STATIC DIELECTRIC ELECTROLYTE PERMITTIVITY IN ELECTRIC DOUBLE LAYER

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1 Dgest Journal of Nanomaterals and Bostructures Vol. 6, No 3, July-September, p STATIC DIELECTRIC ELECTROLYTE PERMITTIVITY IN ELECTRIC DOUBLE LAYER A. I. IOANID *, R. MIRCEA a, T. M. CIUCEANU a Faculty of Physcs, Unversty of Bucharest a Electrcal Engneerng Faculty, POLITEHNICA Unversty of Bucharest Electroknetc phenomena mplyng on flud flow and ther applcatons n technology, bology and medcne are strongly dependent of the electrostatc propertes of the electrc double layer (EDL) defned as the volume solvent regon stuated near to the sold surface, extended over a new charge dstrbuton. Then the solvent s polar, the specfc nteractons at sold/solvent nterface gve to hgh electrc felds near to surface and a feld-dependence of the statc solvent permttvty n the layer from EDL,occurs. (Receved August 8, ; accepted September 8, ) Keywords: Electrc double layer, Polar solvent, Zeta potental, Feld-dependence of permttvty, Flud-flled gap devces.introducton Sold-substrate/flud nterface s a physcal system that gouverns the electroknetc phenomena mplyng on flud flow and ther applcatons n technology, bology and medcne []. Porous materals as porous slcon (PS), are canddates to these applcatons due ther bocompatblty and large surface/volume rato. At nanometrc scale a sngle macromolecule may be controlled va ther electrostatc nteractons wth EDL defned by the sheldng layer that s naturally created wthn the lqud near a charged surface []. The performances of fludc devces depend both of sold-substrate surface (structure, composton, morphology) and flud propertes (polar, multpolar, electrolyte, polelectrolyte, on concentraton, ph). Generally, the complex nteractons at sold-substrate/flud nterface characterse the wettng/dewettng propertes of solds; partculary, for aqueous solvent case, the hydrophobc/hydrophlc propertes of sold. Other system used as fludc devces are the collodal suspensons. It s very mportant and actual the knowledge of the electroknetcal parameters of the complex collodal system as blood and pharmaceutcal products, but and as cement, dyes, nks, clays, paper,water. EDL s the volume solvent regon stuated near the sold surface, extended over the new charge dstrbuton.the spontaneous separaton of charge at sold-lqud nterfaces s ubqutous n all mcro and nanofludc devces, and s essental to electroknetc actuaton flow. The sold surface charge generates an electrc feld whch pulls oppostely charged ons (counterons) toward surface and pushes lke charges (co-ons) away from t. Counterons preferentally concentrate near surface, effectvely sheldng the bulk soluton from the surface charge. Because the nterface charge contans both the postve and negatve ons, the man nteractons are Coulombc type that are long-range n nature and must be properly calculated to correctly model electrolyte mxtures [3]. Orgne of the sold surface charge are the natural reactve surface groups or a strong affnty for ons of one charge or other, the functonalzng reactve surface groups, e.g., amnes, carboxylc acds, oxdes (hydrophlc surface), but and other specfc phenomena for sold surface that not have reactve surface groups and affnty for ons (hydrophobc surface). * Correspondng author: ana_oand@yahoo.com

2 48 Then the solvent s polar, at sold/solvent nterface are compettve the dpole-dpole nteractons. It s shown that strong dpole realgnment, on-on correlaton and fnte-sze effects can greatly modfy the electrc feld and local permttvty near sold surface [4], so that the EDL s an delectrc heterogeneous medum. The man electroknetc phenomena controlled of the EDL charge dstrbuton propertes are []: electrophoress- movement of partcle n a statonary flud by an appled electrc feld; electroosmoss- movement of lqud past a surface by an appled electrc feld; streamng potental- creaton of an electrc feld as a lqud moves past a statonary charged surface; sedmentaton potental- creaton of an electrc feld when a charged partcle moves relatve to statonary flud. Understandng phenomena near the nterface sold/electrolyte s of mportance n surface states of sold, electroknetcs, mcrofludcs, collodal dsperson and electrochemstry of electrolyte. Delectrc effects due to the local modfcaton of the electrolyte low-frequency permttvty gve to the red-green swtchng of porous slcon lumnescence [6]. In ths paper we analyse the relaton between the hdrophobc/hydrophlc propertes of the surface sold and the statc delectrc electrolyte permttvty modfcaton and we propose a model for the effectve measured permttvty of an aqueous solvent n the EDL..Theory..EDL Structure and Propertes Structure of the EDL s wdely descrbed by the usually Gouy-Chapman- (GCS) model that conssts of two layers succedng on the outer normal surface: layer (of bonded by specfc-adsorbng ons and Coulomb nteractons charges) and dffuse layer n that the ons can move freely n any drectons [7]. At mmerson of some sold materals n an aqueous electrolyte, on sold surface develope the charge by the dssocaton any surface stes and by the adsorbton of ons from soluton. Ions become specfcally adsorbed when ther short-range nteractons,other than coulombc, are mportant so that may come nto contact wth the sold surface. They are usually assumed to form a partal or complete monolayer. Ths s the hydrophobc surface case. Ions becomes non-specfcally adsorbed, postvely or negatvely, by ther long-range coulombc nteractons wth surface. They are beleved to retan ther solvaton shell (bonded water molecules) so that have a poston near to the surface but separated from t by one or more molecular solvent layer. Ths s the hydrophlc surface case. Addng the contrbutons of the sold lattce deffects (vacances, multvalent mpurtes) one obtan the ntrnsec charge densty σ that generate the surface potental ψ. IHP s the ntern Helmholtz plane, determned by centers of the adsorbng solvent molecules and ons. On IHP plane the charge densty s σ and the surface potental s ψ (Fg. (a)). We can consder that sold surface charge densty s σ σ + σ and surface potental s ψ s (Fg. (b)). s

3 49 Fg..Charge denstes and potentals n EDL: (a) detaled and (b) smplfed structure. OHP s the outer Helmholtz plane, determned by centers of the counterons bonded by coulombc nteractons, so that the charge densty on OHP surface s σ d, and the potental at OHP s ψ d. Because between the sold surface (IHP) and OHP plane are no ons, we can consder that for a hydrophobc sold surface, IHP conssts n realgnmetng solvent dpoles (e.g. water molecules) and OHP n few hydroxyl-ons bonded at the hydrogen-bonded n above IHP dpole molecules [7], whle for hydrophlc sold surface IHP conssts n dssocated co-ons, adsorbed counterons and OHP conssts n electrostatcaly bonded counterons. Layer between IHP and OHP s called Layer and ther δ thckness depends on the sze of ons. Beyond layer, the solvent charges can move freely manly by dffuson up the bulk solvent. The zeta potental ς s defned as the surface charge generated potental at the dstance at whch the electrcal forces between ons of opposte charge come nto play, (practcally at OHP), ς ψ OHP, so that ths marks the hydrodynamc flow condton at sold/solvent flat nterface, and the stablty lmt for a collodal suspenson respectvely. Beyond the OHP plane the electrostatc forces tend to zero and consequently the ς potental tends to zero. For a gven sold-surface, the solvent ph at whch theς potental s zero s called soelectrc pont (IEP). To obtan the surface charge potental profl that soluton of a Posson-Boltzmann (PB) equaton, t s plausble to take nto account the concentraton varaton wth dstance from sold surface, zero n layer, decreasng for co-ons and ncreasng for counterons n dffuse layer, so that the local concentraton for an type on of valency z, at x dstance, s bulk zeψ ( x ) n ( x ) n exp( ). k BT Posson-Boltzmann equaton for - electrolyte [,7], wth constant permttvty ε and neglectng polarzaton effects (effectve medum approxmaton, EMA), may be wrtten: ψ e bulk zeψ ( x ) n z exp( ). ε ε k BT zeψ ( x ) Because for usual solvents, <<, the PB soluton s a semnfcatve potental over the k BT Debye length, defned by: e λ D ε εk n bulk B T z

4 43 PB equaton approxmaton breaks down at hgh electrolyte concentraton and must be modfed to nclude the effects of on sze for the on dstrbuton at very close to the surface [8]. Thus, n the layer, PB equaton s: ψ Consderng ψ ( x δ ) ψ OHP ς, the potental profl n the layer, x δ, s (Fg.): x ψ ( x ) ψ s + ( ς ψ s ) δ Fg.. Potental dstrbuton n EDL layer. Electrcal feld generated by the surface charge densty n layer s: E ψ x σ s ε ε S where ε S s solvent permttvty n layer. The electrcal feld E modfes the solvent permttvty n layer va an electrostrcton effect so that the solvent permttvty ε S s dfferent from that n the dffuse layer, ε d. PB equaton n the dffuse layer, δ x λd, may be wrtte (for - electrolyte): ψ e ε ε d n b eψ snh k BT Theoretcal studes of the electrostatc propertes for any systems that are not nherently sotropc, as polarzed nterfacal systems predct realstc results f the evaluaton of the longrange electrostatc nteractons take nto account the net polarzaton of the surroundng medum for vacuum boundary condtons [9,]. In ths case, the charge densty s gven by the delectrc dsplacement D, so that D x ρ ( x ) and the boundary condtons may be wrtte: -at sold surface, x,

5 -at OHP plane, x δ, σ ε ε ψ σ s + σ d ε ε S -at one poston from bulk solvent, densty σ ek, σ s S ψ x ψ dffuse + σ d ε ε d x x δ δ < x s + σ d δ x δ 43, takng nto account the electroknetc charge ρ( x' )dx' σ and neutralty condton s now: σ s + σ d σ ek...feld dependence of the statc delectrc permttvty ε S A typcal value of hgh surface charge densty for a fully onzed surface s σ.5cm correspondng to one charge per.5nm. Computatonal studes of the permttvty s of water stressed by an hgh electrc feld [] use values σ ( 3µ C / cm ) that generate an 9 hgh electrc feld E ~ V / m. When a polar lqud s exposed to an external electrc feld t undergoes polarzaton manly by orentatonal polarzaton mechansm. At small electrc felds the macroscopc polarzaton P defned as the total dpole moment of the volume unty, s lnearly proportonal to the appled feld and the proportonalty constant s a measure of the delectrc permttvty ε, P ε ( ε )E. The decrease n ε wth ncreasng solvent onc concentraton s prmarely due to on-solvaton effects. Interactons between ons and solvent molecule nhbe the free rotaton of the solvent molecule. For aqueous solvent, the formaton of the hydraton shell around ons locks orentaton of a great number water molecules n the external feld. These water molecules are excluded from creatng the effectve dpole moment of system, thus causng a decrease of polarzaton and the delectrc constant []. For bulk lqud water, at hgh electrc felds the polarzaton becomes constant and resultng delectrc permttvty falls to unty [3].Ths behavour s descrbed by the classcal pmolecule E Langevn functon L( x ) coth( x ),x where p molecule s the dpole moment of x k BT ρpmolecule water molecule. At concdence lmt, one obtane ε + L( x ), where ρ s atom ε E number densty. Ths dependence s shown n Fg.3 s ek

6 ε S [u.a.] log(p molecule E/k B T) Fg.3. Dependence of the polar solvent delectrc permttvty for hgh felds. Parallel orentaton due the favorable energetc nteracton wth the electrc feld reduces the orentatonal degrees of freedom of the molecular dpoles for other drectons than along axs of the feld and s most stable a new ordered confguraton n whch the orentatonal polarzaton s strongly hndered. It s shown that an extremely hgh nterfacal electrc feld ~ 9 Vm leads to ordered water layers near to an electrode surface [4]. However, reman actve other polarzaton mechansms, as the ntrabond protonc dynamcs that requre a lower delectrc permttvty. Phenomena may be assmlated wth at least one water molecule ordered layer by the nonelectrostatc (hydrophobc) nteractons wth a polar (or weakly onzated) substrate surface. For an onzated surface, a great number of counterons are fxed by electrostatc (hydrophlc) nteractons. In ths case, the water molecules are moblzated n solvaton spheres of solvent ons and one can suppose that the delectrc permttvty decreases by the same above hgh feld mechansm. Delectrc permttvty of a polar solvent decreases n the layer as the surface charge densty ncreases. Decrease s slow for hydrophobc and rapd for hydrophlc substrate surface. 3. Modellng Electroknetcal phenomena at nterface between the electrode and the onc soluton may be measured by any macroscopc observable, as the capactance of the EDL layer system that s a capactor those heterogeneous delectrc conssts of two dfferent homogeneous delectrcs, layer and dffuse layer, connected n seres (Fg.), so that. C EDL C + C dffuse and effectve (measured) delectrc permttvty ε s gven by equaton: where ε S ε and ε d ε bulk 78. λ ε D δ ε S λd δ + ε d

7 433 8 ε d 78 7 effectve permttvty ε S δ /λ D Fg. 4. Dependence of the statc effectve permttvty on the layer thckness. Fg.4 shown a qualtatve ( σ s ) dependence. We have been consdered that λd decreases as the solvent on concentraton ncreases and theδ values are from ~.nm, correspondng to one water molecule layer [5] and ~.9nm for three water molecule layer [3], to λ D ~ nm for low on concentraton []. Then the capactor sze s comparable wth the EDL thckness, the dependence of the capactance of the onc strength of solvent s nsgnfcant. Ths dependence must be taken nto account for the capactor sze greater than λ D. For exemple, for the ε fludc devces as bosensors, ths ε ( σ s ) dependence s crtcal n usng the capactance change as an ndcator of the exstence of target molecules (bomolecules as ssdna, olgonucleotdes) for an gven onc strength [6]. 4.Summary and conclusons Electrcal behavour of EDL s crucal for dfferent applcatons, from bosensors and nano-and mcrofludc devces, to water-flled gaps for hgh technology equpment. Electrcal propertes of EDL depend of both electrode-surface charge densty and on concentraton of polar solvent. The nherently physcal nteractons, hydrophobc or hydrophlc, determne a new on and dpoles dstrbuton near to surface electrode surface, so that the EDL s a strongly nhomogeneous delectrc medum. Due to electrostatc nteractons, the EDL conssts nto a thn flm known as layer, near to electrode-surface, wth bound charge and delectrc propertes dfferent from the remanng bulk solvent n whch the ons are free and a large dffuse layer up to equlbrum on concentraton poston. Hgh solvent on concentraton determnes a strong electrc feld n the layer that should produce on orentaton of the strongly polar water molecules and a polarzaton obeyng of Langevn law. Dpolar orderng reduces the effectve polarzaton and subsequant delectrc permttvty. The strong feld enhancement at the electrode/solvent nterface s caused by both surface electrode propertes (morphology,free or functonalzated, polar or nonpolar) and solvent characterstcs (polar or nonpolar, hgh or low on concentraton, ph), so that the measured permttvty dependence of ths hgh electrc felds s a sensng ndcator of the flud-fllet gap devces.

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