theory of electrophoresis

8/2/2019 Theory of Electrophoresis

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2 Chapter 1

Figure 1.1 A schematic representation of the arrangement of the main components of atypical C E instrument

ily replacing one of the buffer reservoirs (norm ally a t the a no de ) with a sam plereservoir a nd applying either a n electric potential or external p ressure for a fewseconds. After replacing the buffer reservoir, an electric potential is appliedacross the capillary and the separation is performed. Optical (UV-visible orfluorometric) detection of separated analytes can be achieved directly throughthe capillary wall near th e opp osit e en d (normally near the cath od e).CE is very suited to automation, and the arrangement of commercial C Einstrum ents will seem familiar t o tho se with knowledge of modern H P L C . Basicfeatures of a C E instrum ent include an auto sam pler, a detection module, ahigh-voltage power supply, the capillary and, of course, a computer to controleverything. So, i f we consider that the power supply is equivalent to an HPLCpump and the capillary is equivalent to a column, the instrum entation is com-pletely analogous. T hi s is especially so as the software packages used to con trolmost comm ercial C E instr um ent s ar e based heavily on existing H P L C software.

4 Electrophoresis TheoryTh e theory th at governs electrophoresis is directly applicable to CE and can bedealt with very briefly, with reference t o a few equations. As m entioned earlier,electrophoresis is the movement or migration of ions or solutes under theinfluence of an electric field. Therefore, separation by electrophoresis relies on


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Background Theory and Principles of Cap illary Electrophoresis 3differences in the speed of m ig rat ion (mig ration velocity) of ions o r solutes. Now ,ion migration velocity can be expressed as:

where u is ion migration velocity (ms-'), pc is electrophoretic mobility(m 2V - ' s - l ) and E is electric field stre ng th (V m -').T he electric field stren gth is a function of the app lied voltage divided by thetota l capillary length. Electrophoretic mob ility is a facto r th at indicates how fasta given ion or solute may move through a given medium (such as a buffersolution). It is an expression of the balance of forces acting on each individualion; the electrical force acts in favour of motion and the frictional force actsagainst motion. Since these forces are in a steady state during electrophoresis,electrophoretic mobility is a constant (for a given ion under a given set ofconditions). Th e equ atio n describing electrophoretic m obility is:

where q is the charg e on the ion, q is the solution viscosity an d r is the ion radius.Th e charge on the ion (4) is fixed for fully dissociated ions, such a s stron g acids orsmall ions, but can be affected by p H changes in th e case of weak acids o r bases.Th e ion radius ( r )can be affected by the counter-ion present o r by any com plex-ing agents used. From equation (1.2) we can see that differences in elec-trop ho retic mobility will be caused by differences in th e charge-to-size ra tio ofanalyte ions. Higher charge and smaller size confer greater mobility, whereaslower charge an d larger size confer lower m obility.Electrophoretic mobility is probably the most important concept to under-sta nd in electrophoresis. Th is is because elec trophoretic mobility is a charac teris-tic property for any given ion o r solute and will always be a co nstan t. W ha t ismore, it is the defining factor th at decides migration velocities. This is im po rta nt ,because different ions and solutes have different electrophoretic mobilities, sothey also h ave different m igra tion velocities a t the sam e electric field strength. Itfollows that, because of differences in electrophoretic mobility, it is possible tosep ara te mixtures of different ion s an d solutes by using electrophoresis.

5 Electroosmotic Flow (EOF)A vitally im po rta nt feature of CE is the bulk flow of liquid thr ou gh the capillary.This is called t he electroosmo tic flow an d is caused as follows.An un coated fused-silica capillary tu be is typically used for CE.Th e surface ofthe inside of the tub e ha s ionisable silanol groups, which a re in co ntact with th ebuffer during CE. These silanol gr ou ps readily dissociate, giving the capillarywall a negative charge. Therefore, when the capillary is filled with buffer, thenegatively charged ca pillary wall attra cts positively charged ions from the buffer


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4 Chapter I

Figure 1.2 Sterns model of the double-layer charge distribution at a negatively chargedcapillary wall leading to the generation of a zeta potential and EO F

solution, creating an electrical double layer and a potential difference (zetapotential) close to th e capillary wall, as described according t o Sterns model inFigure 1.2. Sterns mod el for a n electrical d ou bl e layer includes a rigid layer ofad sor bed ions an d a diffuse layer, in which ion diffusion m ay occur by therm almo tion. T h e zeta potential is the potential a t an y given poin t in the do uble layeran d decreases exponentially with increasing distan ce from the capillary wallsurface.When a voltage is applied across th e capillary, catio ns in the diffuse layer arefree to migrate tow ards the cathode, carrying the bulk solution with them. Theresult is a n et flow in t he direc tion of th e cath od e, with a velocity described by

where E~ is the dielectric con stan t of a vacuum, E is the dielectric const ant of thebuffer, ( is the zeta potential, q is th e viscosity of the buffer an d E is the appliedelectric field. T he terms enclosed in brackets eq ua te to t he mo bility of the EOFThe relationship between EOF mobility and EOF velocity is analogous tothat between electrophoretic mobility and migration velocity. Indeed, the unitsfor EOF mobility are the sa me a s those for electrophoretic mobility.

(PEOF).


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Background Theory and Principles of Capilla ry Electrophoresis5 14 i

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Figure 1.3 The variation of EOF mobility with changing pH for a typical uncoatedfused-silica capillary (simulated d a ta )

Factors Affecting EOF MobilityThe main variables affecting EOF mobility are the dielectric constant andviscosity of the buffer and the size of the zeta potential. The use of buffer additivesand/or other modifications of the buffer composition may influence the dielectricconstant and viscosity of the buffer. Buffer viscosity will also depend on thetemperature at which the CE separation is performed.

Zeta PotentialThe zeta potential is proportional to the charge density on the capillary wall,which itself is pH dependent. Therefore, EOF mobility will vary according to thebuffer pH, such that at high pH the EOF mobility will be significantly greaterthan at low pH. Figure 1.3 depicts the variation of EOF mobility with pH for atypical fused-silica capillary. Above pH 9, silanols are completely ionised and theEOF mobility is at its greatest. Below pH 4, the ionisation of silanols is low andthe EOF mobility is insignificant. The zeta potential will also depend upon theionic strength of the buffer, because as ionic strength increases, the double layerwill become compressed, which results in a decreased zeta potential and reducedEOF mobility.At pH > 7, the EOF mobility is sufficient to ensure the net migration of mostions towards the cathode, regardless of their charge. Therefore, the observedmigration velocity of a solute may not be directly related to its electro-phoretic mobility. Instead, it is related to a combination of both its elec-trophoretic mobility and the EOF mobility. Therefore, a solutes apparentelectrophoretic mobility (pa), that is calculated from its observed migration


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velocity, is the vector sum of its real (or effective) electrophoretic mobility (p,)and the EOF mobility (pEoF),.e.,

Since samples are normally introduced at the anode and EOF moves from theanode to the cathode, cations have positive p,, neutrals have zero p, and anionshave negative p,. In other words, cations migrate faster than the EOF and anionsmigrate more slowly than the EOF. Neutrals migrate with the same velocity asthe EOF.

Flow Profile in CEA further key feature of EOF is that it has flat flow profile, which is shown inFigure 1.4, alongside the parabolic flow profile generated by an external pump,as used for HPLC. EOF has a flat profile because its driving force ( i e . , charge onthe capillary wall) is uniformly distributed along the capillary, which means thatno pressure drops are encountered and the flow velocity is uniform across thecapillary. This contrasts with pressure-driven flow, such as in HPLC, in whichfrictional forces at the column walls cause a pressure drop across the column,yielding a parabolic or laminar flow profile. The flat profile of EOF is importantbecause it minimises zone broadening, leading to high separation efficiencies hatallow separations on the basis of mobility differences as small as 0.05%.

6 The ElectropherogramThe data output from CE is presented in the form of an electropherogram, whichis analogous to a chromatogram. An electropherogram is a plot of migrationtime 0s. detector response. The detector response is usually concentration de-pendent, such as UV-visible absorbance or fluorescence. The appearance of atypical electropherogram is shown in Figure 1.5 for the separation of a three-component mixture of cationic, neutral and anionic solutes.


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Background Theory and Principles of Capillary ElectrophoresisA

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Detectorresponse

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I0 Migration t imeFigure 1.5 A typical electropherogram showing the separation of a cation, a neutral andan anion7 Summary

CE is based on the principles of electrophoresis.The speed of movem ent o r migration of solutes in CE is determined by theirsize and charge. Small, highly charged solutes will migrate more quicklythan large, less charged solutes.Bulk movem ent of solutes is caused by EOF.Th e speed of EOF can be adjusted by chang ing the buffer pH used.Th e flow profile of EOF is flat, yielding high separation efficiencies.Th e data output from CE is called an electropherogram.

theory of electrophoresis

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