Langmuir 2008, 24, 10709-10716
10709
Polysilazane-Induced Aggregation of Hydrophobic Silver Colloids Vadym Bakumov*,†,‡ and Edwin Kroke*,† Institute of Inorganic Chemistry, TU Bergakademie Freiberg, Leipziger Strasse 29, 09596 Freiberg, Germany, and Department of Chemistry, UniVersity of Konstanz, UniVersita¨tstrasse 10, 78462 Konstanz, Germany ReceiVed April 8, 2008. ReVised Manuscript ReceiVed July 9, 2008 Adsorbing polymers such as polysilazanes induce irreversible coagulation of hydrophobic silver colloids in nonpolar solvents. This is accompanied by broadening of the surface plasmon resonance (SPR) peak. A method to analyze the coagulation kinetics based on von Smoluchowski’s theory utilizing the SPR change is described. The approach allows evaluating extinction spectra of aggregates of small sizes. A model for polymer adsorption kinetics in combination with a modified bridging efficiency model explains the observed coagulation inhibition over time in terms of macromolecules adsorption, spreading, and mutual repulsion.
Introduction Composites consisting of nanometer-sized metal particles in solid dielectric matrixes such as polymers and ceramics are of great interest for technical applications and research. Such systems were mostly produced by in situ reduction of metallic species.1,2 Our approach is based on introducing preprepared metal colloids into polymer solutions. The polymer-nanoparticle composites can be cross-linked and pyrolized to obtain glasses and ceramics if suitable polymers such as polysiloxanes and polysilazanes are used.3a,b During the production of antibacterial with nano-crystalline silver particles (nc-Silver) doped silicon carbonitride ceramics via this method, we encountered silver nanoparticle aggregation, which is accompanied by a color change from yellow to dark brown. We experimentally found that mixing in hot diluted solutions can be applied to avoid the agglomeration at low silver nanoparticle concentration.3c In this paper we describe the phenomenon of polysilazane-induced silver colloid aggregation in more detail and develop a model of polymer bridging dynamics which explains the observed dependencies. The model was combined with the new method which utilizes the optical spectra change to follow the aggregation process. It is known that colloids with low surface coverage in the presence of adsorbing polymers can irreversibly flocculate. Such phase instability is in opposition to the generally reversible flocculation driven by so-called depletion forces. The former is caused by polymer bridging, and schematically shown in Figure 1. Depending on the particular system, this effect should be either controlled and enhanced or suppressed. For instance, polymer bridging was used for the preparation of core-shell composites4 and magnetic wires.5 The phenomenon * Correspondence may be addressed to either author. E-mail:
[email protected];
[email protected]. † TU Bergakademie Freiberg. ‡ University of Konstanz. (1) Korroris, M.; Trapalis, C. C.; Kossionides, S.; Vlastou, R.; Nsouli, B.; Groetzschel, R.; Spartalis, S.; Kordas, G.; Paradellis, T. Nucl. Instrum. Methods Phys. Res., Sect. B 2002, 188, 67–72. (2) Compagnini, G.; Fragala, M. E.; D’Urso, L.; Spinella, C.; Puglisi, O. J. Mater. Res. 2001, 16, 2934–2938. (3) (a) Riedel, R.; Mera, G.; Hauser, R.; Klonczynski, A. J. Ceram. Soc. Jpn. 2006, 114, 425–444. (b) Kroke, E.; Li, Y.-L.; Konetschny, C.; Lecomte, E.; Fasel, C.; Riedel, R. Mater. Sci. Eng. R 2000, 26, 97–199. (c) Bakumov, V.; Gueinzius, K.; Hermann, C.; Schwarz, M.; Kroke, E. J. Eur. Ceram. Soc. 2007, 27, 3287– 3292. (4) Chen, T.-Y.; Somasundaran, P. J. Am. Ceram. Soc. 1998, 81, 11140– 11144. (5) Goubault, C.; Leal-Calderon, F.; Viovy, J.-L.; Bibette, J. Langmuir 2005, 21, 3725–3729.
Figure 1. Polymer bridging: adsorption of polymer chains on both particles.
is mostly discussed in the context of papermaking6 and mineral beneficiation,7 where exhaustiveness and selectivity of flocculation are desirable.8,9 To investigate the dynamics of bridging flocculation, various theoretical10-19 and experimental20-23 attempts were undertaken. Most of the experimental work devoted to this phenomenon deals with coarse colloids. It was shown by Swenson et al. by means of small-angle neutron scattering that bridging of well-stabilized particles occurs when the end-to-end polymer distance corresponds or exceeds the interparticle (6) van de Ven, T.G. M. AdV. Colloid Interface Sci. 2005, 114-115, 147–157. (7) Behl, S.; Moudgil, B. M. J. Colloid Interface Sci. 1993, 161, 437–442. (8) Moudgil, B. M.; Shah, B. D.; Soto, H. S. J. Colloid Interface Sci. 1986, 119, 466–473. (9) Behl, S.; Moudgil, B. M.; Prakash, T. S. J. Colloid Interface Sci. 1993, 161, 414–421. (10) Healy, T. V.; La Mer, V. K. J. Phys. Chem. 1962, 66, 1835–1838. (11) Heath, A. R.; Koh, P. T. L. Combined population balance and CFD modelling of particle aggregation by polymeric flocculant. Third International Conference on CFG in the Minerals and Process Industries; CSIRO Publishing: Victoria, Australia, 2003; pp 339-344. (12) Somasundaran, P.; Runkana, V. Chem. Eng. Res. Des. 2005, 83, 905– 914. (13) Peled, C. R.; Braun, G.; Nir, S. J. Colloid Interface Sci. 1995, 169, 204– 213. (14) Hsu, J.-P.; Lin, D.-P. J. Chem. Soc., Faraday Trans. 1991, 87, 3245– 3250. (15) Bennett, A. J. J. Colloid Interface Sci. 1974, 47, 122–127. (16) Olsen, A.; Franks, G.; Biggs, S.; Jameson, G. J. J. Chem. Phys. 2006, 125, 184906. (17) Molski, A. Colloid Polym. Sci. 1989, 267, 371–375. (18) Hogg, R. J. Colloid Interface Sci. 1984, 102, 232–236. (19) Hsu, J.-P.; Lin, D.-P.; Tseng, S. Colloid Polym. Sci. 1995, 273, 271–278. (20) Lu, C.; Pelton, R. Langmuir 2001, 17, 7770–7776. (21) Cohen-Tannoudji, L.; Bertrand, E.; Bressy, L.; Goubault, C.; Baudry, J.; Klein, J.; Joanny, J.-F.; Bibette, J. Phys. ReV. Lett. 2005, 94, 038301. (22) Gregory, J. J. Colloid Interface Sci. 1972, 42, 448–456. (23) Pelssers, E. G. M.; Cohen Stuart, M. A.; Fleer, G. J. J. Chem. Soc., Faraday Trans. 1990, 86, 1355–1361.
10.1021/la801104b CCC: $40.75 2008 American Chemical Society Published on Web 09/12/2008
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distance.24 The latter condition is fulfilled when the volume fraction of colloid particles is high.25 It was shown that scaling down the colloid size decreases the percolation threshold to a few percent.26,27 For less stabilized colloids aggregation takes place in diluted suspensions, and complex mechanisms of adsorption and collision were suggested.20,23,28 Rheological25,29 and electrostatic30 aspects of polymer bridging were investigated and the influence of shear was pointed out.31 Although no model has yet been recognized as universal, most authors argue that for successful bridging the particle surface should be only partially covered with polymer molecules and bear active polymer tails. “Active” tails in this sense are polymer tails above the glass transition that are present in the appropriate conformation, extend into the solution beyond the electrostatic double layer of the particle, and possess at the same time strong affinity to particle surfaces that will compensate for entropy loss and make the tail’s alignment on the surface of the encountering particle possible. Polymer spreading is the most probable process responsible for deactivation. Moreover, the kinetics of conformational changes were also found to correlate with settling rates,32 which supports the above suggestions. Besides the fact that they are of practical interest, polymeradsorbing colloid systems are worth investigating because insight into polymer dynamics and adhesion processes can be gained.21,24 The referred studies are restricted to aqueous systems where poly(ethylene oxide) or ionic polymers were used as flocculants. However, it will be shown below that the phenomenon of polymer flocculation extends beyond the examined systems. The most common technique to investigate coagulation rates measurement is static light scattering.28 However, more sophisticated setups like single-particle optical sizer23,31 and dynamic light scattering33-35 are being increasingly applied. Colorimetric measurements for studying the aggregation of noble metal colloids can also be useful.36 Karpov et al. pointed out the possibility of time-resolved spectral determination of the aggregation degree in diluted silver sols monitoring the increasing area of the longwave wing of the surface plasmon resonance (SPR) peak.37 Here, we use another approach and report on polysilazane-induced aggregation of hydrophobic silver nanoparticles in unpolar solvents and spectrophotometric kinetic measurements of the process.
BakumoV and Kroke silazanes supplied by this company (Mn ∼ 600 g/mol).38 However, Wan et al. determined higher values of ∼3000 g/mol.39 A solution in toluene of this polymer was purified by centrifugation and filtering (0.2 µm). Silver acetate was purchased from ABCR, and octadecyl amine was from Merck. Synthesis Techniques. Silver nanoparticles were synthesized according to a previously described method.40 In a typical procedure 220 mg of silver acetate was dissolved in a solution of 1 g of octadecyl amine in 10 mL of toluene, heated to 111 °C, kept at reflux overnight, and cooled. Subsequently, 50 mL of acetone was added. The flocculated particles were separated by centrifugation at 2000 rpm. Finally, the sediment was redispersed in heptane. The particle diameter derived from the volume size distribution determined by dynamic light scattering was 7-8 nm. The silver colloid is stable at least within days in heptane without polymer addition. Flocculation Tests. For the quantitative study of the aggregation process an aliquot (100-300 µL) of cold (0 °C) silver colloid was added to a previously incubated (0.5 h at 0 °C) heptane solution (1.7-1.9 mL) of purified KiON Ceraset Polysilazane Ultra and vigorously vortexed for about 7 s. The polymer concentration in the resulting mixture was kept constant at 2 wt %. The samples were immediately transferred into a 1 mm quartz cuvette, and extinction spectra were collected after various periods of time at ambient temperature. The value of optical density determined during the first measurements (arbitrary units) was taken as the initial silver concentration in the mixtures; 1 a.u. at 430 nm corresponds approximately to 1.4 mg/mL of silver in the resulting mixture. Temperature-dependent time-resolved dynamic light scattering (DLS) measurements were performed after mixing was done in a similar way but with toluene being used as the solvent and the polymer concentration maintained at 0.1 wt %. Characterization. UV-vis measurements were performed on a Varian Cary 50 Spectrophotometer. Transmission electron microscopy was performed using a Zeiss CM 80 with accelerating voltage of 80 kV. Samples were prepared by dropping the mixtures on a carbon-coated TEM grid. DLS measurements, also known as photon correlation spectroscopy (PCS), were performed on Malvern Zetasizer Nano ZS with the detector positioned at 178° to the incident 4 mW He-Ne 633 nm laser beam equipped with Peltier element for thermostatic purposes. Spectrophotometric Following of Silver Aggregation. According to Bouguer-Lambert-Beer’s law, when optical length is taken as unity, the extinction at a particular wavelength λ at a given time τ (Aτλ) can be obtained as the sum of contributions from each type of aggregates:
Experimental Section Materials. Commercially available KiON Ceraset Polysilazane Ultra was supplied by KION Corporation. It is a solid colorless powder showing neither a melting point nor a glass transition on the differential scanning calorimetry curve (not shown here). According to information obtained from KION Corp., the molecular mass of this polysilazane is comparable to the other (24) Swenson, J.; Smalley, M. V.; Hatharasinghe, H. L. M. Phys. ReV. Lett. 1998, 81, 5840–5843. (25) Zaman, A. A. Part. Part. Syst. Charact. 2003, 20, 342–350. (26) Spalla, O.; Cabane, B. Colloid Polym. Sci. 1993, 271, 357–371. (27) Surve, M.; Pryamitsyn, V.; Ganesan, V. Langmuir 2006, 22, 969–981. (28) Olsen, A.; Franks, G.; Biggs, S.; Jameson, G. J. J. Chem. Phys. 2005, 123, 20490. (29) Otsubo, Y. Langmuir 1994, 10, 1018–1022. (30) Yu, X.; Somasundaran, P. J. Colloid Interface Sci. 1996, 177, 283–287. (31) Adachi, Y.; Cohen Stuart, M. A.; Fokking, R. J. Colloid Interface Sci. 1994, 167, 346–351. (32) Yu, X.; Somasundaran, P. J. Colloid Interface Sci. 1996, 178, 770–774. (33) Holthoff, H.; Schmitt, A.; Fernandez-Barbero, A.; Borkovec, M.; CabrerizoVilchez, M. A.; Schurtenberger, P.; Hidalgo-Alvarez, R. J. Colloid Interface Sci. 1997, 192, 463–470. (34) Midmore, B. R. J. Chem. Soc., Faraday Trans. 1990, 86, 3763–3768. (35) Chen, K. L.; Mylon, S. E.; Elimelech, M. EnViron. Sci. Technol. 2006, 40, 1516–1523. (36) Rai, R. S.; Ghosh, S. Kolloid Z. 1957, 154, 146–149. (37) Karpov, S. V.; Bas’ko, A. L.; Popov, A. K.; Slabko, V. V. Opt. Spectrosc. 2003, 95, 230–240.
j)n
Aτλ )
∑ ελj · νjτ
(1)
j)1
where νjτ is the concentration of aggregates consisting of j primary particles at time τ, ελj is the extinction coefficient of the aggregate for a given wavelength λ, and n is the maximum size of aggregates considered. Any multi-photon absorption is neglected by this approach since a xenon lamp was used. Besides, we postulate that the optical properties of each type of aggregates remain constant during aggregation (ελj is not a function of time). The theory of M. von Smoluchowski allows us to estimate the concentration of the aggregates:33,41
νjτ )
ν0(E · τ/τ1/2)j-1 (1 + E · τ/τ1/2)j+1
(2)
E is the collision efficiency factor representing the probability of (38) Lukacs, A. KION Corporation, Charlotte, NC, personal communication. (39) Wan, J.; Alizadeh, A.; Taylor, S. T.; Malenfant, P. R. L.; Manoharan, M.; Loureiro, S. M. Chem. Mater. 2005, 17, 5613–5617. (40) Hiramatsu, H.; Osterloh, F. E. Chem. Mater. 2004, 16, 2509–2511. (41) Westgren, A.; Reisto¨tter, J. Naturwissenschaften 1920, 14-15, 277–280. (42) Smellie, R. H.; La Mer, V. K. J. Colloid Sci. 1958, 13, 589–599.
Polysilazane-Induced Aggregation of SilVer Colloids
Langmuir, Vol. 24, No. 19, 2008 10711 model predicts maximum efficiency for a half-covered surface and its main virtue is the explanation of high collision efficiencies, sometimes reaching unity. It is known that for high surface coverage polymers sterically stabilize colloids and the influence of this effect on collision efficiency was recognized.31 Here, we try to express this effect quantitatively considering the close neighborhood of the docking place (Figure 2). Assuming that the particles are free to rotate, collision of two particles would lead to irreVersible bridging only under fulfilment of two conditions: (1) both particles are neither bare nor completely covered; (2) the polymer moieties in the closest neighborhood to the docking place on the first particle do not encounter polymer chains on the second one. The probability of polymer chain collision is proportional to the degree of surface coverage on each particle, and at the boarder cases of full surface coverage and bare particles the probability of ineffective collision solely caused by polymer chain interaction is unity and zero, respectively. The probability that such interactions does not preclude sticking (effective collision) is unity less this value. Interpolation of the condition to the intermediate degrees of surface coverage, θ, the mathematical expression of the above conditions is
Figure 2. Schematic representation of colliding particles at high surface coverage.
Figure 3. Collision efficiency factor calculated within Hogg’s and the present model as a function of surface coverage. Averaged experimental data for monomeric and polymeric bovine serum albumine from ref 43 are depicted for comparison.
effective particle sticking upon collision, τ1/2 is the characteristic half-coagulation time, when the total concentration drops to onehalf of the initial value, and ν0 is the initial concentration of primary particles. To solve or fit the set of equations, the number of measured spectra T should exceed the number of aggregates taken into account: T g n + 1. Model of Collision Efficiency. The attempts to correlate collision efficiency with the degree of surface coverage trace back to that of Smellie and La Mer.42 Later, other authors corrected and extended the model8,16-18 but still stressed the importance of the degree of surface saturation19,43 and/or availability of active polymer tails.20,23 Hogg considered the particles to be free to rotate and to find the appropriate docking place on their counterparts during the collisions.18 For a fraction of covered particle surface θ the probability of successful sticking caused by polymer bridging is unity, less the probability that both particles are bare or completely covered. For two particles of similar size, each can bear up to N polymer molecules and collision efficiency can be expressed as18
E ) [1 - θ2N - (1 - θ)2N] Although the author pointed out that, according to experiments, the optimum surface coverage lies below one-half, the proposed (43) Tirado-Miranda, M.; Schmitt, A.; Callejas-Fernandez, J.; FernandezBarbero, A. Phys. ReV. E 2003, 67, 01140.
E ) [1 - θ2N - (1 - θ)2N] · [1 - θ2]
(3)
Despite the speculative and axiomatic character of the proposed model, the slope of the efficiency decay during surface saturation (Figure 3) corresponds roughly to the experimentally observed data reported in ref 43. The described approach considers neither molecular weight of polymer nor its branching degree and operates only with parameter of particle capacity to adsorb polymer. The maximum number of polymer molecules N one particle can bear was not exactly determined so far. Based on the approach described in ref 18, we chose a number of 10 polymer molecules per particle for the following calculation. Polymer Adsorption and Surface Saturation Dynamics. It was pointed out44 that initially adsorbed polymer molecules with a large fraction of tails may spread over the surface, reducing thus the availability of docking places for the following polymer portions. The kinetics of such an adsorption process was described analytically.45,46 Here we suggest an alternative model (Figure 4) for adsorption from concentrated polymer solutions, based on the following assumptions: (1) The polymer concentration in the solution remains constant; (2) the concentration of active tails, able either to spread over the surface or to bridge to another particle is proportional to the surface coverage. The former assumption is valid since in the present system polymer concentration is an order of magnitude higher than that of silver nanoparticles. The latter assumption means that not only adsorption but also polymer spreading contributes to the number of available tails, which may be reasonable for large branched macromolecules. The fraction of free surface F is unity less the fraction of covered surface fraction, F ) 1 - θ. The rate of surface saturation is expressed by the following equation:
dF ) -Kads·C·F - Kspr·F·(1 - F) dτ
(4a)
Kads and Kspr are the constants of polymer adsorption and spreading, respectively, and C is the polymer concentration. Thus, the rate of surface saturation consists of two similar terms representing two types of processes in the physical model (adsorption itself and spreading) represented by the constants Kads and Kspr. Both rates are proportional to the free surface available and to the polymer concentration in the solution and on the surface, respectively. After rearrangement and introduction of new constants A and B with A ) Kspr and B ) Kads · C + Kspr,
dF ) A·F2 - B·F dτ the variables can be separated. After integration and application of the boundary conditions, the analytical expression of free surface available as one variable function
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BakumoV and Kroke
exp(-Bτ) 1 + A/B[exp(-Bτ) - 1] exp[(-KadsC + Kspr)τ] ) 1 + Kspr/(KadsC + Kspr)[exp[(-KadsC + Kspr)τ] - 1] (4b)
F)
is obtained to model aggregation inhibition. On the basis of the surface saturation model also an average number of adsorbed polymer molecules per particle N can be estimated as follows:
dN ) Kads · C · Nmax · F ) dτ Kads · C · Nmax · exp[-(Kads · C + Kspr) · τ] 1 + Kspr/(KadsC + Kspr) · {exp[-(Kads · C + Kspr) · τ] - 1} (4c) N ) Nmax · Kads · C/Kspr · ln
(
Figure 6. Linear dependencies between extinction at 520 and 430 nm.
)
Kads · C/Kspr + 1 (4d) Kads · C/Kspr + exp[-(Kads · C + Kspr) · τ]
where Nmaxis the number of nonspreading polymer molecules that can be adsorbed on a single particle. The model also defines the amount of adsorbed polymer in equilibrium, i.e., the isotherm of adsorption:
lim
τf∞
( )
(
Kspr N ) Kads · C/Kspr · ln 1 + Nmax Kads · C
)
(4e)
Fitting of Extinction Spectra. Time-dependent extinctionsat 11 wavelength values ranging from 400 to 500 nm caused by clusters consisting of 1-6 primary colloid particles were considered. For each wavelength curve, 11-13 time points from 1 up to 30 min after mixing were taken. About half of them were experimentally determined (Figure 7), and the remaining were graphically interpolated. The gradient method was applied to approximate the observed extinction with eqs 1 - 3 and 4b) in the sense of relative deviation’s mean square minimization and to calculate the variables (e.g., [ελj], θ, A, B). The algorithm was
Figure 4. Schematic representation of branched macromolecule spreading during adsorption.
Figure 7. Rate of relative SPR peak intensity decay for various initial colloid concentrations and polymer content of 2 wt %, λ ) 430 nm.
Figure 8. Time-resolved temperature-dependent particle size measurements obtained by means of DLS in toluene. Each point represents an average value obtained from the corresponding particle size distribution by volume. Inset: Curve of the initial stage of aggregation at 20 °C obtained as averages from the particle size distributions by number.
implemented in C and compiled with Bloodshed DEV C++ compiler, GNU general public license.
Results and Discussion
Figure 5. SPR peak transformation during particle aggregation.
The typical SPR peak change after mixing of stable colloid with polymer is characterized by a decrease of the SPR peak maximum and an increase of the extinction in the longwavelength range (Figure 5). A linear correlation of decreasing extinction in the shortwave range with the increasing extinction in the longwave range was found for the initial stage of aggregation (Figure 6). It can be seen that the bias of this dependency varies
Polysilazane-Induced Aggregation of SilVer Colloids
Figure 9. Arrhenius plots for four various series of nano-silverpolysilazane (0.1 wt %)-toluene system obtained from the slopes of temperature-dependent aggregation curves, measured by means of DLS (Figure 8).
Figure 10. Rate of relative SPR peak intensity decay for three samples with various silver to polymer ratios, λ ) 430 nm. “W1.9U0.5%” means mixture containing 1.9 a.u. of silver sample designated as “W” and 0.5 wt % of polysilazane “Ultra” (see Experimental Section).
Figure 11. Time of half-aggregation τ1/2, ν0 · τ1/2, as a function of initial particle concentration; model of hyperbola is shown for comparison.
for samples of different concentrations. This result may be caused by differences of optical properties and structures of the aggregates. It suggests separate treatment of data for each sample (e.g., [ελj] is not the same for different samples). The rate of decay of the SPR maximum is strongly dependent on the initial colloid concentration (Figure 7), but for all samples a rapid start of aggregation is followed by a rate decrease and saturation after ca. 5-10 min. The rapid start of coagulation can be explained assuming that one silver nanoparticle can rotate freely and bear several polysilazane molecules; and thus in the frame of Hogg’s model18 even small amounts of adsorbed polymer
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Figure 12. Constants of polymer adsorption kinetics, and relative fitting error for samples with different initial concentrations.
Figure 13. Calculated within eqs 3, 4b, and 4d values of θ, N/Nmax, and E as functions of time.
should lead to successful sticking. In other words, it is assumed that upon collision contact time is long enough to produce bridges, insofar free surface area at least on one of the colliding particles is available, and at least one polymer molecule on the other particle is present, and polymer chains in the neighborhood of the docking place do not preclude it. Nevertheless, the flocculation rate is far from being a diffusion-limited process; the latter would be very fast for such tiny nanoparticles and would make timeresolved measurements impossible. In this context the importance of good polymer dissolution and incubation (see Experimental Section) should be stressed. To preclude instantaneous flocculation polymer molecules present in entangled form should be disintegrated6,31 and, probably, converted to a coiled form upon incubation. It was also found that mixing at 0 °C “freezes” aggregation and therefore we assume that the time needed to transfer the sample into a cuvette can be neglected. Besides, the cooling allows a more homogeneous mixing. Since the experimentally determined curves for various initial colloid concentrations possess similar shape (Figure 7), the slow decay rate after several minutes of aggregation cannot be explained in terms of particles depletion entirely and is attributed to surface saturation and steric stabilization (see above) during polymer adsorption. It was possible to obtain temperature-dependent aggregation curves at low (0.1 wt %) polymer concentration using DLS in toluene (which has the same refraction index as the polymer). They show an initial phase of incubation, i.e., particle “activation”, which is attributed to polymer adsorption, followed by a nearly linear phase of growth (Figure 8). With increasing temperature the adsorption rate increases and the initial incubation time becomes shorter. Besides, the growth occurs faster, which is
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reflected by larger slopes of the growth curves. From Arrhenius plots for the growth phase (Figure 9) the apparent activation barrier of 41-48 kJ can be estimated and definitely can not be attributed to the solvent viscosity influencing particle diffusion. Therefore, from this value, rather than physisorption, we suggest irreversible stabilizer (octadecyl amine) substitution caused by the chelate properties of the silazane polymer. The nitrogen atoms present as every other atom in the backbone of the polysilazane are presumably responsible for coordination and adsorption on the silver surface. However, other phenomena occurring on the silver particle surface such as dehydro-coupling reactions between NH2- and Si-H-groups may also be involved. The described features of DLS growth curves coincide qualitatively with UV/vis observations (Figure 10). The decreasing polymer-to-silver ratio leads to higher retention times and a more linear decay of the SPR peak. This linear decay rate (between 10 and 40 min in curves “G2.5U0.2%” and “G2.8U0.2%” in Figure 10) is less dependent on initial colloid content, as compared to higher polymer concentrations (Figure 7). Therefore, at such low polymer concentrations of 0.1-0.2% the aggregation proceeds in a reaction-limited regime and depends on the (from
BakumoV and Kroke
sample to sample slightly varying) amount of residual stabilizer on the particles which is substituted by the silazane polymer to initiate bridging. We have also observed similar optical behavior (not shown here) for silver nanoparticles stabilized additionally by oleic acid; however, in that case significantly higher polymer amount was needed to destabilize the colloid. We are not able to explain the reason for the initial increase of SPR peak immediately after mixing (Figure 10) so far and suggest that the dilution is responsible for this observation. We also believe that a quantitative comparison of DLS and UV/vis results is not reasonable so far since the measurements were conducted with a different series of samples and neither reliable information on interparticle distances in the aggregates in the solution is available nor a suitable dynamic model of the aggregation in the reactionlimited regime can be selected. In particular, we do not know if all particles are equal and if von Smoluchowski’s kinetics is applicable, or if the presence of aggregation centers is essential. Futhermore, the possibility of overestimation of average particle size by DLS in polydisperse suspensions due to highly nonlinear (the power of 6) dependence of scattering intensity on size must be stressed. The attempts to perform time-resolved DLS
Figure 14. Extinction spectra of aggregates consisting of j primary silver particles related to each particle for samples with initial nanoparticle concentrations of 1.0 a.u. (a), 1.4 a.u. (b), 1.8 a.u. (c), 2.1 a.u. (d), 2.6 a.u. (e), and 3.6 a.u. (f).
Polysilazane-Induced Aggregation of SilVer Colloids
measurements with high polymer concentrations failed because of the necessity to optimize the measurements settings for each measurement, when the coagulation already succeeds. In the following discussion we apply the model described in the Experimental Section to six different samples with high (2 wt %) polymer concentration, where “intermediate” (between reaction- and diffusion-limited) aggregation takes place. In Figure 11 half-coagulation times calculated on the basis of the described model are shown and hyperbola points are provided for comparison. von Smoluchowski’s kinetics suggests that the product of τ1/2 and initial concentration ν0 should give a diffusion kinetic constant and thus be independent of concentration. The conditionsdespite strong point scatteringsseems to be fulfilled (Figure 11), and thus the presented theory passes the check on self-consistency. The second sample deviates from this interpretation also in extinction data (Figure 7, ν0 ) 1.4). This may be attributed to experimental errors. The relative fitting errors do not exceed 1% (Figure 12). The constants of adsorption kinetics (Figure 12) also vary moderately and their sum seems to be independent of the particle concentration. It should be pointed out that especially these values strongly depend on the initial mixing conditions, which are difficult to keep strictly constant since a manual technique has been used so far. A conclusion from area between surface saturation and polymer adsorption curves (Figure 13) is the fact that for the investigated concentrations and time range adsorption
Langmuir, Vol. 24, No. 19, 2008 10715
itself has a greater impact than spreading. On the other hand, this is not necessarily the case for lower polymer concentrations (since Kads · C is proportional to the polymer concentration) or higher temperatures (due to increased chain mobility). Diffusion is determined by solvent viscosity, which is less sensitive to temperature increase than polymer chain mobility. Hence, at a certain temperature (e.g., at the boiling point) in diluted solution adsorption and spreading will prevail on collision and surface blockade will occur instantaneously. This method was used by us to preclude phase instability and produce silverdoped polymer-derived ceramics.3c The consistence of these observations testifies to the possibility of spectral following of noble metal colloid coagulation and for the applicability of the proposed models. In addition to the evaluation of kinetic parameters, the described method sheds light on the optical properties of silver aggregates. In Figure 14 evaluated extinction spectra of aggregates consisting of 1-6 primary particles normalized to a single particle are shown. The main feature of all samples is a splitting of the original SPR peak into a doublet upon dimer formation. This result qualitatively validates theoretical predictions that consider nanoparticle electrodynamic interactions.37 The arising short- and long- wavelength maxima are centered at 400-410 nm and 470-480 nm respectively. The relatively small splitting of nearly 70 nm can be attributed to large interparticle distances in the aggregates.47 On the TEM micrograph of the dry mixture (Figure 15) distances in the range of ∼5 nm (which is comparable to the primary particle size) can be seen. However, in the solution distances between the particles in aggregates can be significantly higher and for detailed study of their structure cryo-TEM is needed. The distinct increase of extinction per particle in the region of initial peak for threefold clusters (trimers) as well as further increasingly pronounced peak splitting for higher aggregates may be attributed to the fractal nature of aggregates and needs further verification. It is worth noting that the contribution of high-order aggregates into total extinction is low and even small deviations in extinction as well as approximative character of collision efficiency and surface saturation models lead to significant errors upon evaluation of aggregate’s optical properties. Besides, it should be stressed that the present model considers neither geometric nor temporal variations of aggregate structures and evaluation leads to an “average” extinction coefficient.
Conclusions The kinetics of silver nanoparticle aggregation can be followed spectrophotometrically, allowing evaluation of half-coagulation time as well as extinction spectra of fractals. The instability of hydrophobic silver colloid being mixed with a polysilazane is caused by polymer bridges resulting from particle collision. Mutual repulsion of polymer chains is allegedly responsible for the collision efficiency decrease at high surface coverage. An analytical equation for the surface saturation kinetics accounting for polymer flattening is derived, which is consistent with von Smoluchowski’s kinetics. The extinction spectrum of dimers shows SPR peak splitting, which corresponds with theoretical studies based on electrodynamic interaction between particles reported in the literature. Finally, it should be mentioned that the presented approach for studying SPR coupling and the method of optical following of the coagulation processes is not restricted Figure 15. TEM micrograph showing silver nanoparticles and aggregates (marked with arrows) mainly consisting of two primary particles.
(44) Schneider, H. M.; Frantz, P.; Granick, S. Langmuir 1996, 12, 994–996. (45) van Eijk, M. C. P.; Cohen Stuart, M. A. Langmuir 1997, 13, 5447–5450. (46) Nossal, R.; Ninham, B. Biopolymers 1970, 9, 103–111.
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to bridging aggregation and can be transferred to less complicated colloidal systems. Acknowledgment. This work was in part financially supported in the framework of the Research Priority Programme of the State of Baden-Wuerttemberg, Germany (Project-title: Functional Materials; subproject: Polymer-Derived Metal-Ceramic Nanocomposites). We are grateful for further partial funding by the German Research Foundation (Deutsche Forschunsggemeinschaft, DFG) in the framework of the priority program “NANOMAT” (SPP 1181, Project Numbers KR 1739/13-1 and 13-
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2). We thank Prof. S. Mecking and his work group for access to Zetasizer Nano ZS. The authors are also grateful to Prof. U. Steiner and his research group for access to the UV/vis spectrophotometer and discussions as well as to Christine Dittrich for TEM measurements. Fruitful discussions with Danylo Kats are especially acknowledged. LA801104B (47) Karpov, S. V.; Bas’ko, A. L.; Popov, A. K.; Slabko, V. V.; George, T. F. Optics of Nanostructured Fractal Silver Colloids. In Recent Research DeVelopments in Optics; Research Signpost: Trivandrum, India, 2002.
