference
Zeta potential is the potential at the surface of hydrodynamic shear, also called the slipping plane [1]. That boundary sits inside the electrical double layer. Counter-ions accumulate close to the charged surface and form a strongly bound inner Stern layer; when the particle moves, ions out to some distance from the surface — generally somewhere in the diffuse layer — move with it, and that distance is the slipping plane at which the zeta potential, an apparent surface potential related to the surface charge, is measured [2]. It is not the surface potential itself, and the position of the shear plane is not something the measurement determines.
The IUPAC technical report on electrokinetics treats zeta as a property of charged interfaces that should be independent of the technique used to determine it, then attaches the condition that makes the claim usable: the requirement for obtaining the zeta potential is that electrokinetic theories be correctly used and applied within their range of validity [3]. The same report notes that zeta is often not the only property characterising the electrical state of the interfacial region, because the excess conductivity of the stagnant layer is an additional parameter, and it scopes its recommendations mainly to smooth and homogeneous solid particles and plugs in aqueous systems [3].
The κa criterion decides which equation you are entitled to use
Mobility converts to potential through Henry's function f(κa), in which a is the particle radius and κ−1 is the Debye screening length. Two limits are in routine use. The Smoluchowski approximation sets f(κa) = 1.5 and assumes the electrical double layer is much thinner than the particle, κa >> 1. The Hückel approximation sets f(κa) = 1 and assumes the double layer is much thicker than the particle radius, κa << 1 [2]. Because the potential enters multiplied by f(κa), a single measured mobility maps onto a zeta potential 1.5 times larger in magnitude under Hückel than under Smoluchowski. Two laboratories reporting different potentials for the same material may differ by nothing more than that choice.
κ−1 is set by the ionic strength of the medium, so κa is a joint property of the particle and the buffer rather than of the particle alone [2]. A few-nanometre micelle in millimolar buffer and a several-hundred-nanometre aggregate in 150 mM saline sit at opposite ends of the criterion, and one software default cannot be correct for both. Skoglund and colleagues stated the failure plainly for metal nanoparticles: particle size is seldom included specifically in the standard ways of determining zeta potential, and there are cases in which both the Hückel and the Smoluchowski approximations are invalid, although corrections are possible using approximations of the Henry function, which improved their analysis [2]. The bridging expression they applied, which they attribute to Ohshima, converges to the Hückel result for small particles at low ionic strength and to Smoluchowski for larger particles at relatively higher ionic strength [2].
The closed form is itself an approximation. Doane and colleagues, reviewing nanoparticle zeta potentials, identify when the numerical solution of O'Brien and White should be adopted in preference to Henry's closed-form analytical approximation, and note that interpreting electrophoretic mobility, especially for ligand-coated particles, can be a complex undertaking [4]. The technique they review has furnished zeta potentials for analytes with sizes ranging from a few nanometres to several micrometres [4] — the whole range peptide assemblies occupy, and the reason the model question has to be answered per system rather than settled once.
Zeta potential is not a stability number
Pochapski and colleagues took experimental electrophoretic mobility data for magnetite (Fe3O4) nanoparticles and showed that inappropriate selection of the electrokinetic model can compromise interpretation of the results [5]. Their particles formed mass fractal aggregates in solution, so the zeta potential could not be determined under ideal conditions where mobility depends on the particle radius; the Dukhin number estimated from potentiometric titration indicated that stagnant layer conduction could not be neglected for that system; and models that do not consider stagnant layer conduction grossly underestimated the zeta potential [5]. DLVO interaction energy predictions for the colloidal stability of those dispersions likewise depended on which electrokinetic model had been used to calculate the potential, and the authors concluded that, contrary to many reports in the literature, high zeta potential values do not necessarily reflect high colloidal stability for charge-stabilised nanoparticle dispersions [5].
That was an inorganic oxide, not a peptide. What transfers is the structure of the argument rather than the numbers: a stability threshold is a statement about one system's balance of attraction and repulsion, computed from a potential that has already absorbed an assumed f(κa) and an assumed handling of surface conduction. Lowry and colleagues draw the reporting consequence: nanoparticle zeta potentials are easy to measure and have been proposed as a required property for complete nanoparticle characterisation, but relevant metadata must be reported alongside them for the values to be scientifically useful [6].
A value without its buffer is uninterpretable
Increased ionic strength screens surface charges and reduces the Debye length, and the consequences reach past the number itself [2]. In the same study, solutions of high ionic strength (150 mM NaCl) induced a higher extent of particle agglomeration than 10 mM NaCl for citrate-capped silver nanoparticles, which further complicates prediction of the zeta potential through sedimentation and broadening of the zeta potential distribution [2]. A potential quoted without its electrolyte and concentration cannot be compared with anything, because both the conversion factor and the object being measured have moved.
Austin and colleagues used micro-electrophoresis with a diffusion barrier to reach high and saturated ionic strengths, and reproduced the theoretically predicted asymptotic, non-zero electrophoretic mobility with increasing ionic strength, a cationic Hofmeister series dependency, charge inversion, and a continuously decreasing variation in mobility with pH as molarity increases [7]. The last of those matters for anyone titrating a peptide assembly to find where its mobility crosses zero: the pH dependence flattens as salt rises, so an apparent electrokinetic zero measured in one electrolyte does not transfer to another. This is where the measurement meets the isoelectric point guide — the crossing you observe belongs to the assembled particle in a stated electrolyte, not to the sequence.
Electrodes, Joule heating and dilution
The sample sits in a field between electrodes, and both the field and the electrodes act on it. Applying the field over long timescales creates an electro-osmotic flow along the cell wall; at high ionic strength the current drives significant Joule heating, which increases the uncertainty in the measured electrophoretic mobility; and with the dispersed phase close to the electrode surface, catastrophic effects including large aggregated particle size fractions and outgassing were observed for all salts tested [7]. The remedy adopted there was to isolate the dispersed phase from the electrode surface with a diffusion barrier, which prevented the outgassing, precipitation and sample degradation otherwise seen [7].
The same approach was characterised earlier for proteins. Corbett and colleagues loaded a small sample volume into a much larger volume of dispersant containing the electrodes and recorded the measurement before the sample could diffuse to them, reducing sample volumes by up to two orders of magnitude to around 50 µL with no reduction in measurement sensitivity, retrieving samples usefully intact, and demonstrating BSA mobility up to 75 °C and 1 M buffer concentration and lysozyme down to 0.5 mg/mL with good agreement with literature values [10]. Those were globular proteins rather than peptide assemblies, but the geometry of the problem — a scarce, salt-sensitive biomolecule in a conductive buffer next to a polarising electrode — is the one a peptide nanostructure presents.
Dilution is the other intervention that changes the sample. Measuring at or close to neat concentration is desirable because it minimises any change in zeta potential caused by dilution, and for both a titanium dioxide and a polyurethane dispersion the measured electrophoretic mobility showed a gradual decrease as sample concentration increased [1]. For a peptide system the risk runs the other way as well: diluting a hydrogel precursor into the instrument's optical working range can take it below the concentration at which the assembly exists.
A validated protocol does not travel
Varenne and colleagues standardised an ELS protocol and built a validation methodology around it, testing robustness against the batch of measurement cells, the sample temperature, the type of measurement cell and the analyst, and reporting uncertainties of 14% and 12% for negatively and positively charged reference standards respectively [8]. That list of factors is worth reading as a list of things that will move your answer. A later protocol from the same group, based on Fast Field Reversal mode and validated within the framework of the Smoluchowski approximation, could be applied to soft nanomaterials including polymer-based nanoparticles and liposomes but appeared unsuitable for dense nanomaterials including rutile titanium dioxide nanoparticles [9]. Validation is material-class specific.
Peptide assemblies, not peptide molecules
Nap and colleagues built a theoretical model to describe and predict the charge on self-assembled peptide amphiphiles as a function of pH and ion concentration, computed for nanofibres of the sequence C16−V2A2E2, treating charge regulation of the carboxylic acid groups through the acid–base equilibrium of the glutamic acid residues and the possibility of ion condensation [11]. They found the charges on the glutamic acid residues of the nanofibre to be much lower than for the same functional group in aqueous solution, with strong coupling between charging via the acid–base equilibrium and the local dielectric environment, and concluded that an accurate model of peptide amphiphile self-assembly must take charge regulation and ion condensation into account together with that coupling [11]. The same paper states the measurement caveat directly: zeta potential measurement gives electrophoretic mobility, from which the electrostatic surface potential and charge can be estimated, but the method is best used for spherical particles and can be more challenging to interpret for filamentous or fibrous structures [11].
Two things follow. Sequence-level pKa arithmetic does not give the charge carried by the assembled fibre [11], so a calculated monomer pI is not a prediction of where the fibre's mobility vanishes. And a high-aspect-ratio fibre is not the sphere that Henry's function was written for [11], so the quantity you can defend reporting for a nanofibre suspension is the mobility, with any derived potential flagged as model-dependent.
Used within those limits the measurement earns its place. Toksoz and colleagues studied nanofibre formation by self-assembling peptide amphiphiles using pH and zeta potential measurements alongside FT-IR, circular dichroism, rheology, atomic force microscopy, scanning electron microscopy and transmission electron microscopy, and found that aggregation of the peptides was triggered upon neutralisation of the charged residues by pH change or by addition of electrolyte or biomacromolecules [12]. That is the defensible reading: the electrokinetic signal tracks when electrostatic repulsion has been removed, cross-checked against structural and rheological evidence rather than standing alone, which is the pairing the self-assembly guide develops. Martin and colleagues likewise used zeta potential together with electrical impedance spectroscopy to monitor gelation across four diphenylalanine-based peptides bearing different heterocyclic capping groups, with the differing gelation times for each hydrogel coming from the impedance data [13].
A separate use is to measure a peptide through its effect on a particle that does satisfy the model. Freire and colleagues derived and tested a mathematical model to obtain lipid/water partition constants from ζ-potential data and evaluated it on two antimicrobial peptides, comparing the results with values from fluorescence spectroscopy [14]. The electrokinetic object there is the lipid vesicle; the peptide is detected by the shift it produces as it partitions. When you report such a result, say what was in the tube.
What to record
A review of DLS and zeta potential practice locates the recurring problem in inadequate understanding of the operating principles together with critical issues such as sample preparation and interpretation of the data [15]. The mitigation is bookkeeping rather than instrumentation. Report the electrophoretic mobility next to the potential; the electrolyte and its concentration, the pH and the temperature; the radius used to evaluate κa and the model or f(κa) applied; the cell type, cell batch and operator [6, 8]. Report the distribution as well as the mean, and run the blank — in biomolecule-containing cell medium the signal from proteins can interfere with the measured zeta potential, so the intensity distribution of the blank should be presented alongside that of the sample [2]. None of this makes the number more accurate. It makes it possible for a reader to work out what the number meant.