The electrified interface.

Transcription

1 Physial and Intefaial Eletohemisty 3 Exess negative Eletode Solution + + Potential elmholtz Laye s Letue 5 Eletode/solution Intefae Exess positive x a..6 nm istane L The eletified intefae. The intefae between two dissimila intefaes is eletified. Almost all sufaes ay an exess eleti hage. ene when two dissimila phases ome into ontat, hage sepaation ous in the intefaial egion whih esults in the geneation of an intefaial potential diffeene o eleti field. ow does this happen? E field geneated Bottom line : an eletial ouble laye is set up at M/S intefae. Exess positive Exess negative

2 Eletoneutality is valid in bulk solution. onside a metal eletode in ontat with an aqueous solution ontaining salt (e.g Kl (aq)). The solution ontains solvated haged ions and solvent dipoles. Foes expeiened by ions and solvent moleules in bulk of solution ae isotopi : spheial symmety opeates. Ions and wate moleules (on a time aveage) expeiene foes whih ae position and dietion independent. Thee is no net alignment of solvent dipoles, and positive and negative ions ae equally distibuted thoughout any volume element of the solution. Eletoneutality opeates in bulk solution egion vey fa fom eletode sufae. Eletoneutality beaks down in sufae egion. What about the solution egion next to the eletode sufae? In this egion foes expeiened by ions and solvent dipoles ae no longe isotopi and homogeneous. The foes ae anisotopi beause of the pesene of the eletode phase. New solvent stutue, diffeent fom that of the bulk, develops beause of the phase bounday. Eletoneutality beaks down on the solution side of the intefae. Thee will be a net oientation of solvent dipoles and a net exess hage in any volume element of the solution adaent to the eletode sufae. The solution side of the intefae beomes eletified.

3 Intefaial hage sepaation geneates high intefaial Efield. One the solution side of the intefae beomes eletified (aquies a net o exess hage), an eleti field will opeate aoss the phase bounday. Sine the metalli phase ontains haged patiles, the latte will espond to this E field. The fee eletons will move away fom o move towads the intefae depending on the dietion of the E field. Thus a net hage will be indued on the metal, whih will be equal in magnitude and opposite in sign to that on the solution side of the phase bounday. Thus hage sepaation ous aoss the M/S intefae, and this gives ise to an intefaial potential diffeene. Typially the potential diffeene is a.. V. oweve the spatial dimensions of the intefae egion ae vey small, typially nm thik. Thus the eleti field stength pesent at the M/S intefae will be typially 7 Vm whih is vey lage. Eletified intefae. Fomal definition. Tem eletified intefae used to desibe the aangement of hages and oiented solvent dipoles at the intefae between an eletode and an eletolyte solution. We now pesent some simple appoximate models to desibe the popeties of the eletified intefae. We examine thee simple models : elmholtz ompat laye model Gouyhapman diffuse laye model Sten model. A key idea whih we develop involves the epesentation of intefaial stutue in tems of an eletial equivalent iuit element (speifially a single apaito o seies of apaitos). We initially adopt a simple pitoial desiption. This will be followed by a moe quantitative mathematial analysis. 3

4 Eletode Exess positive L Exess negative Solution Eleti field pesent at intefae x Simple epesentation of eletode/solution intephase egion : elmholtz ompat laye model. Eletode Exess positive Exess negative Solution Stutue of thin double laye egion modelled as a paallel plate apaito with a plate sepaation of moleula dimension. L Potential x a..6 nm elmholtz Laye s istane L 6 F m Numeial alulations Using the elmholtz Model. We need the following Relationships fom basi Physis. Sufae on metal (m ) x istane between plates of apaito elmholtz apaitane (Fm ) Intefaial Potential diffeene (V) = pemittivity of vauum = x Fm = dieleti onstant of solution. ( bulk) 78 ( elmholtz) 5 6 E x Eleti field Stength (Vm ) Exess negative Eletode Exess positive Solution L Potential x a..6 nm elmholtz Laye s istane A fundamental poblem is assigning a value fo the dieleti onstant of the solvent in the thin elmholtz egion. Solvent stutue in this egion diffes onsideably fom that of the bulk solution. ave onsideable dieleti satuation effets and so dieleti onstant will be muh lowe than that assoiated with the bulk solution. The dieleti onstant may also vay apidly with distane in intefae egion. 4

5 Potential istibution in elmholtz ompat Laye. Potential distibution obtained using the PoissonBoltzmann equation whih elates hage density and eletostati potential. d dx Ions teated as point hages. ene an assume that exess between eletode sufae and OP is zeo, hene =. x M S M x x (x) Radius of solvated ion = x M x d dx d dx x Linea potential pofile in ompat laye. S x x x M x M M S x S Simple models ae not always good ones. The simple elmholtz pitue is not omplete sine it pedits: The double laye apaitane is a onstant independent of ion onentation and eletode potential Wheeas: Expeiment indiates that the double laye apaitane vaies with both of these quantities in a definite manne. A moe elaboate model is equied. 5

6 The diffuse double laye. ow does a 3 distibution of hage aise? We have negleted the disodeing effet of the themal motion of the ions in the solution. This opposes the odeing tendeny due to opeation of eletostati foes in the intefae egion. Themal and eletostati foes esults in an equilibium. The exess s S ountebalaning the exess hage density s M on the metal, is at a maximum lose to the eletode sufae. It diminishes in an appoximate exponential manne with ineasing distane fom the eletode sufae, giving ise to a diffuse spae hage laye adaent to the eletode. etailed analysis indiates that the thikness of the diffuse laye egion will depend both on the potential applied t the eletode, and on the onentation of ions pesent in the eletolyte solution. Gouyhapman model of diffuse double laye. Eletode Exess positive Exess negative hage density Solution OP L a. nm In the Gouyhapman model of the intefae egion, it is assumed that the exess hage density on the solution side of the intefae an be epesented in tems of a thee dimensional spae hage. s x iffuse laye thikness 6

7 At potential of Zeo hage:, L Gouyhapman model of diffuse double laye. Eletode Exess positive M Exess negative hage density Solution 4ze L sinh hage density in diffuse laye d ze L osh L kbt osh osh L, osh Valid when, is L small. L a. nm osh s x L = ebye Length. Measues diffuse laye thikness. iffuse laye thikness. The diffuse laye thikness is alled the ebye Length and is given the symbol L. In many books this is denoted as /. Fo a z,z eletolyte the ebye length is given by the expession aoss. / kbt RT Evaluation of the onstants gives a L useful expession fo omputation. z e z F / L 6.3 z T e8 L / m mol m 3 o mm Note that the ebye Length ineases as the ioni onentation deeases. The diffuse laye thikness will be geatest fo the most dilute solutions. L /m e9 e /mol m 3 (,) eletolyte, wate = 78, T = 98K 7

8 Sten model of the intefae egion. Neithe the elmholtz ompat laye model no the Gouy hapman diffuse laye model is totally satisfatoy. In the G model the solvated ions ae modelled as point hages. This neglet of ion size is unealisti. In eality the solvated ion an only appoah the eletode sufae to a distane equal to its solvated adius a. ene a moe logial appoah is to ombine the featues of the elmholtz and Gouy hapman models. This was done by Sten. The Sten model is as follows. Next to the eletode we have a egion of high eleti field and low dieleti onstant ( value a. 6) with a ow of fimly held ounte ions. Beyond that thee is an ioni atmosphee (the diffuse laye) whee thee is a balane between the odeing eletostati foe and disodeing themal motions. The dieleti onstant ineases apidly with distane in this egion. The eletial potential vaies linealy with distane (a. hydated ion adius) within the inne ompat laye and deeases in an appoximate exponential manne with distane within the diffuse laye, deaying to zeo in the bulk solution. Sten model of solid/solution intephase egion. L L Seies aangement of apaitos. The smalle of the two apaitanes will detemine the oveall apaitane. If and ae of vey diffeent size then the tem ontaining the lage one may be negleted. The diffuse laye apaitane will pedominate when the solution onentation is low. 8

9 A easonable model of the eletode/solution intefae. Linea potential Vaiation with distane The eletode/solution intefae is modelled as a seies aangement of two apaitos. This is an equivalent iuit epesentation of the intefae. Exponential Vaiation of Potential with distane x Fom basi physis : L ompat laye L Seies aangement of apaitos. Total apaitane L iffuse laye The PoissonBoltzmann equation (I). Fom lassial eletostatis we use the Poisson equation whih elates the dieleti displaement veto and the loal volume density of hage (the numbe of hages pe unit volume). E ivegene opeato E pemittivity pemittivity of vauum eleti field veto dieleti onstant 8.854x Eleti field veto E an be elated to the eletostati potential using basi physis. E This is the fom of the Poisson Gadient opeato equation whih elates the and the eletostati potential. Fm 9

10 The PoissonBoltzmann equation (II). We now need to evaluate the. The volume density of hage is obtained by adding togethe the podut of the hage q and onentation of eah ioni speies in the solution next to the eletode sufae. Ion valene q z e fundamental hage We use the Boltzmann equation of statistial mehanis to obtain a elationship between the loal ounteion onentation and the bulk onentation. To do this we need to evaluate the wok w done in binging the ion fom a efeene point at infinity, up to a point distane fom the eletode sufae. We assume that this wok is puely eletial in natue. w ) q z e( ) ( w exp kbt z e( ) exp kbt The PoissonBoltzmann equation (III). We ae now in a position to wite down the PB equation. This is a faily ompliated equation to solve fom fist piniples. The exat fom of the diffeential equation depends on the geomety. We shall assume a z,z eletolyte suh as Kl o Nal. The geomety detemines the fom that the opeato takes. A plana geomety is used fo maoeletodes, wheeas a spheial geomety is adopted fo ultamioeletodes. d x Plana geomety dx d dx d d d d Spheial geomety d d ze d ze d ze sinh kbt ( ) z L z z e z z e ( ) z e exp kbt z,z valent eletolyte ze ze ze exp exp kbt kbt ze ze sinh kbt ze ze exp exp kbt kbt kbt ze ebye Length, z,z eletolyte The PB equation is solved fo.

11 The Poisson Boltzmann equation (IV). The PB equation fully desibes the petinent eletial popeties of the diffuse laye. oweve it an only be solved analytially fo a few speial situations. Fo the most geneal ases a numeial solution has to be adopted. The PB equation fo flat plana sufaes an be igoously solved fo z,z eletolytes. This annot be done igoously fo spheial sufaes. Appoximate solutions of vaying degees of auay have been podued. A easonable appoah valid both fo plana and spheial intefaes involves the ebyeukel appoximation, whih esults in the tansfomation of the PB equation into a linea fom as indiated aoss. This appoximation will be valid povided that the potential at the sufae of the eletode is not too lage. Appoximate fom appoximation Of potential distibution Plana geomety d dx ze k T B x x exp exp L Poisson/Boltzmann equation : plana sufae. d sinh d Nomalised potential ze kbt ze k T B Vaiation of eletostati potential with distane in the diffuse laye egion. The potential is effetively exponentially deaying with distane fom solid sufae. Neglet ompat laye x x L Nomalised distane exp Small sufae potential ebyeukel appoximation Lage sufae potential tanh exp tanh tanh Full solution of PB equation Thikness of iffuse laye exp

12 hage density in diffuse laye egion. x dx d If the potential applied to the metal sufae is small we an assume a linea appoximation and Fo a z,z eletolyte the loal hage density is given by ze exp ze sinh exp ze sinh d ze sinh d sinh 4ze 4ze ebye Length d sinh d d d sinh osh sinh sinh z e k T 4ze 4ze ze kbt Note that the sign of is opposite to that of. ene a positive implies that negative ions ae attated to intefae and vie vesa. B iffuse Laye apaitane We define the diffeential apaitane of the diffuse laye as L d d d M d BT d 4ze ze k hage density within diffuse laye is d sinh We eall that ebye Length (diffuse laye thikness is kbt ze z e k T B z e k T z e k T z e k T ze osh kbt osh B B B d sinh d osh ze osh kbt depends on potential. It is not onstant.

13 Vaiation of diffuse laye apaitane with potential. ow good is the diffuse laye Theoy in patie? iffuse laye model also applies fo olloidal patile/solution intefae. ouble laye modelling still being Pefomed at eseah level to vaious degees of sophistiation. 3

14 Eletoneutality beakdown in diffuse laye egion : Plana sufae. ounte ion exess tanh oth f f f lntanh f ln tanh ounteion onentation ineases lose to haged solid sufae and oion onentation deeases lose to haged sufae. oion depletion Typial vaiation of L with applied potential. g/aqueous Kl intefae. apaitane maximum Moden models inopoating speifi adsoption of ions in the inne ompat laye, allied with a model fo the wate stutue in the inne laye explain the apaitane maximum onstant apaity Region. Explained by elmholtz model apaitane minimum Explained by Gouyhapman model 4

15 The BM tiple laye Model of the metal/solution Intefae. One uently aepted model is the BM model. It epesents the situation on the solution side of the intefae in tems of a tiple laye. an inne helmholtz plane (IP) is intodued and is egaded as the lous of the eletial entes of speifially adsobed ions. These anions ae stongly adsobed onto the eletode sufae and ae patially desolvated. This fat auses a evesal of eletostati potential in the egion between the IP and the OP. x A pimay and seonday wate laye is intodued with diffeing dieleti popeties. x The pimay wate laye ( = 5) is loated immediately adaent to the metal eletode sufae. The seonday wate laye (e = 36) is loated as a hydation sphee aound a solvated ation and anion. 5

16 Polaizable and nonpolaizable intefaes. L Intefaial stutue Eletode/solution intefae No leakage of hage aoss M/S intefae Ideally Polaizable Intefae : R T Eletial equivalent iuit R T Ideally nonpolaizable Intefae: R T hage tansfe ous aoss M/S intefae Measues ET Aoss intefae Simple equivalent iuit epesentation of eletode/solution intefae egion. L haging uent i i L R S Resistane of solution Faadai uent i F i i i F R T Solution Eletode Evaluation of L (and hene i ) always neessay when making kineti measuements at shot timesales. ouble laye haging uent always pesent in addition to Faadai uent in eletohemial measuements. 6

17 Expeimental inteogation of eletode/solution intefaes. onventional eletohemial tehniques. Based on measuement of uent, potential and hage. V, RV, RRV, PSA, IS et. Applied both to maosized and mioeletodes. Theoy, instumentation, and patie well developed. No diet infomation on miosopi stutue of eletode/solution intefae. Spetosopi tehniques. Povides useful hemial infomation anout speies at intefaes. FTIR, Raman, UV/VIS, XPS, EXAFS, Ellipsomety, E/NMR (new tehnique, vey speialised, limited appliation at pesent). Sanning pobe miosopy. igh esolution topogaphial imaging of eletode sufaes with atomi esolution. Sufae eativity also pobed with high spatial esolution. STM, AFM, SEM. Refe to: P.A. histensen, A. amnett, Tehniques and Mehanisms in Eletohemisty, hapman and all, UK, 994 fo details onening Spetosopi tehniques. 7