Supplementary Information. Fundamental Growth Principles of Colloidal Metal Nanoparticles

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1 Electronc Supplementary Materal (ESI) for CrystEngComm. Ths journal s The Royal Socety of Chemstry 2015 Supplementary Informaton Fundamental Growth Prncples of Collodal Metal Nanopartcles Jörg Polte* a a Humboldt-Unverstät zu Berln, Department of Chemstry, Brook-Taylor-Strasse 2, Berln, Germany S1 Short Introducton to the concepts of collodal stablty One of the most mportant aspects n collod scence s the mechansm of (metal) nanopartcle stablzaton n the dspersng medum. In general, partcles at the nanoscale are unstable and tend to agglomerate because at short nterpartcle dstances they are attracted to each other by van der Waals, electrostatc or magnetc forces. Wthout any counteractve repulsve forces nanopartcles aggregate, agglomerate or undergo coalescent processes. In the theory of collodal chemstry such repulsve forces can be acheved by electrostatc or sterc stablzaton. 47 Electrostatc stablzed nanopartcles possess at least one electrcal double layer due to a surface chargng. The resultng Coulomb repulson forces between the partcles decays exponentally wth partcle to partcle dstance. If the electrostatc repulson s suffcently hgh, t prevents the partcles from any knd of coagulaton. Ths s well known for the classcal gold nanopartcle synthess by reducton of tetrachloroaurc acd wth sodum ctrate where the gold nanopartcles are surrounded by an electrcal double layer formed by adsorbed ctrate and chlorde ons as well as the catons whch are attracted to them. 4 In the followng secton, mportant partcle nteractons are dscussed brefly. S1.1 Van der Waals Interacton - Nanopartcle Attracton Force The common way to descrbe ntermolecular forces s to use the so called Lennard-Jones potental whch s an expresson for the nteracton energy of the par potental W(r) of two molecules at a dstance r: W(D) = C + B (5) r 6 r 12 wth the constants C and B for the attractve Van der Waals and repulsve Born repulson, respectvely. 48,49 At frst, the second term (Born repulson) wll be neglected. The Van der Waals nteracton energy W a (D) between two partcles wth radus R 1 and R 2 can be theoretcally obtaned by addng all the ntermolecular forces between all consttuent molecules of the partcles,

2 W a (D) = V dv 1 ρ 1 ρ 2 ( C r 6)dV 2 1 V 2 whch fnally yelds for two sphercal partcles: π 2 ρ 1 ρ 2 2R W a (D) = C 6 [ 1 R 2 2R + 1 R 2 c 2 (R 1 + R 2 ) 2 c 2 (R 1 R 2 ) ( c 2 (R + ln 1 + R 2 ) 2)] 2 (7) 2 c 2 (R 1 R 2 ) wth the electron densty ρ, the center to center dstance between the two partcles c and the dstance between the two partcle surfaces D (D = c (R 1 + R 2 )). For two dentcal partcles wth R = R 1 = R 2 and D R (partcles n close proxmty) the equaton reduces to approx.: (6) π 2 ρ 1 ρ 2 CR W a (D) = 12D wth the Hamaker constant A. = AR 12D (8) The fndngs from Eq. (7) and (8) show that the surface nteracton potental (thus the surface forces) decays less wth respect to dstance D than the nteracton potental between two molecules ( 1/D compared to 1/r 6 ) and that the potental s proportonal to the partcle sze ( W a (D)~R ). S1.2 Electrostatc Interacton - Nanopartcle Repulson Force The attractve Van der Waals nteractons dscussed beforehand can promote reversble agglomeraton or even rreversble aggregaton of suspended partcles. The preparaton of stable nanopartcles demands forces opposng the Van der Waals attracton. Ths can be provded by the partcle surface charge resultng n a repulsve nterpartcle forces. In soluton, solvated ons surround the partcles and sheld ther surface charge. Ths can be descrbed usng the Stern-Gouy-Chapman theory n whch the surface potental decreases wthn two layers known as the electrc double layer (EDL) - a compact nner and a dffuse outer layer. The ons n the nner layer (Stern layer) are strongly bound and n the outer layer (dffuse layer) less frmly assocated. Wthn the dffuse layer a boundary exsts, known as the slppng plane, n whch the partcle acts as a sngle entty. The potental at ths boundary s called the Zeta Potental ( ζ potental). Ths s llustrated n Fgure 2a together wth the correspondng cross-secton and the decrease of the electrc potental. The thckness of ths double layer s called Debye length λ ( κ 1 ) and can be quantfed usng smple electrostatcs. Obvously, the dstrbuton of the electrc surface potental ψ(x) s requred for the descrpton of the double layer. The Posson equaton states: (9) = ρ(x) dx 2 wth x as the dstance from the partcle surface, the electrcal potental ψ(x), the permttvty of vacuum ( ), delectrc constant of the soluton and the charge densty. The ε 8.854e 12 CJ 1 m 1 ε 0 ρ physcal meanng of the Posson equaton s that the total electrc flux through a closed surface around the partcle s proportonal to the total electrc surface charge (Gauss's flux theorem whch s

3 one of the four Maxwell equatons n classcal electrodynamcs). The on dstrbuton n the dffuse layer s determned by the balance between the electrostatc attractve force and the Brownan force of thermal dffuson descrbed by Boltzmann: n (x) = n exp( ez Ψ(x) T ) wth the concentraton of on n, n as the concentraton of on at x =, the valency of on z, the Boltzmann constant and the temparature T. The varaton of the co-on and counter-on concentraton can be descrbed usng the Boltzmann dstrbuton and s dsplayed n Fgure 2b. Wth ρ(x) = n (x)z e as the sum of all charges at dstance x, Eq. (9) can be rewrtten as: ez = z dx ( 2 en exp( Ψ(x) (11) T )). Due to the small potental the exponental functons can be lnearzed ( exp ( ± x) = 1 ± x +..) known as the Debye-Hückel lnearzaton (DHL) yeldng: z = z dx ( 2 en - 2 e2 n 2 Ψ(x) T ) and because of the charge neutralty, the frst term s zero whch fnally gves: (10) (12) wth the Debye constant κ = dx 2 z 2 e2 n 2 Ψ(x) = κ 2 Ψ(x) T (13) z κ = [ 2 e2 n 2 ]2. T The Debye screenng length λ D whch measures the dffuse layer thckness s defned as λ D = κ 1. The smple soluton for the dfferental equaton (Eq. (9)) s: (14) ψ(x) = ψ o (x)exp ( κx) (15) wth the surface potental ψ 0 at x = 0. Ths equaton descrbes the decrease of the electrc surface potental n the EDL, but actually the nteracton between at least two EDLs are of nterest to descrbe collodal stablty. The forces due to the EDL are caused by the overlap of the electrc potental dstrbuton and the overlap of the on concentraton (osmotc pressure). Fnally, for the EDL nterpartcle force between two sphercal partcles wth radus R and surface to surface dstance D usng the Derjagun approxmaton the followng expresson s found to be a good approach (constant surface potental and partcle rad much larger than the thckness of the EDL are assumed) 48 : F (D) = 2π κrψ 2 δ exp ( κd) (16) W R = wth the nterpartcle energy D : F(D)dD W R (D) = 2π Rψ 2 δ exp ( κd) (17)

4 Fgure 2 (a) Formed electrc double layer (EDL) around a nanopartcle due to the Gouy-Chapman model whch conssts of the nner Stern layer and the outer dffuse layer (b) correspondng decrease of the counter- and co-on concentraton wth respect to the dstance from the partcle surface; (c) schematc of the EDL, Van der Waals and total nteracton potental (TIP) of two nanopartcles; (d) and (e) nfluence of the on concentraton and the partcle sze on the TIP. S1.3 DLVO Theory More than 70 years ago, two Russan (Derjagun and Landau) and two Dutch (Verwey and Overbeek) scentsts developed a theory of collodal stablty whch s stll seen as one of the groundbreakng characterzaton models n the physcs and chemstry of collods - the DLVO theory. 50 The basc assumpton s that the total force between collodal partcles s the addton of the Van der Waals (attractve) and the EDL (repulsve) forces. In the DLVO theory the effect of Van der Waals and double layer forces are combned, so that the potental nteracton energy between two partcles or two surfaces n a lqud s assumed to be the sum of the Van der Waals and EDL nteracton energy: W total (D) = W a (D) + W r (D) (18) whch can be rewrtten wth Eq. (8) and (17) for two dentcal partcles wth radus proxmty to: R n close W total (D) = W a (D) + W r (D) = AR 12D + 2π Rψ2 δ exp ( κd) (19) Note that n partcular the second term changes wth dfferent assumptons (constant surface potental or surface charge, thn EDL compared to the partcle sze and vce versa etc.) A representatve resultng total nteracton potental (TIP) s dsplayed n Fgure 2c. The TIP demonstrates some fundamental features that become mportant n the explanaton of partcle growth processes. The shape of the curve s the consequence of the exponental and steep decay of the repulsve and attractve term, respectvely. The resultng maxmum of the curve represents the aggregaton barrer and determnes the collodal stablty. The barrer creates effectvely an actvaton energy for aggregaton that two partcles have to overcome when they collde. In ths pcture several factors affect the stablty of the system (.e. the barrer): () the on type and concentraton, () the value of the surface potental and () the partcle sze. Although, Eq. (16) s

5 lmted to two dentcal partcles, t descrbes the propertes of the whole system qute well snce the expressons for sphercal partcles wth dfferent szes show smlar dependences wth respect to sze, surface charge, and on concentraton of the soluton. The Van der Waals attracton s relatvely ndependent of the on concentraton, but the repulsve term strongly depends on t snce the counter-ons are the domnant ons n the Stern and dffuse layer. The on concentraton s drectly proportonal to κ and thus to the exponental decrease of the surface potental. Ths means that the hgher the on concentraton (n partcular the counter-on concentraton) the smaller s the EDL. In Fgure 2d t s shown how the on concentraton n prncple affects the TIP. Moreover, Eq. (19) (.e. wth the assumpton of a constant surface potental and a thn EDL), reveals that n close proxmty the partcle sze s proportonal to both the attractve and repulsve terms. Consequently, the TIP s drectly proportonal to the radus whch means that wth ncreasng sze the shape of the curve and the poston of the maxmum remans whereas the aggregaton barrer ncreases. As a more general rule, one can state that n almost all cases the aggregaton barrer ncreases wth ncreasng sze and therefore also the collodal stablty. Ths s llustrated n Fgure 2e. S1.4 Sterc Stablzaton Sterc stablzaton s a process n whch collodal partcles are prevented from aggregatng by adsorpton of large molecules at the partcle surface, such as polymers or surfactants, provdng a protectve layer. The preventon of coagulaton of these large molecules can be explaned va smple mechansms. The densty of the adsorbed molecules n the nterpartcle space would ncrease tremendously, f the nterpartcle dstance would become smaller and smaller. Ths would cause a decrease n entropy, thus an ncrease of the free energy whch s energetcally less favorable. Due to the ncreased densty, osmotc repulsve forces would also ncrease. Furthermore, a hghly soluble molecule counteracts agglomeraton. 51 Hence, the nteracton potental descrbed n the DLVO theory has to be extended by a further term W sterc descrbng the repulsve forces due to the sterc stablzaton : W total (D) = W a (D) + W r (D) + W sterc (20) W sterc The repulsve nteracton potental s not a long range nteracton and does not sgnfcantly depend on the partcle sze snce the stablty s manly determned by parameters such as polymer concentraton, temperature, average chan length and the solublty of the polymer. 48,52 S2 Experment wth subsequent addton A smple experment whch llustrates the concentraton nfluence on the growth, s the separaton of the NaBH 4 synthess n several growth steps. The experment consst of three dfferent mxng condtons of the precursor and reducng agent soluton whereby all three fnal collodal solutons have the same fnal concentratons. In all synthetc procedures the reacton mxtures were contnuously strred wth a teflon bar exactly fttng the reacton glass at 350 rpm. For each experment a 3 mm NaBH 4 soluton was freshly prepared by dssolvng mg of NaBH 4 n 1 l of MllQ water.

6 In the standard synthess Au NP s were syntheszed by the fast 1:1 mxng of 5 ml of a 0.5 mm HAuCl 4 soluton wth 5 ml of a 3 mm NaBH 4 soluton usng Eppendorf ppettes. Ths synthess results n Au NP s wth a mean radus of 1.66 nm and a polydspersty of 10% that are stable for several mnutes wthout the addton of any stablzng agent. In the second experment the synthess s separated n two steps. In the frst step, 5 ml of Au-NP s wth a radus of 1.66 nm were syntheszed as descrbed above. In a second step, 2.5 ml of a 3 mm NaBH 4 soluton were added to the strred AuNP soluton followed by the rapd addton of 2.5 ml of a 0.5 mm HAuCl 4 soluton usng Eppendorf ppettes. The resultng NP s have a mean radus of nm and a polydspersty of 10 %. In the thrd experment the addton of HAuCl 4 s separated n 30 steps. 5ml of Au-NP s wth a radus of 1.66 nm were syntheszed as descrbed above. 2.5 ml of a 3 mm NaBH 4 soluton were added to the strred Au-NP s soluton, followed by the addton of 2.5 ml of a 0.5 mm HAuCl 4 n 30 alquots of 83 µl every 5-10 s usng an Eppendorf ppette. The resultng NP s have a mean radus of 1.92 nm and a polydspersty of 10 %. The scatterng curves of the respectve fnal NP s are dsplayed n Fg. 1. Fg. 1: (a) Standard synthess of Au NP, mean radus: 1.66 nm; (b) addton of NaBH 4 to and HAuCl 4 to AuNP s, mean radus: 1.75 nm, (c) dropwse addton of NaBH 4 to HAuCl 4 and AuNP s, mean radus: 1.92 nm; the polydspersty for all partcles s 10%. The frst experment s the standard synthess by mxng 1:1 the two reactants to obtan a 5ml collodal soluton wth a fnal gold concentraton of 0.25mmol (e.g. mxng wth Eppendorf ppettes 0.5mmol HAuCl 4 wth 3mmol NaBH4 soluton n less than a second). The partcles grow by coalescence to a sze of ap-prox. 1.5 nm and are collodal stable for mnutes (e.g. wthn further 60mn they grow to a sze of approx. 1.8 nm). The addton of an approprate stablzng agents such as PVP prevents the further growth to 1.8nm. The second mxng comprses the separaton of the synthess n two steps. At frst 2.5ml of a collodal gold soluton wth the standard synthess (wth 1:1 mxng) s prepared and subsequently at frst 1,25ml of 3mmol NaBH 4 and then 1,25ml of a 0.5mmol HAuCl 4 soluton s added. For the thrd order, the 1,25ml HAuCl 4 soluton s added to the 2.5ml collodal gold soluton (also prepared wth the standard procedure) n 30 steps wth addtons of around 40µl every 5-10s (note that every growth step comprses around 3-4s). As expected the fnal partcles of the frst mxng condton (standard 1:1 mxng) have a mean radus of 1.44 nm at a polydspersty of 10%. For the second mxng condton at whch HAuCl4 s reduced n the presence of exstng partcles (wth 1.44nm) the fnal mean radus ncreased to 1.64 nm. The experment revealed that around 50% of the added HAuCl 4 grow on exstng partcles and the remanng gold salt creates new partcles. Therefore the fnal partcle concentraton n the second procedure equates to 75% of

7 the concentraton n the frst procedure. The growth mechansm of the second procedure can be deduced from known mechanstc knowledge of the standard synthess. The exstng partcles wth a sze of around 1.5 nm are collodal stable. The addton of HAuCl 4 (to the collodal soluton wth suffcently BH 4 - ons) wll lead to an almost mmedate reducton. The gold atoms can ether grow on exstng partcles or form small metal clusters (dmers etc.) whch are not collodal stable. The probablty for the growth on exstng partcles wll be much lower than the formaton of small clusters whch s caused by the hgher aggregaton barrer but manly due to the relatvely low concentraton of the exstng partcles. Wth the same argumentaton the formed small molecular lke metal clusters wll further grow due to coalescence wth themselves whereby the correspondng aggregaton probablty wll decrease wth ncreasng sze caused by the ncreasng aggregaton barrer and decreasng concentraton. Consequently, less partcles are created and more of the added gold salt grow onto exstng partcles. Thus, the fnal mean radus of the thrd procedure (.e. 30 addtons of around 40µl) s 1.75 nm and around 90% of the added gold salt grow onto the exstng partcles.