Kelly Robinson 1 and Ravi Sharma 2

Transcription

1 Electrophoretic Mobility Estimated from the Transient Current in a Parallel Plate Cell Kelly Robinson 1 and Ravi Sharma 1 Electrostatic Answers LLC Rochester, NY 14450, USA Kelly.Robinson@ElectrostaticAnswers.com Bausch and Lomb Rochester, NY Ravi.Sharma@Bausch.com This work was funded by the Eastman Kodak Company and was accomplished while both authors were employed there. 1 1

2 Outline Introduction Surfactants, micelles and charge Electrophoresis and mobility Current in a parallel plate cell. Estimating mobility bl from current measurements. Summary

3 Introduction Separation of cells, bacteria, proteins, peptides, (DNA), viruses, membranes, or organelles according to their electrophoretic mobility [1] Characterization ti of nanoparticles, viruses, and liposomes [] Electronic displays [3, 4, 5] Imaging using liquid toners [6] Electrical conduction in nonpolar liquids (including antistatic additives to prevent fires and explosions [7] [1] Bauer, Johann, MaxPlanck Institute, Martinsried, Germany, Free Flow Electrophoresis (FFE), Copyright , The American Electrophoresis Society, 6/5/007. [] Gale, Bruce K., University of Utah, A Decade of Progress in Microscale Electrical FieldFlow Fractionation, Copyright , The American Electrophoresis Society, 6/5/007. [3] E Ink Corporation Technology Electronic Paper Displays, E Ink Corporation, 6/5/007. [4] Liang, RC., S. CJ Tseng, ZA. G. Wu, HM. Zang, HK. Chuang, Electrophoretic display and novel process for its manufacture, US Patent 6,788,449, SiPix Imaging, Inc., 9/7/004. [5] Kim, Junhyung, John L. Anderson, Stephen Garoff, and Luc J. M. Schlangen, Ionic conduction and Electrode polarization in a Doped Nonpolar Liquid, Langmuir, Vol. 1 (005), pg [6] Ertel; John P., Encapsulated liquid toner printing apparatus, US Patent 5,93,41, HewlettPackard Company, July 13, [7] Morrison, Ian D. and Sydney Ross, Colloidal Dispersions, Suspensions, Emulsions, and Foams, WileyInterscience, 00, pp

4 Surfactants Surfactants (Surface Active Agents) are molecules composed of a nonpolar chain terminated with a polar group such as stearic acid. Polar group, miscible in polar liquids Nonpolar chain, miscible in nonpolar liquids 4 4

5 (Inverse) Micelles Above the critical micelle concentration (CMC), surfactant molecules find each other and form clusters or micelles. In a nonpolar liquid such a dodecane, the nonpolar chains of the surfactant molecules are oriented outward forming inverse micelles. Nonpolar exterior Enclosed polar interior ~0 nm 5 5

6 Inverse Micelles can be charged The polar interior of inverse micelles capture water, salt, and other impurities. Some inverse micelles carry charge resulting from collisions between neutral, inverse micelles, charge separation within the polar interior of the aggregate, and the formation of oppositely charged inverse micelles [5]. Also, nearby counter ions in the fluid are bound to the charged, inverse micelles by coulombic attraction. A dispersion of a surfactant in a nonpolar liquid is analogous to a weakly ionized i plasma. 6 6

7 Electrophoresis When an electric field is applied, loosely bound counter ions are stripped from the charged, inverse micelle. The micelle carries a net charge and becomes a mobile charge carrier. E applied 7 7

8 Polarization The electric field from the separated charge opposes the applied electric field. The total field is reduced, and the motion of charge carriers decreases. eases E applied E separated charge 8 8

9 Cell Current Governing Eq. r J = ( nqb) r E r E r J b n q Ohmic Current Electric field Current density Mobility Charge carrier number density Charge per carrier J = x ( nqb) E x ( nu) 0 n r = t r r U = be n t x Charge conservation ( nbe ) = 0 Velocity x = 9 9

10 Cell Separation of Variables n t x ( nbe ) 0 x = Let n( x,t) Ν( x) T( t) E( x,t) E( x) T( t) T N dt d dt N dt 1 T dt dt d bt NE dx bt NT d dx ( ) = 0 ( NE) 1 d b NE N dx = 0 ( ) 0 = Conservation of charge ( x ) Ν #/m 3 E T ( x) ( t ) V/m 1 (dimensionless) Separation is achieved

11 Cell Time dependence 1 dt 1 d = b NE T dt N dx d T dt T () t 1 T τ = 0 1 = t 1 τ ( ) = 1 τ Constant with units of s

12 Cell Transient Current ( x,t) = E( x) T( t) ; n( x,t) N( x) T( t) qbn( x) E( x) J ( x) E = J(x,t) = nqbe = qbnet EP () t = AJ( x = 0,t) = I = t 1 τ t 1 τ I EP,1 IEP, t t 1 1 τ 1 τ I ( t ) x = I ss I = EP t 1 τ Ideal current, 1 EP species Expected current, with EP species 1 1

13 Experimental Apparatus Electrode gap C empty =.73 pf d=566 μm Insulator with adjustable spacer to vary the electrode gap Guarded stainless steel electrode 13.6 mm dia. to center of insulators Grounded Stainless Steel Electrode High Voltage Electrode Overflow well Fluid well holds ~1 ml fluid 13 13

14 Cell Photo Overflow well Electrode gap C empty = pf d=566 μm Fluid well holds ~1 ml fluid Clamping collar adjusts electrode gap Guarded stainless steel electrode 13.6 mm dia. to center of insulators High Voltage Electrode 14 14

15 So, species are resolved whose time constants differ by about 5X

16 Estimating Mobility n t n 1 nb τ d d b Vτ r ( nbe) = 0 V d 0 Conservation of charge Estimate using characteristic time and characteristic distance. Estimated mobility

17 Estimating Number Density r r J = nqbe I EP d V nq A Vτ d τ IEP n qad Current density Estimates using characteristic time and characteristic distance. Estimated number density of charge carriers Parameter Species 1 Species I EP [na] τ [s] 1.89 s 9.95 s m b [ ] 34x10 3.4x x10 7 V s # m n [ ] 1.4x x ns m σ [ ] A elec = 46. mm d gap = 566 mm 17 17

18 Summary y( (1/) To conserve charge, the time dependence of the current must be: I EP init () t = I t 11 τ The mobility and number density of charge carriers are estimated by: b d V τ n Iτ qad 18 18

19 Summary (/) In a 1% solution of OLOA in dodecane, charged species are present. The properties of the species at 0.5 V (E=880 V/m) are summarized below. Parameter Species 1 Species I EP [na] τ [s] 1.89 s 9.95 s m b [ ] 3.4x x10 7 V s # m n [ ] 1.4x x ns m σ [ ] A elec = 46. mm d gap = 566 mm 19 19