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Dynamic Light Scattering Based Microelectrophoresis:Main Prospects and LimitationsVuk Uskoković aa Therapeutic Micro and Nanotechnology Laboratory, Department of Bioengineering andTherapeutic Sciences , University of California, Mission Bay Campus , San Francisco ,California , USAAccepted author version posted online: 19 Dec 2011.Published online: 07 Dec 2012.

To cite this article: Vuk Uskoković (2012) Dynamic Light Scattering Based Microelectrophoresis: Main Prospects andLimitations, Journal of Dispersion Science and Technology, 33:12, 1762-1786, DOI: 10.1080/01932691.2011.625523

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Dynamic Light Scattering Based Microelectrophoresis:Main Prospects and Limitations

Vuk UskokovicTherapeutic Micro and Nanotechnology Laboratory, Department of Bioengineering and TherapeuticSciences, University of California, Mission Bay Campus, San Francisco, California, USA

Microelectrophoresis based on the dynamic light scattering (DLS) effect has been a major tool forassessing and controlling the conditions for stability of colloidal systems. However, both the DLSmethods for characterization of the hydrodynamic size of dispersed submicron particles and thetheory behind the electrokinetic phenomena are associated with fundamental and practical approx-imations that limit their sensitivity and information output. Some of these fundamental limitations,including the spherical approximation of DLS measurements and an inability of microelectro-phoretic analyses of colloidal systems to detect discrete charges and differ between differentlycharged particle surfaces due to rotational diffusion and particle orientation averaging, are revis-ited in this work. Along with that, the main prospects of these two analytical methods are men-tioned. A detailed review of the role of zeta potential in processes of biochemical nature is giventoo. It is argued that although zeta potential has been used as one of the main parameters incontrolling the stability of colloidal dispersions, its application potentials are much broader.Manipulating surface charges of interacting species in designing complex soft matter morpholo-gies using the concept of zeta potential, intensively investigated recently, is given as one of theexamples. Branching out from the field of colloid chemistry, DLS and zeta potential analysesare now increasingly finding application in drug delivery, biotechnologies, physical chemistry ofnanoscale phenomena and other research fields that stand on the frontier of the contemporaryscience. Coupling the DLS-based microelectrophoretic systems with complementary characteriza-tion methods is mentioned as one of the prosperous paths for increasing the information output ofthese two analytical techniques.

Keywords Colloidal system, dynamic light scattering, microelectrophoresis

INTRODUCTION

Zeta Potential represents a basic law of Nature, and it plays a

vital role in all forms of plant and animal life. It is the force that

maintains the discreteness of the billions of circulating cells,

which nourish the organism. The stability of simple inorganic

man–made systems is governed by these same laws.[1]

Surface charge of particles in sols has been used for cen-turies to regulate the stability of colloidal suspensions.[2]

The ancient Egyptians used to render many colloids, fromclays to inks, stable by electrostatic means, without beingaware.[3–6] In 1857, Michael Faraday described the prep-aration of colloidal gold sols which are still stable and ondisplay in the British Museum.[7] Although Faraday used

different salt contents to control the electrostatic repulsionbetween the particles and, therefore, the extent of theiraggregation (nowadays known as the ‘‘salting out’’ effect),neither was he aware that he had been indeed manipulatingwith the surface charge of the particles, although he was onthe right track of explaining the cause of the stability of hissols. ‘‘There is probably some physical change in the con-dition of the particles, caused by the presence of the saltand such affecting media, which is not a change of the goldas gold, but rather a change of the relation of the surface ofthe particles to the surrounding medium,‘‘[8] stands writtenin his extensive treatise. The Gouy-Chapman model of theparticle-solution interface then postulated a separation ofcharges at the interface and the formation of the so-calleddouble layer composed of counterions and co-ions, some ofwhich are, as later pointed out by Stern, tightly bound tothe surface and some of which are free to diffuse.

Built on the basis of this model, DLVO theory developedin 1940s by Derjaguin and Landau and Verwey and Over-beek, separately, explained the stability of colloids byinvoking a balance between the repulsive electric doublelayer forces and the attractive, short-range van der Waals

Received 21 July 2011; accepted 13 September 2011.The author acknowledges the NIH grant DE021416 for

support.Address correspondence to Vuk Uskokovic, Therapeutic

Micro and Nanotechnology Laboratory, Department of Bioengi-neering and Therapeutic Sciences, University of California, 17004th Street, QB3 204, Mission Bay Campus, San Francisco, CA94158-2330707, USA. E-mail: Vuk.Uskokovic@ucsf.edu

Journal of Dispersion Science and Technology, 33:1762–1786, 2012

Copyright # Taylor & Francis Group, LLC

ISSN: 0193-2691 print=1532-2351 online

DOI: 10.1080/01932691.2011.625523

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forces.[9,10] Ever since the propositions of this theory, it hasbeen used as the theoretical basis in controlling the stabilityof colloidal dispersions for various technologies—foods,pharmaceutics, cosmetics, photography, electronics, agro-chemicals, paints, building materials, etc. Opposing theexclusively attractive and short-range van der Waals inter-actions, the charged nature of suspended particles inducestheir repulsion and is a critical factor in controlling the stab-ility of colloidal systems. As small particles tend to aggre-gate and phase separate due to their high interfacial freeenergies, ensuring relatively high surface charges on the par-ticles is oftentimes a necessary precondition for keepingtheir colloidal suspensions stable. A measurable quantityused to control the intensity of the repulsive electrostaticinteraction between the charged colloidal particles is zetapotential (f potential). Typically, f potential of� 15mV isconsidered as the threshold for agglomeration, whereas� 30mV is considered as the limit above which the colloidalsystem becomes thoroughly stable. In between 15 and30mV, the system may be either agglomerated or dispersed.

To measure the distribution of f potential of suspendedparticles, an electric field is applied to the suspension.Electrophoretic mobility (l) of the charged particles mov-ing across the field is measured in terms of changes in theintensity of the scattered light caused by the light-scatteringparticles moving in the alternate electric field and is furtherused to calculate f potential of the particles according toSmoluchowski equation, in which g is the viscosity coef-ficient of the medium, n is the electrophoretic velocity, eis the dielectric constant of the medium, and E is the gradi-ent of the electric field applied:

n ¼ gn=eE ¼ gl=e½Volt�: ½1�

Since the measurement of the particle size typically pre-sents the first step in characterization of colloids usingDLS, the next section will deal with fundamentals of thesemeasurements using the dynamic light scattering (DLS)effect, also known as photon correlation spectroscopy(PCS) and quasi-elastic light scattering (QELS), which isthe technique on which this work will focus.

DYNAMIC LIGHT SCATTERING

Particles, micelles and molecules in suspension undergoBrownian motion, which is the random zigzag motioncaused by collisions with solvent molecules that themselvesare randomly moving owing to their thermal energy(Figure 1). The name for this ubiquitous random motionof particles in any given medium was given after the botan-ist who first observed this phenomenon with pollen grains‘‘dancing’’ on the surface of the water. An essential featureof Brownian motion is that smaller and lighter particles are‘‘kicked’’ further by the solvent molecules and, thus, experi-

ence more rapid zigzag motion. According to the classicalkinetic gas theory, every particle in the suspension has anequal kinetic energy, Ek¼mt2=2¼ 3kT=2 (along a singleaxis the thermal energy is equal to kT=2). So, with adecrease in size, the mass will get lower and the velocity willgo up, and vice versa.

Hence, particles in suspension undergo random, Brow-nian motion, the velocity of which is proportional to theparticle mass, which can be represented as the product ofsize and density. The DLS devices are built on the principleof extracting information about diffusion and size proper-ties of dispersed colloidal entities exactly from this seem-ingly random, Brownian motion.

All materials are capable of scattering light (Tyndalleffect) and only perfectly homogeneous systems, whichneither pure liquids nor dust-free gases are, would be anexception to this rule. There are different types of scatter-ing, depending on the size of the particle as the scatteringentity: Rayleigh (when the particles are small compared tothe wavelength of the light: <circa k=20), Debye (whenthe particles are large and their refractive index is not sig-nificantly different from that of the dispersion medium),and Mie (when the particles are large and their refractiveindex is significantly different from that of the dispersionmedium). For systems analyzable using the DLS method,Rayleigh scattering presents the dominant scattering mech-anism. According to Rayleigh’s theory released in 1871, asan electromagnetic wave hits the particle, it induces oscillat-ing dipoles in the particle, which then acts as a secondarysource for the emission of the scattered radiation of thesame wavelength as the incident light in all directions, pro-vided that the particle is stationary with respect to the lightsource. Light scattered by a moving particle will experiencea Doppler shift to slightly higher or lower frequenciesdepending on whether the particle is moving towards oraway from the observer=detector. Illuminating particles or

FIG. 1. An example of Brownian motion: a dust particle is

bombarded by air molecules (a) and randomly moves in space (b). Note

that dust particles dispersed in air are also a form of colloidal systems,

known as aerosol or smoke. Sols, gels, foams and latexes present other

common form of colloids where solids, liquids, gases and macromolecules

are dispersed in liquid (sols, foams, and saps) and solid phases (gels),

respectively.

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molecules in suspension with a monochromatic and coher-ent, laser light results in fluctuations of the intensity of thescattered light at a rate that is dependent on the particle size.Since the suspended particles are randomly moving backand forth with respect to the light source, time-dependentfluctuation of the intensity of the light scattered off the par-ticles results, owing to the Doppler effect (Figure 2).

In the case of Rayleigh scattering, the intensity of lightscattered from a particle is proportional to the square ofthe particle mass. Analysis of the intensity fluctuationsresulting from the Doppler effect that the particles undergoin their Brownian motion yields the particle velocity and,hence, the particle size from the Stokes-Einstein relationship:

D ¼ kbT=6pgr ½2�

D is the measured translational diffusion coefficient[m2=s]; g is the viscosity coefficient of the medium [Ns=m2]; kb is the Boltzmann constant (1.38� 10�23 J=K); T isthe absolute temperature; and r is the Stokes or hydrody-namic radius of the particle. It is not the effective radiusof a hydrated molecule in solution, as often mentioned.Rather it is the radius of a hard sphere that diffuses atthe same rate as the molecule. The behavior of this sphereincludes hydration and shape effects. Since most moleculesare not perfectly spherical, the Stokes radius is smaller than

the effective radius (or the rotational radius). A moreextended molecule will have a larger Stokes radius whencompared to a more compact molecule of the same molecu-lar weight.

The translational diffusion coefficient (D) correspond-ingly depends not only on the size of the particle, but onmultiple other factors, including the topology and chemicalordering of the particle surface as well as the ionic strengthand the ionic composition of the medium. A direct conse-quence of this is that the particle size estimated usingDLS turns out to be typically larger than that obtainedduring any of the electron microscopy analyses, duringwhich the particle is looked at in isolation, away from itsdynamic colloidal environment.[11]

Diffusion coefficient has [cm2s�1] units and represents afactor of proportionality in Fick’s law, representing theamount of substance diffusing across a unit area througha unit concentration gradient in unit time. As such, it doesnot depend on concentration of the particles, but presents acoefficient that describes how proportional concentrationof the particles is to their flux. Typically, D of a compoundis circa 104 times higher in air than in water. For example,CO2 in air has D¼ 16mm2=s, while in water its diffusioncoefficient is only 0.0016mm2=s. For biological molecules,D normally ranges from 10�11 to 10�10m2=s. D alsoincreases with both temperature and pressure. According

FIG. 2. A set of drawings depicting the Doppler effect on which the DLS measurement device relies in determining the size of the dispersed particles.

The Doppler effect occurs when the source of waves is moving relative to the detector. Red shifts to lower frequencies result when the source moves away

from the detector, while blue shifts to higher frequencies occur when the source moves towards the detector, independently of the waves in question:

electromagnetic (galaxies in the image) or mechanical waves of pressure (train whistle). (Figure available in color online.)

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to Einstein’s equation, where x is the mean Browniandisplacement of a particle along a given axis after time t:

x ¼ ð2DtÞ1=2 ½3�

Combining the former two equations (Equations (2) and(3)), one can calculate that an uncharged particle with 1 nmin radius will travel 1.23mm in an hour during itsBrownian motion in water at 20�C, whereas an unchargedparticle with 1 mm in radius will cross only 39 mm during thesame period of time.

The DLS device measures D by looking at the Dopplershift of dispersed particles as they randomly move backand forth with respect to the light source. Distribution ofthe particle size and its average are calculated from thehalf-width of the peak on the scattering intensity versuslight frequency curve (Figure 3). If one were to look at staticscattering entities, only the natural width of the peak ofintensity of the scattered light versus scattering frequency,xo would remain. Smaller particles produce a more inten-sive Doppler effect than the bigger and less movable ones.So, the half-width of the peak of intensity of the scatteredlight versus scattering frequency, Dx1=2 is directly pro-portional to the diffusion coefficient of the particle andinversely to its size:

Dx1=2 ¼ Dð4pnoxo sinðh=2Þ=cÞ2 ½4�

The raw function that the DLS device draws during themeasurement is the correlation function versus time curve(G(s)), and is related to the diffusion coefficient of the dis-persed particles. In general, quasi-random physical eventscould be described with the use of correlation functions,mathematical constructs designed to reflect the average timespans during which the signals followed remain correlated.The characteristic of greatly damped phenomena thatinclude diffusion is that correlation functions describing

them decay approximately exponentially, with a distinctivetime constant known as the ‘‘correlation time,’’ s.

GðsÞ ¼ IðtÞ � Iðtþ sÞ ¼ A½1þ B expð�2CsÞ� ½5�

C ¼ Dq2 ½6�

q ¼ 4pn sinðh=2Þ=ko ½7�

D ¼ kbT=6pgr ½8�

I is the scattered light intensity; t is the initial time; s isthe delay time; A is the amplitude or intercept of the corre-lation function; B is the baseline; D is the diffusion coef-ficient; q is the scattering vector magnitude; ko is thevacuum laser wavelength; n is the medium refractive index;h is the scattering angle; and r is the hydrodynamic radius.This exponentially decaying curve falls to zero at timewhen the particle in its movement exceeds the wavelengthof the laser light. The slope of the logarithm of this func-tion (the so-called ‘‘first cumulant’’) could be used to calcu-late the particle size, r, whereas the curvature indicatesnonlinearity due to polydispersity and can be used to esti-mate its range (Figure 4).

FIG. 3. Light intensity versus frequency curve with the denoted half-

width of the main peak from which the diffusion coefficient is calculated.

FIG. 4. Cumulants analysis used to calculate the average D and

polydispersity index (PdI) from the logarithmic autocorrelation curve (a)

and a comparison of two exponentially decaying autocorrelation curves,

one for a suspension medium (pure water) and another one for a poly-

meric dispersion (b). Obviously, the scattering from rapidly diffusing sol-

vent molecules remains correlated only for a very short time, inaccessible

to the correlator. Reprinted with permission of Malvern Instruments,

Ltd., www.malvern.com.[11]

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EFFECT OF IMPURITIES ON THE PARTICLE SIZE

One of the essential factors that affect the quality andreliability of DLS analyses are impurities. The followingexample demonstrates the drastic influence that they mayexert. Figure 5a shows the particle size distribution of asample with the major peak at�2 nm, derived from the lightscattered off small colloidal particles, and a minor peak at�80 nm, derived from the light scattered off aggregates ofthe small particles or relatively large impurities. Althoughthis minor peak accounts for less than one-third of the over-all scattered light, since intensity is directly proportional tothe particle mass and the mass increases in proportion to r3,the total mass represented by this peak is only �0.05% ofthe total. Figure 5b shows the size distribution of an evenmore impure=aggregated sample, where additional aggre-gate peaks are visible at �10 nm and �4 mm. The largestaggregate (4% of the intensity of the scattered light) in thiscase represents less than 1 ppm of the total mass. Also, themain peak at �2 nm possesses a sharp shoulder at �10 nm.Although the light intensity represented by the former peakis only 3.5 times higher than that of the latter peak, the scat-tering mass is more than 60 times greater for the former,

2 nm sized particles versus the latter, 10 nm ones. In general,because the scattering intensity is the function of r3, a par-ticle with 1 nm in diameter will scatter 106 times less lightthan a particle with 10 nm in radius.

This sensitivity of DLS measurements to impurities is aseeming weakness that could be transformed into strength.Namely, protein solutions or suspensions tend to easilyaggregate and repeated freezing=thawing cycles or pro-longed aging frequently result in this undesired aggregation.When it comes to DLS analyses of protein solutions or sus-pensions, however, this technique can prove to be of greatuse in evaluating the stability of these systems. Since theselarge clumps of protein typically grow from trace amountsof markedly smaller precursor aggregates, DLS can presentvaluable means for detecting such segregation process longbefore apparent aggregation marked by visible particulatesfloating in the suspension has taken place. As such, DLSpresents a valuable tool for assessing the stability of proteinsolutions or suspensions, especially since it allows for study-ing protein sols directly in their formulation buffers as wellas at either very low or very high concentrations (0.01–100mg=ml). Deviations of the highly concentrated samplesfrom the ideal conditions due to the so-called ‘‘molecularcrowding’’ effect, although, make the data analysis burden-some at times. The latter effect, common to intracellularenvironments, describes altering of the properties of macro-molecules in highly concentrated solutions. It is associatedwith the protein molecules capturing solvent moleculesand increasing the effective concentration and viscosity ofthe medium. This, in turn, often modifies the behavior ofthe proteins compared to the one evidenced in test-tubeassays at lower concentrations.

SPHERICAL APPROXIMATION

The central fundamental problem that the DLS faces inanalyzing the particle size is the spherical particle shapeapproximation that it employs. Although common sensethinking may prompt us to assume that elongation of par-ticles will produce a bimodal distribution of sizes, any elon-gation will, in fact, produce a single peak at the sizes thatwould correspond to the averaged particle dimension.Hence, every elongated particle will not be detected as such,but rather as a spherical one with the diameter averagedover the three axes.[13] The reason is that in addition toBrownian, translational diffusion of suspended particles,they also undergo rotational diffusion around their axes.The latter form of diffusion contributes to randomizationof the particle orientation, implying that any particle deviat-ing from the spherical shape would be treated as an ‘‘ellip-soid of revolution,’’ which is characterized by its axial ratio,that is, the ratio of the single half-axis, a, to the radius ofrevolution, b. For this reason, it cannot be expected fromelongated particles to produce multiple peaks, presumably

FIG. 5. Particle size distribution curves expressed in terms of the

intensity of the scattered light for two protein samples forming aggregates

in suspension.

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one corresponding to their width and another to length. Theaforementioned Stokes-Einstein relationship is thence usedto calculate the mean particle size.

For a dispersion of rod-like particles, for example, thetranslational diffusion coefficient (Do) of the particle canbe represented[14] by a linear combination of the diffusioncoefficients parallel and perpendicular to the long axis ofthe rod, DII and DI:

Do ¼ 1=3�DII þ 2=3�DI: ½9�

For very diluted dispersions, particle interactionsbecome negligible and the overall expression for the dif-fusion coefficient can be written in the following way:[15]

Do ¼ kT=2pglef ½10�

lef ¼ l½lnðl=dÞ þ 0:316þ 0:5825d=lþ 0:050ðd=lÞ2��1: ½11�

The length of the rod is represented with l; d is thediameter of the rod; and lef represents an effective averageparticle length. For rod-like particles with large aspectratio, the last three terms within square brackets can beneglected.[16]

Hence, by knowing the shape and the dimensions of theparticles, one can calculate the expected measured hydrody-namic radius using the spherical approximation applied bythe device. In the example of 4� 25 nm sized CdS rods, adifference was detected between the measured and the cal-culated values, and the authors concluded that the forma-tion of dimers had had to take place in the suspension.[17]

For one such deduction to be made, a priori information,typically coming from microscopic analyses, has to beobtained.

Whenever one works with elongated particles, one canalso apply the hydrodynamic Brenner theory to estimatethe hydrodynamic radius of the particle that will be givenas the output by the device. Barbara Jachimska et al. have,thus, shown[18] that for the case of fibrinogen, which isknown to have the length l¼ 47.5 nm and the molecular vol-ume n¼ 387 nm3, the other two dimensions can be calcu-lated as 3.2 nm each. Hence, the aspect ratio, k, would be47.5=3.2¼ 15. Assuming that a monolayer of water dipolesis adsorbed on each side of the molecule (proteins in generalare strongly hydrated), and knowing that its thickness is0.145 nm, the hydrodynamic width would be 3.2þ 2�0.145¼ 3.5 nm. The effective aspect ratio, k�, would, thus,be equal to 13.6. Then, one can apply Brenner equation:[19]

rh ¼ L=2ða1 ln 2k� � a2Þ ½12�

a1¼ 1 and a2¼ 0.11 for cylinders (rods); a1¼ 11=12 anda2¼ 0.31 for bend cylinders forming a semicircle (semi-torus); and a1¼ 11=12 and a2¼ 1.2 for cylinders bent to

form torus.[20] One can, thus, calculate the hydrodynamicradius (rh) for various a1 and a2, and by comparison withthe size measurement outcomes infer which shape fits mostthe results obtained. In other words, as previously noticed,by knowing the molecular shape, one can deduce detailsregarding the shape of the aggregates or molecules in sol-ution, but not vice versa.

In order to assess how self-assembly of colloidal entitiesproceeds over a reaction coordinate (time, concentration ofa reactant, etc.), the decay rate (1=s) can be measuredinstead of the particle size and plotted against time orenzyme concentration. A mirrored sigmoidal curve reach-ing a plateau at lower decay rates would, thus, indicateattainment of a state of lower mobility, which the decayrate is the direct indicator of. As oftentimes fibers areassembled from the initial spheres, one would detect onesuch drop in the decay rate, that is, the mobility or the dif-fusion coefficient of the particles. Widening of the fibers ortheir elongation would correspond to the same drop. Ingeneral, translational diffusion coefficient (D) may be moreappropriate to plot against time or concentration while fol-lowing the protein self-assembly since particle size as aparameter becomes meaningless if we know that the spheri-cal approximation fails.

SOURCES OF THE SURFACE CHARGE

As already mentioned, owing to charge separationeffects, particles in suspension acquire surface charge,which is typically screened at a certain distance from theparticle surface.[21] There are three sources of electricalcharges on particle surfaces:

1. Ionization: Proteins are examples of particles with intrin-sic surface charges primarily deriving from the protona-tion and deprotonation of acidic and basic side chains ofamino acid residues. Also, ionization of the end aminoand carboxyl groups determine the charge of the wholemolecule and, thus, of its aggregates. Thus, proteinsare normally positively charged at low pH values whenamino group (-NH2) becomes �NHþ

3 and carboxylgroup is also protonated (�COOHþ

2 ). But at higherpH values, amino group and carboxyl group becomedeprotonated (-NH- and -COO-), so that the protein asa whole becomes negatively charged. In the case ofhydrous metal oxide sols, hydroxyl groups (M–OH)become deprotonated at high pH values, transformingfrom –OH to O-,, thus, also contributing to the forma-tion of negatively charged particle surface, whereas theybecome protonated, transforming from –OH to OHþ

2 atlow pH values. The same argument applies for the caseof silica, typically negatively charged at neutral pHvalues. Metal ions on the metal oxide particle surfaceare likewise bound to OH groups owing to hydration

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effects and deprotonation of these groups is what makesthese particles negatively charged. Similarly to silanolgroups that render silica particles in aqueous medianegatively charged, gold particles form a micelle-likesheet of oxide groups on their surface (refer toFigure 11), which makes covalent conjugation of variousfunctional molecules thereto possible and makes themnegatively charged too, unlike the typically positivelycharged silver particles under physiological conditions.

2. Adsorption of Species: The surface charge of many typesof particles derives from selective adsorption of ions,such as metals, anions, protons or hydroxyl groups.Ions in general adsorb more easily on hydrophobic sur-faces, such as lipids, rather than on hydrated ones,which include proteins and polysaccharides. Becausecations are usually more hydrated than anions and,therefore, have a greater tendency to reside in the bulkaqueous medium, whereas bigger, less hydrated andmore polarizing anions have the tendency to be specifi-cally adsorbed, surfaces in contact with aqueous mediaare most often negatively charged. Owing to this effect,even oil droplets, alcohol monolayers and air bubbles inwater are negatively charged, except under very acidicconditions.[22–25] The effect of increased interfacial ten-sion between water and air=oil following the additionof electrolyte can also be interpreted by referring to lightand more movable cations moving away from thewater-air and water-oil interfaces more than anions

and leaving the interfaces negatively charged. In theabsence of surface-active species, the surface charge ofmetal oxides is solely due to adsorption=desorption ofprotons. Whether this proton adsorption=desorptionequals protonation=deprotonation of discreet surfacesites is still questionable, although it is accepted as suchin most models. If surfactant ions are present, theiradsorption will usually determine the surface charge.Finally, although adsorption of bipolar molecules doesnot contribute to the net surface charge, it does affecta rearrangement of the double layer composition, whichindirectly leads to modified f potential of the particles.

3. Selective dissolution of ionic compounds: In these cases, itis either anions or cations comprising the particles thatare preferentially dissolved,, thus, contributing to theimbalance in electroneutrality of the particle as a whole.Such is the case with AgI particles, which upon dissol-ution tend to preferentially release smaller and moremobile Agþ ions into the solution and retain heavierand less mobile I- within the crystal lattice. Conse-quently, although the solubility product (aAgþaI-) forAgI is equal to 10�16, the point of zero charge (PZC) doesnot exist at pAg 8 but is displaced to pAg 5.5 (pI 10.5).

As shown in Figure 6a, f potential is actually a differ-ence in electric potentials between that of the bulk and neu-tral liquid and that at a certain distance from the particlesurface, corresponding to the so-called slipping or shear

FIG. 6. Distribution of counterions in the double layer surrounding a negatively charged colloidal particle. Reprinted from Shaw[28] (this article was

published in Introduction to Colloid and Surface Chemistry, D. J. Shaw, # Elsevier [2003]). Stern layer of counterions is depicted as tightly bound to the

charged particle surface. The electric potential at the boundary of the shear plane compared to the neutral medium at the distance that surpasses the

Debye length (1=j) equals f potential. (Figure available in color online.)

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plane. The latter is the boundary of the sphere composed ofboth firmly adsorbed ions (Stern layer) and some of the dif-fusing ions surrounding the charged particle. Hence, thedistance from the particle surface at which f potential ismeasured is further away from Stern layer. However, theexact location of the shear plane is an unknown featureof the electric double layer. Still, as can be seen fromFigure 6b, f potential is normally taken to be just a bitlower than Wd, which is the potential at the boundary ofthe Stern layer. Experiments have shown that evenassuming that these two potentials are identical, especiallyfor lyophobic surfaces, would not produce a significanterror. Any differences between the two would most likelybe pronounced at high surface potentials and high electro-lyte concentrations due to the effect of compression of thediffusion layer of charges that leads to a higher slope of the

surface potential versus distance curve between the Sternlayer boundary and the slipping plane.

Strictly speaking, isoelectric potential is, thus, never themeasure of the surface potential. Counterions are typicallymostly present within this cloud of ions (composed of partlyfixed ions in Stern layer and partly diffusing and replaceableions outside of it but still within the shear plane) that movestogether with the particle, thus, contributing to typicallylower f potential compared to the surface potential. Still,sometimes it is the case that co-ions are dominant in thislayer (either as (a) overlapping with or lying over the layerof counterions confined very close to the particle surface, or(b) due to specific adsorption in spite of the electrostaticrepulsion), and in those cases f potential will be higher thanthe surface potential (Figure 7b). Also, sometimes, parti-cularly when polyvalent ions act as counterions, this layerof counterions may be sufficiently strong to induce thereversal of charges (Figure 7a). This is why aluminum ionsare frequently used to produce ‘‘salting out’’ aggregationeffects. In that case, f potential would be of a different signcompared to the surface potential.

To sum up, f potential should be, strictly saying, namedvoltage as it is effectively the electric potential differenceand its units, Volts, denote that. It is the difference betweenthe potential of the medium (considered as neutral) and thepotential at a certain distance from the particle surface.This distance is normally taken to be beyond the Sternlayer and at the boundary of the so-called shear=slippingplane. Another important boundary=layer is Debye length,which corresponds to the distance from the particle surfaceat which surface potential is completely screened andreaches zero. It normally, but not necessarily lies furtheraway from the Stern layer and shear plane.

Just as one often confuses f potential with the surfacecharge, isoelectric point (the zero value of f potential, IEPin general or pI in case of proteins) is often confused withthe point of zero (surface) charge (PZC). Whereas the

FIG. 8. Compression of the electrical double layer following an increase in the ionic strength of the medium (a) and a f potential versus pH curve for

a suspension of a recombinant protein in the absence of the background electrolyte (-o-) and in the presence of 150mM KCl (-D-) (b).

FIG. 7. Examples of polyvalent ions adsorbed onto a charged particle

and reversing its effective charge (a), and of specific adsorption of ions of

the same charge as the particle, contributing to an effective increase of the

effective charge (b). These are the two cases when the surface charge

cannot be readily estimated from f potential—the presence of polyvalent

ions (a) and specific adsorption that transcends the electrostatic repulsion

(b). Reprinted from Shaw[28] (this article was published in Introduction to

Colloid and Surface Chemistry, D. J. Shaw, # Elsevier [2003]).

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former quantities correspond to certain distances from theparticle surface, the latter are associated with the veryparticle surface. PZC is taken as equal to IEP only in theabsence of ions that screen the charge on the particle surface.(This would ideally happen only in vacuum, which is, enpassant, the only particle-medium interface which we canbe literally called ‘‘surface’’; everything else is an interface).Hence, a particle with the zero surface charge may have anon-zero value of f potential owing to the effect of doublelayer of charges surrounding it and, thus, may move in theelectric field, whereas the particle at the IEP may not havezero surface charge and still be stationary in the electric field.

Smoluchowski equation typically used to convert themeasured electrophoretic mobility to f potential has its lim-itations too. First of all, it is mainly applicable for mediumthicknesses of the double layer and low-to-medium ionicstrengths. It also applies only when the ratio of the doublelayer curvature to its thickness is so high that it can beassumed that the surface is almost flat. When the particleitself is small and the layer of ionic charges surroundingit is thin too, so that the given ratio is small and thecharged particle could be treated as a point charge, Huckelequation, the conditions for which are mostly found atextremely low ionic strengths (I< 10�5M for 10 nm sizedparticles) or nonpolar solvents, is applicable:

n ¼ 1:5gn=e½Volt� ½13�

EFFECT OF IONIC STRENGTH

Ionic strength plays a role in screening ion-ion interac-tions (as well as the ones between charged colloidal parti-cles) in the solution. Namely, surface charge density isequal to: r¼ ejwo, where e is the dielectric constant ofthe medium (inversely proportional to the ionic strength),wo is the surface potential, and 1=j is the length of the dif-fuse double layer of ions surrounding the particle surface.The latter can be divided to the Stern layer composed of

FIG. 9. Van der Waals force remains unchanged while electrostatic field gets suppressed in the vicinity of the particle following an increase in the

ionic strength of the dispersion medium. The local energy maximum existing at low ionic strengths (a) disappears at high ionic strengths (b), yielding an

unstable colloidal (or cellular as in this example) suspension as the result. (Figure available in color online.)

FIG. 11. An electron micrograph showing negatively charged nano-

sized gold particles adsorbed on electronegative plate-shaped kaolin crys-

tals, and the scheme depicting the negatively charged surface structure of

gold nanoparticles in water. Although kaolin platelets are negatively

charged as a whole, their edges are electropositive and as such attract

the gold particles onto them. Reprinted with permission from Riddick.[1]

(Figure available in color online.)

FIG. 10. The effect of the type and concentration of electrolytes on fpotential. Reprinted with permission from Zeta-Meter Inc.[38]

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adsorbed counterions and a diffuse layer of both counter-ions and co-ions, yielding as a sum the distance from theparticle surface to the slipping plane, the electric potentialat which corresponds to the measured f potential of theparticle. The slipping plane separates the mobile fluid fromthe fluid that remains attached to the particle surface andmoves together with it, similar to a cloud of charges, a partof which is bound to the particle and a part of which is ofdiffuse character. Another name for 1=j is Debye lengthand is, as already noted, usually taken as the distance fromthe charged particle surface at which the electrical neu-trality is reestablished. It can be represented as:

j�1 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie0erkT2NAe2I

s½14�

I is the ionic strength of the medium in mol=m3; e0 is thepermittivity of free space; er is the dielectric constant of themedium; k is the Boltzmann constant; T is temperature inK; NA is the Avogadro number; e is the elementary charge.A simpler expression for Debye length when water is usedthe dispersion medium is the following:

j�1ðnmÞ ¼ 10ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIðmMÞ

p ½15�

The initially proposed model of charged particle surfacein solution was by Helmholtz in 1850, and it merelydescribed the charge on the particle surface as balancedby an equal charge in the liquid phase. Only the subsequentupgrade of this model by invoking the diffuse nature oflayer of ions due to thermal motion and its double layerstructure yielded the so-called Gouy-Chapman model.The addition of inert electrolyte compresses the diffuselayer of charged ions and co-ions around each of the dis-persed and charged particles. Namely, a higher concen-tration of co-ions and counterions implies screening ofthe particle surface charge at a distance closer to the par-ticle. (This explains why f potential drops upon theaddition of electrolyte: wo exponentially decays with thedistance from the surface, and f potential is measured atsome distance from the particle surface; as with theaddition of electrolyte this potential decays faster, the fpotential will correspondingly be lower.) In other words,1=j decreases, which entails either an increase in r or adecrease in wo, or both. For example, in the case of AgIparticles whose potential depends on the concentration ofsilver and iodide ions in the solution, the addition of elec-trolyte and the corresponding drop in j leads to adsorptionof potential-determining silver or iodide ions whichincreases r but keeps wo constant. In case of an ionogenicsurface, however, r stays constant, but wo drops.

As shown in Figure 8a, increasing ionic strength causesthe double layer of ions around the charged particle surfaceto shrink owing to a higher concentration of ions in the dis-persion. Consequently, the absolute value of f potentialdecreases at any given pH following an increase in the ionicstrength, as shown in Figure 8b. IEP, on the other hand, issupposed to remain the same, provided the electrolyte isinert. However, as shown in Figure 9, van der Waals forcesdominating at shorter particle-particle distances are notinfluenced by the change in the ionic strength. Note that fpotential could be used in DLVO theory to calculate theinteraction force or energy as a function of the distancebetween the particles based on the balance between the repul-sive electrostatic and attractive van derWaals forces. Coagu-lation is a direct consequence of this interaction energy, andmaximum coagulation rates, aggregate sizes and sedimen-tation rates all coincide with the pI=IEP for the given system.

It is well known that Nature disperses colloids almostexclusively on the negative side. Most cells and biologicalsurfaces are, thus, negatively charged. One of the reasonsbehind the negative charge of biological surfaces is thelower mobility of OH- ions compared to that of protons,which makes the former more prone to adsorption on theparticle surface. The effect of the ionic strength on destabi-lization of biological colloids is, therefore, such that theyare primarily sensitive to the valence of the cation ratherthan to that of the anion. Critical coagulation concentration(ccc) of the cation can be calculated using the followingempirical formula, where v is the valence of the cation:

ccc ¼ 0:8=v6 ½16�

So, for monovalent Naþ ccc¼ 0.8M; for divalent Ca2þ

ccc¼ 12.5mM; and for trivalent Al3þ ccc¼ 1mM. Hence,10mM is the ionic strength high enough to induce rapidcoagulation of colloidal dispersions if multivalent ionsare present. Equation (16) gives a general picture, but needsto be readjusted for a specific material in question sincesome compounds are more sensitive to the ‘‘salting out’’effect and some are less. Thus, for example, in the case ofnegatively charged As2S3 sols (where valence of the cationis decisive), ccc for NaCl is 50mM, for ZnCl2 it is 0.7mM,and for AlCl3 it is 0.1mM, whereas for positively chargedFe(OH)3 (where valence of the anion is critical), ccc forNaCl is 9mM, for K2SO4 it is 0.2mM, and for K2Cr2O7

it is 0.2mM. For the As2S3 sol, ccc values are in the ratio1:0.015: 0.0018 as the counterion valence increases from 1to 3, which is in agreement with the DLVO theory whichstates that the ratios should be 1:2�6:3�6 (1:0.0156:0.0014).

Schulze-Hardy rule has accordingly stated that ccc for atypical lyophobic (solvent-fearing, as opposed to lyophilic-solvent-loving) sol is extremely sensitive and inverselyproportional to the valence of the counterion. Note thatadding two or more electrolytes together to a colloid may

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have different effects on the colloidal stability. Thus, if cccfor a mixture of two electrolytes, A and B, corresponds toconcentrations of the two components, ca and cb, whereascccs of A and B taken separately are coa and cob, then theeffects of the electrolytes are said to be additive if (ca=c

oa)

þ (cb=cob)¼ 1; they are synergistic if (ca=c

oa) þ (cb=c

ob)< 1;

and antagonistic if (ca=coa) þ (cb=c

ob)> 1. Note also that

the addition of small amounts of a hydrophilic colloid toa hydrophobic sol may make the latter more sensitive toflocculation by electrolyte, which is the phenomenonknown as sensitization.[29] Higher concentrations of thesame hydrophilic colloid usually protect the hydrophobicsol from flocculation, and this phenomenon is called pro-tective action. The fact that the stability of colloids tendsto be sensitive to ionic strength of the background electro-lyte also limits the pH ranges for which reliable f potentialinformation can be collected because not only 2> pH> 12tends to dissolve many particles, but it also possessesintrinsically high ionic strengths.

Thomas Riddick, the originator of the idea that f poten-tial of particles dispersed in blood could be used as a controlparameter in treating various cardiovascular diseases thatinvolve pathological coagulation, such as atherosclerosis,claimed that some salts act as coagulants and other as dis-persants.[1] Aluminum salts and others that comprisedivalent or trivalent cations, thus, act as coagulants forthe negatively charged colloids (which most biological sys-tems are), whereas potassium citrate acts as a dispersant.The former were in his classification named as 2:1 or 3:1salts (because of having divalent or trivalent cations andmonovalent anions), while the latter was named 1:3(because potassium is monovalent and citrate is a trivalention). Figure 10 shows how this rule can be used to predictthe direction in which f potential of a colloid will changeupon the addition of a given salt. Hence, it is multivalentions that play a decisive role in shifting the value of f poten-tial in the direction of their valence. Thus, 3:1 and 2:1 saltswill tend to shift the f potential in the þdirection, and 1:2,1:3 and 1:4 salts will shift it in the – direction. Recently,the same concept was invoked to explain the aggregationof cholesterol particles, pointing out that a control over fpotential may be used to prevent the formation of patho-logical cholesteric deposits, including atherosclerotic plaqueand gallstones.[30–32] These findings are on the line of Tho-mas Riddick’s invoking f potential to explain the ‘‘saltingout’’ effect of ions on coagulation in blood, including theeffect of thrombosis.[1] It is also worth noting that Naturenever disperses its entities using exceptionally high negativef potential values. Human blood platelets, for example,have a f potential of �14� 2mV in their physiologicalenvironment,[33] which is right at the aforementionedthreshold for dispersion=agglomeration. Human bloodtoo is supersaturated with respect to more than one calciumphosphate phase, speaking in favor of Nature’s tendency to

keep its systems in the states of metastability from whichthey can transition to any of the sides depending on theneeds of the system. To keep its entities ‘‘at the edge’’ wherethey might interact but also be well dispersed, depending onthe biological needs of the moment, is, thus, ‘‘Nature’sway,’’ the one symbolized by the Way, an epitome of simul-taneous connection and separation, as has been elaboratedby the author on different occasions.[34–37]

OTHER APPLICATIONS OF THE CONCEPT OF f;POTENTIAL IN BIOCHEMISTRY

That f potential is important in governing many interac-tions in the world of biochemistry can be seen from theincreasing usage of this term in various biochemical con-texts. It is known that enzyme-ligand binding is favoredunder conditions of electrostatic attraction, which isespecially true for enzymatic reactions that rely on theacid=base conjugate mechanism.[39] Also, enzyme immobili-zation is known to depend not only on the chemical interac-tion specificity, but on the difference in the surface potentialsbetween the enzyme molecule and the matrix carrier.[40]

Electrostatic effects have been regularly relied on in the elec-trophoretic separation of peptides, and the protein adsorp-tion has been shown to be directly dependent on themagnitude of the difference between the f potentials of theprotein and the adsorbent.[41] Deviations of f potential ofcells from the expected values have been used to concludeabout their membrane abnormalities.[42] Charge on the cellmembrane, originating from phosphoryl and carboxylgroups of macromolecules that constitute it,[43] can bemanipulated to prevent cellular aggregation, which is aneffect detrimental for cellular electrophoresis techniques.[44]

It can also be assessed to differ between metabolically activeand inactive cells,[45] as well as between rich, starved anddead ones.[46] Antibiotics have, thus, been shown to inducea rapid change in bacterial f potential,[47] and the same effectwas observed on fungal cells following the application ofantifungal drugs.[48] In fact, different bacterial strains couldbe distinguished between based on their specific electro-phoretic response.[49] The role of f potential in viral-hostinteractions has been proposed as well,[50] and the transfec-tion efficiency was said to be predictable by referring to theparameter of f potential.[51,52] The adhesion of pathogensresiding in the oral cavity and binding to saliva has beenshown to be governed by the surface charge attraction.[53,54]

The membrane glycoproteins contribute to the negativecharge of virus entities and cells at the physiological pH,and f potential of polioviruses was taken advantage of forthe purpose of eliminating them from contaminatedwaters.[55] The same approach was used to flocculateblue-green algae in eutrophic lakes.[56] Flocculation of cellsduring their removal from fermentation broth has been alsocorrelated with the parameter of f potential.[57]

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Essentially, most biological structures carry a netnegative charge,[58] and it was shown that medical implantsfor substitution of hard tissues carrying negative fpotentials help in promoting bone regeneration andosseointegration.[59] This might also explain the recentlyshown good adhesion of cells onto positively charged apa-tite and poor adhesion and growth on negatively chargedapatite surfaces.[60] It was similarly proposed that f poten-tial could be used to predict the attachment of biomaterialsto osteoblasts and bone.[61] Another study demonstratedthat the nucleation and growth of calcium phosphates onthe surface of 45S5 bioactive glass can be followed by asses-sing the temporal variations in f potential over time.[62] Evi-dence was also offered in support of an approach whereinthe wound healing process could be assisted by endowingcells with relatively high f potentials.[63] Inorganic particlesused as ingredients in skin care cosmetic products have beenshown to accelerate skin permeability barrier recovery whenthey are provided with negative f potential values.[64] Thesorption of nanoparticles applied for drug and gene deliveryby the target cells can also be controlled using the f poten-tial.[65] Changes in the f potential of cells incubated withnanoparticles have been taken as an indication of the vitalrole that the cell membrane charge plays in maintainingthe cell endocytosis capacity.[66] It was, thus, shown that fpotential of cells could be monitored to follow the interna-lization of nanoparticles; whereas the binding of positivelycharged nanoparticles on the cell plasma membrane shiftsits f potential to more positive values, the subsequentinternalization, mainly via vesicular-transport-based endo-cytosis, reestablishes the initial negative value.[67] Thisobservation is in agreement with a similar change in the fpotential of multilamellar liposomes consisting of phospha-tidylcholine following their encapsulation of a drug.[68–70]

Aging of drug-containing microcapsules and release of theentrapped drugs can also be correlated with specific f poten-tial changes of the drug carriers.[71] Among many otherparticles conjugated with surface agents, f potential hasbeen used to estimate the surface characteristics of calcium-phosphate=DNA complexes too. If DNA coats the parti-cles, they carry a strong negative charge; if calcium phos-phate is uncoated, the particle charge is only slightlynegative.[72] A similar f potential shift from that of the coreparticle to that of the coating applies for all other core-shellsystems.[73] Orientation of amphiphilic or bipolar moleculesconjugated to the particle surface can also be assessed usingf potential measurements.[74] Zeta potential shifts to posi-tive values when carbohydrates become attached to theparticle surface, and the interest in functionalizing nanopar-ticles for intracellular drug or gene delivery with sugars isconnected with the finding that polysaccharides residing onthe surface of Gram-negative bacteria have a role in enhanc-ing cell penetration. Convenient for following the adsorptionof species onto dispersed particles of interest, f potential

analyses have also recently been used to detect binding ofamelogenin nanospheres onto apatite crystals under variousconditions[75] and correspondingly improve the understand-ing of the mechanism of amelogenesis, a biomineralizationprocess during which a finely structured protein gel directsthe growth of hierarchically ordered enamel crystals, thehardest material in the vertebrate body.[76] Finally, the brainitself, as a whole, has a specific f potential, which implies thatthe extracellular translational motion is governed by electro-kinetic effects under this naturally occurring electric field inaddition to diffusion and tissue tortuosity.[77]

ANALYZING COMPLEX CERAMICS

This section will deal with the main practical and funda-mental challenges in the analysis of ceramic particles usingDLS microelectrophoresis, and hydroxyapatite (HAP), themain mineral constituent of hard tissues, will be used as theexample.[78]

The problem with analyzing HAP and other complexceramics and minerals with respect to f potential is thatat the mineral surface, changes in pH do not only shiftthe surface charge by changing the distribution of protonand hydroxyl groups hydrating the interface, but they alsoinfluence selective dissolution of the surface ions, whichthen induces rearrangement of the surface charge layers,,thus, oftentimes shifting the f potential values in unpredict-able ways. Typically, HAP undergoes a shift in the f poten-tial depending on the immersion time, which is an effectrelated to ion exchange between the hydrated layer aroundthe material and the material surface, leading to dissolutionand re-precipitation of new phases defined by the ioniccomposition of the solution, the material surface activityand the presence of additives.[79] This selective leaching ofions has been the source of great unpredictability and irre-producibility of the electrophoretic analyses of apatitepowders. For HAP, the PZC in calcium-free solutions issaid to occur at pH 7.3. For more alkaline solutions thesurface should be negatively charged, whereas for moreacidic solutions it should be positively charged. However,ions other than Hþ and OH- can adjust the surface charge,and in calcium-containing solutions Ca2þ ions bind to thesurface at pH> 7, leaving the surface neutral rather thannegative.[80] As already said, HAP also undergoes dissol-ution depending on the pH and these dissolved ions canhave a decisive effect on f potential of the particle. Conse-quently, whereas some studies report negatively chargedparticles in the entire pH range in which HAP is the stablephase (4–11),[81] others report IEP values at anywherebetween 5 and 7.5, below which the particles become posi-tively charged.[82,83] There are, however, reports[84] on IEPof HAP suspensions detected at pHs as high as 10.

In addition, HAP, like many other materials, has twotypes of crystal planes, each one of which carries a different

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charge: positive on a-planes and negative on c-planes. Zetapotential analyses are not able to differ between the twoand often it happens that an electrostatic attraction thatleads to specific adsorption is observed between two typesof particles carrying the same net charge. In such cases,planes or edges of one of the particles carry the oppositecharge compared to the particles as wholes, inducing theelectrostatic attraction and adsorption to occur. One suchexample is shown in Figure 11. Similarly, streaming poten-tial measurements of f potential of sapphire monocrystalsyielded a difference equivalent to 2 pH units between theIEPs of different crystal planes, indicating the existenceof a pH window within which different crystal planeswould carry opposite charges.[85] Also, assuming a uniformdistribution of surface charges is another approximationthat is known to yield significant discrepancies wheneverdiscrete or alternate charges, as in the case of HAP, com-prise the surface.[86] Such finer levels of charge distributioncould be analyzed only by means of techniques more soph-isticated than colloidal electrophoresis.

Buffers do not necessarily need to be used when proteinsare analyzed because proteins act as buffers per se throughtheir titratable residues. If the experiments are carried outunder atmospheric conditions, an amount of CO2 will bedissolved in the solution and will enter the equilibrium withcarbonate ions that CO2 forms upon dissolution in water.Carbonate=bicarbonate system also has a bufferingcapacity and is, as such, utilized by living organisms, inaddition to the intrinsic buffering capacity of proteinsand phosphate species. Buffers are mixtures of weak acidsor bases and their salts and their purpose is to resist drasticchanges in pH produced by adding a strong acid or base tothe system. The cause of their acting in such a way can beseen from the titration curve of a weak acid with a strongbase (Figure 12a). The curve appears as a 90o rotated

sigmoidal curve, and the range of stability of pH with theaddition of the titrant presents the buffering range for thatparticular buffer. The middle of this range, thehalf-equivalence point, is equal to pKa of the given acid,so that the buffering range is usually taken aspH¼ pKaþ�1. When HAP is analyzed, however, theuse of buffers is recommended in order to eliminate themeasurement error due to extensive pH fluctuations andinstability. Tris and Bis-Tris are commonly used to stabi-lize the pH of organic and biological systems, and couldbe used in the 8.3� 1 and 6.8� 1 ranges of pH, respectively(note that HCl is the complementary acid for these twosalts, which implies that Cl- ions are required for both Trisand Bis-Tris to act as buffers); glycine=HCl and glycine=KOH could be used as buffers in 2–4 and 10–12 rangesof pH, respectively; citric and phosphoric acids, which havethree pKa values each present additional common options.However, it is vital to remember that components of buf-fers usually show specific adsorption and were thus, forexample, excluded from the most extensive compilationof PZCs and IEPs up to date.[27]

Although protonation=deprotonation reactions in sol-ution are some of fastest ones and the same is expected tobe the case for surface protonation=deprotonation, pHchanges are often detected during sample incubation, sug-gesting that there might be analytically detrimental kineticeffects on the adsorption equilibrium. In the case of surfacesthat undergo selective dissolution and possibly phase transi-tions of surface layers, as is the case with calcium phos-phates, longer equilibration times may be required. Theprocedure used by Somasundaran et al. was, thus, to soakapatite powders in KNO3 solutions and age them as suchovernight as well as to equilibrate the samples for 1 hourat any given pH.[87] Another main concern for calciumphosphates is their tendency to aggregate over time

FIG. 12. (a) The titration curve of a weak acid, acetic acid, with a strong base, NaOH, showing pH¼pKa �1 as the buffering range for the given

acid=base pair. (b) The buffering capacity of phosphoric acid is strongest at the points of intersection of the curves that represent the amount of different

phosphate species as the products of dissociation of phosphoric acid: pHs 2, 7, and 12. Reprinted from Dorozhkin.[90] (Figure available in color online.)

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(namely, calcium phosphates particles are typically com-posed of smaller, nanosized subunits), which may affectthe particle size and f potential values alike. Sodium hexam-etaphosphate (0.1 wt%) used in food industry as a defloccu-lant could be applied to stabilize dispersions of HAP andenable more reliable DLS measurements.[88] Prolongedultrasonication (>30 minutes); bubbling of inert gases toeliminate the effects of surface-active CO2; extensive incu-bation to allow the sediments to settle down, with or with-out centrifugation; and the use of supernatants only areother measures routinely applied to obtain more reproduc-ible and reliable results. Optimization of the solid-to-liquidweight ratios, typically recommended for DLS measure-ments to be in the range 5� 10�5 to 5� 10�3, presentsanother strategy for improving the measurement quality.Calcium carbonates share numerous properties with cal-cium phosphates, including the high mobility of the surfacelayer and a high tendency to undergo Ostwald ripening andagglomeration, which implies that in their case too,similarly to HAP and other calcium phosphates, greatdiscrepancies between values for IEP=PZC reported in theliterature exist.[89]

The size and shape of inorganic particles normally do notaffect surface charge density, r, but they do affect f poten-tial since particles with the same surface charge but of dif-ferent sizes and shapes will move with different velocitiesin the electric field; hence, their electrophoretic mobility,from which f potential is calculated, will be different. Typi-cally, an increase in temperature leads to a drop in the fpotential for inorganic samples, whereas an increase inpressure may have different effects depending on the chemi-cal nature of the sample and its ionic environment.[91] A lin-ear decrease in the PZC for alumina particles was observedin 10–40�C range with an increase in temperature, owing tothe thermal desorption of protons from the particle=sol-ution interface.[92] Also, although increasing ionic strengthtends to push the f potential values closer to IEP at anygiven pH, the IEP itself is normally not subject to changefollowing changes in the ionic strength. Unlike f potential,with surface charge density, r, this trend follows theopposite direction: it increases following an increase in theconcentration of an inert electrolyte. By definition, inertelectrolyte is composed of ions that react with the surfaceonly by a Coulombic force and do not get specificallyadsorbed to it. This can be verified by evidencing no shiftin the PZC=IEP at different electrolyte concentrations. Spe-cific adsorption of cations leads to a shift in the PZC=IEP tolower values, and vice versa for anions. Any combination ofNaþ, Kþ on the cation side and of Cl-, NO�

3 , and ClO�4 on

the anion side has been accepted as inert for metal oxides.However, although halide ions are usually inert with respectto metal oxides, they are potential determining for silverhalides, which makes the term ‘‘inert electrolyte’’ veryrelative. Still, to these rules there are exceptions since a

particular combination of the particle surface compositionand the double layer ions may trigger specific adsorptionand other counterintuitive effects that may follow. Thiscan be exemplified by the case of dispersions of ice inwater.[93] In those cases, whereas the IEP is detected atpH 3.0, the PZC is found at pH 7.0, which altogether withthe evidenced shift in the IEP depending on the NaCl con-centration directly implies complex specific adsorption ofions at the interface between water and water. The com-plexity and versatility of water as a dispersing medium withrespect to the surface charge properties of the interfaces in itis, thus, also implicit.

ZETA POTENTIAL OF PROTEINS

Amino acids as basic building blocks of proteins arenormally negatively charged at high pH values and posi-tively charged at low pH values. Simply speaking, eachamino acid has a carboxyl (-COOH) group at one of itsends and an amino (-NH2) group at another. In an acidicenvironment, the free ions are predominantly protons.With a plenty of protons surrounding the protein, -COOHgroup does not tend to dissociate to -COO- and Hþ, and,thus, remains neutral. In contrast, -NH2 group will tendto be protonated and, thus, become -NHþ

3 . Hence, thenet charge of the molecule will be positive. At high pHvalues, hydroxyl ions will be the dominant ions in the sol-ution. Thus, the protons from -COOH groups would read-ily be released into the solution to combine with free OH-

ions and yield water. As a result, -COOH group will tendto dissociate into -COO- and Hþ. Protonation of –NH2 willbe suppressed, however, and it will remain in neutral, NH2

form. So, the net charge will be negative (Figure 13).This can be also described through La Chatelier’s

principle. Namely, the dissociation constant for COOH$ COO- þHþ reaction is always constant. La Chatelier’sprinciple says that as concentration of any of the reactantsis increased, all the concentrations will change so thatthe dissociation constant remains the same. The latter isgiven as:

K ¼ ½COO��½Hþ�=½COOH�: ½17�

So, as the concentration of protons is increased bylowering the pH, the concentration of COOH has to goup in order for the K to remain constant.

FIG. 13. Dissociation of an amino acid depending on the pH.

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To calculate the isoelectric point (pI) of an amino acid,the following equation can be used in case when no proto-nation of the side chain takes place:

pI ¼ ðpKa þ pKbÞ=2: ½18�Alternatively, when the side chain is also titratable, the

following equation is valid:

pI ¼ ðpKa þ pKb þ pKrÞ=3: ½19�

The same equation (Equation (19)) could be appliedfor estimating the pI of a protein molecule as a whole. Inthat case, pKa is the pK value of –COOH group at theC-terminal; pKb is the pK value of -NH2 group at theN-terminal; and pKr is the average pK value of the activeacid and base groups in the side chains of the so-calledtitratable residues (the ones with acidic or alkaline sidechains). In the case of polypeptides, pKa and pKb of aminoacids other than the ones on terminals do not contribute topI because their COOH and NH2 groups form peptidebonds.

To estimate the extent of dissociation of acid=base pairsof individual titratable side chains at any given pH, theHenderson-Hasselbalch equation can be used:

Ka ¼½Hþ�½A��½HA� ½20�

pH ¼ pKa þ log10½A��½HA� : ½21�

Note that pK of a compound is equal to pH at whichone half of its molecules are protonated and the other halfare not. Note also that since the Henderson-Hasselbalchequation does not account for the ionization of water itself,it is not useful for calculating pH of solutions of strongacids or bases (pH� 1 or 14).

The general trend is that pK values of amino acidsdecrease with temperature: not much although, by �0.05to 0.2 units as the temperature is increased from 25 to37�C. On one hand, this may be seen as a consequence ofthe fact that the pH of neutral water drops by �0.2 unitsfollowing the increase in temperature from 25 to 37�C.On the other hand, it can be, all by itself, treated as differ-ent depending on whether the protonation=deprotonationreaction is exothermic or endothermic, while referring toLa Chatelier’s principle. Namely, according to Le Chate-lier’s principle, raising the temperature of exothermic reac-tions pushes the system back towards the reactants, whichis observed as a decrease in the equilibrium constant value(or an increase in the pK value), whereas raising thetemperature of endothermic reactions pushes the systemtowards the products, which results in an increase in theequilibrium constant value (or a decrease in the pK).

Empirically speaking, pKb decreases in all cases, whereaspKa may decrease, stay constant or increase following anincrease in temperature. Thus, the overall effect of increas-ing temperature is typically a lower combined pK of theamino acid or a protein. And as pK values get lower, sodoes pI. This may explain why pI detected at 37�C is lowerby almost 0.5 pH units relative to pI detected at 25�C. Thisalso explains why pH of organic buffers, such as Tris=Bis-Tris, decreases following an increase in temperature.In case of Tris and other organic buffers, one often detectsa change in the pH by 0.5 units following a transition from25 to 37�C. Thus, pure aqueous Tris buffer at pH 6.8 at25�C will exhibit pH 6.46 when heated to 37�C. In fact,as the temperature increases, pKa of Tris decreases at anapproximate rate of 0.03 units=�C. In the case of phosphatebuffers, this change is almost negligible. Thus, pH 7 bufferhas pH 7.00 at 25�C and pH 6.98 at 37�C; pH 10 buffer haspH 10.00 at 25�C and pH 9.90 at 37�C; and pH 4 buffer haspH 4.00 at 25�C and pH 4.02 at 37�C.

However, notice also that a phosphate buffer with pH7.00 at 25�C is neutral, whereas having pH 6.98 at 37�Cmeans that it has become basic. This is why. Namely, dis-sociation of water to hydrogen (or hydroxonium, H3O

þ,strictly speaking, as free protons are always bound withhydrogen bonds to water molecule monomers, dimersor trimers) and hydroxyl ions (H2O(l) $ Hþ(aq) þOH�

ðaqÞ) is an endothermic process, capturing thermal

energy from the surrounding. As one increases the heatcontent of the system by bringing the temperature up,one instigates more of the dissociation, according to LaChatelier’s principle. The effect of this is an increase ofthe dissociation constant of water, Kw, as temperatureincreases. Table 1 shows Kw values for water at differenttemperatures:

This does not mean, however, that water with pH 6.77 at40�C will be acidic. It means that neutral pH is 6.77 at40�C. Water with pH 7 at 40�C will, thus, be basic.Namely, in the case of pure water, the number of free

TABLE 1Equilibrium constants for dissociation of pure water and

the neutral pH values at different temperatures

T (�C) Kw (mol2 dm�6) pH

0 0.114� 10�14 7.4710 0.293� 10�14 7.2720 0.681� 10�14 7.0825 1.008� 10�14 7.0030 1.471� 10�14 6.9240 2.916� 10�14 6.7750 5.476� 10�14 6.63

100 51.3� 10�14 6.14

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hydrogen ions and hydroxide ions is always balanced.Hence, pure water remains pH neutral at all temperatures,even though its pH changes with temperature.

In view of this, note that the real concentration of freeprotons as defined by Kw is subject to change even for thephosphate buffers following a change in temperature.Namely, although pH of the pH 7 phosphate bufferchanges from 7.00 to 6.98 as temperature is increasedfrom 25 to 37�C, pH of neutral water changes from 7.0to 6.8 with the same temperature change. Hence, it canbe said that concentration of free protons, in fact,decreases with increasing the temperature by about 0.2pH units. On the other hand, Tris buffers exhibit a dropof about 0.5 pH units with an increase in temperaturefrom 25 to 37�C. In view of the mentioned change inthe pH of neutral water following this change in tempera-ture, this drop accounts for only 0.3 instead of 0.5 pHunits, and is, thus, almost similar in magnitude to theone exhibited by the pH 7 phosphate buffer, althoughin a different direction.

Zeta potential analyses of proteins may be significantlyhampered due to high ionic strengths of the conductivemedia in which they are dissolved or suspended. Theconsequence of this is that destabilization and disinte-gration of the protein structure often occurs during theanalysis owing to the electric field effect. Namely, highionic strengths increase electrical conductivity of thedispersing medium, which makes the dissolved proteinmore prone to ‘‘cooking.’’ The magnitude of this effectvaries depending on the sensitivity of a particular protein,which implies that there are no precisely defined standardoperation procedures that would apply for proteins ingeneral. Essentially, a tradeoff between the intensity ofthe electric field in which the charged particles ormolecules move and susceptibility of the macromoleculesanalyzed has to be ensured. The higher the intensity of thefield, the more precise is the measurement, but the higherare the chances that the protein will disintegrate too. Aswith every other method, a compromise between power-fulness and sensitivity needs to be found. Thus, manyadvanced measurement settings offer very intensive fields,thereby increasing the measurement precision for the rela-tively robust inorganic particles, but present imperfectsolutions for the organics. Even Tris as a default organicbuffer in biochemistry may disintegrate under thesesettings at conductivities as low as 1 mS=cm. High ionicstrengths essentially either increase the surface tensionof the solvent and intensify the hydrophobic forces, orincrease the solubility of the nonpolar protein residues,thus, unbalancing the protein secondary and tertiarystructures by different mechanisms. According to theHofmeister series,[94–96] which was confirmed as validfor inorganic particles as well,[97] the following ionsare arranged in the direction on their increasing

destabilization (aggregation or unfolding) of proteins:

F� ¼ SO2�4 < HPO2�

4 < CH3COO� < Cl� < NO�3

< Br� < ClO3� < I� < ClO4� < SCN� ½22�

NH4þ < Kþ < Naþ < Liþ < Mg2þ < Ca2þ < CH6Nþ3

½23�Be that as it may, to take pK values of all amino acids

that comprise a protein into account when calculating itspI would be a mistake. Namely, as all amino acid residuesexcept those at the C- and N-terminals have their aminoand carboxyl groups involved in forming peptide bonds,only those with free acidic or basic side chains should beincluded in the intrinsic charge calculations. Only Cys=C,Asp=D, Glu=E, His=H, Lys=K, Arg=R, and Tyr=Y (andthe amino- and carboxyl-termini of the peptide) amino acidresidues, that is, only those containing the so-called titrat-able side chains are, thus, considered[98] (i.e, only the oneswith acidic or basic side chains, as shown in Table 2), andmany online algorithms[99] work on this principle. On theother hand, taking into account only these amino acids isagain an approximation. Strictly speaking, a deeply buriedresidue may not necessarily undergo dissociation and, ifthat is so, it should be excluded from contributing to theintrinsic molecular charge. Since water is mostly excluded

TABLE 2pK values of the 20 biological amino acids, including those

of the side chains of seven titratable residues

Amino Acid a-carboxylic acid a-amino Side chain

Alanine 2.35 9.87Arginine 2.01 9.04 12.48Asparagine 2.02 8.80Aspartic Acid 2.10 9.82 3.86Cysteine 2.05 10.25 8.00Glutamic Acid 2.10 9.47 4.07Glutamine 2.17 9.13Glycine 2.35 9.78Histidine 1.77 9.18 6.10Isoleucine 2.32 9.76Leucine 2.33 9.74Lysine 2.18 8.95 10.53Methionine 2.28 9.21Phenylalanine 2.58 9.24Proline 2.00 10.60Serine 2.21 9.15Threonine 2.09 9.10Tryptophan 2.38 9.39Tyrosine 2.20 9.11 10.07Valine 2.29 9.72

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from the predominantly hydrophobic and nonpolarinterior of the protein, and whenever present it occupiesrigid positions in space where it contributes in highly direc-tional hydrogen bonds, it is difficult to predict the extent ofdissociation of buried charged side chains. This is howeverthought to be a rare case since the crucial role of hydro-phobic forces in determining the active conformation ofthe protein dictates that it is energetically unfavorable tohave a charged residue buried in the deep interior of theprotein. The protein core is typically made up only ofnon-titratable, hydrophobic and neutral amino acids. Thenonpolar residues such as Val=V, Leu=L, Ile=I, Met=M,and Phe=F are, thus, mostly found in the interior of theprotein; the charged polar residues such as Arg=R, His=H, Lys=K, Asp=D, and Glu=E are normally located onthe protein surface, in contact with the aqueous solvent;and uncharged polar groups such as Ser=S, Thr=T, Gln=Q, and Tyr=Y may occur in the interior of the protein(typically as H-bonded, which mitigates their polarity),although they are still prevalently exposed on the surface,in contact with the water molecules. Still, the energeticallyunfavorable packing of charges may happen under certainconditions. Namely, charged residues could be packedinside of the protein as covalent bonds between -SH groupsof two cystein residues, forming an S-S bond (disulfidebridge); as salt bridges where opposite charges neutralizeeach other; or as metal coordination complexes. On theother hand, the dielectric constant in the interior of theprotein is 2–40 times less (e¼ 2–40) than in the bulk water(e¼ 80), which implies more intensive electric field effectsto take place therein.[100] Also, it is worth noting that evenresidues with nonacidic or non-basic side chains can inducecharge on their surface through polarization effects, weakbonding and coordination of ions. Furthermore, pK valuesfor individual amino acid residues are empirically deter-mined for amino acids alone and not as parts of a peptidechain, let alone folded into specific three-dimensional con-firmations where they may be forming weak bonds withother residues. Just as increasing the length of an aliphaticchain decreases the frequency of C-C vibrations, a similarsynergetic effect occurs herein as well. Amine groups in achain would not possess the same pK values as in isolation;surrounding cationic amine groups will, for example, elec-trostatically suppress the protonation of the neighboringamines.[101] Increasing the length of a polyamine chain will,thus, decrease the protonated fraction of its amine groupconstituents. pK values of given acid-base pairs of titrat-able side chains of amino acid residues can vary by as muchas several pH units depending on the microenvironment.For example, Asp=D residue in nonpolar environment orin close proximity to another Asp=D would attract protonsmore strongly than otherwise and, hence, have a higherpK.[102] pK values of amino acids also change dependingon the ionic strength of the solution. Hence, pI values of

proteins are subject to significant variations and are intrin-sically determined by the content of the titratable residuesand extrinsically by the adsorption of ionic species and theeffect of the diffuse double layer of charges. Hence, pIvalues range from as low as less than 1.0 for pepsin to4.9 for human serum albumin to 5.4 for human fibrinogento 6.6 for collagen to 7.1 for human hemoglobin to 9.4 forribonuclease A to 10.8 for histone to 11.0 for lysozyme to12.1 for salmine in salmon.[102] Finally, f potential is adescriptive quality that is merely indicative of the surfacecharge of the particle.[27] Because the actual distance fromthe particle surface at which f potential is measured isunknown and depends on the nature of the particle andthe suspension medium (it could be anywhere betweenthe Stern layer and the Debye length, that is, the outerboundary of the diffuse layer), f potential is merely looselyindicative of the surface charge of the particle. Zeta poten-tial versus pH curves can still be specific to different mate-rials, which justifies the occasional use of the term‘‘electrophoretic fingerprinting’’ (Figure 14).

From the raw electrophoretic mobility data, one can alsoestimate the effective (uncompensated) charge on molecules(Ne) as a function of pH and ionic strength, which is ofinterest in predicting the deposition propensity and interac-tion energy, kinetics and mechanisms on various interfaces.For that purpose, one uses Lorenz-Stokes relationship:[18]

Ne ¼ 6pg� 108rhl=1:602 ½24�g is viscosity [g(cm s)�1]; rh is the hydrodynamic radius

[cm] (determined from the diffusion coefficient measured

FIG. 14. Zeta potentials and electrophoretic mobility of different

compounds versus pH: hydrocarbon oil droplets (a), sulphonated poly-

styrene latex (b), arabic acid as carboxylated polymer (c), and serum albu-

min (d). Note that there are polymers (b), typically containing periodically

arranged heavily charged, phosphorylated or sulphonated groups along

their chains,[103] possessing linear and flat f potential versus pH curves.

Reprinted from Shaw[28] (this article was published in Introduction to

Colloid and Surface Chemistry, D. J. Shaw, # Elsevier [2003]).

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using DLS and the Stokes-Einstein relationship); and l isthe electrophoretic mobility [lm cm s�1 V�1]. This equationis considered to be more reliable than the titration methodwhich typically tends to overestimate charge on molecules,presumably owing to ion exchange processes. If Ne is >10(10–25, approximately), the surface charge is high and theaggregation of the protein is excluded for the given pHvalues. Also, it may imply that a significant rearrangementof the flexible parts of the tertiary structure of the moleculeis expected to occur, in analogy with the behavior of poly-electrolyte chains. However, it is important to emphasizethat this is the number of uncompensated and not totalcharges on the protein molecule=particle. As even in purewater free hydronium ions and hydroxyl groups form dueto dissociation of water, there will always be ions screeningthe surface charge of the particle=molecule itself. The num-ber of charges calculated from the electrophoretic mobilitydata will, thus, not account for the particle=molecule perse, regardless of the properties of the medium in which itis dispersed, but for the given particle=molecule and theions adsorbed thereon and diffusing between the particlesurface and the slipping plane. For, an essential principleof colloid chemistry is that both sides of an interface needto be referred to when describing and explaining any pro-perty emanating from it; or, as Ludwig Wittgenstein wouldhave put it, ‘‘in order to draw a limit to thinking, we needto think both sides to this limit.’’[104]

PRACTICAL LIMITATIONS OF f; POTENTIALANALYSES

Different specimens made up of an identical chemicalcomposition typically give nonidentical f potential versuspH curves and yield different IEPs. Representing each sin-gle curve of this type as a narrow line, as is often seen in theliterature, instead of a spread of values around each datapoint is, thus, quite misleading. When standard deviationsof the error are not denoted in the graphs, one shouldimagine them in both X and Y directions for each datapoint. The bar along Y axis would originate from theinherent unrepeatability of f potential measurements, ascaused by uncontrollable variations in: (a) the extent ofparticle aggregation and polydispersity (i.e., imperfect stab-ility of even the most stable suspensions); (b) temperature;(c) concentration of the background inert electrolyte; (d)the type and concentration of impurities; (e) interatomicdistances that affect the acidity of surface oxygen atoms.Moreover, the same Brownian motion on which the DLSdevice relies in measuring the particle size of a colloid isthe source of an intrinsic error during the measurementsof f potential. The DLS device, therefore, takes the averagemobility of an ensemble of particles into account, whichimplies that the measurement error becomes more pro-nounced at high polydispersities. Spherical approximation

mentioned in the previous section accounts for anadditional source of uncertainty. Namely, when the parti-cles are anisotropic with respect to their shape, the electro-static force exerted during f potential measurements willdepend on their orientation. However, an orientationallyaveraged mobility could be considered by assuming thatthe electric field is too low to align the rod-like particles.Still, due to high polydispersity, it is convenient to treatthe particles as spheres, although in this approximationthe absolute value of the f potential may change by a factorof 0.8–1.5 depending on the particle orientation.[105]

The bar along X axis, on the other hand, would orig-inate from the error of pH measurements, which are saidto be the main source of uncertainty in microelectrophore-tic analyses.[27] Since the second decimal digit of pH valuesis usually uncertain and unstable, such mistakenly reportedoverly precise values should have been rounded to 0.1 pHunit. Although pH measurements are sometimes presentedwith the precision of the third decimal digit,[106] reports ofPZCs=pIs with precision down to the second decimal digitare claimed to be due to carelessness and inaccuracy in esti-mation of the error rather than to extraordinary accuracy.pH values for solutions either partially or completely com-posed of nonaqueous solvents are also frequently reportedbased on the direct pH electrode output, without a priornormalization for the water content,[107] which is, however,known to be a complex and not perfectly clear procedure,particularly when nanosized domains of water=oil phasescomprise the solvent.[108] Ethanol, for example, does nothave pH even though a pH electrode will respond with asignal when immersed in it. However, pKa of ethanol is15.9, which means that when dissolved in water, at pH15.9 a half of its molecules will be in C2H5O

- form andanother half will exist as C2H5OH. Basically, pH of dilutedethanol solutions in water is practically the same as that ofwater; it can be calculated from two equilibriums—pKw

(negative logarithm of the ion product for water:14.00346 at 25�C) and pKa for ethanol (�15.9)—usingHenderson-Hasselbalch equation.

How critical errors in pH measurements can be duringthe interpretation of microelectrophoretic data is demon-strated in Figure 15. According to Kosmulski, there aremultiple reasons for this inevitable spread of pH valuesmeasured, starting from the trivial ones which includeimproper contact between the electrode and the solution,errors in calibration (old calibration buffers?), worn ordefective electrodes, inadequate flow rate between the refer-ence electrode and the solution on a clogged electrode, etc.,but ending at some fundamental reasons that include thefollowing:

a. pH is minus the logarithm of the activity of protonsrather than of their concentration. Yet, at I> 10mM,this difference is already higher than 0.1 pH units.

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b. Nonbuffered systems can display fluctuations 1 pH unitwide, and very dilute dispersions (<10�6M) are parti-cularly sensitive to this effect. This effect may be miti-gated by buffering the system, although a tradeoffexists there too. Namely, buffer components are usuallysurface-active and also the extensive addition of acid=base to adjust the pH would substantially modify thebackground ionic strength.

c. Most pH electrodes are very sensitive to Naþ and Liþ

salts at pH> 12. Namely, every electrode in certainextent confuses these two ions for Hþ ions, implyingthat in their presence the measured pH will be lowerthan the real.

d. For very concentrated dispersions, the solid surfaceacts as a buffer partially; however, the tendency ofthe system to be less stable and segregate then appears.

e. In suspensions, pH measurements are affected by thelocal gradient of the pH and shifting the electrode upand down can sometimes induce a difference in pHhigher than 0.2 pH units. This is the consequence ofthe gradient of numerous physical properties of themedium, ranging from density to viscosity to pH, asone is moving away from or approaching the interface.A thin gel layer is, thus, present on the accuratelyresponsive electrode; however, its degradation leadingto erroneous measurements may result followinglong-term immersion in: hygroscopic or nonaqueoussolutions; in HF acid below pH 4 or strongly alkalinesolutions at elevated temperatures; in colloids compris-ing abrasive particles (SiO2, Al2O3, soil samples, etc.);or during storage in dry conditions.[109,110]

f. The standard pH scale is designed for room tempera-ture, atmospheric pressure, I< 1M, and water as the

solvent. Using the pH electrode outside of this scalerequires its calibration under the nonstandard con-ditions, for which, however, most limitations outlinedabove still apply.

In addition to temperature affecting the pH electrodecalibration curve slope (Figure 16), every sample exhibitsinternal temperature-dependent chemical equilibriums, pre-disposing it to possess a unique pH versus temperaturerelationship.[112] Therefore, even though a pH electrodemay be hypothetically perfectly calibrated, the pH-meterwould be unable to correct pH values for temperatureeffects with a perfect precision. Then, the heat content isnever uniformly distributed throughout the sample, whichimplies local variations in temperature, and different sen-sors in the system (such as pH electrode and thermocouple)will then respond to different environments. Every electrodealso leaks some of its electrolyte content into the solutionduring a continuous measurement, thereby manifestingthe general principle that there is no measurement withoutan interaction in which the measuring device modifies theproperties of the measured system. The greater the leakagerate, the more precise the measurement, which reflects thegeneral trend of all measurements: the greater the inter-ference with the measured system, the more informationwill be gathered, but the more changes will be introducedin the system as well, which at the same time makes themeasurement results less reliable. Finally, every electrodepresents a foreign surface which can influence nucleation,and that becomes particularly critical when one works withmetastable, lowly supersaturated systems. The latter will beincreasingly exploited in future because many natural

FIG. 15. To explain the discrepant data point in terms of the error in

a f potential measurement solely, a broad margin of error has to be

allowed. Yet, it can be explained by allowing relatively narrow margin

of error in the pH.

FIG. 16. The scope of the temperature-induced pH measurement

error for a range of temperatures, as calculated using the Nernst equation:

E¼Eo—2.3RT(-log[Hþ])=F, where E is the electric potential measured,

Eo is the standard electric potential, R is the gas constant, T is the tem-

perature, and F is the Faraday constant. Reprinted with permission from

Queeney.[111] (Figure available in color online.)

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self-assembly processes, including biomineralization, occurexactly under conditions of low supersaturation when phasetransformations are governed by subtle interactions con-veyed by weak chemical forces.[113–115]

The greater spread is typically found in the vicinity of theIEP because dispersions are inherently unstable in thatrange. Quite often, f potential values are immensely scat-tered in this range and interpolation based on arbitrarilyconnecting data points from þand – sides of the f potentialversus pH curve is carried out; depending on the concave-ness of the sigmoidal curve drawn, the IEP detected mayvary significantly. Extrapolation is done when IEP is verylow or very high and the f potential data are available onlyon the þor only on the – side (typically on the – side, as isthe case with silicates). If all these effects account for the dif-ference that is less than a single pH unit in terms of IEP,they are considered acceptable. If it is greater than a singlepH unit, then impurities could be blamed. Impurities in sus-pension are normally concentrated on the particle surface,and tiny amounts thereof may be enough to drasticallyinterfere with the f potential output. As for impurities, sili-cate and carbonate ions present the main ones, as they arepresent in water and other reagents and are also adsorbedfrom air and leach from parts of the device. The reasonwhy distilled water at atmospheric conditions, typicallyused in the lab, is acidic rather than neutral (it has pH5.7) is due to the effect of dissolution of carbon dioxideand the formation of carbonic acid and carbonate ions.The sorption of carbonates and silicates leads to an increasein the negative charge and, thus, a shift of IEP to lowervalues. Long contacts of dilute dispersions of metal oxideswith neutral or basic solutions in glass containers at roomtemperature have been known to result in decreased pIowing to silica leaching out of the glassware and adsorbingonto the particle surface.[27] Storing colloids in plastic con-tainers is known to minimize the presence of silica contami-nants; however, it has been documented that rubber,polyethylene and Teflon all undergo chemical degradationover time and may significantly disrupt experimental repro-ducibility.[116] Typical distilled (de-ionized) water contains afew solutes at a level higher than 0.01mM (a few ppm), afew dozens of solutes at a level higher than 1 nM, and hun-dreds of solutes at a level higher than 10 pM. Then, waterunder atmospheric conditions contains approximately5mM of dissolved gas, which adds up to a single gas mol-ecule per each 3 nm (note that oils contain 10 times morethan that). The effects of the dissolved gas on variouschemical transformations in wet conditions are mostlyunknown, except for the fact that their presence can be com-parable to defects in a solid body.[117] There are many cases,however, in which the gas content significantly influencesthe reaction taking place in the system. For example, thefirst nucleation stage in precipitation of ferrites involves oxi-dation of ferric ions. The oxygen content of the solution

can, thus, exert a critical effect on the kinetics of the overallprocess, the particle size, the microstructure and crystalstoichiometry of the precipitated powders, and, therefore,its properties, including the magnetic ones.[118] Yet, anotherexample comes from the recent synthesis of vaterite inreverse micelles of SDS=hexane=water microemulsion.[119]

The formation of calcium carbonate is in this case triggeredby continuous purging of nitrogen gas through the microe-mulsion. This leads to a gradual removal of carbon dioxidebubbles, which are, however, unable to escape from the dis-persed water phase and become trapped at the oil-waterinterface where they form a gas-water interface and providea nucleation surface for the formation of vaterite crystals.Gas bubbles (strictly speaking, these are cavities, as bubblesare defined as possessing a boundary of a different phasebeyond which the same phase as the one comprising thebubble exists) are known for their ability to intensify hydro-phobic forces, as shown in the case of a 10-fold decrease inflocculation rates upon the removal of dissolved gas in acolloid system composed of paraffin and stearic acid.[120]

Just as repeated adsorption=desorption of water duringthawing=freezing cycles can induce denaturation of pro-teins, gaseous cavities can too disrupt their native confor-mations and, thus, affect f potential measurements, whichexplains why vortexing protein solutions and suspensionsis not always recommended.[121] The effect of the gaseouscontent on pH measurements was evidenced before andinvoked to explain variations in the measurement outcomesdepending on the stirring rates.[122] As for recombinant pro-teins, for which the average purity is around 90wt%(95wt% is considered high purity), the effect of remnantsof the purification and lyophilization processes, such asvarious types of silica beads or shorter polypeptide seg-ments, can be a cause of variation of the results from onesample=batch to another. Another one of the rarely men-tioned effects that leads to a shift in the f potential versuspH curves, including the extrapolated IEP, depends onwhether an acid or base titration is carried out. Typically,an overlap of these two types of f potential versus pH curvesresults in a hysteresis instead of a perfect overlap. Aspointed out by Kosmulski, ‘‘Reversibility of titration (acidtitration vs. base titration) is not guaranteed, but this is sel-dom examined; that is, titration in only one direction isreported in most studies. The system tends to ‘remember’its state from the past: this phenomenon is called hyster-esis.’’[27] This hysteresis loop also typically narrows as thetitration rate decreases, presumably owing to leaving moretime for the system to transform from a mildly metastablestate to a state that lies closer to adsorption equilibrium.

PROSPECT OF COMBINATORIAL TECHNIQUES

DLS electrophoresis has found innumerable applicationsin the fields of colloid and soft chemistry. It has been used to

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characterize colloid dispersions and to gather crucialinsights into the particle=solution interface parameters thatpromote the desired stabilization or phase segregation pro-cesses.[123] Deposition of oppositely charged layers has beenroutinely applied in multilayered thin film technologies,[124]

and fabrication of nanoparticles with functionalized sur-faces or complex core-shell structures routinely relies on fpotential measurements.[125–127] Yet, one of the most pros-perous paths for the future of this method lies in the possi-bility of its real-time coupling with other spectroscopic ormicroscopic methods, which would enrich the informationcontent of the characterization outcomes. An upgrade ofthe DLS electrophoresis measurement apparatus with agel permeation chromatographer, for example, enables dif-ferentiating between protein monomers and dimers, andgives indication of the protein conformation—globular,random coil or elongated, for example—by calculating theslope of the density versus molecular weight curves.[128] Infact, changes in the particle size and f potential in parallelare routinely followed to additionally support insightsabout the interaction of given entities, and a similar combi-natorial principle could be applied with numerous otherexperimental techniques. Some of these methods that wereused in combination with the DLS electrophoresis so asto gain more profound insights into the mechanisms ofthe investigated physicochemical transformationshave been small angle x-ray scattering (SAXS),[129]

circular dichroism (CD),[130] isothermal titrationcalorimetry,[131] microbalance, rheological, and conduc-tivity analyzers,[132–137] flow fractionation technologies,[138]

various infrared spectroscopies,[139,140] x-ray photoelectronspectroscopy,[141] nuclear magnetic resonance,[142] UV-visspectroscopy,[143] electron spin resonance spectroscopy,[144]

surface enhanced Raman spectroscopy,[145] a range ofelectron, optical, and atomic force microscopictechniques,[146–148] and many other. The main risk,however, is that the complemented methods may give con-trasting and incompatible information. On one occasion,for example, the DLS indicated a sharp increase in the par-ticle size following an increase in temperature, whereas thisincrease was absent in the complementary SAXS analy-ses.[149] Also, estimating the melting point of hemoglobinas the onset of change in the particle size due to aggregationyielded 38�C as the outcome, which is lower in comparisonwith the results of CD studies and unlikely to apply tophysiological conditions.[150]

In parallel with miniaturization of critical boundaries intechnological devices and functional materials that entailsthe progress in nanoscience and nanoengineering, the reac-tion systems and the characterization interfaces will tend tobecome smaller and finer as well.[151,152] Ultrafine stream-ing potential measurements of f potential in microfluidicdevices, which are designed to offer in situ optimizationof reaction conditions based on an ultrafast feedback from

an array of characterization techniques,[153] ranging fromvarious spectroscopic and microscopic analyses to micro-electrophoretic ones, seem especially prospective in thiscontext.[154–156]

To sum up, electrophoresis presents an invaluable and,yet, not perfectly quantifiable tool in controlling the inter-action and stability of finely dispersed particles. Althoughelectrostatic effects have been proposed as the first step inthe merging of self-assembling peptide entities, it was alsoobserved that the following steps dominated by molecularrecognition interactions using more subtle forces and shortranges start to take over, exerting the decisive influences onthe assembling systems.[157] The complexity of chemicalsystems utilized to yield advanced materials and assembliesis too high to allow for their control via long-range andnondirectional electrostatic forces. Probing static nanos-tructures at the fine scale is already an enormous chal-lenge[158] and understanding the dynamic evolution ofbio-nano-morphologies at an ultrafine scale and withrespect to the short-range and highly directional weakforces stands forth as an even greater one.[2,159–161]

One example of how weak forces can have a decisiveinfluence on the stability of colloidal systems, prevailingover the effect of electrostatic forces, comes from the fre-quently observed effect of thickening of colloidal disper-sions following specific adsorption of phosphate ionsonto the particle surface.[162] Namely, although one mayexpect the adsorbed multivalent phosphate ions to repulseeach other and prevent particle-particle contact, it turnsout that phosphate ions coating the particles engage inhydrogen bonding with each other, promoting interparticleattraction and aggregation. On the other hand, citrate ionsspecifically adsorbed on the particle surface undergo intra-molecular hydrogen bonding between -OH and the free ter-minal carboxylic group, which prevents the formation ofintermolecular and interparticle hydrogen bonds, resultingin steric repulsion and increased stability of the suspension.Also, the fact that cells whose surface is negatively chargeddisplay preferential uptake of negatively charged nanopar-ticles, rather than those that are positively charged[163] (asin concert with the already mentioned negative surfacecharge of most biological entities) indicates the prime roleof molecular recognition interactions of subtler naturecompared to the long-range electrostatic forces in the reignof soft- and bio- chemistry. Numerous other effects ofattraction of likewise charged colloidal particles,[164–168]

which may seem anomalous from the perspective of soleelectrostatic interactions, can be understood only by refer-ring to finer and more directional physicochemical forces.These examples provide arguments against the simple andstraightforward application of the criterion of electrostaticrepulsion in analyzing and predicting the conditions of col-loid stability or aggregation propensity, while disregardingthe interaction specificities on a fine, molecular scale.

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SUMMARY

Fundamentals of two analytical methods that find per-vasive usage in colloid chemistry, DLS, and microelectro-phoresis, have been discussed, along with pointing out themain limitations of the two.Most importantly, the sphericalapproximation integrated in the measuring apparatus ofDLS devices and the limited spatial sensitivity and aninability to fully discern double-layer effects from the sur-face charge ones in microelectrophoretic measurementsstand forth as the critical limitations of the two. Thesetwo methods are now increasingly finding application indrug delivery, biotechnologies, nanoscience, and otherresearch fields that stand on the frontier of the contempor-ary science and developing more precise equipment and bet-ter quantitative models for probing fine particles withrespect to their dimensions and surface charge propertiesis a vital precondition for an ever greater presence thereofin the modern scientific arena. Also, upgrading or comple-menting the standard DLS settings with different spectro-scopic and microscopic methods can be seen as aprospective path and some of these combinatory character-ization techniques were mentioned in this work.

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