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Oxidative dissolution of silver nanoparticles: A new theoretical approach
Accepted Manuscript Oxidative dissolution of silver nanoparticles: A new theoretical approach Zbigniew Adamczyk, Magdalena Oćwieja, Halina Mrowiec, Stanisław Walas, Dawid Lupa PII: DOI: Reference:
S0021-9797(15)30435-5 http://dx.doi.org/10.1016/j.jcis.2015.12.051 YJCIS 20976
To appear in:
Journal of Colloid and Interface Science
Received Date: Accepted Date:
23 November 2015 27 December 2015
Please cite this article as: Z. Adamczyk, M. Oćwieja, H. Mrowiec, S. Walas, D. Lupa, Oxidative dissolution of silver nanoparticles: A new theoretical approach, Journal of Colloid and Interface Science (2015), doi: http://dx.doi.org/ 10.1016/j.jcis.2015.12.051
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Oxidative dissolution of silver nanoparticles: a new theoretical approach
Zbigniew Adamczyk1*, Magdalena Oćwieja1, Halina Mrowiec2, Stanisław Walas2, Dawid Lupa1 ([email protected], [email protected], [email protected], [email protected]) 1
Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, 30-239 Cracow, Poland 2
Jagiellonian University, Faculty of Chemistry, Ingardena 3, 30-060 Cracow, Poland
*Corresponding author Zbigniew Adamczyk Jerzy Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences Niezapominajek 8 30-239 Cracow, Poland phone: +48126395104 fax: +48124251923 e-mail: [email protected]
1
Graphical abstract
2
Abstract A general model of an oxidative dissolution of silver particle suspensions was developed that rigorously considers the bulk and surface solute transport. A two-step surface reaction scheme was considered that comprises the formation of the silver oxide phase by direct oxidation and the acidic dissolution of this phase leading to silver ion release. By considering this, a complete set of equations is formulated describing oxygen and silver ion transport to and from particles’ surfaces. These equations are solved in some limiting cases pertinent to nanoparticle dissolution in dilute suspensions. The obtained kinetic equations were used for the interpretation of experimental data pertinent to the dissolution kinetics of citrate-stabilized silver nanoparticles. In these kinetic measurements the role of pH and bulk suspension concentration was quantitatively evaluated by using the atomic absorption spectrometry (AAS). It was shown that the theoretical model adequately reflects the main features of the experimental results, especially the significant increase in the dissolution rate for lower pH. Also the presence of two kinetic regimes was quantitatively explained in terms of the decrease in the coverage of the fast dissolving oxide layer. The overall silver dissolution rate constants pertinent to these two regimes were determined. Keywords kinetics of silver nanoparticle dissolution; oxidative dissolution of silver nanoparticles; silver nanoparticle dissolution; silver ion release; theoretical model of silver nanoparticle dissolution. Highlights
A general model describing oxidative dissolution of silver nanoparticles was developed. Kinetics of silver ion release from nanoparticle suspensions was quantitatively determined. Two stage kinetics of silver nanoparticle dissolution was confirmed. The kinetic constants pertinent to both stages were quantitatively evaluated.
3
1. Introduction
Silver nanoparticles are widely applied in science and many branches of the industry [1,2] because of their excellent antibacterial [3], antifungal [4] and antiviraial [5] activities. However, the widespread exploitation of silver nanoparticles may lead to their uncontrolled penetration into the environment, especially into aquatic systems. Indeed, the toxicity of silver nanoparticles to various micro-organisms [6], invertebrates [7], crop plants [8] and even human cells [9,10] was confirmed. As shown in recent works [11-19] this adverse activity of nanoparticles is mainly due to silver ion leaching from their surfaces. Because of major practical significance of this issue, much effort was devoted to experimentally determine mechanisms and kinetics of silver nanoparticle dissolution both in aqueous suspension [11-13, 20-29] and from monolayers deposited on solid substrates [30]. In 2010 Liu et al. published two pioneering works [12,13] devoted to the issues of silver nanoparticle dissolution. It was confirmed that under aerobic conditions the dissolution kinetics of silver nanoparticles depends on pH, temperature and the presence of natural organic matter (NOM). Taking into account the influence of other chemical compounds, especially NOM, on a nanoparticle dissolution, the empirical kinetic law comprising a first order reaction was proposed. It was also shown that for higher nanoparticle concentrations, the nanoparticle dissolution process becomes more complicated due to a possible depletion of oxygen and the chemical reactions which can increase pH [12]. The attention of Zhang and coworkers [22] was focused on the influence of a nanoparticle size on the rate of silver ion release. Their study carried out for three various sizes of citrate-stabilized silver nanoparticles revealed that the dissolution efficiency was increased for smaller particle size amount of leached silver ions decreases when the size of nanoparticles increases. The authors also developed a theoretical model for describing nanoparticle dissolution kinetics based on the hard sphere collision theory and using the Arrhernius equation. The size-controlled dissolution of thiol functionalized methoxyl polyethylene glycol (PEGSH) silver nanoparticles, at neutral and acidic conditions, was studied by Peretyazhko et al. [29]. It was confirmed that the particle dissolution rate depends on their size and pH, which was also observed in other works [11-13,22]. On the other hand, in other publications the attention was focused on the surface coating effect on the kinetics of silver ion release [11, 15,25]. Dobias and Bernier-Latmani [15] compared the dissolution of three types of silver nanoparticles stabilized by common 4
organic capping agents: polyvinylpyrrolidone (PVP), tannic acid and citrate anions. Their studies showed that in the case of two first stabilizing agents, the release on silver ions was more efficient than in the case of citrate-stabilized nanoparticles. The author assumed that citrate ions may act as reducing agents at nanoparticle surface, reducing the oxide layer and decreasing their solubility. On the other hand, the contradictory results were obtained by Lenhart group [25]. It was found that the low molecular weight capping agents, such as citrate ions, did not inhibit silver ion release while nanoparticles stabilized by high-molecular weight surfactants were more prone to dissolution. Despite a scatter of these experimental data it is generally recognized that silver particle dissolution only proceeds in solutions containing oxygen or another oxidizing agent and its efficiency significantly increases for lower pHs (mild acidic conditions) [1113,22,28,29]. It is also confirmed that smaller particles of sizes below 10 nm dissolve faster than larger particles and that the dissolution rate is the largest at initial stages [13,22,29]. For longer times the dissolution rate systematically decreases, therefore the maximum dissolved amount usually varies between 5 and 30% [12,13,22,28,29]. It is also shown that the temperature increases dissolution rate although this effect was rather moderate [11,12]. However, contrary to the extensive experimental effort, little attention was devoted to systematize these facts in terms of a comprehensive theoretical approach with the exception of the work of Zhang et al. [2011] where an on-step dissolution model was proposed. The obtained experimental data were rationalized in terms of a single exponential kinetic model by postulating a surface controlled dissolution mechanism of silver nanoparticles. Given the deficit of theoretical approaches the main goal of this work is to develop a general model of an oxidative dissolution of silver particle suspensions that rigorously considers the bulk and surface solute transport steps. In contrast to previous models, a twostep surface reaction scheme is considered. It comprises the formation of the silver oxide phase on the bare silver particle surface by direct oxidation and the second reaction described the acidic dissolution of this phase leading to silver ion release. By considering this, a complete set of equations is formulated describing oxygen and silver ion transport to and from particles’ surfaces. These equations are solved in some limiting cases pertinent to nanoparticle dissolution in dilute suspensions. The obtained kinetic equations are used for the interpretation of experimental data that allows one to quantitatively determine the bare silver oxidation rate constant and the oxide layer dissolution rate constant. It is also shown that the model explains the main features of literature data, especially the nonlinear dissolution
5
kinetics for longer times and the increase in dissolution rate for smaller particles in terms of the presence of the oxide layer.
2. Experimental section 2.1.Materials Silver nitrate, sodium borohydride and trisodium citrate were purchased from Sigma Aldrich. Nitric acid and hydrogen peroxide were supplied from Avantor Performance Materials S.A. (formerly POCH S.A.) and (poly(allylamine hydrochloride) (PAH 70 kDa) was obtained from Polyscience. Mica sheets for the silver nanoparticle deposition were purchased from Continental Trade. All chemical reagents and solvents were commercial products and were applied without further purification. Ultrapure water was obtained using the Milli-Q Elix&Simplicity 185 purification system from Millipore SA Molsheim, France. Citrate-stabilized silver nanoparticles were synthesized according to the previously described method [31] with some modifications. Briefly, a solution containing 0.42 M sodium borohydride and 5.69 mM trisodium citrate was prepared in 1.5 L of deionized water using a mechanical stirring with a constant speed rate of 170 rpm. Afterwards, continuing the stirring, 500 mL of an aqueous solution of silver nitrate (1 mM) was added dropwise (using a peristaltic pump, speed of addition 10 mL min-1) into the reduction mixture. The synthesis was carried out at room temperature (298 K) and the stirring was continued over 1 h. After this period of time, the obtained silver suspension was purified using Amicon Ultrafiltration Cell equipped with a cellulose membrane (NMWL 100kDa). The ultrafiltration was continued until the conductivity of the suspension reached a value of 20 μS cm-1. For calibration of silver determination by flame atomic absorption spectrometry (FAAS) standards were prepared form Ag stock standard solution Certipur®, Merck Darmstadt, Germany.
2.2.Methods 2.2.1. Characterization of silver nanoparticle suspension The weight concentration of silver in the purified suspension was determined precisely using two independent methods. In the first approach [31], the silver nanoparticle concentration was calculated based on the experimentally measured density of suspension and the effluent obtained during the ultrafiltration. These values were determined using a highprecision DMA 5000M densitometer from Anton Paar company according the procedure described previously [31]. In the second procedure, the total silver concentration in the suspension was determined by FAAS Accordingly, 200 µL of the suspension was digested in 6
the mixture of nitric acid, and hydrogen peroxide (30%) according to the procedure of Peretyazhko [29]. The obtained solution was analyzed using Atomic Absorption Spectrometer PinAAcle 900Z from Perkin Elmer company. The size distribution and morphology of silver nanoparticles were determined by transmission electron microscopy (TEM). A drop of silver suspension was placed on a copper grid coated with a carbon film, air dried and imaged with the use of FEI Tecnai G2 microscope [31]. Additionally, the silver nanoparticles deposited on (poly(allylamine hydrochloride)-covered mica sheets [31] were characterized using atomic force microscope (AFM) according to the procedure presented elsewhere [31,32]. This measurements were carried out using the NT-MDT Solver Pro instrument with the SMENA SFC050L scanning head. The imaging was done in semi-contact mode using composite probes possessing a silicon body, polysilicon levers and high resolution silicon tips. The analysis of obtained micrographs and images was done using MultiScan Base software. The stability of silver nanoparticles in the suspension was monitored by UV-vis measurements using UV-1800 spectrometer from Continental Trade. The diffusion coefficients of nanoparticles were measured using dynamic light scattering (DLS) technique using the ZetaSizer NanoZS apparatus. The same instrument was applied in order to determine the electrokinetic properties of nanoparticles. Knowing the electrophoretic mobility and hydrodynamic diameter of nanoparticles, the values of zeta potential were calculated using Henry’s equation [31].
2.2.2 Ion release experiments The experiments of silver ion release from the nanoparticles were conducted immediately after the purification and the determination of silver weight concentration in the suspension. Then, the stock solution of nanoparticles was diluted with deionized water of a controlled temperature (298 K) to a desired initial concentration (5 mg L -1, 10 mg L-1 and 30 mg L-1). In the additional part of experiments, the natural pH of the samples (usually 6.2) was adjusted to pH 3.5 using nitric acid. The dissolved oxygen (DO) concentration in the prepared solutions was determined using the oxygen probe COG-1t connected with the oxygen meter CPO-505 obtained from Elmetron company. Afterwards, the silver suspension of controlled properties (pH, DO, silver concentration, temperature) was divided onto the samples of an initial volume of 10 mL. Each sample was used for the determination of silver ion concentration released after a given period of time. Indeed, for a given periods of time, the silver ion determination was repeated twice. The ultrafiltration method was applied in order to 7
separate silver ions from the nanoparticles. The separation was carried out using Amicon Ultrafiltration Cell (Model 8010) equipped with a cellulose membrane (NMWL 30 kDa, Merck Millipore). The clear effluents were tested using UV-vis measurements and DLS techniques. The absence of plasmon resonance optical absorption peak at a wavelength 396 nm and the lack of nanoparticles detectable for DLS technique, confirmed that the method of separation was optimized correctly. The effluents contained only leached silver ions were fixed using nitric acid ( 2% v/v). They were stored in polypropylene tubes at the temperature of 277 K. The concentration of leached silver ions was determined by flame atomic absorption spectrometry. The concentration of released silver ions for a given period of time was determined from the three independent measurements.
3. Results and discussion
3.1.The theoretical model In order to quantitatively interpret the experimental results a phenomenological cell model of oxidative dissolution of silver particle suspensions is developed. Accordingly, it is assumed that a particle in the suspension is confined within a spherical cell of the diameter db,, see Fig. 1.
Fig.1. A schematic representation of silver particles with the outer boundary (cell boundary). 8
For spherically shape particles db can be calculated from the relationship 1
3 db 102 d s mx s cs
(1)
where ds is the particle diameter, s is silver particle density, cs is the silver particle concentration in the bulk expressed in mg L -1 (ppm) and mx is the maximum packing (volume fraction) of spheres in 3D is ca. 0.62 [33]. From Eq.(1) one can calculate that for a typical value of cs equal to 10 mg L-1, particle size equal to 10 nm and s = 10.49 g cm-3 one has db = 866 nm. Different transport conditions can be treated by formulating appropriate boundary conditions at the cell's boundary as previously discussed in Ref.[34] where surfactant adsorption/desorption processes at liquid emulsions were studied. For example in the case of unstirred suspension, where the oxygen and ion transport is solely due to diffusion one formulates the symmetry boundary conditions. In this case concentrations of all dissolved species change in time everywhere in the suspension. On the other hand, in the case of a wellstirred suspension, concentrations of all species considered in the mass balance remain uniform within the cell and equal to bulk reference concentrations. It is also useful to estimate the characteristic relaxation times of establishing the stationary transport conditions pertinent to our system. This can be done by considering that relaxation time for the diffusion transport to a spherical interface is given by the simple expression [35,36]:
t1
d s2
(2)
4D
where D is the effective diffusion coefficient of the solute comprising the Brownian motion of the particle. By assuming dp = 10 nm (10-6 cm) and by considering that the oxygen and silver ion diffusion coefficients in water equal to 2.1∙10-5 and 1.65∙10-5 cm2 s-1 , respectively (at T=298 K [37]) one can calculate from Eq.(2) that the relaxation times are equal to 1.2∙10-8 and 1.5∙10-8 s, for oxygen and silver ion, respectively. This demonstrates that the local steady state
9
transport near the silver particle is established very fast compared to typical dissolution experiments times. Analogously, the diffusion relaxation times for oxygen and silver ion transport across ds d r b is given by 2 2
the cell
d t2 t1 b ds 4 Dox db2
2
(3)
By considering Eq.(1) one obtains explicitly 2
3 t2 104 mx s t1 cs
(4)
Accordingly, t2 equals to 8.9∙10-5 and 1.1∙10-4 seconds for cb=10 mg L-1 for the oxygen and silver ion transport, respectively. It should be mentioned that t2 is also a good estimate of the particle dissolution time under bulk transport dominated transport. Given the fact that the typical experimental dissolution times are of the order of 10 6 seconds [11-13,22,29], i.e., by the factor of 1014 larger than t1 one can deduce that the silver dissolution kinetics is surface reaction controlled. It should be mentioned that the assumption of a dominant reaction dissolution regime of silver particles was intuitively accepted in Refs. [12,13,22,28]. However, in contrast to these approaches, where an one-step reaction was considered, in this work we assume a more general scheme where the silver particle dissolution is governed by the two irreversible surface reactions as proposed in Ref. [25,28] 2Ag(s) + ½ O2 → Ag2O(s) Ag2O(s) + 2H+ → 2Ag+ + H2O
(5)
The first reaction describes the formation of the silver oxide phase on the bare silver particle surface and the second reaction described the acidic dissolution of this phase. By assuming irreversibility of these reactions, one can formulate the following kinetic equation characterizing the oxide layer mass balance
10
q dmox S k1cop B k2 H Box mox dt
(6)
where mox is the oxide layer mass, S is the particle surface area, k1 is the oxidation rate constant, c0 is subsurface oxygen concentration, B is the fraction of the available (bare) surface area of the particle, k2 is the dissolution rate constant, H is the hydrogen ion subsurface concentration, Box is the fraction of the available surface of the oxide layer and p, q are exponents characterizing the reaction order. In the general case, the surface mass balance equation, Eq.(7) is coupled with the bulk oxygen diffusion equation in the form: cox D ox 2cox t
(7)
where cox is the oxygen concentration in the suspension, D ox is the effective oxygen diffusion coefficient in the bulk and t is the diffusion time. The boundary and initial conditions for Eq.(3) are cox 0 r
at
r
db 2
(i) symmetry
(8)
cox coxi
at
r
db 2
(ii) well-stirred solution
(9)
cox cox i mox moxi
for at
ds d r b 2 2 t 0 ds r 2
(10)
k cox dmox p 2 Dox S t k c t B ( t ) B m t 10 ox ox dt r 0 k'
(11)
where cox i is the oxygen concentration at the cell’s surface at the distance of d b (see Fig. 1), r is the radial distance from the silver particle center, moxi is the initial mass of the oxide layer
11
q
on silver particles, k 2 k2 k ' H and k '
4M Ag M O2
, MAg , M O2 are the molar masses of silver
and dioxygen, respectively. It should be mentioned that the initial condition, Eq.(10) reflects the fact that the initial mass of the oxide layer can be different in various experiments. This effect, which was not considered in previous approaches, may lead to a significant spread of the short-time dissolution kinetics as observed experimentally [12,13,29]. Analogously, the silver ion bulk diffusion equation has the form : cAg t
D Ag 2cAg
(12)
where c Ag is the silver concentration in the suspension, D Ag is the silver ion diffusion coefficient, with the following boundary and initial conditions:
cAg 0 c Ag r
dmAg dt
0
for
ds d r b, 2 2
t 0
at
r
db , 2
t 0
(13)
k S t 2 Box mox t 0 k'
(14)
c D Ag Ag r
where mAg is the dissolved silver mass. Eqs.(6-14) represent a complete boundary value problem that describes silver particle dissolution kinetics governed by both surface reaction and bulk transport. However, it should be mentioned that by formulating these equation one tacitly assumes that the hydrogen ion concentration (pH value) in the suspension remains constant during the dissolution process. Due to non-linear character of Eqs.(6-14) their solution in the general case is only feasible by using numerical methods. However, as above estimated, in the case of silver nanoparticle suspensions appearing in practice the relaxation time of establishing quasistationary transport conditions is very short compared to the overall dissolution times. Therefore, the oxygen and silver ion concentrations in the cell are uniform at all times. This implies that:
12
cAg t
coxi k '
mAg
for
v1
mAg v1
coxi
ds d r b , t 0 2 2
mox (t ) v1
(15)
where v1 is the cell’s volume. Because the diffusion within the cell is very fast, Eqs. (11,14) simplify to: dmox k S t k1c p t B t 2 Box mox t dt k'
dmAg dt
(16)
S t k 2 Box mox t
with the following constrains: cox coxi k 'cAg
case (i) symmetry
cox coxi
case (ii) well –stirred solution
(17)
2
S t k '' msi mAg 3 2
6 3 3 where k '' and msi = msi d s is the initial mass of the silver particle. 6 s The initial conditions for Eq.(16) are cox coxi ms msi t 0 mAg 0 mox moxi
(18)
By assuming that all the silver oxide is available for hydrogen ions, i.e., Box = 1 and by assuming that the one can express the available surface function for the bare silver is given in the Langmuir model expressed as 13
B mox 1
mox (t ) Γ ox (t ) S (t )
(19)
where, Γ ox is the coverage (2D density) of the Ag2O layer, one can transform Eq. (16) to the form dmox m k p ox 2 S k1co 1 mox dt Γ S ox k'
dmAg dt
S k2 mox
(20)
with the initial conditions:
mAg 0 ms msi t 0 mox moxi 2 S Si k '' msi 3
cox coxi
cox coxi k 'c Ag cox coxi
(21)
(i ) t 0 (ii )
Eqs.(20-21) represent a general initial value problem that exactly describes the dissolution kinetics of silver particles for arbitrary time scale. However, since these equation are coupled and non-linear their solution is only feasible by using numerical methods. Interesting analytical solutions can be derived for shorter times where the size of the particles and their surface area do not change appreciably, if mAg msi . Consequently 2
S Si k '' mAg 3 Si ,
cox coxi k 'mAg coxi
(22)
In this case, the equation system, Eq.(20) becomes decoupled and can be integrated to the form 14
mox
moxi
dX k cp k 1 oxi p 2 k1coxi X Γ ox Si k '
Si t
(23)
where X is the dummy variable After evaluating the definite integral, Eq. (23) yields the following expression
mox m m moxi e Kt
(24)
where
k1coxp i
Γ ox Si
k' Γ ox
K
m
k2
(25)
k1coxp i Γ ox Si
k1coxp i
k2
Γ ox S i
k'
Thus, the expression for the silver ion mass becomes
mAg Si k 2 mt Si k 2 moxi m
1 e Kt K
(26)
Eq. (26) can be converted to a simpler form
mAg K1t K 2 1 e Kt
(27)
where
K1 Si k 2
k1coxp i Γ ox Si
kc p 1 oxi
k2
Γ ox Si
k'
15
k1coxp i Γ ox Si K 2 Si k 2 moxi k k1coxp i 2 Γ ox Si k'
Γ ox p k2 kc Γ S 1 oxi ox i k'
(28)
Because the k 2 constants depends on the hydrogen ion concentration (pH) one can predict from Eq.(27-28) that the silver particle dissolution kinetics is a complex and nonlinear function of pH. Eqs.(26-28) can be used for the interpretation of the dissolution kinetics of silver particles for shorter times where the particle mass change remain not too significant. In this way, the oxide layer and bare silver dissolution kinetic constants can be determined. From Eq. (27) one can derive various asymptotic solutions: short times, where t
(i)
1 K
mAg K1 KK 2 t
longer times t
(ii)
(29)
1 K
mAg K1t (iii)
(30)
fast oxide layer dissolution rate compared to bare silver dissolution where K2 >> K1 that occurs at low pHs. In this case one has
k2
K Si
k' K1 Si k 'coxp i k1 k1coxp i K 2 k moxi q k2 H '
(31) k 'm oxi
In this case, Eq.(27) becomes S k H t mAg k ' Si coxp i k1t ' k ' moxi 1 e i 2 q
(32)
16
q
As indicated by Eq. (31), the k2 H constant characterizing dissolution rate of the silver oxide layer can be experimentally determined from the dependence valid for shorter times:
m ln 1 ' Ag k mox i q kox Si k2 H t
(33)
q
where kox Si k2 H is the rate constant of silver oxide dissolution. On the other hand, for longer times where kox t >> 1, Eq. (32) simplifies to the linear form mAg k 'moxi k ' Si coxp i k1t k 'moxi kbt
(34)
where kb = k ' Si coxp i k1 is the rate constant of bare silver dissolution. One can notice from Eq.(34) that in this case the overall dissolution rate is governed by the bare silver ion dissolution rate that is independent of pH. This implies that for higher pHs the bare silver dissolution rate may become larger than the oxide layer dissolution rate that significantly decreases with pH (see Eq.(28)). In this case, where k1coxp i k2 Γox S the expressions for the K, K1 and K2 constants simplify to
K k ' Si coxp i k1 / moxi kb / k ' moxi q
K1 k ' moxi Si k2 H k 'moxi kox
(35)
2
k 'm S k H q oxi i 2 k 'm K2 oxi Si ki coxp i
2
kox kb
2
where moxi Si Γox Given the fact that the q exponent is positive and larger than unity, one can deduce form Eq.(35) and Eq.(27) that both the bare and silver oxide dissolution kinetics vanishes for higher pHs. In the former case this effect is due to the presence of the oxide layer whose 17
dissolution rate becomes very low at higher pHs. Therefore, it remains at the particles’ surfaces blocking the bare silver contact with oxygen. It should also be mentioned that the above derived expressions for the single particle dissolution kinetics can be converted to more convenient forms by introducing the experimentally accessible bulk silver ion concentration c
Ag
that is connected with mAg
through the linear dependence:
cAg
cs m msi Ag
(36)
By considering this, Eq.(32), valid for low pHs, assumes the form cAg cs k b' t m 1 e koxt
where k b'
6k 'coxp i k1 ds s
, m k'
(37)
moxi msi
is the normalized mass of the oxidized silver.
On the other hand, for high pHs one obtains the following expression cAg cs k1' t m ' 1 e koxt
where k1' m kox , m' m k ' moxi (
(38)
kox 2 ) kb
3.2.Experimental results 3.2.1. Physicochemical properties of silver nanoparticles
The
silver
nanoparticles
were
synthesized
using
sodium
borohydride
as
a reducing agent of silver ions, and trisodium citrate as a stabilizing agent. Among various chemical reagents applied during the preparation of silver suspensions, this combinations of reagents is the most popular [1] and equally often used in the studies of nanoparticle dissolution [12,13,28]. Sodium borohydride belongs to strong reducing compounds [1], therefore it was assumed that thanks to their excess in the reaction mixture, the reduction proceeds with 100% yield. However, herein it was revealed that after 60 min of the addition of sodium borohydride, the concentration of silver ions in the reaction mixture amounted to 18
178 µg L-1. Thus, in order to remove the unreacted silver ions and other chemical residues, the ultrafiltration method was used. Afterwards, the weight concentration of nanoparticles in the purified suspension was determined using the aforementioned techniques. It was found that the concentration of stock solution amounted to 71.8 mg L -1. The optical properties of silver nanoparticles were determined with the use UV-vis spectroscopy. As can be seen in Fig. 2, the silver suspension of concentration 20 mg L-1 and pH 6.2, shows a single visible excitation band at the wavelength of 390 nm, which is related to the plasmon resonance of spherical nanoparticles [1]. Observed plasmon band is narrow and symmetric which indicates that the sample does not contain agglomerated particles. Additionally, one can notice that the position of the band does not change with the decrease of pH to the value of 3.5 although the absorbance decreases from 2.874 to 2.458. On the basis of this fact, one can indicate that the silver nanoparticles under acidic conditions are unstable. It is worth mentioning that the changes in absorbance and integrated area of absorption peak were used by Zook et al. in order to determine kinetics of silver nanoparticle dissolution [24].
3.5
3.0
2.5
A
2.0
1.5
1.0
0.5
0.0 300
400
500
600
700
[nm]
Fig. 2. The extinction spectra of silver nanoparticle suspension for concentration of 20 mg L -1 recorded for pH: (___) 6.2 and (___) 3.5. The peak of the spectrum maximum extinction occurs at λ= 390 nm. The micrographs from TEM and AFM images allowed to determine the morphology and size distribution of nanoparticles. As can be seen in Fig.3, the nanoparticles exhibit quasispherical shape and quite narrow size distribution. The average size (diameter) of nanoparticles, determined from TEM micrographs, equaled 12±4 nm. As can be noticed in 19
Fig. 3b, this value remains in compliance with the results obtained from AFM analysis. The additional measurements carried out with the use of DLS, showed that the hydrodynamic diameter of nanoparticles amounted to 14 ± 5 nm in the case of pH 6.2 and 16 ±7 nm for pH 3.5. This data also remains in a good agreement with the results received from the microscopic analysis.
a)
b)
c) 160 140
TEM AFM
120
Count
100 80 60 40 20 0 0
10
20
30
40
50
d [nm]
Fig. 3. a) TEM micrograph, b) AFM image (2µm x2µm ) and c) size distribution of silver nanoparticles.
20
Taking into account that the changes in the physicochemical properties of silver nanoparticles have an essential significance for the description of mechanisms of their oxidative dissolution [29], parallel to the release experiments, the stability of nanoparticles were determined using electrophoretic mobility measurements. Knowing the size of nanoparticles and values of electrophoretic mobility, the zeta potential of nanoparticles, which is much more representative parameter, was calculated using Henry’s model [31,32]. The dependence of nanoparticle zeta potential on time for pH 3.5 and 6.2 was presented on Fig. 4. As can be seen, the nanoparticles were negatively charged for both tested pH values. At pH 3.5 the initial value of zeta potential equaled -67 mV. The increase of nanoparticle zeta potential to the value of -58 mV at pH 3.5 is caused by the increase of ionic strength due to the addition of nitric acid. Interestingly, at pH 6.2 the zeta potential of nanoparticles remained at a constant value over the entire range of tested time. Otherwise, at pH 3.5 one can observe a significant increase of the zeta potential to the value of -48 mV and then its stabilization at this level.
Fig. 4. Dependence of zeta potential of silver nanoparticles on time determined for the suspension concentration of 30 mg L -1 at T=298 K. The solid lines represent nonlinear fits of experimental data.
3.2.2. Kinetics of silver particle dissolution
In Fig. 5 the short-term silver nanoparticle dissolution kinetics, measured for three various bulk suspension concentrations equal to 30, 10 and 5 mg L-1 at pH 3.5, is shown. 21
As can be seen, the kinetics is fast and quasi-linear for the time below 5000 seconds (about 1.4 hours) and monotonically increases with the bulk suspension concentration. Afterwards, for longer times, the kinetic considerably slows down, hence the maximum amount of the dissolved silver (that is equal to the silver ion appearing in the solution) is only 6-8% of the initial concentration after the time of 20.000 seconds (ca. 5.5 hours). This behavior qualitatively confirms the above formulated hypothesis about a fast dissolution of the oxide layer compared to a slow oxidation of the bare silver. It should be mentioned that analogous kinetic runs were previously observed by Maurer –Jones et al. [27] Pertyazhko et al. [29], Liu et al. [12,13], Zhang et al. [22] and Mittelman et al. [28]. In the latter references, the experimental data were fitted by a one–step, first order dissolution model yielding an exponential function for describing the dissolution kinetics. However, it was observed that for longer times this model evidently failed (Pertyazhko et al. [29], Mittelman et al. [28]) because the amount of dissolved silver increased linearly with time instead of attaining a constant value as implied by the exponential function.
3.0
2.5
1
-1
c Ag+ [mg L ]
2.0
1.5 2 1.0 3 0.5
0.0 0
5000
10000
15000
20000
t [s]
Fig. 5. The shorter time kinetics of silver nanoparticles dissolution determined for three various suspension concentrations: 1. (●) 30 mg L-1 , 2. (○) 10 mg L-1, and 3. (▄) 5 mg L-1, at a constant pH 3.5 and temperature 298 K. The initial concentration of dissolved oxygen was 7.8 mg L-1. Three solid lines 1-3 show the theoretical results calculated from Eq.(37). This confirms that the theoretical model developed in this work, predicting a two-stage kinetics characterized by the constants kox
and kb
can be more appropriate for the
interpretation of experimental data. It should be mentioned that in order to apply this model
22
one also needs the m parameter representing the amount of the oxidized silver to the initial silver particle mass. This parameter can be quite precisely estimated by postulating that the silver oxide layer is solely formed in the reaction with surface exposed silver atoms forming
a shell of the thickness da. Consequently, m can be calculated from the formula
m
mAg msi
msi mc msi
3d 3d 2 d 3
(39)
where mc is the mass of the core part of the unoxidized silver particle and d
da . ds
By knowing m one can calculate the coverage of the oxide
Γ ox
s ds m 6k '
(40)
As can be noticed form Eq.(39), for a constant da, the m parameter systematically decreases with the particle size that confirms a faster dissolution rate for smaller particles in accordance to what has been observed in the literature [13,22,29]. By assuming that da is equal to the distance between two crystallographic planes in the elementary cell of silver
metal (cubic face centered), i.e., 0.29 nm [33] one obtains m = 0.072 (7.2%) for the silver particle size of 12 nm used in our work. This fairly well agrees with experimental observations (see Fig. 5). Analogously, for particles of the size 4.8 nm studied in the work of
Liu et al. [12], one obtains m = 0.17 (17%). By using this value, the kinetic runs shown in Fig. 5 were fitted by the two stage model expressed by Eq.(37), depicted by solid lines in Fig. 5. In this way the optimum values of the kox and kb' constants were obtained that were equal to 2.5∙10-4 and 3.2∙10-7 s-1, respectively. It should be mentioned that the influence of the kb' constant is rather minor for this range of dissolution times, therefore, the kox constant, which has not been explicitly determined in the literature, is obtained with a relative precision of ±7%.
23
If kox is known one can calculate the k2 constant pertinent to the oxide layer dissolution kinetic from the dependence
k2
kox Si H
(41)
q
For q = 2 one has k2 = 5.5∙1014 (cm2 s mol2)-1. Additionally, by using kox one can calculate the normalized dissolution flux of the silver ions jAg, a parameter of essential significance, that is given by the expression
jAg
s ds m kox 6
(42)
For kox = 2.5x10-4 s-1, m =0.07 one has jAg = 3.7∙10-11 g cm-2 s-1 . It should be noted that this parameter is independent of the coverage of the silver oxide layer, the concentration of the suspension and the particle size. However, it is dependent on pH as implied by Eq.(41). Although jAg has not been given before in the literature one can calculate this parameter from the silver foil dissolution kinetic measurements presented by Liu et al. [13]. These experiments were performed in acetic acid solution at pH 4, similar to our conditions. In Liu et al. experiments the geometrical surface are of the foil Sf was equal to 0.16 cm2 and the volume of the cell vc was equal to 2 cm3. After the time of 12 hours the concentration of silver ions in the suspension (mAg) was ca. 7.5∙10-4 g. Hence, the silver ion calculated from the equation
j Ag
mAg
(43)
S f vct
was equal to 2.2∙10-11 g cm-2 s-1 . Given a significant experimental error for the short time dissolution kinetics and the difference in pH (that is expected to decrease the dissolution rate), the agreement with our results is satisfactory. This fact is significant confirming that the silver dissolution processes are surface reaction controlled as assumed above. This can be quantitatively proven by considering that the bulk transport controlled regime the dissolution flux from silver nanoparticles should be 24
j Ag kc s
where kc
2 Ds s ds
(44)
2 Ds is the mass transfer rate constant pertinent to spherical particles [36]. Taking ds
Ds = 1.65∙10-5 cm2 s-1 as before one obtains from Eq.(44), jAg =2.9∙102 g cm-2 s-1 . Thus, the
ratio of the experimental to the bulk transport fluxes kc is equal to 1.1∙10-13. As can be noticed the real silver ion flux (dissolution rate) is almost 13 orders of magnitude smaller than the bulk controlled flux that unequivocally confirms the surface reaction controlled regime. This finding has an essential practical significance indicating that kox and jAg
are universal
quantities valid for arbitrary particle size and shape, oxide layer coverage as well as transport regime, either diffusion or flow (mixing). Additionally by knowing the flux ratio one can calculate the activation energy (barrier height) b for the dissolution of the oxide layer from the formula [33] 1
2 b k c b e kT kT
(45)
This can be iteratively solved yielding an approximate expression for b 1 ln k c ln k c ln kT 2
(46)
By using the above flux ration one obtains b = 30 kT that corresponds to 75 kJ mol-1 at the temperature of 298 K. It should be mentioned that a similar value of 77 kJ mol-1 was experimentally obtained by Liu and Hurt [12] for the dissolution of 4.8 nm silver particles.
25
6 1 5
-1
c Ag+ [mg L ]
4
3
2
2
1
0 0
105
2x105
3x105
4x105
5x105
t [s]
Fig. 6. Long-time kinetics of silver particle dissolution. Initial suspension concentration 30 mg L-1, T = 298 K, pH 3.5 (upper curve (1)) and 6.2 (lower curve (2)). The concentration of dissolved oxygen was 7.4 mg L-1 for pH 3.5 and 7.8 mg L-1 for pH 6.2. The solid lines show the theoretical results calculated from Eq. (38). In an analogous way, the silver dissolution flux under the stationary dissolution regime governed by the kb' constant can be calculated. However, in order to increase the precision of the kb' determination, long-time dissolution kinetic runs were carried out, shown in Fig. 6. It can be seen that the experimental data are in agreement with the theoretical results derived from Eq.(37) by assuming a two stage dissolution model (depicted by the solid line 1 in Fig. 6). The best fit value of the kb' constant was equal to 3.2 ± 0.2∙10-7 s-1 that is close to the previous value derived from the shorter time dissolution kinetics. It should be noted that kb' is
independent of m , bulk suspension concentration and kox that makes its determination quite reliable. Hence, the k1 rate constant pertinent to the bare silver oxidation can be calculated from the dependence
kb' k1 Si k 'coxp i
(47)
26
By considering that in our case coxi = 7.8 mg L-1 = 2.4∙10-4 mol L-1, k ' = 13.5 and assuming 1 6 2 1/2 -1 p one obtains from Eq.(47) k1 = 1.1∙10 (cm s mol ) . 2
Analogously as before, by using kb' one can calculate the normalized dissolution flux under the stationary regime from the formula
j Ag
s ds ' kb 6
(48)
It was equal to 6.7∙10-13 g cm-2 s-1 that is 47 times smaller than the silver ion flux stemming from oxide dissolution, which means that also in this case the silver dissolution rate is solely surface reaction controlled. It should be observed, however, that contrary to silver oxide dissolution flux, the stationary flux depends on the dissolved oxygen concentration. By using the above value of the flux one can calculate from Eq.(46) that the activation energy for the stationary dissolution is equal to 34 kT that corresponds to 82 kJ mol-1 at the temperature of 298 K. It is interesting to mention that such two stage kinetics of silver nanoparticle dissolution was also observed in the work of Mittelman at al. [28] (for the experimental conditions pH 4, particle size 11 nm, bulk particle concentration 3 mg L-1). The long time (10-50 hours) experimental data acquired for the oxygen concentration of 9 mg L-1 are well fitted by an linear dependence having the slope of 6.5∙10-7 mg (s L) -1. This gives kb' = 1.9 ∙10-7 s-1 (corrected for the oxygen concentration). Consequently, the silver ion flux is equal to 3.9∙10-13 g cm-2 s-1. This value is close to our value if one considers the experimental error and the difference in pH that is expected to decrease the dissolution rate. Another factor that should be considered in the long time dissolution runs, where the amount of the dissolver silver exceeds 10% of the initial mass, is the decrease in the surface area of the particles that slows down the kinetics. This effect is quantitatively considered in our theoretical model via Eq.(16) whose solution is only possible by numerical methods and is not discussed in this work. One can estimate that the reduction in the dissolution rate is of 1
mAg mAg 3 20% . Another factors that can decrease the longthe order , i.e., ca. 6% for ms ms
27
time dissolution kinetics are the depletion of oxygen concentration in the suspension and the aggregation of nanoparticles that was reported in a few works [12,22,29] It is also interesting to mention that the increase in pH significantly decreases the dissolution rate of nanoparticles that is in accordance with theoretical predictions derived from Eq.(35), see curve 2 in Fig. 6. Even at the dissolution time of 5 days, the amount of dissolved silver nanoparticles is only 1.5% of their initial mass. This result, which agrees with previous data reported in the literature [12,27-29], has practical implication confirming that silver nanoparticle deposition processes aimed at obtaining high density monolayers within the time period of a few hours [38] are not influenced by the dissolution effects.
4. Conclusions The general model of an oxidative dissolution of silver particle suspensions developed in this work enables a quantitative analysis of experimental kinetic data obtained under various physicochemical conditions. The main finding derived from the model is that the overall silver ion release process is surface reaction controlled. This has an important implication showing that the kinetic parameters obtained for silver particle suspensions can be directly transferred to particle monolayers and solid silver dissolution runs. Because of its flexibility, the model adequately reflects the main features of the experimental results, especially the significant increase in the dissolution rate for lower pH. Also, the experimentally observed two kinetic regimes differing in time scale by orders of magnitude are in agreement with theoretical predictions confirming the essential role of the oxide layer present at silver particles. Hence, at lower pHs, the silver ion release mechanism consist in rapid dissolution of oxide layer with the oxidation of bare silver being much slower. This results in the decrease in the oxide coverage that attains a stationary state independent of the initial coverage. The kinetic measurements performed in this work for citrate stabilized silver nanoparticles interpreted in terms of this model allowed one to determine the kinetic rate constant for the silver oxide and for the stationary dissolution (referred to as bare silver dissolution) regimes. By using these constants, the silver ion flux was acquired equal to 3.1x10-11 and 6.7x10-13 g cm-2 s-1 for the silver oxide and bare dissolution regimes, respectively (at pH 3.5). These values are agree with the literature data characterized by a relatively large spread. Given the fact that the limiting flux for the particle suspension dissolution is known from the theory, the activation energy of this process can be calculated by using the experimental flux 28
data. It was shown that that the activation energy is equal to 75 and 82 kJ mol-1 for the oxide and the stationary dissolution, respectively.
ACKNOWLEDGMENTS This work was financially supported by the Research Grant: POIG 01.01.02-12-028/ 09-00. FAAS measurements were carried out with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/0)
Literature. [1] T.M. Tolaymat, A.M.E. Badawy, A. Genaidy, K. G. Scheckel, T. P. Luxton, M. Suidan, Sci. Total. Environ. 408 (2010) 999-1006. [2] A. Ravindran, P. Chandran, S. Sudheer Khan, Colloid. Surf. B. Biointerfaces 105 (2013) 342-352. [3] B. Le Ouay, F. Stellacci, Nanotoday 10 (2015) 339-354. [4] M.J. Kasprowicz, M. Kozioł, A. Groczyca, Can. J. Microbiol. 56 (2010) 247-253. [5] D. Baram-Pinto, S. Shukla, N. Perkas, A. Gedanken, R. Sarid, Bioconjugate. Chem. 20 (2009) 1497-1502. [6] A. Turner, D. Brice, M. T. Brown, Ecotoxicology 21 (2012) 148-154. [7] J. Fabrega, S. N. Luooma, Ch. R. Tyler, T.S. Galloway, J.R. Lead, Environ. Int. 37 (2011) 517-531. [8] R.G. Haverkamp, A.T. Marshall, J. Nanopart. Res. 11 (2009) 1453-1463. [9] R. de Lima, A.B. Seabra, N. Durán, J. Appl. Toxicol. 32 (2012) 867-879. [10] A. Barbasz, Oćwieja, J. Barbasz, Appl. Biochem. Biotech. 176 (2015) 817-834. [11] S. Kittler, C. Greulich, J. Diendorf, M. Kőller, M. Epple, Chem. Mater. 22 (2010) 4548-4554. [12] J. Liu, R.H. Hurt, Environ. Sci. Technol. 44 (2010) 2169-2175. [13] J. Liu, D.A. Sonshine, S. Shervani, R.H. Hurt, ACS Nano 4 (2010) 6903-6913. [14] C. Levard, E. Matt Hotze, G. V. Lowry, G.E. Brown, Environ. Sci. Technol. 46 (2012) 6900-6814. [15] J. Dobias, R. Bernier-Latmani, Environ Sci. Technol. 47 (2012) 4140-4146. [16] C. Greulich, D. Braun, A. Peetsch, J. Diendorf, B. Siebers, M. Epple, M. Köller, RCS Advances 2 (2012) 6981-6987. [17] C. Marambio-Jones, E. M. Hoek, J. Nanopart,. Res. 12 (2010) 1531-1551.
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[18] Z-M. Xiu, Q. Zhang, H.L. Puppala, V.L. Colvin, P.J.J. Alvarez, Nano Lett. 12 (2012) 4271−4275. [19] C-N. Lok, C-M. Ho, R. Chen, Q-Y. He, W-Y. Yu, H. Sun, P. K-H., Tam, J-F. Chiu, CM. Che, J. Biol. Inorg. Chem. 12 (2007) 527-534. [20] T. Pal, T.K Sau, N.R. Jana, Langmuir 13 (1997) 1481-1485. [21] C-M. Ho, S.K-W. Yau, C-N. Lok, M-H. So, C-M. Che, Chem. Asian J. 5 (2010) 285-293. [22] W. Zhang, Y. Yao, N. Sullivan, Y. Chen, Environ. Sci. Technol. 45 (2011) 4422-4428. [23] G.A. Sotiriou, A. Meyer, T.N. Knijnenburg, S. Panke, S.E. Pratsinis, Langmuir 28 (2012) 15929-15936. [24] J.M. Zook, E.S. Long, D. Cleveland, C.L.A. Geronimo, R.I. MacCuspie, Anal. Bioanal. Chem. 401 (2011) 1993-2002. [25] X. Li, J.J. Lenhart, H.W. Walker, Langmuir 28 (2012) 1095-1104. [26] R. Ma, C. Levard, S.M. Marinakos, Y. Cheng, J. Liu, F.M. Michel, G.E. Brown, G.V. Lowry, Environ. Sci. Technol. 46 (2012) 752-759. [27] M.A. Maurer-Jones, M. P.S. Mousavi, L.D. Chen, P. Bühlmann, Ch.L. Haynes, Chem. Sci. 4 (2013) 2564-2572. [28] A.M. Mittelman, A. Taghavt, Y. Wang, L.M. Abriola, K.D. Pennell, J. Nanopart. Res. 15 (2013) 1765. [29] T.S. Peretyazhko, Q. Zang, V.L. Colvin, Environ. Sci. Technol. 48 (2013) 11954-11961. [30] R.D. Kent, J. Vikesland, Environ. Sci. Technol. 46 (2012) 6977-6984. [31] M. Oćwieja, Z. Adamczyk, M. Morga, A. Michna, J. Colloid. Interface. Sci. 364 (2011) 39-48. [32] M. Oćwieja, Z. Adamczyk, K. Kubiak, J. Colloid. Interface. Sci. 76 (2012) 1-11. [33] K.A. Gschneidner, O.D. McMasters, D.G. Alexander, R.F. Venteicher, Metall. Trans. 1 (1970) 1961-1971. [34] Z. Adamczyk, J. Petlicki, J. Colloid. Interface. Sci.118 (1987) 20-49. [35] von Smoluchowski, M. Bull. Acad. Sci. Cracovie, Classe Sci. Math. Natur. 1 (1903) 182. [36] Z. Adamczyk, Particles at Interfaces: Interactions, Deposition, Structure. First ed., Elsevier, Academic Press, Amsterdam, 2006. [37] E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems. Third ed., Cambridge University Press, 2009. [38] M. Oćwieja, Z. Adamczyk, M. Morga, K. Kubiak, Adv. Colloid Interface Sci. 222 (2015) 530-563.
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S0021-9797(15)30435-5 http://dx.doi.org/10.1016/j.jcis.2015.12.051 YJCIS 20976
To appear in:
Journal of Colloid and Interface Science
Received Date: Accepted Date:
23 November 2015 27 December 2015
Please cite this article as: Z. Adamczyk, M. Oćwieja, H. Mrowiec, S. Walas, D. Lupa, Oxidative dissolution of silver nanoparticles: A new theoretical approach, Journal of Colloid and Interface Science (2015), doi: http://dx.doi.org/ 10.1016/j.jcis.2015.12.051
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Oxidative dissolution of silver nanoparticles: a new theoretical approach
Zbigniew Adamczyk1*, Magdalena Oćwieja1, Halina Mrowiec2, Stanisław Walas2, Dawid Lupa1 ([email protected], [email protected], [email protected], [email protected]) 1
Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, 30-239 Cracow, Poland 2
Jagiellonian University, Faculty of Chemistry, Ingardena 3, 30-060 Cracow, Poland
*Corresponding author Zbigniew Adamczyk Jerzy Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences Niezapominajek 8 30-239 Cracow, Poland phone: +48126395104 fax: +48124251923 e-mail: [email protected]
1
Graphical abstract
2
Abstract A general model of an oxidative dissolution of silver particle suspensions was developed that rigorously considers the bulk and surface solute transport. A two-step surface reaction scheme was considered that comprises the formation of the silver oxide phase by direct oxidation and the acidic dissolution of this phase leading to silver ion release. By considering this, a complete set of equations is formulated describing oxygen and silver ion transport to and from particles’ surfaces. These equations are solved in some limiting cases pertinent to nanoparticle dissolution in dilute suspensions. The obtained kinetic equations were used for the interpretation of experimental data pertinent to the dissolution kinetics of citrate-stabilized silver nanoparticles. In these kinetic measurements the role of pH and bulk suspension concentration was quantitatively evaluated by using the atomic absorption spectrometry (AAS). It was shown that the theoretical model adequately reflects the main features of the experimental results, especially the significant increase in the dissolution rate for lower pH. Also the presence of two kinetic regimes was quantitatively explained in terms of the decrease in the coverage of the fast dissolving oxide layer. The overall silver dissolution rate constants pertinent to these two regimes were determined. Keywords kinetics of silver nanoparticle dissolution; oxidative dissolution of silver nanoparticles; silver nanoparticle dissolution; silver ion release; theoretical model of silver nanoparticle dissolution. Highlights
A general model describing oxidative dissolution of silver nanoparticles was developed. Kinetics of silver ion release from nanoparticle suspensions was quantitatively determined. Two stage kinetics of silver nanoparticle dissolution was confirmed. The kinetic constants pertinent to both stages were quantitatively evaluated.
3
1. Introduction
Silver nanoparticles are widely applied in science and many branches of the industry [1,2] because of their excellent antibacterial [3], antifungal [4] and antiviraial [5] activities. However, the widespread exploitation of silver nanoparticles may lead to their uncontrolled penetration into the environment, especially into aquatic systems. Indeed, the toxicity of silver nanoparticles to various micro-organisms [6], invertebrates [7], crop plants [8] and even human cells [9,10] was confirmed. As shown in recent works [11-19] this adverse activity of nanoparticles is mainly due to silver ion leaching from their surfaces. Because of major practical significance of this issue, much effort was devoted to experimentally determine mechanisms and kinetics of silver nanoparticle dissolution both in aqueous suspension [11-13, 20-29] and from monolayers deposited on solid substrates [30]. In 2010 Liu et al. published two pioneering works [12,13] devoted to the issues of silver nanoparticle dissolution. It was confirmed that under aerobic conditions the dissolution kinetics of silver nanoparticles depends on pH, temperature and the presence of natural organic matter (NOM). Taking into account the influence of other chemical compounds, especially NOM, on a nanoparticle dissolution, the empirical kinetic law comprising a first order reaction was proposed. It was also shown that for higher nanoparticle concentrations, the nanoparticle dissolution process becomes more complicated due to a possible depletion of oxygen and the chemical reactions which can increase pH [12]. The attention of Zhang and coworkers [22] was focused on the influence of a nanoparticle size on the rate of silver ion release. Their study carried out for three various sizes of citrate-stabilized silver nanoparticles revealed that the dissolution efficiency was increased for smaller particle size amount of leached silver ions decreases when the size of nanoparticles increases. The authors also developed a theoretical model for describing nanoparticle dissolution kinetics based on the hard sphere collision theory and using the Arrhernius equation. The size-controlled dissolution of thiol functionalized methoxyl polyethylene glycol (PEGSH) silver nanoparticles, at neutral and acidic conditions, was studied by Peretyazhko et al. [29]. It was confirmed that the particle dissolution rate depends on their size and pH, which was also observed in other works [11-13,22]. On the other hand, in other publications the attention was focused on the surface coating effect on the kinetics of silver ion release [11, 15,25]. Dobias and Bernier-Latmani [15] compared the dissolution of three types of silver nanoparticles stabilized by common 4
organic capping agents: polyvinylpyrrolidone (PVP), tannic acid and citrate anions. Their studies showed that in the case of two first stabilizing agents, the release on silver ions was more efficient than in the case of citrate-stabilized nanoparticles. The author assumed that citrate ions may act as reducing agents at nanoparticle surface, reducing the oxide layer and decreasing their solubility. On the other hand, the contradictory results were obtained by Lenhart group [25]. It was found that the low molecular weight capping agents, such as citrate ions, did not inhibit silver ion release while nanoparticles stabilized by high-molecular weight surfactants were more prone to dissolution. Despite a scatter of these experimental data it is generally recognized that silver particle dissolution only proceeds in solutions containing oxygen or another oxidizing agent and its efficiency significantly increases for lower pHs (mild acidic conditions) [1113,22,28,29]. It is also confirmed that smaller particles of sizes below 10 nm dissolve faster than larger particles and that the dissolution rate is the largest at initial stages [13,22,29]. For longer times the dissolution rate systematically decreases, therefore the maximum dissolved amount usually varies between 5 and 30% [12,13,22,28,29]. It is also shown that the temperature increases dissolution rate although this effect was rather moderate [11,12]. However, contrary to the extensive experimental effort, little attention was devoted to systematize these facts in terms of a comprehensive theoretical approach with the exception of the work of Zhang et al. [2011] where an on-step dissolution model was proposed. The obtained experimental data were rationalized in terms of a single exponential kinetic model by postulating a surface controlled dissolution mechanism of silver nanoparticles. Given the deficit of theoretical approaches the main goal of this work is to develop a general model of an oxidative dissolution of silver particle suspensions that rigorously considers the bulk and surface solute transport steps. In contrast to previous models, a twostep surface reaction scheme is considered. It comprises the formation of the silver oxide phase on the bare silver particle surface by direct oxidation and the second reaction described the acidic dissolution of this phase leading to silver ion release. By considering this, a complete set of equations is formulated describing oxygen and silver ion transport to and from particles’ surfaces. These equations are solved in some limiting cases pertinent to nanoparticle dissolution in dilute suspensions. The obtained kinetic equations are used for the interpretation of experimental data that allows one to quantitatively determine the bare silver oxidation rate constant and the oxide layer dissolution rate constant. It is also shown that the model explains the main features of literature data, especially the nonlinear dissolution
5
kinetics for longer times and the increase in dissolution rate for smaller particles in terms of the presence of the oxide layer.
2. Experimental section 2.1.Materials Silver nitrate, sodium borohydride and trisodium citrate were purchased from Sigma Aldrich. Nitric acid and hydrogen peroxide were supplied from Avantor Performance Materials S.A. (formerly POCH S.A.) and (poly(allylamine hydrochloride) (PAH 70 kDa) was obtained from Polyscience. Mica sheets for the silver nanoparticle deposition were purchased from Continental Trade. All chemical reagents and solvents were commercial products and were applied without further purification. Ultrapure water was obtained using the Milli-Q Elix&Simplicity 185 purification system from Millipore SA Molsheim, France. Citrate-stabilized silver nanoparticles were synthesized according to the previously described method [31] with some modifications. Briefly, a solution containing 0.42 M sodium borohydride and 5.69 mM trisodium citrate was prepared in 1.5 L of deionized water using a mechanical stirring with a constant speed rate of 170 rpm. Afterwards, continuing the stirring, 500 mL of an aqueous solution of silver nitrate (1 mM) was added dropwise (using a peristaltic pump, speed of addition 10 mL min-1) into the reduction mixture. The synthesis was carried out at room temperature (298 K) and the stirring was continued over 1 h. After this period of time, the obtained silver suspension was purified using Amicon Ultrafiltration Cell equipped with a cellulose membrane (NMWL 100kDa). The ultrafiltration was continued until the conductivity of the suspension reached a value of 20 μS cm-1. For calibration of silver determination by flame atomic absorption spectrometry (FAAS) standards were prepared form Ag stock standard solution Certipur®, Merck Darmstadt, Germany.
2.2.Methods 2.2.1. Characterization of silver nanoparticle suspension The weight concentration of silver in the purified suspension was determined precisely using two independent methods. In the first approach [31], the silver nanoparticle concentration was calculated based on the experimentally measured density of suspension and the effluent obtained during the ultrafiltration. These values were determined using a highprecision DMA 5000M densitometer from Anton Paar company according the procedure described previously [31]. In the second procedure, the total silver concentration in the suspension was determined by FAAS Accordingly, 200 µL of the suspension was digested in 6
the mixture of nitric acid, and hydrogen peroxide (30%) according to the procedure of Peretyazhko [29]. The obtained solution was analyzed using Atomic Absorption Spectrometer PinAAcle 900Z from Perkin Elmer company. The size distribution and morphology of silver nanoparticles were determined by transmission electron microscopy (TEM). A drop of silver suspension was placed on a copper grid coated with a carbon film, air dried and imaged with the use of FEI Tecnai G2 microscope [31]. Additionally, the silver nanoparticles deposited on (poly(allylamine hydrochloride)-covered mica sheets [31] were characterized using atomic force microscope (AFM) according to the procedure presented elsewhere [31,32]. This measurements were carried out using the NT-MDT Solver Pro instrument with the SMENA SFC050L scanning head. The imaging was done in semi-contact mode using composite probes possessing a silicon body, polysilicon levers and high resolution silicon tips. The analysis of obtained micrographs and images was done using MultiScan Base software. The stability of silver nanoparticles in the suspension was monitored by UV-vis measurements using UV-1800 spectrometer from Continental Trade. The diffusion coefficients of nanoparticles were measured using dynamic light scattering (DLS) technique using the ZetaSizer NanoZS apparatus. The same instrument was applied in order to determine the electrokinetic properties of nanoparticles. Knowing the electrophoretic mobility and hydrodynamic diameter of nanoparticles, the values of zeta potential were calculated using Henry’s equation [31].
2.2.2 Ion release experiments The experiments of silver ion release from the nanoparticles were conducted immediately after the purification and the determination of silver weight concentration in the suspension. Then, the stock solution of nanoparticles was diluted with deionized water of a controlled temperature (298 K) to a desired initial concentration (5 mg L -1, 10 mg L-1 and 30 mg L-1). In the additional part of experiments, the natural pH of the samples (usually 6.2) was adjusted to pH 3.5 using nitric acid. The dissolved oxygen (DO) concentration in the prepared solutions was determined using the oxygen probe COG-1t connected with the oxygen meter CPO-505 obtained from Elmetron company. Afterwards, the silver suspension of controlled properties (pH, DO, silver concentration, temperature) was divided onto the samples of an initial volume of 10 mL. Each sample was used for the determination of silver ion concentration released after a given period of time. Indeed, for a given periods of time, the silver ion determination was repeated twice. The ultrafiltration method was applied in order to 7
separate silver ions from the nanoparticles. The separation was carried out using Amicon Ultrafiltration Cell (Model 8010) equipped with a cellulose membrane (NMWL 30 kDa, Merck Millipore). The clear effluents were tested using UV-vis measurements and DLS techniques. The absence of plasmon resonance optical absorption peak at a wavelength 396 nm and the lack of nanoparticles detectable for DLS technique, confirmed that the method of separation was optimized correctly. The effluents contained only leached silver ions were fixed using nitric acid ( 2% v/v). They were stored in polypropylene tubes at the temperature of 277 K. The concentration of leached silver ions was determined by flame atomic absorption spectrometry. The concentration of released silver ions for a given period of time was determined from the three independent measurements.
3. Results and discussion
3.1.The theoretical model In order to quantitatively interpret the experimental results a phenomenological cell model of oxidative dissolution of silver particle suspensions is developed. Accordingly, it is assumed that a particle in the suspension is confined within a spherical cell of the diameter db,, see Fig. 1.
Fig.1. A schematic representation of silver particles with the outer boundary (cell boundary). 8
For spherically shape particles db can be calculated from the relationship 1
3 db 102 d s mx s cs
(1)
where ds is the particle diameter, s is silver particle density, cs is the silver particle concentration in the bulk expressed in mg L -1 (ppm) and mx is the maximum packing (volume fraction) of spheres in 3D is ca. 0.62 [33]. From Eq.(1) one can calculate that for a typical value of cs equal to 10 mg L-1, particle size equal to 10 nm and s = 10.49 g cm-3 one has db = 866 nm. Different transport conditions can be treated by formulating appropriate boundary conditions at the cell's boundary as previously discussed in Ref.[34] where surfactant adsorption/desorption processes at liquid emulsions were studied. For example in the case of unstirred suspension, where the oxygen and ion transport is solely due to diffusion one formulates the symmetry boundary conditions. In this case concentrations of all dissolved species change in time everywhere in the suspension. On the other hand, in the case of a wellstirred suspension, concentrations of all species considered in the mass balance remain uniform within the cell and equal to bulk reference concentrations. It is also useful to estimate the characteristic relaxation times of establishing the stationary transport conditions pertinent to our system. This can be done by considering that relaxation time for the diffusion transport to a spherical interface is given by the simple expression [35,36]:
t1
d s2
(2)
4D
where D is the effective diffusion coefficient of the solute comprising the Brownian motion of the particle. By assuming dp = 10 nm (10-6 cm) and by considering that the oxygen and silver ion diffusion coefficients in water equal to 2.1∙10-5 and 1.65∙10-5 cm2 s-1 , respectively (at T=298 K [37]) one can calculate from Eq.(2) that the relaxation times are equal to 1.2∙10-8 and 1.5∙10-8 s, for oxygen and silver ion, respectively. This demonstrates that the local steady state
9
transport near the silver particle is established very fast compared to typical dissolution experiments times. Analogously, the diffusion relaxation times for oxygen and silver ion transport across ds d r b is given by 2 2
the cell
d t2 t1 b ds 4 Dox db2
2
(3)
By considering Eq.(1) one obtains explicitly 2
3 t2 104 mx s t1 cs
(4)
Accordingly, t2 equals to 8.9∙10-5 and 1.1∙10-4 seconds for cb=10 mg L-1 for the oxygen and silver ion transport, respectively. It should be mentioned that t2 is also a good estimate of the particle dissolution time under bulk transport dominated transport. Given the fact that the typical experimental dissolution times are of the order of 10 6 seconds [11-13,22,29], i.e., by the factor of 1014 larger than t1 one can deduce that the silver dissolution kinetics is surface reaction controlled. It should be mentioned that the assumption of a dominant reaction dissolution regime of silver particles was intuitively accepted in Refs. [12,13,22,28]. However, in contrast to these approaches, where an one-step reaction was considered, in this work we assume a more general scheme where the silver particle dissolution is governed by the two irreversible surface reactions as proposed in Ref. [25,28] 2Ag(s) + ½ O2 → Ag2O(s) Ag2O(s) + 2H+ → 2Ag+ + H2O
(5)
The first reaction describes the formation of the silver oxide phase on the bare silver particle surface and the second reaction described the acidic dissolution of this phase. By assuming irreversibility of these reactions, one can formulate the following kinetic equation characterizing the oxide layer mass balance
10
q dmox S k1cop B k2 H Box mox dt
(6)
where mox is the oxide layer mass, S is the particle surface area, k1 is the oxidation rate constant, c0 is subsurface oxygen concentration, B is the fraction of the available (bare) surface area of the particle, k2 is the dissolution rate constant, H is the hydrogen ion subsurface concentration, Box is the fraction of the available surface of the oxide layer and p, q are exponents characterizing the reaction order. In the general case, the surface mass balance equation, Eq.(7) is coupled with the bulk oxygen diffusion equation in the form: cox D ox 2cox t
(7)
where cox is the oxygen concentration in the suspension, D ox is the effective oxygen diffusion coefficient in the bulk and t is the diffusion time. The boundary and initial conditions for Eq.(3) are cox 0 r
at
r
db 2
(i) symmetry
(8)
cox coxi
at
r
db 2
(ii) well-stirred solution
(9)
cox cox i mox moxi
for at
ds d r b 2 2 t 0 ds r 2
(10)
k cox dmox p 2 Dox S t k c t B ( t ) B m t 10 ox ox dt r 0 k'
(11)
where cox i is the oxygen concentration at the cell’s surface at the distance of d b (see Fig. 1), r is the radial distance from the silver particle center, moxi is the initial mass of the oxide layer
11
q
on silver particles, k 2 k2 k ' H and k '
4M Ag M O2
, MAg , M O2 are the molar masses of silver
and dioxygen, respectively. It should be mentioned that the initial condition, Eq.(10) reflects the fact that the initial mass of the oxide layer can be different in various experiments. This effect, which was not considered in previous approaches, may lead to a significant spread of the short-time dissolution kinetics as observed experimentally [12,13,29]. Analogously, the silver ion bulk diffusion equation has the form : cAg t
D Ag 2cAg
(12)
where c Ag is the silver concentration in the suspension, D Ag is the silver ion diffusion coefficient, with the following boundary and initial conditions:
cAg 0 c Ag r
dmAg dt
0
for
ds d r b, 2 2
t 0
at
r
db , 2
t 0
(13)
k S t 2 Box mox t 0 k'
(14)
c D Ag Ag r
where mAg is the dissolved silver mass. Eqs.(6-14) represent a complete boundary value problem that describes silver particle dissolution kinetics governed by both surface reaction and bulk transport. However, it should be mentioned that by formulating these equation one tacitly assumes that the hydrogen ion concentration (pH value) in the suspension remains constant during the dissolution process. Due to non-linear character of Eqs.(6-14) their solution in the general case is only feasible by using numerical methods. However, as above estimated, in the case of silver nanoparticle suspensions appearing in practice the relaxation time of establishing quasistationary transport conditions is very short compared to the overall dissolution times. Therefore, the oxygen and silver ion concentrations in the cell are uniform at all times. This implies that:
12
cAg t
coxi k '
mAg
for
v1
mAg v1
coxi
ds d r b , t 0 2 2
mox (t ) v1
(15)
where v1 is the cell’s volume. Because the diffusion within the cell is very fast, Eqs. (11,14) simplify to: dmox k S t k1c p t B t 2 Box mox t dt k'
dmAg dt
(16)
S t k 2 Box mox t
with the following constrains: cox coxi k 'cAg
case (i) symmetry
cox coxi
case (ii) well –stirred solution
(17)
2
S t k '' msi mAg 3 2
6 3 3 where k '' and msi = msi d s is the initial mass of the silver particle. 6 s The initial conditions for Eq.(16) are cox coxi ms msi t 0 mAg 0 mox moxi
(18)
By assuming that all the silver oxide is available for hydrogen ions, i.e., Box = 1 and by assuming that the one can express the available surface function for the bare silver is given in the Langmuir model expressed as 13
B mox 1
mox (t ) Γ ox (t ) S (t )
(19)
where, Γ ox is the coverage (2D density) of the Ag2O layer, one can transform Eq. (16) to the form dmox m k p ox 2 S k1co 1 mox dt Γ S ox k'
dmAg dt
S k2 mox
(20)
with the initial conditions:
mAg 0 ms msi t 0 mox moxi 2 S Si k '' msi 3
cox coxi
cox coxi k 'c Ag cox coxi
(21)
(i ) t 0 (ii )
Eqs.(20-21) represent a general initial value problem that exactly describes the dissolution kinetics of silver particles for arbitrary time scale. However, since these equation are coupled and non-linear their solution is only feasible by using numerical methods. Interesting analytical solutions can be derived for shorter times where the size of the particles and their surface area do not change appreciably, if mAg msi . Consequently 2
S Si k '' mAg 3 Si ,
cox coxi k 'mAg coxi
(22)
In this case, the equation system, Eq.(20) becomes decoupled and can be integrated to the form 14
mox
moxi
dX k cp k 1 oxi p 2 k1coxi X Γ ox Si k '
Si t
(23)
where X is the dummy variable After evaluating the definite integral, Eq. (23) yields the following expression
mox m m moxi e Kt
(24)
where
k1coxp i
Γ ox Si
k' Γ ox
K
m
k2
(25)
k1coxp i Γ ox Si
k1coxp i
k2
Γ ox S i
k'
Thus, the expression for the silver ion mass becomes
mAg Si k 2 mt Si k 2 moxi m
1 e Kt K
(26)
Eq. (26) can be converted to a simpler form
mAg K1t K 2 1 e Kt
(27)
where
K1 Si k 2
k1coxp i Γ ox Si
kc p 1 oxi
k2
Γ ox Si
k'
15
k1coxp i Γ ox Si K 2 Si k 2 moxi k k1coxp i 2 Γ ox Si k'
Γ ox p k2 kc Γ S 1 oxi ox i k'
(28)
Because the k 2 constants depends on the hydrogen ion concentration (pH) one can predict from Eq.(27-28) that the silver particle dissolution kinetics is a complex and nonlinear function of pH. Eqs.(26-28) can be used for the interpretation of the dissolution kinetics of silver particles for shorter times where the particle mass change remain not too significant. In this way, the oxide layer and bare silver dissolution kinetic constants can be determined. From Eq. (27) one can derive various asymptotic solutions: short times, where t
(i)
1 K
mAg K1 KK 2 t
longer times t
(ii)
(29)
1 K
mAg K1t (iii)
(30)
fast oxide layer dissolution rate compared to bare silver dissolution where K2 >> K1 that occurs at low pHs. In this case one has
k2
K Si
k' K1 Si k 'coxp i k1 k1coxp i K 2 k moxi q k2 H '
(31) k 'm oxi
In this case, Eq.(27) becomes S k H t mAg k ' Si coxp i k1t ' k ' moxi 1 e i 2 q
(32)
16
q
As indicated by Eq. (31), the k2 H constant characterizing dissolution rate of the silver oxide layer can be experimentally determined from the dependence valid for shorter times:
m ln 1 ' Ag k mox i q kox Si k2 H t
(33)
q
where kox Si k2 H is the rate constant of silver oxide dissolution. On the other hand, for longer times where kox t >> 1, Eq. (32) simplifies to the linear form mAg k 'moxi k ' Si coxp i k1t k 'moxi kbt
(34)
where kb = k ' Si coxp i k1 is the rate constant of bare silver dissolution. One can notice from Eq.(34) that in this case the overall dissolution rate is governed by the bare silver ion dissolution rate that is independent of pH. This implies that for higher pHs the bare silver dissolution rate may become larger than the oxide layer dissolution rate that significantly decreases with pH (see Eq.(28)). In this case, where k1coxp i k2 Γox S the expressions for the K, K1 and K2 constants simplify to
K k ' Si coxp i k1 / moxi kb / k ' moxi q
K1 k ' moxi Si k2 H k 'moxi kox
(35)
2
k 'm S k H q oxi i 2 k 'm K2 oxi Si ki coxp i
2
kox kb
2
where moxi Si Γox Given the fact that the q exponent is positive and larger than unity, one can deduce form Eq.(35) and Eq.(27) that both the bare and silver oxide dissolution kinetics vanishes for higher pHs. In the former case this effect is due to the presence of the oxide layer whose 17
dissolution rate becomes very low at higher pHs. Therefore, it remains at the particles’ surfaces blocking the bare silver contact with oxygen. It should also be mentioned that the above derived expressions for the single particle dissolution kinetics can be converted to more convenient forms by introducing the experimentally accessible bulk silver ion concentration c
Ag
that is connected with mAg
through the linear dependence:
cAg
cs m msi Ag
(36)
By considering this, Eq.(32), valid for low pHs, assumes the form cAg cs k b' t m 1 e koxt
where k b'
6k 'coxp i k1 ds s
, m k'
(37)
moxi msi
is the normalized mass of the oxidized silver.
On the other hand, for high pHs one obtains the following expression cAg cs k1' t m ' 1 e koxt
where k1' m kox , m' m k ' moxi (
(38)
kox 2 ) kb
3.2.Experimental results 3.2.1. Physicochemical properties of silver nanoparticles
The
silver
nanoparticles
were
synthesized
using
sodium
borohydride
as
a reducing agent of silver ions, and trisodium citrate as a stabilizing agent. Among various chemical reagents applied during the preparation of silver suspensions, this combinations of reagents is the most popular [1] and equally often used in the studies of nanoparticle dissolution [12,13,28]. Sodium borohydride belongs to strong reducing compounds [1], therefore it was assumed that thanks to their excess in the reaction mixture, the reduction proceeds with 100% yield. However, herein it was revealed that after 60 min of the addition of sodium borohydride, the concentration of silver ions in the reaction mixture amounted to 18
178 µg L-1. Thus, in order to remove the unreacted silver ions and other chemical residues, the ultrafiltration method was used. Afterwards, the weight concentration of nanoparticles in the purified suspension was determined using the aforementioned techniques. It was found that the concentration of stock solution amounted to 71.8 mg L -1. The optical properties of silver nanoparticles were determined with the use UV-vis spectroscopy. As can be seen in Fig. 2, the silver suspension of concentration 20 mg L-1 and pH 6.2, shows a single visible excitation band at the wavelength of 390 nm, which is related to the plasmon resonance of spherical nanoparticles [1]. Observed plasmon band is narrow and symmetric which indicates that the sample does not contain agglomerated particles. Additionally, one can notice that the position of the band does not change with the decrease of pH to the value of 3.5 although the absorbance decreases from 2.874 to 2.458. On the basis of this fact, one can indicate that the silver nanoparticles under acidic conditions are unstable. It is worth mentioning that the changes in absorbance and integrated area of absorption peak were used by Zook et al. in order to determine kinetics of silver nanoparticle dissolution [24].
3.5
3.0
2.5
A
2.0
1.5
1.0
0.5
0.0 300
400
500
600
700
[nm]
Fig. 2. The extinction spectra of silver nanoparticle suspension for concentration of 20 mg L -1 recorded for pH: (___) 6.2 and (___) 3.5. The peak of the spectrum maximum extinction occurs at λ= 390 nm. The micrographs from TEM and AFM images allowed to determine the morphology and size distribution of nanoparticles. As can be seen in Fig.3, the nanoparticles exhibit quasispherical shape and quite narrow size distribution. The average size (diameter) of nanoparticles, determined from TEM micrographs, equaled 12±4 nm. As can be noticed in 19
Fig. 3b, this value remains in compliance with the results obtained from AFM analysis. The additional measurements carried out with the use of DLS, showed that the hydrodynamic diameter of nanoparticles amounted to 14 ± 5 nm in the case of pH 6.2 and 16 ±7 nm for pH 3.5. This data also remains in a good agreement with the results received from the microscopic analysis.
a)
b)
c) 160 140
TEM AFM
120
Count
100 80 60 40 20 0 0
10
20
30
40
50
d [nm]
Fig. 3. a) TEM micrograph, b) AFM image (2µm x2µm ) and c) size distribution of silver nanoparticles.
20
Taking into account that the changes in the physicochemical properties of silver nanoparticles have an essential significance for the description of mechanisms of their oxidative dissolution [29], parallel to the release experiments, the stability of nanoparticles were determined using electrophoretic mobility measurements. Knowing the size of nanoparticles and values of electrophoretic mobility, the zeta potential of nanoparticles, which is much more representative parameter, was calculated using Henry’s model [31,32]. The dependence of nanoparticle zeta potential on time for pH 3.5 and 6.2 was presented on Fig. 4. As can be seen, the nanoparticles were negatively charged for both tested pH values. At pH 3.5 the initial value of zeta potential equaled -67 mV. The increase of nanoparticle zeta potential to the value of -58 mV at pH 3.5 is caused by the increase of ionic strength due to the addition of nitric acid. Interestingly, at pH 6.2 the zeta potential of nanoparticles remained at a constant value over the entire range of tested time. Otherwise, at pH 3.5 one can observe a significant increase of the zeta potential to the value of -48 mV and then its stabilization at this level.
Fig. 4. Dependence of zeta potential of silver nanoparticles on time determined for the suspension concentration of 30 mg L -1 at T=298 K. The solid lines represent nonlinear fits of experimental data.
3.2.2. Kinetics of silver particle dissolution
In Fig. 5 the short-term silver nanoparticle dissolution kinetics, measured for three various bulk suspension concentrations equal to 30, 10 and 5 mg L-1 at pH 3.5, is shown. 21
As can be seen, the kinetics is fast and quasi-linear for the time below 5000 seconds (about 1.4 hours) and monotonically increases with the bulk suspension concentration. Afterwards, for longer times, the kinetic considerably slows down, hence the maximum amount of the dissolved silver (that is equal to the silver ion appearing in the solution) is only 6-8% of the initial concentration after the time of 20.000 seconds (ca. 5.5 hours). This behavior qualitatively confirms the above formulated hypothesis about a fast dissolution of the oxide layer compared to a slow oxidation of the bare silver. It should be mentioned that analogous kinetic runs were previously observed by Maurer –Jones et al. [27] Pertyazhko et al. [29], Liu et al. [12,13], Zhang et al. [22] and Mittelman et al. [28]. In the latter references, the experimental data were fitted by a one–step, first order dissolution model yielding an exponential function for describing the dissolution kinetics. However, it was observed that for longer times this model evidently failed (Pertyazhko et al. [29], Mittelman et al. [28]) because the amount of dissolved silver increased linearly with time instead of attaining a constant value as implied by the exponential function.
3.0
2.5
1
-1
c Ag+ [mg L ]
2.0
1.5 2 1.0 3 0.5
0.0 0
5000
10000
15000
20000
t [s]
Fig. 5. The shorter time kinetics of silver nanoparticles dissolution determined for three various suspension concentrations: 1. (●) 30 mg L-1 , 2. (○) 10 mg L-1, and 3. (▄) 5 mg L-1, at a constant pH 3.5 and temperature 298 K. The initial concentration of dissolved oxygen was 7.8 mg L-1. Three solid lines 1-3 show the theoretical results calculated from Eq.(37). This confirms that the theoretical model developed in this work, predicting a two-stage kinetics characterized by the constants kox
and kb
can be more appropriate for the
interpretation of experimental data. It should be mentioned that in order to apply this model
22
one also needs the m parameter representing the amount of the oxidized silver to the initial silver particle mass. This parameter can be quite precisely estimated by postulating that the silver oxide layer is solely formed in the reaction with surface exposed silver atoms forming
a shell of the thickness da. Consequently, m can be calculated from the formula
m
mAg msi
msi mc msi
3d 3d 2 d 3
(39)
where mc is the mass of the core part of the unoxidized silver particle and d
da . ds
By knowing m one can calculate the coverage of the oxide
Γ ox
s ds m 6k '
(40)
As can be noticed form Eq.(39), for a constant da, the m parameter systematically decreases with the particle size that confirms a faster dissolution rate for smaller particles in accordance to what has been observed in the literature [13,22,29]. By assuming that da is equal to the distance between two crystallographic planes in the elementary cell of silver
metal (cubic face centered), i.e., 0.29 nm [33] one obtains m = 0.072 (7.2%) for the silver particle size of 12 nm used in our work. This fairly well agrees with experimental observations (see Fig. 5). Analogously, for particles of the size 4.8 nm studied in the work of
Liu et al. [12], one obtains m = 0.17 (17%). By using this value, the kinetic runs shown in Fig. 5 were fitted by the two stage model expressed by Eq.(37), depicted by solid lines in Fig. 5. In this way the optimum values of the kox and kb' constants were obtained that were equal to 2.5∙10-4 and 3.2∙10-7 s-1, respectively. It should be mentioned that the influence of the kb' constant is rather minor for this range of dissolution times, therefore, the kox constant, which has not been explicitly determined in the literature, is obtained with a relative precision of ±7%.
23
If kox is known one can calculate the k2 constant pertinent to the oxide layer dissolution kinetic from the dependence
k2
kox Si H
(41)
q
For q = 2 one has k2 = 5.5∙1014 (cm2 s mol2)-1. Additionally, by using kox one can calculate the normalized dissolution flux of the silver ions jAg, a parameter of essential significance, that is given by the expression
jAg
s ds m kox 6
(42)
For kox = 2.5x10-4 s-1, m =0.07 one has jAg = 3.7∙10-11 g cm-2 s-1 . It should be noted that this parameter is independent of the coverage of the silver oxide layer, the concentration of the suspension and the particle size. However, it is dependent on pH as implied by Eq.(41). Although jAg has not been given before in the literature one can calculate this parameter from the silver foil dissolution kinetic measurements presented by Liu et al. [13]. These experiments were performed in acetic acid solution at pH 4, similar to our conditions. In Liu et al. experiments the geometrical surface are of the foil Sf was equal to 0.16 cm2 and the volume of the cell vc was equal to 2 cm3. After the time of 12 hours the concentration of silver ions in the suspension (mAg) was ca. 7.5∙10-4 g. Hence, the silver ion calculated from the equation
j Ag
mAg
(43)
S f vct
was equal to 2.2∙10-11 g cm-2 s-1 . Given a significant experimental error for the short time dissolution kinetics and the difference in pH (that is expected to decrease the dissolution rate), the agreement with our results is satisfactory. This fact is significant confirming that the silver dissolution processes are surface reaction controlled as assumed above. This can be quantitatively proven by considering that the bulk transport controlled regime the dissolution flux from silver nanoparticles should be 24
j Ag kc s
where kc
2 Ds s ds
(44)
2 Ds is the mass transfer rate constant pertinent to spherical particles [36]. Taking ds
Ds = 1.65∙10-5 cm2 s-1 as before one obtains from Eq.(44), jAg =2.9∙102 g cm-2 s-1 . Thus, the
ratio of the experimental to the bulk transport fluxes kc is equal to 1.1∙10-13. As can be noticed the real silver ion flux (dissolution rate) is almost 13 orders of magnitude smaller than the bulk controlled flux that unequivocally confirms the surface reaction controlled regime. This finding has an essential practical significance indicating that kox and jAg
are universal
quantities valid for arbitrary particle size and shape, oxide layer coverage as well as transport regime, either diffusion or flow (mixing). Additionally by knowing the flux ratio one can calculate the activation energy (barrier height) b for the dissolution of the oxide layer from the formula [33] 1
2 b k c b e kT kT
(45)
This can be iteratively solved yielding an approximate expression for b 1 ln k c ln k c ln kT 2
(46)
By using the above flux ration one obtains b = 30 kT that corresponds to 75 kJ mol-1 at the temperature of 298 K. It should be mentioned that a similar value of 77 kJ mol-1 was experimentally obtained by Liu and Hurt [12] for the dissolution of 4.8 nm silver particles.
25
6 1 5
-1
c Ag+ [mg L ]
4
3
2
2
1
0 0
105
2x105
3x105
4x105
5x105
t [s]
Fig. 6. Long-time kinetics of silver particle dissolution. Initial suspension concentration 30 mg L-1, T = 298 K, pH 3.5 (upper curve (1)) and 6.2 (lower curve (2)). The concentration of dissolved oxygen was 7.4 mg L-1 for pH 3.5 and 7.8 mg L-1 for pH 6.2. The solid lines show the theoretical results calculated from Eq. (38). In an analogous way, the silver dissolution flux under the stationary dissolution regime governed by the kb' constant can be calculated. However, in order to increase the precision of the kb' determination, long-time dissolution kinetic runs were carried out, shown in Fig. 6. It can be seen that the experimental data are in agreement with the theoretical results derived from Eq.(37) by assuming a two stage dissolution model (depicted by the solid line 1 in Fig. 6). The best fit value of the kb' constant was equal to 3.2 ± 0.2∙10-7 s-1 that is close to the previous value derived from the shorter time dissolution kinetics. It should be noted that kb' is
independent of m , bulk suspension concentration and kox that makes its determination quite reliable. Hence, the k1 rate constant pertinent to the bare silver oxidation can be calculated from the dependence
kb' k1 Si k 'coxp i
(47)
26
By considering that in our case coxi = 7.8 mg L-1 = 2.4∙10-4 mol L-1, k ' = 13.5 and assuming 1 6 2 1/2 -1 p one obtains from Eq.(47) k1 = 1.1∙10 (cm s mol ) . 2
Analogously as before, by using kb' one can calculate the normalized dissolution flux under the stationary regime from the formula
j Ag
s ds ' kb 6
(48)
It was equal to 6.7∙10-13 g cm-2 s-1 that is 47 times smaller than the silver ion flux stemming from oxide dissolution, which means that also in this case the silver dissolution rate is solely surface reaction controlled. It should be observed, however, that contrary to silver oxide dissolution flux, the stationary flux depends on the dissolved oxygen concentration. By using the above value of the flux one can calculate from Eq.(46) that the activation energy for the stationary dissolution is equal to 34 kT that corresponds to 82 kJ mol-1 at the temperature of 298 K. It is interesting to mention that such two stage kinetics of silver nanoparticle dissolution was also observed in the work of Mittelman at al. [28] (for the experimental conditions pH 4, particle size 11 nm, bulk particle concentration 3 mg L-1). The long time (10-50 hours) experimental data acquired for the oxygen concentration of 9 mg L-1 are well fitted by an linear dependence having the slope of 6.5∙10-7 mg (s L) -1. This gives kb' = 1.9 ∙10-7 s-1 (corrected for the oxygen concentration). Consequently, the silver ion flux is equal to 3.9∙10-13 g cm-2 s-1. This value is close to our value if one considers the experimental error and the difference in pH that is expected to decrease the dissolution rate. Another factor that should be considered in the long time dissolution runs, where the amount of the dissolver silver exceeds 10% of the initial mass, is the decrease in the surface area of the particles that slows down the kinetics. This effect is quantitatively considered in our theoretical model via Eq.(16) whose solution is only possible by numerical methods and is not discussed in this work. One can estimate that the reduction in the dissolution rate is of 1
mAg mAg 3 20% . Another factors that can decrease the longthe order , i.e., ca. 6% for ms ms
27
time dissolution kinetics are the depletion of oxygen concentration in the suspension and the aggregation of nanoparticles that was reported in a few works [12,22,29] It is also interesting to mention that the increase in pH significantly decreases the dissolution rate of nanoparticles that is in accordance with theoretical predictions derived from Eq.(35), see curve 2 in Fig. 6. Even at the dissolution time of 5 days, the amount of dissolved silver nanoparticles is only 1.5% of their initial mass. This result, which agrees with previous data reported in the literature [12,27-29], has practical implication confirming that silver nanoparticle deposition processes aimed at obtaining high density monolayers within the time period of a few hours [38] are not influenced by the dissolution effects.
4. Conclusions The general model of an oxidative dissolution of silver particle suspensions developed in this work enables a quantitative analysis of experimental kinetic data obtained under various physicochemical conditions. The main finding derived from the model is that the overall silver ion release process is surface reaction controlled. This has an important implication showing that the kinetic parameters obtained for silver particle suspensions can be directly transferred to particle monolayers and solid silver dissolution runs. Because of its flexibility, the model adequately reflects the main features of the experimental results, especially the significant increase in the dissolution rate for lower pH. Also, the experimentally observed two kinetic regimes differing in time scale by orders of magnitude are in agreement with theoretical predictions confirming the essential role of the oxide layer present at silver particles. Hence, at lower pHs, the silver ion release mechanism consist in rapid dissolution of oxide layer with the oxidation of bare silver being much slower. This results in the decrease in the oxide coverage that attains a stationary state independent of the initial coverage. The kinetic measurements performed in this work for citrate stabilized silver nanoparticles interpreted in terms of this model allowed one to determine the kinetic rate constant for the silver oxide and for the stationary dissolution (referred to as bare silver dissolution) regimes. By using these constants, the silver ion flux was acquired equal to 3.1x10-11 and 6.7x10-13 g cm-2 s-1 for the silver oxide and bare dissolution regimes, respectively (at pH 3.5). These values are agree with the literature data characterized by a relatively large spread. Given the fact that the limiting flux for the particle suspension dissolution is known from the theory, the activation energy of this process can be calculated by using the experimental flux 28
data. It was shown that that the activation energy is equal to 75 and 82 kJ mol-1 for the oxide and the stationary dissolution, respectively.
ACKNOWLEDGMENTS This work was financially supported by the Research Grant: POIG 01.01.02-12-028/ 09-00. FAAS measurements were carried out with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/0)
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