Thermodynamic Model of Charging the Gas/Water Interface

Transcription

1 pubs.acs.org/jpcc Thermodynamc Model of Chargng the Gas/Water Interface Nkola Kallay, Tajana Preocǎnn,*, Atđa Selman, Davor Kovacěvc, Johannes Luẗzenkrchen, Hromch Nakahara, and Osamu Shbata Department of Chemstry, Faculty of Scence, Unversty of Zagreb, Horvatovac 10a, Zagreb, Croata Insttut fu r Nukleare Entsorgung (INE), Karlsruher Insttut fu r Technologe (KIT), Postfach 3640, 7601 Karlsruhe, Germany Faculty of Pharmaceutcal Scences, Nagasak Internatonal Unversty, 85-7 Hus Ten Bosch, Sasebo, Nagasak , Japan ABSTRACT: In ths work, chargng of the water layer at the gas/water nterface s analyzed expermentally and theoretcally. Expermental data on the surface tenson and surface potental n the acdc range are presented. Lterature electroknetc data ndcate that the soelectrc pont of the gas/ water nterface s ph 3.8. In the acdc regon, a plot of the surface potental versus ph has a slope of 55% of the Nernstan value. The surface tenson exhbts a mnmum at ph 3.8. A thermodynamc model based on the dstrbuton of ons between the bulk and the nterface s developed. The nterpretaton of the surface and electroknetc potental data provded equlbrum constants for the dstrbuton of ons between the bulk and the nterface and the onzaton equlbrum constant of nterfacal water. A sgnfcantly hgher onzaton of nterfacal water wth respect to the bulk phase was observed. The affnty of hydrogen and hydroxde ons to accumulate at the nterface s hgher than the affnty to accumulate n the bulk of the soluton, especally for hydroxde ons. The mnmum of the surface tenson at the soelectrc pont s presented and analyzed. The thermodynamc concept, n accordance wth the Gbbs sotherm, takes nto account the varaton of the composton at the nterface. The effect of electrolytes on the surface tenson, that s, the JonesRay effect, s also dscussed. 1. INTRODUCTION The state of water at nterfaces s an mportant subject, but there are stll controverses between theory and experment as to whether the water at gaseous nterfaces s postvely or negatvely charged. 1 There are at least two open questons. The frst queston s whether the ons from the bulk of the soluton are accumulated or depleted from the nterfacal layer. If there s accumulaton or depleton, the second queston concerns the nature of the ons that can be accumulated or depleted and under whch condtons these processes occur. In other words, the second queston s related to the dfference n affntes of ons to the bulk and to the nterface. If ons tend to accumulate at the nterface, a dfference n the affntes of anons and catons can result n an nterfacal electrcal charge, whch, n turn, depends on ther bulk concentratons (actvtes). The same apples f ons are depleted from the nterface and dfferences n depleton occur. For example, Tan et al. found expermentally that odde ons n soluton tend to appear at the gas/water nterface. In ths case, the expermental result agrees wth theory. However, wth respect to hydrogen and hydroxde ons, the dsagreement could not be more severe. For pure water, the predomnance of hydroxde versus hydrogen ons, or vce versa, results n a very fundamental queston of whether the pure water/gas nterface s negatvely or postvely charged. Accordng to theoretcal smulatons, 310 nterfacal water should be postvely charged. For example, Pegram and Record 5 concluded that the nterfacal concentraton of H ons s 50% hgher than that n the bulk, whereas the nterfacal concentraton of OH ons s about 60% of ther bulk concentraton. They further concluded that the onzaton equlbrum constant of nterfacal water s approxmately equal to that n the bulk soluton. On the bass of molecular dynamc smulatons, Baer et al. 11 concluded that there s no sgnfcant preference for or averson to H 3 O and OH ons at the nterface. However, they found that the solvaton shell of H 3 O was only slghtly dependent on ts poston, n contrast to the OH ons whose solvaton shells near the arwater nterface changed, whch caused a dfferent nterfacal propensty for water self-ons. However, most expermental fndngs have shown the opposte. 118 There are exceptons n both approaches. For example, Vaćha et al. 19 suggested that the ansotropy of the water hydrogen-bond dstrbuton at the nterface results n a regon of net negatve charge at 5 Å below the Gbbs dvdng surface. The estmated potental was found to be mv, whch s stll sgnfcantly lower than the expermental electroknetc potental. Kudn and Car 0 explaned the negatve charge of hydrophobc surfaces n terms of smulatons, whereas on the expermental sde, Wnter et al., 1 for example, dd not fnd evdence for an enhanced hydroxde propensty. In general, expermental electroknetc Receved: July 5, 014 Revsed: December 14, 014 Publshed: December 15, Amercan Chemcal Socety 997 J. Phys. Chem. C 015, 119,

2 data suggest a negatve nterfacal charge n a broad ph regon above the soelectrc pont. 118 Therefore, t could be expected that a negatve surface charge should be observable through surface tenson measurements because of a strong affnty of hydroxde ons for the surface.,3 However, surface tenson data for the gas/water nterface, over a wde ph range, were not prevously avalable, and only Lorenz 4 reported a JonesRay effect when changng the acd concentraton at rather acdc condtons (.e., ph < 3). In a prevous artcle, Beatte et al. 3 reported surface tenson data over the full ph range. Ther experments were performed n the absence and n the presence of 0.01 mol dm 3 salt solutons. In the absence of salt, the surface tenson ph curve was found to be flat. However, a small local mnmum was found around ph 4. Drect ttraton measurements on ol 5 showed that the uptake of hydroxde ons does stablze the ol/water system by chargng the nterface. Several expermental technques such as measurement of the surface potental 6 and dsjonng pressure, 7 atomc force mcroscopy, 8,9 and some spectroscopc methods 30 do suggest a negatve surface charge, whereas other spectroscopc data 31 exclude strong surface enhancement of hydroxde ons and the absence of changes n the surface propensty of hydroxde ons. 3 To analyze the ssue of the nterfacal charge of water, one should frst consder and defne the regon carryng an excess of postve or negatve charge. It s obvous that bulk water and nterface water at equlbrum are overall uncharged. Regardng electroknetc data, 33 one should be aware that the negatve electroknetc charge apples to the so-called stagnant electroknetc layer. A negatve electroknetc potental and charge means that the stagnant layer, the thckness of whch s assumed 34 to be 1 nm, bears a net negatve charge. The thckness of the entre dffuse layer s a few Debye dstances l D, (e.g., for aqueous solutons at room temperature and an onc strength of 10 mol dm 3, l D 3 nm), so that the dffuse layer extends as far as 10 nm from the surface. The dffuse layer s dvded by the shear or slp plane nto a stagnant layer and a moble part (where the term moble s wth respect to the surface plane dvdng the two phases). The charge of the stagnant layer s compensated by the charge of the moble layer. The orentaton of water dpoles at the surface can cause charge separaton, but ths cannot drectly affect the electroknetc phenomena, as the shear plane smply cannot be located wthn water dpoles, dvdng postve from negatve sdes of the water molecules. However, n prncple, the local feld caused by orented dpoles could affect the dstrbuton of other ons at the nterface and cause charge separaton wthn the entre electrcal nterfacal layer. Ths hypothess can be analyzed by consderng electroknetc data for pure neutral water (ph 7) exhbtng a negatve electroknetc charge. The only ons present n pure water are OH and H ons. If they were bound equally at the gas/water surface, the nterface would be electroneutral. If H (H 3 O ) ons were bound to surface H O molecules, the process could be smply consdered as an accumulaton of H ons at the surface. The same would apply to OH ons. Therefore, the electroknetc data showng a generally negatve surface charge (charge of the electroknetc stagnant layer) for ph > 4 and a postve charge for ph < 3 could be nterpreted as the unsymmetrcal accumulaton (or depleton) of OH and H ons n (or from) the stagnant part of the nterfacal layer. Consequently, a thermodynamc treatment based on the dstrbuton of these ons between the bulk and the nterface can be appled. Such an approach s correct f the fracton of these ons at the surface s low so that the fracton of neutral water molecules remans practcally 1. The same apples for other ons present n the system. The effect of electrolytes on the surface tenson, partcularly at hgh electrolyte concentratons, s well-establshed, and several models exst. Also, the macroscopc data and the computatonal results are consstent for these condtons. At low concentratons (curously at the mllmolar concentraton range), the JonesRay effect occurs, 3537 whch has been hotly debated snce the frst publcaton about t but was recently confrmed 38,39 by spectroscopc methods for the mllmolar concentraton range. It s obvous that the nterpretaton of surface tenson requres consderaton of the composton of the nterfacal layer. It can be expected that the addton of acd or base, that s, a change n ph, would affect the surface tenson n dfferent ways so that one could expect dfferent behavor n the soelectrc regon around ph 34. Electroknetc data 40 for water at nert surfaces, such as hydrocarbon/water nterfaces 5,41,4 (whch are frequently termed ol/water nterfaces), Teflon/water nterfaces, 43,44 ce/ water nterfaces, 45,46 and some mneral and metal aqueous surfaces are smlar to those for gas/water nterfaces. 47 All of these nterfaces exhbt low soelectrc ponts between ph and ph 4, and t has been suggested that ther nterfacal charges are governed by smlar mechansms. 45,48 The goal of the present study was to contrbute to the understandng of chargng of gas/water nterfaces. The ph dependency of the surface potental at the ar/water nterface was measured and compared to electroknetc data from the lterature. A thermodynamc nterpretaton was developed consderng the dstrbuton of ons between the bulk and the nterface, as well as the onzaton of the nterfacal water. To explan the mnmum n the surface tenson around ph 4, as ndcated n a prevous report, 3 addtonal experments were performed n ths ph regon. The thermodynamc equlbrum constants for the dstrbuton of hydrogen (hydronum) and hydroxde ons between the bulk and nterface provde nsght nto the state and processes at gas/water nterfaces. Addtonally, the proposed model enables the evaluaton of the degree of onzaton of nterfacal water, whch has been estmated to be hgher at the nterface than n the bulk of the soluton. 47,49 A thermodynamc model, n accordance wth the well-known Gbbs equaton, was developed on the bass of chemcal potentals of onc speces n the bulk of the soluton and at the nterface. Such an approach enabled a consderaton of complex and varable compostons at the nterface. Ths approach would yeld thermodynamc equlbrum parameters and model nherent nformaton on the composton of the nterfacal layer. The thermodynamc treatment s necessarly lmted wth respect to the detaled molecular orgn of the macroscopcally observed behavor. However, beyond our smple thermodynamc approach, t s expected that a theoretcal analyss of the new data wll be helpful n elucdatng the effects on the molecular level. Beyond the ph dependence, our thermodynamc model wll be appled to demonstrate and elucdate the mnmum of surface tenson at the gas/aqueous electrolyte soluton 50 n the vcnty of the nterfacal electroneutralty pont, that s, the JonesRay effect Thermodynamc Bass. To compare the onzaton of nterfacal water wth the onzaton of bulk water, as well as to study the equlbrum at the gas/water nterface, a straghtforward thermodynamc model should be derved. The fact that the values of the thermodynamc equlbrum constants depend 998 J. Phys. Chem. C 015, 119,

3 on the defnton and choce of the standard state should be taken nto account. 51 The chemcal potental, that s, the partal molar Gbbs energy (μ B ), of any speces B nvolved n a chemcal reacton s generally, at standard pressure (p = 1 bar), gven by μ(b) = μ (B) RT ln a(b) (1) where a(b) s the relatve actvty of speces B. For condensed systems (lquds and solds), the above relaton holds for pressures not sgnfcantly dfferent from the standard value, p =10 5 Pa. Relatve actvty depends on the arbtrary choce of the standard state. The (relatve) actvty depends on the composton of the system and nteractons between speces. For speces B, the relatve actvty s gven by a(b) = y(b) r(b) () where y(b) s the actvty coeffcent of speces B descrbng the devaton from the assumed dealty and the respectve nteractons occurrng n real systems. The term r(b) s the relatve content of speces B whch depends on the composton of the system. Several quanttes can be used to descrbe the composton of a system: () the relatve content of the bulk solvent, () the relatve content of a solute dssolved n the bulk of the soluton, and () the relatve content of nterfacal speces. () Relatve Content of the Bulk Solvent. The common practce, as recommended by IUPAC, 33 consders the solvent as a component of the mxture so that the relatve content of solvent speces s defned n terms of ts amount (.e., mole) fracton, x r(b) = x(b) (3) where the standard state s the pure component, that s, x =1. () Relatve Content of a Solute Dssolved n the Bulk of the Soluton. For solute speces B dssolved n the bulk lqud soluton, such as H (aq), OH (aq), K (aq), and NO 3 (aq), the relatve content s commonly defned n terms of molar concentraton as c(b) r(b) = = [B] c (4) where c = 1 mol dm 3, so that the square brackets denote the numercal value of the concentraton f t s expressed n moles per cubc decmeter. The relatve actvty for a solute speces based on concentraton s c ac (B) = y (B) (B) = y(b)[b] c (5) However, the relatve content of solute B can also be defned n terms of ts amount (mole) fracton, as n eq 3. Accordngly, the relatve actvty for solute speces B based on the amount (mole) fracton s ax (B) = y(b) x(b) (6) () Relatve Content of Interfacal Speces. The quantty that s consdered for the defnton of the standard composton at the nterface s ether the amount fracton or surface concentraton (amount dvded by surface area). Accordngly, the relatve content for nterfacal speces B based on the amount fracton s rx ( B) = x( B) (7) Consequently, the relatve actvty of an nterfacal speces on the bass of amount (mole) fracton s ax ( B) = y( B) x( B) (8) In the nterpretaton of nterfacal equlbrum, the effect of electrostatc potental on charged nterfacal speces should be taken nto account. The dfference between the chemcal potental of nterfacal speces B n the real and deal states s therefore gven by the actvty coeffcent y, whch s generally defned as μ real deal (B) μ (B) = RT ln y(b) For the nterfacal speces B of charge number z( B) exposed to the electrostatc potental Ψ, the devaton from dealty s predomnantly due to the electrostatc nteractons, so that real deal μ ( B) μ ( B) = RT ln y( B) = z( B) FΨ (10) where F denotes the Faraday constant. Accordngly, the actvty coeffcent of nterfacal speces B of charge number z( B) s gven by z( B) FΨ y( B) = exp RT (9) (11) For ons n soluton, actvty coeffcents can be calculated usng the DebyeHu ckel or Daves equatons wthn the approprate ranges of onc strength (.e., at low salt content). The reacton Gbbs energy Δ r G s zero n the equlbrum state and s related to the chemcal potentals of speces nvolved n the reacton multpled by ther correspondng stochometrc coeffcents ν νμ νμ ln Δ G = = RT a r ν =Δ G RT ln a = 0 r ν (1) Followng eqs 1 and 1, the thermodynamc equlbrum constant s generally defned by = Δ rg K exp = a RT ν (13) 1.. Ionzaton of Bulk and Interfacal Water. Ionzaton of bulk water s commonly represented by H O( ) H (aq) OH (aq), Kw,bulk = a(h ) a(oh ) a(h O) (14) where K w,bulk s the thermodynamc equlbrum constant for the onzaton of bulk water. To smplfy the notaton, the bulk speces n the equatons wll be denoted smply as H O, H, and OH, for example. Accordng to the conventon, the actvty of solvent molecules s defned n terms of the amount (mole) fracton, so that, for dlute solutons, y H O 1 and x H O 1, whch results n a H O 1 and the thermodynamc equlbrum constant as w,bulk (15) K = a(h ) a(oh ) 999 J. Phys. Chem. C 015, 119,

4 Conventonally, the actvtes of solute speces are defned on the concentraton bass as n eq 8, so that the correspondng thermodynamc equlbrum constant for the onzaton of bulk water s w,bulk, c (16) K = y(h )[H ] y(oh )[OH ] Accordng to the lterature, 5 the value of the conventonal thermodynamc equlbrum constant based on concentraton for the onzaton of bulk water at 5 C, K w,bulk,c, s equal to For the purpose of ths study, to quanttatvely compare the nterface and bulk of the soluton, t s sutable to use the equlbrum constant for bulk water onzaton based on the amount fractons of solute speces, whch s gven by w,bulk, x (17) K = y(h ) x(h ) y(oh ) x(oh ) The two equlbrum constants are related, and K w,bulk,x could be smply recalculated from K w,bulk,c. In relatvely dlute aqueous solutons, for solute speces B, the relatonshp between the bulk concentraton and the amount fracton s c(b) M(HO) x(b) = = [B] ρ(h O) (18) where M and ρ are the molar mass and ρ densty, respectvely, of water. Consequently, the water onzaton thermodynamc equlbrum constant based on the amount fracton s K w,bulk,x = at 5 C, and the degree of the bulk water onzaton n the neutral solutons at ph 7 s therefore 1/ 9 3 bulk w,bulk,x α = ( K ) = = ppm (19) Because of the dfferent physcal and chemcal propertes of water at nert hydrophobc surfaces wth respect to bulk water, 53,54 the onzaton of nterfacal water s represented by HO H OH, a( H ) a( OH ) Kw,nt = a( H ) a( OH ) a( HO) (0) Note that the actvty of neutral water molecules s unty (a H O 1) f the degree of onzaton s suffcently low (x H O 1). At the nterface, t s more sutable to ntroduce amount fractons of nterfacal speces (eq 8) w,nt, x (1) K = y( H ) x( H ) y( OH ) x( OH ) Assumng that devaton from dealty for the above nterfacal speces s predomnantly due to electrostatc nteractons 55 and determned by the electrostatc potental at the plane dvdng the gas phase from bulk water (surface potental Ψ 0 ), the actvty coeffcents of nterfacal H and OH speces accordng to eq 10 are y( H ) = exp( FΨ0 / RT) () y( OH ) = exp( FΨ0 / RT) (3) Multplyng eqs and 3 leads to y( H ) y( OH ) = 1, so that eq 1 s reduced to w,nt, x (4) K = x( H ) x( OH ) The degree of nterfacal water dssocaton, α nt, s related to the correspondng nterfacal equlbrum constant based on amount fractons, K w,nt,x,byα nt =(K w,nt,x ) 1/. The known values of amount fractons of hydronum and hydroxde ons enable the evaluaton of the thermodynamc equlbrum constant and the degree of nterfacal water onzaton. Note that the actvty coeffcents for bulk soluton speces change wth the electrolyte concentraton n an on-specfc way at concentratons hgher than 0.5 mol dm 3. The concentraton lmt for the surface speces mght be lower, f the occurrence of on-specfc behavor s taken as a threshold, 34,56 but stll hgher than the concentraton ranges treated n the present work Chargng of Interfacal Water. Chargng of the water layer at the gas/water nterface could, n prncple, be represented by several dfferent stochometres (reacton equatons). Assumng the presence of negatve surface stes, Leroy et al. 57 appled a surface complexaton model. In the present artcle, the dstrbuton of H and OH between bulk and nterface s not consdered n terms of a surface complexaton (ste-bndng) model, but rather s descrbed by a dstrbuton equlbrum nvolvng dstrbuton equlbrum constants applcable for hgh fractons of neutral water molecules. Our smplfed model of the nterfacal water layer s presented n Fgure 1. Fgure 1. Interfacal water layer at the gas/aqueous electrolyte soluton nterface. Potentals wthn the nterfacal layer are ndcated. However, the dstances between planes are not representatve but rather are for llustraton. As t s common practce, to smplfy the system, we consder the accumulaton of ons n dealzed planes. For thermodynamc consderatons, only the states of reactants and products are relevant. To be able to compare equlbrum constants of dfferent processes, one should be consstent n defnng reacton stochometres and the correspondng equlbrum constants. The accumulaton of hydrogen (hydronum) and hydroxde ons at the nterface s represented as the dstrbuton of H ons between the bulk of the soluton and the nterfacal regon H(aq) H (5) 1000 J. Phys. Chem. C 015, 119,

5 and the dstrbuton of OH ons between the bulk of the soluton and the nterfacal regon OH (aq) OH (6) The correspondng thermodynamc equlbrum constants can be defned dependng on the choce of the standard state. The standard states are defned here n terms of concentraton for bulk soluton speces (eq 8) and amount fractons for nterfacal speces (eq 7), whereas actvty coeffcents for nterfacal speces are gven by eq 11. Accordngly, the thermodynamc equlbrum constants of reactons 5 and 6 are K (H ) = K (OH ) = exp( Ψ0 F/ RT) x( H ) ac (H ) (7) exp( Ψ0 F/ RT) x( OH ) ac (OH ) (8) where Ψ 0 denotes the surface potental, that s, the electrostatc potental affectng the state of nterfacal H and OH ons. Accordng to eqs 7 and 8, the surface potental Ψ 0 s related to the bulk ph by RT K (H ) RT x( H ) Ψ 0 = ln ln F K (OH ) Kw,bulk,c F x( OH ) RT ln 10 ph F (9) Equaton 9 suggests that the slope of the Ψ 0 (ph) functon should be lower n magntude than the Nernstan slope [(RT ln 10)/F] because of the ph dependency of the rato of H and OH fractons at the nterface. The surface s electrcally neutral f the amounts of H and OH at the surface are equal, that s, x( H )=x( OH ), and consequently, the surface potental s zero (Ψ 0 = 0). Accordng to eq 9, the electroneutralty pont ph eln s related to the equlbrum constants descrbng postve and negatve chargng, that s, to the values of the thermodynamc constants for the accumulaton of postve H ons and negatve OH ons, respectvely ph eln = 1 K log (H ) K (OH ) K w,bulk,c (30) In the case of symmetrcal, or lack of, counteron assocaton, the electroneutralty pont concdes wth the soelectrc pont: ph eln =ph ep. 58 Accordng to eq 9, the ph dependence of the surface potental can be expressed as RT ln 10 Ψ 0 = αn (ph eln ph) F (31) where α N s the devaton of the actual Ψ 0 (ph) slope from the Nernstan slope defned as F dψ 0 α N = RT ln 10 d(ph) 1 d{ln[ x( H )/ x( OH )]} = 1 ln 10 d(ph) (3) Because, n prncple, the ncrease n ph lowers the fracton of nterfacal H ons and ncreases the fracton of OH ons, the dervatve of the logarthm of ther rato wth respect to ph s negatve, causng α N to be postve and less than 1. However, f both fractons were hgh, α N would be close to 1. The dstrbuton of counterons (catons C and anons A ) between the bulk and the nterface should also be consdered. The correspondng reactons are and C(aq) C (33) A (aq) A (34) In our nterfacal model, counterons wthn the nterfacal layer are affected by the nterfacal electrostatc potental Ψ β, whch les between Ψ 0 and the ζ potental. The correspondng equlbrum constants, based on concentratons n the bulk of the soluton and amount fractons at the nterface, are K (C ) = K (A ) = Ψ β exp( F/ RT) x( C ) ac (C ) (35) exp( Ψ β F/ RT) x( A ) ac (A ) (36) The surface charge densty at the gas/water nterface (q 0 )s related to the surface concentratons of the ons n the nterfacal regon q = F[ Γ( H ) Γ( OH )] 0 (37) The surface concentratons of nterfacal speces are related to the correspondng amount fractons x( B) x( B) Γ ( B) = /3 Ls Mr(HO) u L ρ(h O) (38) where s s the surface area occuped by one H O molecule, L s Avogadro s number, M r (H O) s the relatve molar mass of water, and u s the unfed atomc mass constant. The counterons ( C and A ) are also dstrbuted wthn the nterfacal water layer, and t s assumed that they are exposed to the surface potental Ψ β. The surface charge densty at the β plane (q β ) s gven by the surface concentraton of assocated counterons q = F[ Γ( C ) Γ( A)] β (39) A net surface charge densty of the nner layer (q IL ) can be acqured by the unequal adsorpton of postvely and negatvely charged ons and s related to the surface concentraton of the nterfacal speces q = q q = F[ Γ( H ) Γ ( OH ) Γ( C ) IL 0 β Γ( A)] (40) Because of the overall charge neutralty of the nterfacal water layer, the net surface charge densty of the nner layer (q IL ) s compensated by the charge of the dffuse layer (q DL ). The GouyChapman theory provdes the relatonshp between the potental at the onset of the dffuse layer Ψ β and the net surface charge densty for 1:1 electrolytes at suffcently low concentratons = = ε Ψ βf q q 8RT I snh DL IL c RT (41) 1001 J. Phys. Chem. C 015, 119,

6 The same theory enables the calculaton of Ψ β from the measured electroknetc potentals ζ Ψ = β RT F exp( l κ ζ e ) tan( F /4 RT) ln exp( le κ) tan( Fζ/4 RT) (4) where l e s the electroknetc slp- (shear-) plane separaton and κ s the recprocal Debye dstance determned by the onc strength (I c ) 1 FIc κ = = l εrt D (43) 1.4. Surface Tenson of a Gas n Contact wth an Aqueous Electrolyte Soluton. The change n the composton of the nterface n the presence of an acd or base, or even a neutral electrolyte, should, n prncple, affect the surface (nterfacal) tenson. Ths problem cannot be analyzed by the commonly used smple form of the Gbbs adsorpton sotherm 59 because the change n bulk composton changes the composton of the nterface nvolvng dfferent knds of onc speces. Nevertheless, the analyss employed n ths study s n accordance wth the Gbbs concept. 60 Therefore, the problem s consdered on the bass of a (chemcal) equaton descrbng the transfer of one water molecule from the bulk of the soluton to the nterface, takng nto account the transfer of accompanyng ons H O( ) ν( OH )OH (aq) ν( H )H (aq) ν( A )A (aq) ν( C )C (aq) H O ν( OH ) OH ν( H ) H ν( A) A ν( C ) C (44) In ths equaton, ν represents the number of speces (H,OH, C, and A ) that accompany one water molecule n the process. If the values of ν are low, specfcally below or around 10 3, the fracton of neutral water molecules at the surface s very close to 1 and nearly constant, so that the coeffcents ν n eq 43 are equal to the amount (mole) fracton of relevant speces at the surface, x. Stochometrc coeffcents (ν) for speces nvolved n the process are negatve for reactants, x(oh ), x(h ), x(a ), and x(c ), and postve for product speces, x( OH ), x( H ), x( A ), and x( C ). Accordng to eq 1, the reacton Gbbs energy s the sum of the products of the chemcal potentals and correspondng stochometrc coeffcents of all speces nvolved n a chemcal reacton. To calculate the Gbbs energy of reacton 44, the chemcal potentals of all speces n aqueous soluton and all nterfacal speces should be taken nto account. Chemcal potentals for solute speces, as well as for nterfacal speces, do not depend on the choce of the standard state, eqs 111. However, ther standard values depend on the choce of the standard state. In the analyss of the ph dependency of the surface tenson, the standard values of the chemcal potentals and relatve actvtes for solute speces are based on molar concentratons, whereas for nterfacal speces, amount fractons are ntroduced. For nterfacal speces B, the standard chemcal potental can be separated nto the chemcal contrbuton μ ( B) and the contrbuton assocated wth the nterfacal tenson μ σ ( B) μ ( B) = μ ( B) μ σ ( B) (45) Upon ntroducng ths formalsm nto eqs 1, 7, and 10, the chemcal potentals of the nterfacal speces become σ μ( OH ) = μ ( OH ) μ ( OH ) RT ln x( OH ) ΨF σ μ( H ) = μ ( H ) μ ( H ) RT ln x( H ) ΨF σ μ( A) = μ ( A) μ ( A ) RT ln x( A ) ΨF β 0 σ μ( C ) = μ ( C ) μ ( C ) RT ln x( C ) ΨF β μ( HO) = μ ( HO) μ ( HO) RT ln x( H O) σ 0 (46) Note that, at the surface, H and OH ons are exposed to surface potental Ψ 0, whereas counterons dstrbuted wthn the dffuse part of the nterfacal layer are exposed to the (average) potental Ψ β. Consequently, the surface tenson (σ) s the sum of contrbutons of all nterfacal speces nvolved n the reacton 1 σ σ = [( ν B) μ ( B)] sl B (47) where s denotes the area occuped by one water molecule at the surface and ν( B) represents the stochometrc coeffcents, that s, the mole fractons (x), of nterfacal speces B. Accordngly, the surface tenson s gven by 1 σ = [ σ σ μ μ sl x ( OH ) ( OH ) x ( H ) ( H ) σ σ x( C ) μ ( C ) x( A) μ ( A) σ x( HO) μ ( H O)] (48) where the mole fractons x of nterfacal speces are determned by nterfacal equlbrum constants, surface potentals, and bulk concentratons (eqs 7, 8, 35, and 36). Note that x( H O) x[h O( )] 1.. EXPERIMENTAL SECTION.1. Surface Potental Measurements. Surface potentals were measured at 5 C usng an onzng 41 Am electrode postoned at a certan level above the gas/soluton nterface and a reference electrode mmersed n an dentcal soluton. The expermental procedure and setup were descrbed n detal prevously. 61 The ph was adjusted by addton of sodum hydroxde soluton to the ntal soluton of hydrochlorc acd (1 10 mol dm 3 ) so that the onc strength n the acdc regon was kept constant at I c = 1 10 mol dm 3. The measurements provde surface potental data on a relatve scale. The absolute values of the surface potental data were obtaned by settng them to zero (electroneutralty pont) at the soelectrc pont, ph eln =ph ep = 3.8. In the acdc ph range (ph < 3), surface potental s then postve and decreases wth ncreasng ph wth the slope of the Ψ 0 (ph) functon beng lower than the Nernstan slope (α N 0.55). Electroknetc potental data of gas bubbles were taken from the lterature. 16,17 In calculatons, the smoothed curve and the value of the soelectrc pont ph ep = 3.8 were used. The electroknetc 100 J. Phys. Chem. C 015, 119,

7 measurements of gas bubbles n aqueous solutons are tedous, and measured electroknetc potentals are affected by the nstablty of bubbles, by addtonal bubble movement due to buoyancy, and by the model used for the calculaton of electroknetc potentals from the measured mobltes. 6.. Surface Tenson Measurements. Surface tensons of aqueous solutons of hydrochlorc acd were measured on a KRU SS Processor tensometer K100 at 5.0 ± 0.1 C. Water was deonzed and boled pror to use. Durng experments, the measurng system was under an argon atmosphere to avod dssoluton and the nfluence of carbon doxde. Specal care was taken to avod any traces of surfactants. For all nterfacal surface tenson measurements, the followng procedure was appled: Chromesulfurc acd was used to remove organc matter from the glassware. Glassware was soaked n chrome sulfurc acd and left overnght. After that, the chromesulfurc acd was removed by ntense washng wth regular dstlled and deonzed water. Before each measurement, the rng was mmersed for 10 mn n chromesulfurc acd. Then, t was extensvely washed wth dstlled and deonzed water. After beng washed, t was exposed to the reducton flame of a Bunsen burner to remove mpurtes from the rng. In the experments, HCl was gradually added to (a) pure water up to a concentraton of 1 10 mol dm 3 (to ph ), n whch case the onc strength was ncreased, and (b) mol dm 3 NaCl soluton up to a concentraton of mol dm 3 (to ph 3), also resultng n an ncrease n onc strength. It was found that the surface tenson exhbts a mnmum n the soelectrc regon around ph RESULTS AND INTERPRETATION OF DATA 3.1. Evaluaton of Equlbrum Constants from Interfacal Potentals. Two dfferent nterfacal electrostatc potentals characterzng the gas/water nterface are expermentally avalable. The frst s the surface potental Ψ 0, measured n the present work wth an onzng 41 Am electrode, whereas the second s the electroknetc ζ potental measured by electrophoress of gas bubbles. 16,17 The data are shown n Fgure. Accordng to eqs 9 and 31, the devaton of the surface potental values from the Nernst equaton provdes the rato of the surface amount (mole) fractons of postve and negatve surface groups. Ths rato s equal to the rato of ther amounts and, consequently, to the rato of ther surface concentratons. The electroknetc ζ potental s related to the net charge of the surface wthn the shear plane, that s, to the dfference n the surface concentratons of postve and negatve nterfacal speces, and s nfluenced by the onc strength. To calculate the dfference between the Ψ β and ζ potentals, the Gouy Chapman theory was appled (eqs 3943). At frst, a certan value of the shear-plane separaton l e was assumed, and the potental at the onset of the dffuse layer Ψ β was calculated usng eq 4. The choce of shear-plane separaton n the range of 0.5 nm < l e <.5 nm does not sgnfcantly affect the fnal result of the calculatons. In the second step, the surface charge densty of the dffuse layer (q DL ), whch s equal n magntude but opposte n sgn to the net surface charge densty (q IL = q DL ), was calculated usng eq 41. To calculate the dfference n surface concentratons and fractons of postve (H ) and negatve (OH ) ons at the surface from the net surface charge densty (q IL ), the surface concentratons of assocated counterons A and C should be known (eq 39). These concentratons were calculated from the correspondng Fgure. Dependency of the surface potental ( ) at the gas/water nterface on ph at ϑ =5 C and I c =1 10 mol dm 3 ;ph ep = ph eln = 3.8. The results are compared wth the values of the zeta potental of gas bubbles n aqueous soluton publshed by ( ) Yang and co-workers 16 (I c =1 10 mol dm 3 ) and by ( ) Takahash 17 (varable onc strength). The Nernstan slope s presented as a dashed lne, whereas the sold lne represents the surface potental functon correspondng to a reduced slope, α N = A smoothed zeta potental functon used n the nterpretaton s presented as a dotted lne ( ). thermodynamc equlbrum constants, whch were treated as adjustable parameters. Once the dfference (eqs 39 and 40) and rato (eq 9) of surface concentratons of nterfacal water speces OH and H are known, ther ndvdual values can be calculated. The ndvdual values of surface concentratons can be transformed nto the mole fractons of nterfacal speces usng eq 38. Wth values for the potentals Ψ 0 and Ψ β, as well as the mole fractons of nterfacal speces, the thermodynamc equlbrum constants for the dstrbuton of postve H and negatve OH ons between the bulk of the soluton and the nterface were evaluated by means of eqs 7, 8, 35, and 36. The thermodynamc equlbrum constants K (H ) and K (OH ) for the dstrbuton of H and OH ons between the bulk and the nterface, based on the bulk concentratons and nterfacal mole fractons, were calculated for the examned ph values and are presented n Fgure 3. The values of thermodynamc equlbrum constants should not depend on ph, so that the constancy of the obtaned values of K (H ) and K (OH ) was used as a crteron whle adjustng values of equlbrum constants for the dstrbutons of Na and Cl counterons K (Na ) and K (Cl ). The values of counteron dstrbuton equlbrum constants were adjusted to obtan constant K (H ) and K (OH ) values. However, as can be concluded from Fgure 3, these values depend on the choce of l e. An ncrease of l e by 1 nm results n an ncrease of the logarthms of the K (H ) and K (OH ) values by approxmately 0.. For l e =1± 0.5 nm, the followng values were obtaned: log K (H ) = 1.31 ± 0.1, log K (OH )= 7.63 ± 0.1. The adjusted dstrbuton equlbrum constants for counterons dd not depend on the choce of l e, and the fnal values were log K (Na ) = log K (Cl )=0.74. These values of dstrbuton equlbrum constants are based on amount fractons of nterfacal speces and ther concentratons n the 1003 J. Phys. Chem. C 015, 119,

8 Fgure 3. Calculated equlbrum constants log K (H ) and log K (OH ) for the dstrbuton of H and OH ons between the bulk and nterface, characterzng the chargng of the gas/water nterface as a functon of ph at ϑ =5 C, I c =10 mol dm 3 (NaCl). ph eln =ph ep = 3.8 and log K (Na ) = log K (Cl )=0.74 for slpplane separaton. l e = 1 nm (heavy lne), l e = 0.5 nm (lower thn lne), and l e = 1.5 nm (upper thn lne). bulk of the soluton. Accordng to eq 18, the ntroducton of the amount (mole) fracton bass for both solute and nterfacal speces results n the followng values of dstrbuton equlbrum constants: log K x,x (H ) = 3.06 ± 0.1, log K x,x (OH ) 9.38 ± 0.1. Regardless of the uncertanty connected to the choce of l e, the values of the dstrbuton equlbrum constants are hgh, ndcatng the preference of H and OH ons for the surface, wth ths preference beng markedly more pronounced for OH ons. Accordng to the above results, the equlbrum constant of nterfacal water onzaton based on amount fractons (eqs 4, 7, and 8) s equal to log K w,nt,x = log- [K (H ) K (OH ) K w,bulk,c ] = 5.06 ± 0.. Consequently, the degree of nterfacal water dssocaton s evaluated as α nt = (.95 ± 0.1) 10 3, whch s approxmately 10 6 tmes hgher than n the bulk of the soluton. 3.. Surface Tenson. The measured surface tenson data for hydrochlorc acd added to pure water and to 10 3 mol dm 3 sodum chlorde soluton as a functon of ph are presented n Fgure 4. The dependency of surface tenson on ph was calculated on the bass of the developed thermodynamc model. The ndvdual values of mole fractons of the nterfacal speces were calculated, usng eq 48, from the thermodynamc equlbrum constant (evaluated by the procedure descrbed n the prevous secton), bulk concentratons of ons, and correspondng surface potentals. The electroneutralty pont was taken to be at the soelectrc pont of ph eln =ph ep = 3.8, and the slp-plane separaton was assumed to be l e = 1 nm. The values of μ σ ( B) for all nterfacal speces were adjusted to ft the expermental surface tenson data (Fgure 4) as follows: μ σ ( H )=5.8 kj mol 1, μ σ ( OH )=5.0 kj mol 1, μ σ ( Na )=4.5 kj mol 1, μ σ ( Cl )=4.1 kj mol 1, μ σ ( H O) = 4. kj mol 1. Fgure 4. Surface tenson of the gas/water nterface as a functon of ph: addton of hydrochlorc acd to pure water (two runs are presented, Δ, ) and addton of hydrochlorc acd to sodum chlorde c =10 3 mol dm 3 (two runs are presented,, ). The lnes were calculated from equlbrum parameters obtaned from the nterpretaton of electroknetc and surface potental data by means of eq 48. The sold lne corresponds to the addton of hydrochlorc acd to pure water, whereas the dashed lne corresponds to the addton of hydrochlorc acd to sodum chlorde c =10 3 mol dm 3. In the calculatons, the followng parameters were used: ph eln =ph ep = 3.8, ϑ = 5.0 C, l e = 1 nm, log K (H ) = 1.31, log K (OH ) = 7.63, log K (C ) = log K (A )=0.74. Adjusted values of contrbutons to surface tenson were as follows: μ σ ( H )=5.8 kj mol 1, μ σ ( OH )=5.0 kj mol 1, μ σ ( Na )=4.5 kj mol 1, μ σ ( Cl )= 4.1 kj mol 1, μ σ ( H O) = 4. kj mol 1. The presence of sodum chlorde (10 3 mol dm 3 ) dd not sgnfcantly affect the calculated surface tenson functon. 4. DISCUSSION AND CONCLUSIONS In the frst step of the nterpretaton, the values of the dstrbuton equlbrum constants for the accumulaton of H and OH, as well as counterons Na and Cl, were obtaned from expermental surface and electroknetc potentals. The thermodynamc model used n ths work nvolves approxmatons related to the electrostatc potentals affectng the states of onc speces at the nterface. As wll be shown, these approxmatons do not affect the man concluson that H and OH ons exhbt a preference for the nterfacal layer and that the onzaton of nterfacal water s markedly more pronounced compared to that of bulk water. At the electroneutralty pont, where Ψ 0 = 0, the fracton of nterfacal hydronum ons s more than 10 3 tmes hgher than the amount of hydronum ons n the bulk of the soluton. At the same tme, the fracton of nterfacal hydroxde ons s 10 9 tmes hgher. From these data, t s obvous that the affnty of hydroxde ons toward the nterface s much more pronounced than the affnty of hydronum ons. Electrostatc potentals Ψ 0 affectng the state of nterfacal OH and H ons are determned by the electroneutralty pont ph eln (Ψ 0 = 0) and the devaton from the Nernstan potental, α N. Both parameters ph eln and α N affect the values of the equlbrum dstrbuton constants of OH and H ons. However, calculatons performed nvolvng devatons from the expermental values stll result n markedly hgher degrees 1004 J. Phys. Chem. C 015, 119,

9 of onzaton for nterfacal water and markedly hgher affntes of OH ons for the nterfacal regon wth respect to H ons. Electrostatc potentals affectng the state of counterons dstrbuted wthn the dffuse part of the nterfacal layer Ψ β cannot be drectly measured and should be between the ζ and Ψ 0 potentals. The best approxmaton s to use expermentally avalable electroknetc ζ potentals (Fgure ) and to apply GouyChapman theory (eq 4) assumng reasonable values of the slp-plane separaton, for example, l e = 1 nm. The mnmum possble value of l e s zero. In such a case, the counterons would be located n the electroknetc slp plane (.e., n the e plane, Ψ β = ζ). Consequently, the logarthm of the dstrbuton equlbrum constants for H and OH ons would be lower by 0. wth respect to the values calculated for l e = 1 nm. The maxmum possble l e value could be estmated by comparng expermental Ψ 0 and ζ electroknetc potentals. Equaton 4 provdes the dstance between the e and 0 planes. The maxmum l e value corresponds to the assumpton that 0 the and β planes are dentcal. In that case, the counterons would be dstrbuted n the same layer as the H and OH ons, that s, n the 0 plane, Ψ β = Ψ 0. Accordng to the expermental data presented n Fgure 3, the maxmum possble l e value would be.5 nm, leadng to values of the logarthm of the dstrbuton equlbrum constants for H and OH ons that are hgher by 0.3 wth respect to the values calculated for l e = 1 nm. The value of the slp-plane separaton was consdered as representatve because t agrees wth fndngs for metal oxde surfaces. 63 The equlbrum constants for the dstrbutons of OH and H ons between the bulk and the nterface were obtaned by applyng the crteron of ther constancy as a functon of ph. The varaton of l e dd not affect the constancy of the K (H ) and K (OH ) values. However, the varaton of the counteron dstrbuton equlbrum constants results n a ph dependency of the K (H ) and K (OH ) values. The values of K (Na ) and K (Cl ) were treated as adjustable parameters and were fnally found to be approxmately equal, whch s n accordance wth publshed electroknetc data, suggestng that the soelectrc pont does not sgnfcantly depend on the electrolyte concentraton. In prncple, one should consder the possble change n water densty at the nterface. Introducng a value of 0.5 g cm 3, the values for the logarthms of the dstrbuton equlbrum constants for H and OH would be hgher by 0.4, whch would not affect the conclusons. The avalable electroknetc data as taken from the lterature (Fgure ) showed sgnfcant dscrepances, and a smoothed ζ(ph) functon was used n the calculatons. The error n ζ potental values dd not sgnfcantly affect the results. In the second step of the nterpretaton, the surface tenson data are analyzed. An approprate form of the Gbbs sotherm s derved that consders the process n whch solute onc speces (.e., hydronum and hydroxde ons as well as counterons) and solvent molecules (.e., water) are dstrbuted between the bulk soluton phase and the gas/water nterface (the water surface). The appled thermodynamc approach s n accordance wth the orgnal Gbbs sotherm. It s based on chemcal potentals (.e., partal molar Gbbs energes) and takes nto account the dstrbutons of several speces and ther varable concentratons at the nterface. Equatons 46 and 47 can easly be reduced to the classcal Gbbs equaton. For example, the effect of a surfactant on the nterfacal tenson could be consdered by eq 46 by equatng the chemcal potentals of nterfacal and bulk speces and ntroducng a concentraton dependence of the latter. In the case of constant composton of the surface, the term ncludng the amount (mole) fracton of nterfacal speces s constant. Also, at constant composton of the nterface, the surface potental s constant, causng the electrostatc term to be constant and ndependent of the bulk concentraton. In the case of uncharged speces, ths term smply dmnshes. By ntroducng the obtaned μ σ value nto eq 47 and takng the dervatve wth respect to the logarthm of the bulk concentraton, the common form of the Gbbs adsorpton sotherm can be easly obtaned. The developed model was used to nterpret the surface tenson of an aqueous electrolyte soluton as a functon of ph and as a functon of the concentraton of electrolyte ons. As shown n Fgure 4. the model agrees wth the expermentally obtaned mnmum n the surface tenson at the soelectrc pont. In the analyss, the equlbrum parameters obtaned by nterpretaton of surface and electroknetc data were used. The contrbutons of chemcal potentals of dfferent nteractng speces, μ σ, were used as adjustable parameters for the evaluaton of surface tenson. The obtaned values of chemcal potentals depend on the nature of the nterfacal speces and are n the range from 4 to6 kj/mol. The above analyss of the expermental data suggests that the negatve charge at the gas/water nterface n a broad ph regon (ph > 4) s due to preferental accumulaton of OH ons at the surface compared to H ons. Both ons exhbt a pronounced affnty for the surface, but the affnty s markedly more pronounced for OH ons. Accordngly, the onzaton of the surface layer of water s approxmately 10 6 tmes hgher than that of the bulk of the soluton, whch agrees wth the theoretcal predctons of Coluss and co-workers. 64,65 However, the majorty of the surface water molecules stll reman uncharged. In the analyss, a thermodynamc model based on the dstrbuton of OH and H ons between the nterface and the bulk phase was appled. The approach assumes that the amount (mole) fracton of neutral water molecules at the surface remans close to 1, whch was shown to be the case because the fractons of nterfacal OH and H onc speces were found to be suffcently low. Despte the relatvely low accuracy of the obtaned values, one can defntely conclude that both OH and H show a tendency to be transferred to the surface. However, ths tendency s sgnfcantly more pronounced for OH ons. The fact that some theoretcal analyses suggest opposte conclusons mght be explaned as follows: Frst, the results of ths study suggest that whole nterfacal layer, from the electroknetc slp plane to the surface plane, s negatvely charged above ph 4, whereas theoretcal studes deal wth a defned plane or thn layer wthn the nterfacal layer. The problem s most easly analyzed by consderng the negatve electroknetc charge of the gas/pure water nterface, that s, at ph 7. The only ons present n pure water are H and OH, so that a negatve nterfacal charge could only be due to the preferental accumulaton of OH ons at the surface. Because ther bulk concentratons are equal, one can conclude that H ons exhbt a lesser affnty to the nterface than OH ons. A shallow mnmum n surface tenson was observed n the soelectrc ph regon (Fgure 4). The theoretcal analyss predcts such a mnmum and thus explans the expermental fndng. The obtaned values of the parameters are not accurate, but t s clear that the decrease n chemcal potental related to the transfer of OH and H ons from the bulk to the nterface should produce a mnmum n the surface tenson n the soelectrc regon. The values obtaned by nterpretng the 1005 J. Phys. Chem. C 015, 119,

10 electroknetc and surface potental data therefore agree wth the surface tenson data. The proposed procedure could also be appled to the effect of neutral electrolytes (whch are not surface-actve agents) on the surface tenson. Such an analyss requres surface potental and electroknetc data of gas/aqueous electrolyte soluton for dfferent concentratons of electrolytes. Measured surface tenson data 50 of sodum chlorde aqueous solutons are compared to our model calculatons n Fgure 5. For the Fgure 5. Surface tenson of sodum chlorde aqueous soluton at ph 6. JonesRay effect: ( ) lterature data 66 and surface tenson calculated usng constant devaton from the Nernstan potental (α N = 0.55, sold lne) and adjustable devaton from the Nernstan potental (values are gven near correspondng expermental ponts, dashed lne). Other parameters used n the calculatons were as follows: ph eln =ph ep =3.8, ϑ = 5.0 C, l e = 1 nm, I c =10 mol dm 3, log K (H ) = 1.31, log K (OH ) = 7.64, log K (C )=0.74, log K (A )=0.74, μ σ ( H )=5.8 kj mol 1, μ σ ( OH )=5.0 kj mol 1, μ σ ( Na )=4.5 kj mol 1, μ σ ( Cl )=4.1 kj mol 1, μ σ ( H O) = 4. kj mol 1. calculaton of surface tenson, the avalable lterature data for electroknetc potentals, 16 estmated surface potental values, and calculated thermodynamc equlbrum parameters were used. The calculated values were found to depend strongly on the choce of the parameter α N (devaton from the Nernstan slope). Usng a constant α N value, good agreement wth expermental data was found only for NaCl concentratons above 10 3 mol dm 3. Wth the value gven above, the observed mnmum was not obtaned n the smulatons. However, by slghtly changng the parameter α N (±0.01) for calculatng surface potental the model follows the expermentally obtaned 46 JonesRay effect. It can be concluded that the above analyss does not contradct to the observed JonesRay effect but cannot be used for ts predcton because of the uncertan dependency of α N value. In concluson, one can state that the controverses between the phenomenologcal (macroscopc) and theoretcal approaches on the molecular scale stll exst, whch means that further research s necessary. Addtonal expermental methods should be developed and appled. The fnal goal wll be acheved when the theoretcal predctons match the expermental fndngs. Ths s mportant because the phenomenologcal approach, as presented n ths study, does not provde reasons for the behavor of the system on the molecular scale. AUTHOR INFORMATION Correspondng Author *E-mal: tajana@chem.pmf.hr. Fax: Tel.: Author Contrbutons The manuscrpt was wrtten through contrbutons of all authors. All authors have gven approval to the fnal verson of the manuscrpt. 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