Article pubs.acs.org/JPCC
Structural Evolution of Aqueous Zirconium Acetate by TimeResolved Small-Angle X‑ray Scattering and Rheology Martin Bremholm,*,† Henrik Birkedal,‡ Bo Brummerstedt Iversen,† and Jan Skov Pedersen‡ †
Department of Chemistry and Interdisciplinary Nanoscience Center, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark ‡ Department of Chemistry and iNANO, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus, Denmark ABSTRACT: The nanostructure and viscosity of aqueous zirconium acetate solutions was investigated by combining small-angle X-ray scattering (SAXS) and rheology measurements. The structural evolution at concentrations of 22, 43, and 220 mM was furthermore investigated by time-resolved SAXS at a moderate temperature of 85 °C. Modeling of the SAXS data revealed that zirconium acetate exists as extended oligomer chains with an average contour length of 100 ± 15 Å and radius of 4.9 ± 0.9 Å. This chain radius corresponds to a radius of gyration of 3.8 Å for a sphere-like object, which is similar to that for individual cyclic tetramers, [Zr(OH)2·4H2O]48+, suggesting that the chains consist of connected tetramers. Their suspension in the aqueous solution is stabilized by their charge as corroborated by addition of NaCl, which lowers the stabilizing potential and leads to chain growth and aggregation upon aging at room temperature. The time-resolved SAXS measurements allow a detailed characterization of the polymerization to lengths of several hundred Angstroms. The radius of the polymeric chains remains constant throughout the reactions showing that the growth is one-dimensional. After the initial polymerization the SAXS data furthermore reveal the formation of polymeric clusters. Timeresolved rheology is used to follow the formation of a viscoelastic solid gel. The formation kinetics of these clusters matches the time evolution of the viscosity, providing a direct structural mechanism for the gel formation.
■
acetate complexes in solution exists. Cölfen et al.6 studied aqueous solutions of Zr(SO4)2·4H2O, which is argued to be different from the weak ligand complexes, such as the zirconyl halides and the nitrate, because the sulfate forms strong complexes with zirconium and can act as a bridging ligand. A broad range of complexes are thus expected to form depending on the pH and the Zr4+/SO42− ratio. Similar arguments apply for the acetate, which can act as both a simple ligand and a bridging ligand.7 Geiculescu et al.8,9 reported small-angle X-ray scattering (SAXS) and powder X-ray diffraction (PXRD) studies of dry gel powders and thin films prepared from aqueous solutions of zirconium acetate. Although the studies focused on dried products, the results are relevant to the present study. In particular, they determined the stoichiometry of zirconium and acetate complexes in the aqueous phase at various pH values: at pH ≤ 1 zirconium exists as a [Zr(OH)3]+ complex, at pH near 2 a 1:1 Zr(OH)3Ac complex forms, while at pH > 3 a 1:2 complex forms [Zr(OH)3Ac2]−. Furthermore, they suggest the dry gels consist of short rod-like clusters with a radius of gyration of 18 Å and cross-section radius of 12 Å, which stack into aggregates with lengths of 60 Å. Berry et al.10 studied the transformation of zirconium acetate to ZrO2 by reflux boiling and by hydrothermal treatment and investigated the effect of
INTRODUCTION Few materials show as much potential and industrial applicability as zirconia-based ceramics. Existing applications include solid oxide fuel cells, catalysts, bioimplants, gas sensors, cutting tools, abrasives, bearings, and many more.1 A wide variety of methods for production of zirconia-based ceramics exist, but syntheses in the aqueous phase using zirconyl salts are particularly favorable because of the low processing temperatures and inexpensive, environmentally friendly precursors. There is a great interest in understanding the relation between the complex chemistry of zirconium salts in aqueous solution and the formation of solids.2 In addition to a basic research interest in complex chemistry, an improved fundamental understanding of zirconium salt aqueous chemistry leads to control of the zirconia crystal phase and overall crystallinity and, equally important, the microstructural properties such as crystallite size, porosity, and surface area. All these properties are of fundamental importance in applications of zirconia. It is well-known that zirconium ions are strongly hydrolyzed in aqueous solutions, but the detailed structures of the hydrolyzed species are only known in a few cases. The complex structures of zirconyl salts, such as zirconyl chloride ZrOCl2 and zirconyl nitrate ZrO(NO3)2, are the most studied.3,4 The solid-state structure of the zirconyl halides has been determined by crystallography to form the tetramer complex, [Zr(OH)2· 4H2O]48+ (ICSD 27437),5 which is believed to exist in solution as well. However, zirconium acetate has not been crystallized, and furthermore no conclusive work on the structure of the © 2015 American Chemical Society
Received: January 22, 2015 Revised: April 21, 2015 Published: April 22, 2015 12660
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
Figure 1. SAXS data (symbols) and model fits (solid lines) of zirconium acetate solutions at room temperature. (A) Untreated zirconium acetate of various concentrations. The red dashed line indicates the shift of the maxima. (B) Same data divided by the concentration. The red dashed line shows the power law, I ∝ q−1.5.
pH on the crystalline phase of final products by PXRD and Raman spectroscopy. The hydrolysis of zirconium in aqueous solutions has been investigated using several experimental techniques including EXAFS,11 SAXS,12,13 dynamic light scattering (DLS), and ultracentrifugation.6 Heating of zirconium solutions or an increase of pH result in polymerization,14 and specifically for zirconium acetate, such treatments result in polymerization into [Zr(OH)4]n, which has been suggested to have a two-dimensional structure.15 The formation of sheets was also assumed more recently by Berry et al.10 in a study of zirconium acetate. Chaumont et al.12 studied the alcohol-based hydrolysis and condensation of zirconium tetrapropoxide in npropanol and acetic acid by SAXS. They showed that under these conditions nearly rigid linear polymeric chains form. Similar chemistry was more recently studied in greater detail by Riello et al.13 Using systematic variation of chemical parameters they found that a general two-step mechanism consists of a growth stage followed by diffusion-limited aggregation. The transformation from the complex species in solution to solid particles is a complicated process and requires insight into solution chemistry, coordination chemistry, polymerization, and nucleation.16 Detailed studies of the transformation require noninvasive techniques, which can access the early stages of the transformation. SAXS is very powerful in this respect because of the high sensitivity in diluted systems and because it can be performed with a time resolution suitable for following the progression of the complex species without perturbing the system.17,18 Here, we report SAXS studies of zirconium acetate solutions at ambient conditions and time-resolved measurements at elevated temperatures and compare the found behavior to time-resolved rheological measurements.
SAXS measurements were performed on a modified Bruker AXS NanoSTAR SAXS camera with a three pinhole collimated beam and a rotating copper anode X-ray generator.19 The setup uses a gas proportional position-sensitive HiSTAR detector from Bruker AXS. Several different configurations of the NanoSTAR were used. For the time-resolved measurements, we used two pinholes (0.75 mmØ and 0.4 mmØ), separated by 925 mm, with an antiscatter pinhole in front of the sample (1.0 mmØ) at a distance of 485 mm from the second pinhole. The sample−detector distance was 46.7 cm, and a beamstop of 3.0 mmØ was used. To extend the probed q-range for static measurements this configuration was combined with measurements performed with three pinholes (0.5 mmØ, 0.15 mmØ, and 0.5 mmØ) with the same distances and a sample detector distance of 106.7 cm and a beamstop of 2.0 mmØ. A few measurements were also done with the first configuration with the detector at 66.7 cm. Samples were loaded in borosilicate capillaries (diameter of about 2.0 mm, wall thickness 0.01 mm) and flame-sealed. The sealed capillaries were then placed in the sample chamber, which was evacuated to a pressure of 10−3 mbar. Time-resolved measurements were performed at a constant temperature of 85 °C with time resolutions of 30, 120, and 600 s depending on the aging stage. The scattering vector range (q-range) was 0.015−0.50 Å−1, where q is the modulus of the scattering vector (4π sin θ)/λ, where 2θ is the scattering angle and λ the X-ray wavelength (here λ = 1.54 Å). The temperature was controlled by a Peltier-heated sample holder, which reaches the set temperature within 2 min. SAXS data for individual samples were measured at room temperature for 60 min to improve the statistics on the starting sol and the final aged sol, and for these measurements the qrange was increased to 0.005−0.50 Å−1 by merging measurements at two detector distances. Additionally, data were collected for untreated solutions and for solutions aged at 85 °C for 24 h in a standard oven. The SAXS data were corrected for absorption and scattering through measurements of the capillary with solvent at room temperature. The data do not contain any sharp features, and instrumental smearing was therefore not considered in the analysis. Rheological measurements were performed using an Anton Paar Physica MCR 501 rotational rheometer using isothermal oscillatory measurements with 1% strain at a frequency of 1 Hz and a time resolution of 15 s. The sample container was a stainless steel concentric cylinder (Anton Paar, CC27-SS), and the sample solution covered the oscillating bob completely
■
EXPERIMENTAL METHODS An aqueous solution of zirconium(IV) acetate in diluted acetic acid containing 15−16 wt % Zr (2.2 M) (Sigma-Aldrich 413801, density 1.279 g mL−1) was used as received and was diluted by a factor of 5, 10, 25, 50, and 100 resulting in Zr concentrations of 0.44, 0.22, 0.087, 0.044, and 0.022 M. NaCl (Fluka 71379) was dissolved in deionized water to a stock solution of 1.0 M, which was mixed with water and zirconium acetate to prepare five solutions with a fixed Zr(ac) 4 concentration of 0.087 M and NaCl concentrations of 0.20, 0.30, 0.40, 0.50, and 0.60 M. SAXS data were measured on freshly prepared samples as well as samples aged in sealed vials for 10 days at room temperature. 12661
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C (Seale method20). The large sample volume (∼20 mL) combined with an evaporation trap minimized the effect of evaporation and allowed a steady sample environment for at least 10 h. SAXS Modeling. The SAXS data are shown in Figure 1A for four concentrations. The same data divided by the zirconium concentration are shown in Figure 1B. At intermediate q the data display a power-law behavior I(q) ∝ q−1.5. For one-dimensional objects, i.e., objects for which one axis is much larger than the other two axes, the expected behavior is I(q) ∝ q−1 at intermediate q. Flexibility and random walk polymer behavior results in I(q) ∝ q−2, whereas selfavoidance for such chains gives I(q) ∝ q−1.667 (see, e.g., refs 21 and 22). Hence the data have a behavior which is similar to that of flexible self-avoiding chains. The form factor of such chains can be described as a product of the form factor related to the length PL(q) and a form factor of the cross section, PCS(q)23 I(q) = nΔρ2 V 2PL(q)PCS(q)
account by multiplying the intensity expression by a structure factor for the clusters Scluster(q) = 1 + Scl exp( −R g 2q2 /3)
where Rg is the radius of gyration of the clusters and Scl is the cluster scale factor.
■
RESULTS The SAXS data collected at ambient conditions were of excellent quality and cover a wide q-range (0.005 < q < 0.5 Å−1). Figure 1A shows the absorption-corrected SAXS data, and Figure 1B shows the same data divided by the zirconium concentration. The linear dashed line at the intermediate qrange (0.1 < q < 0.3 Å−1) in Figure 1B, I(q) ∝ q−1.5, suggests that the solution contains rod-like objects. The data display a pronounced correlation peak at the lower q-range at the lowest concentrations, demonstrating that there are strong interactions in the system. Since the species in solution are expected to be negatively charged, the correlation peak can be associated with electrostatic interactions, and the rod- or polymer-like objects can be expected to be stabilized in solution by this electrostatic repulsion (see below). The SAXS data were modeled by the PRISM-related expressions given in the Experimental Methods. The model expression produces excellent fits to the data as shown by the black solid lines in Figure 1. The PRISM model is described in further detail in ref 24. The model expression includes the following seven parameters: L, average contour length of the chains; σL/L, polydispersity of contour length; b, Kuhn length; R, chain cross-section radius; νRPA strength of interparticle interactions: Rc, range of interparticle interactions. The Kuhn length characterizes the flexibility and is equal to two times the persistence length. The polydispersity of the chains was set to σL/L = 1 as expected for random formation and breaking of the chains.27 The refinements show some variation depending on the concentration. In the concentration range from 22 to 435 mM all chain radii are in the range 3.9(3)− 5.79(12) Å, and the lengths are in the range 87(2)−115(6) Å. These changes may partly be attributed to correlations between parameters, and some variation is also expected when the system is diluted and the effect of the structure factor is reduced. Therefore, rather than using the standard errors (SEs) from individual refinements we conservatively estimate an effective SE from the spread of parameters and thus obtain R = 4.9(9) Å and L = 100(15) Å. The Kuhn length, the distance over which the polymer is rigid, is found to vary only little and is determined to be 36(2) Å. Figure 2 shows SAXS data of zirconium acetate heated at 85 °C for 24 h for concentrations of 22 and 87 mM, and for reference the data for the untreated samples are also shown. For the lowest concentration (22 mM) the intensity changes only a little at large q-values, while at lower q values (q ≈ 0.015 Å−1) the intensity increases by almost an order of magnitude. This shows that at the low concentration of 22 mM the chain length increases and that aggregation into larger structures (∼100 Å) occurs. However, it should be noted that visual inspection of sample vials as well as rheological measurements (see below) show that gelling does not occur for the case of 22 mM. For the larger concentration of 87 mM the change is more drastic, an increase by a factor of ∼50 at low q (q ≈ 0.015 Å−1), which shows that more pronounced aggregation occurs. Furthermore, the slope for the intermediate q range changes
(1)
where n is the number density of chains; Δρ is the excess scattering length density; and V is the volume of a chain. The scattering data display a correlation peak with maxima at q-values in the range 0.025−0.05 Å−1 dependent on the concentration (indicated by a red dashed line in Figure 1A), which shows that there are strong interparticle interactions in the system. The interaction potential was assumed to be dominated by the electrostatic repulsion between the chain structures formed in the solutions. The effects were in this work described by an expression based on the Polymer Reference Interaction Site Model (PRISM) which has been derived from Monte Carlo simulations on wormlike micelles interacting with a screened Coulomb potential.24 Including polydispersity of the chain lengths,25 we obtain the following expression for the intensity I(q) = scale
PKP(q , L , σL/L , b)PCS(q , R ) 1 + νRPAc(q , R c , σc)PKP(q , L , σL/L , b)
(2)
where PKP(q, L, σL/L, b) is the scattering function of polydisperse infinitely thin semiflexible self-avoiding chains,26 with number-average contour length L and polydispersity described by a Schultz distribution of relative width σL/L which was fixed at unity so that the size distribution is exponential. The parameter b is the Kuhn length, which is equivalent to a random walk step length. The function PCS(q,R) is the crosssection scattering function of chains with a homogeneous circular cross section with radius R ⎡ 2J (qR ) ⎤2 ⎥ PCS(q , R ) = ⎢ 1 ⎣ qR ⎦
(3)
where J1(x) is the first-order Bessel function of the first kind. The parameter νRPA describes the strength of the interparticle interactions and increases with the concentration. The function c(q,Rc,σc) is the direct correlation function which from simulations24 has been found to follow c(q , R c , σc) =
sin(qR c) exp( −q2σc2) qR c
(5)
(4)
where Rc and σc are related as Rc = 2 ln(σc) + 2. For aged samples, the scattering intensity at low q increased, and this was attributed to aggregation of the chains and cluster formation. In the model this aggregation was taken into 12662
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
Figure 2. SAXS data, I(q)/C, for zirconium acetate samples with concentrations of 22 and 87 mM aged at 85 °C for 24 h and as a reference the data for untreated samples as shown as well.
to approximately −2, and the scattering intensity decreases at the largest q-values (q ≈ 0.2 Å−1). The aggregation of the chains of organometallic complexes is in general prevented by an electrostatic interaction potential. Upon even subtle heating the stabilization is not sufficient, and the chains may grow to significant lengths without aggregation; i.e., the complexes still display significant electrostatic repulsion. For zirconium acetate the electrostatic stabilization must be due to the anionic acetate species. The interaction potential is assumed to be dominated by the electrostatic repulsion and the attractive van der Waals as described by the classical DLVO theory.28−30 Addition of salt results in a decrease of the electrostatic repulsion, and at a sufficiently high salt concentration aggregation is expected. We investigated this by studying the behavior of an 87 mM zirconium acetate solution with increasing concentrations of NaCl from 200 to 600 mM. The addition of NaCl did not lead to any visual change for several days, but after 10 days of aging a clear progression of aggregation was observed as shown by the photograph of the sample vials after 10 days (Figure 3A). Figure 3B,C compares SAXS data of freshly prepared (Figure 3B) and 10-day-aged (Figure 3C) samples with varying salt concentration together with the corresponding model fits. The freshly prepared Zr(Ac)4/NaCl solutions clearly show that the correlations at low q disappear, and the structure factor is redundant, i.e., S(q) ≈ 1. The increase in intensity at low q follows the order in which the samples were measured and show that a small degree of aggregation has already taken place in less than the approximately 2 h it took to complete these measurements. In agreement with the fits to data without NaCl, we find that the chain lengths are maintained at approximately 100 Å, while the radius is slightly reduced to 4.2(3) Å. Upon aging, the PRISM expression alone does not provide good fits to the data as the intensity at low q increases dramatically. We therefore included an extra cluster term in the expression for the intensity (eq 5 in Experimental Methods), which depends on a scale factor and a radius of gyration of the clusters, Rg. Using this model, we find that the chains have grown to lengths in excess of 400 Å for all samples and that the data do not allow an accurate determination of the length. The Kuhn length, however, remains almost the same with an average of LKuhn = 27(2) Å. The radii are gradually reduced to 3.83(8) Å for 200 mM NaCl and 2.5(3) Å for 600 mM. The observed reduction of the radius is assigned to the gradual change in the contrast between the solvent and the Zr species.
Figure 3. (A) Photograph of five vials with a concentration of 87 mM Zr(Ac)4 and increasing concentration NaCl from 200 to 600 mM taken after aging for 10 days at room temperature. (B) SAXS of samples right after addition of NaCl to give concentrations of 200, 400, and 600 mM and fitted to the PRISM model. (C) Same samples measured after aging for 10 days.
Furthermore, we find that clusters have formed with an average radius of gyration, Rg = 78(12) Å. The cluster sizes tend to be smaller for the lowest salt concentration, but only small variations were found. Time-Resolved SAXS and Rheology Measurements. To investigate the detailed behavior of the system at elevated temperature, we performed time-resolved SAXS and rheology measurements of zirconia acetate solutions at 85 °C. For the rheology analysis we measured SAXS data for samples of aqueous zirconium acetate with concentrations of 43, 87, 220, and 2200 mM for up to 6 h. The time-resolved rheological characterization during aging is used to investigate a macroscopic property of the system, the complex viscosity, for comparison with microscopic SAXS modeling. The complex viscosity function is equal to the difference between the dynamic viscosity and the out-of-phase viscosity or imaginary part of the complex viscosity: η*(iω) = η′(ω) − iη″(ω), where η* is the complex viscosity; η′ is the dynamic viscosity; and η″ is the out-of-phase viscosity. Figure 4 shows time-resolved measurements of the norm of the complex viscosity, |η*|, for concentrations of 43, 87, and 220 mM at a temperature of 85 °C. 12663
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
At 220 and 87 mM these slope changes occur at t = 10 min and t = 60 min, respectively. Time-Resolved SAXS. The evolution of nanostructure leading to gelation was investigated by time-resolved SAXS for concentrations of 22, 87, and 220 mM. Figure 5 shows a series of SAXS data collected on 220 mM zirconium acetate at 85 °C to study the chain growth, aggregation, and gel formation in the course of 22.5 h. The SAXS invariant for the series is approximately constant showing that the amount of material and the scattering contrast are unchanged throughout. All data were modeled with the PRISM model with the addition of a cluster term when required to model the data. The cluster term was included at all times for the 220 mM sample, while it was only required after some heating for the remaining samples (25 min for 87 mM and 55 min for min for 22 mM). Figure 6 shows the evolution of selected PRIMS parameters for the 22, 87, and 220 mM data. The radius for the highest concentration (220 mM) is on average 4.23(2) Å but shows some fluctuation and the largest SE (4.06(7) < R < 4.57(7) Å) in the early stage (t < 30 min) where data collection time is limited to 30 s. In the later stage, where longer exposure times are used, the radii converge to the average value. Similarly, the lower concentrations (87 and 22 mM) produce lower data quality, particularly at the early stages, and some irregular changes occur over time. Furthermore, there is only negligible systematic change, and we interpret these results as the radius being essentially constant with both time and concentration. For the chain length similar arguments apply regarding the data quality, but for this parameter we observe clear trends with both time and concentration. For the highest concentration the length grows to more than 400 Å in 20 min. When the length is well beyond 400 Å, the exact value has no influence on the quality of the fit, and for the remaining data sets the length was fixed at 2000 Å. For the lower concentrations the growth is significantly slower and reaches an average length of only ∼300 Å during the experiment. The parameter Rc describes the range of the interchain correlations and is displayed in Figure 6C. The parameter was refined to large values and fluctuating values for the case of 22 mM, and it was fixed at 160 Å, which gave good fits to the data. Overall, the Rc values decrease with increasing concentration in agreement with the simulations by Cannavacciuolo et al.24 For
Figure 4. Complex viscosity, |η*|, during aging at 85 °C for concentrations of 43, 87, and 220 mM. The inset shows the first 30 min to highlight the slope increase at t = 10 min for the sample with a concentration of 220 mM.
The 87, 220, and 2200 mM samples form rigid gels, while the 43 mM sample shows little change in viscosity during the first 3.5 h. The viscosity of the undiluted zirconium acetate (2200 mM) rapidly turns into a viscoelastic solid with a viscosity of 25 kPa s at which point the gel structure is disrupted due to the oscillating strain, and the measurement was therefore terminated (data now shown). Thus, the analysis here focuses on the lower concentrations of 43, 87, and 220 mM. Visual inspection of the 43 mM sample confirmed that the sample does not form a gel within 24 h. The initial complex viscosity at room temperature was 0.1 Pa·s, and we could not measure any significant increase during the first 3.5 h of aging at 85 °C, indicating that there is no significant entanglement of the chains. The sensitivity of these measurements is limited for low viscosity liquids, and no detailed interpretation of the subtle and irregular variation in viscosity of the 43 mM sample is appropriate. For both 87 and 220 mM concentrations an increase in slope is observed, the onset of which was reproduced in more than three experiments. This increase in slope can be interpreted as the point at which the polymer gel extends throughout the volume of the sample container, i.e., a gel point. Further growth serves to increase the entanglement and gel formation, and thus the viscosity increases more rapidly.
Figure 5. Time-resolved SAXS data for 220 mM zirconium acetate aqueous solution measured for 22.5 h at 85 °C. 12664
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
Figure 6. Selected parameters from the PRISM modeling of zirconium acetate solution. (A) Chain radius, R. (B) Chain length, L. (C) The correlation radius, Rc (fixed to 160 Å for 22 mM). (D) Cluster Scale (Rg = 100 Å).
Viscosity and Comparison of SAXS Results with Rheology. There are in general no direct relations between parameters from SAXS and observables in rheology, e.g., the occurrence of a “gel point”. However, an almost perfect correlation between the evolution of the SAXS cluster scale and the complex viscosity was found as illustrated in Figure 7.
systems with a low ionic strength, like the present ones, the electrostatic repulsions are quite long-ranged, and therefore Rc reflects the interparticle/interchain distance. This distance is larger for the lower concentration, and this explains the overall behavior. At short aging times (less than 11 min), the lengths of the chains are comparable to Rc. For longer times, the situation is more complicated as the chains grow in length, and in addition they aggregate to polymer clusters. Therefore, Rc in this region is probably related to an interchain distance of the entangled network, in which the chains form as they grow in length. The growth of the chains causes the number density of chains to decrease, and therefore the interchain distance increases. This explains the increase of Rc which occurs as the chain growth sets in. In Zimm’s classical approach νRPA = 2A2Mc, where A2 is the second virial coefficient, M the mass, and c the concentration.31 So νRPA/M is proportional to A2, and when the radius is constant, it furthermore follows that νRPA/L is proportional to A2. We do not put too much emphasis on the variation of νRPA/ L but note that it increases by a factor of 2 as the chains grow toward the gel point and then decreases toward the initial value, which shows that the strength of the interchain interactions only changes modestly throughout the measurements. For modeling of the aggregation we fixed the radius of gyration Rg of the cluster aggregate to 100 Å, the approximate value found for the samples aged at 85 °C for 24 h. For the lowest concentrations the degree of aggregation was limited, and the scale factor is small and increases slowly (Figure 6D). For the concentration of 220 mM the aggregation is very significant and shows a large upturn after 20 min, simultaneous with the significant increase in chain length. The cluster scale for the intermediate concentration (87 mM) shows large fluctuations, and this is possibly due to correlations with the chain lengths which also show significant fluctuation.
Figure 7. Comparison of the evolution of the complex viscosity and the cluster scale for 220 mM zirconium acetate aqueous solution at 85 °C.
During the first 3 h these two parameters increase in a similar fashion. However, the viscosity appears to continue to increase, while the cluster scale reaches a maximum probably due to structural evolution outside the length scale window probed by SAXS. Thus, the combined analysis of rheology and SAXS results provides a structural model of gelation: cross-links are formed by aggregation of the formed polymers leading to increasing viscosity and gelation. The critical extent of a polymeric reaction for which the gel point occurs depends on the concentration of the polymeric species and only when the concentration is sufficiently high; i.e., for concentrations ≤43 12665
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
in some previous studies. We found that these linear oligomer species are electrostatically stabilized, and their behavior can be explained by the classical DVLO theory. A model expression for the SAXS intensity based on the Polymer Reference Interaction Site Model (PRISM) was found to describe the system very accurately and allowed a detailed modeling of the time-resolved SAXS data collected at 85 °C as the polymeric chains grow and form a hydrogel. Aggregation occurs simultaneously with chain growth. Except for the lowest concentrations, where no gelling occurs, it was found that the increase in viscosity followed the increase in the degree of aggregation of the polymers, i.e., the cluster scale factor, strongly suggesting that cluster formation is necessary for the formation of sufficient cross-link densities required for gelation. A review of the existing literature combined with the present results provides important clues on the structure of the oligomers; however, the details of the local atomic geometry and connectivity of the chain structures remain elusive, and further investigation by local techniques is required, e.g., NMR, EXAFS, or PDF.
mM gelling will never occur. At these low concentrations the polymer lengths increase, and clusters of these do form; however, compared to the higher concentrations this has little impact on the viscosity of the resulting sol since the polymer clusters stay isolated from each other.
■
DISCUSSION
Structure of Zirconium Acetate Complexes. The SAXS data show that even at room temperature extended oligomers are present with a length of approximately 100 Å and radii of 4.9 ± 0.9 Å. In contrast to the general mechanism for zirconium with noncomplexing precursor anions proposed in the early work by Clearfield,15 the present SAXS data show that aqueous solutions of zirconium acetate are not dominated by individual cyclic tetramers and that sheets of tetramer units do not form at any stage. The calculated radius of gyration for an individual cyclic tetramer is 3.8 Å3 based on the crystalline structure of zirconyl chloride.5 The true shape is as an intermediate between a sphere (R = (5/3)1/2RG) and a thin disc (R = √2RG), and from this we can constrain the numerical cross-section radius of an individual cyclic tetramer to the range 4.9−5.4 Å. This distance matches well the observed radius of the polymer chain in the present study, and these must therefore consist of tetramer units, which polymerize to form extended chains. To maintain an almost unchanged chain radius during growth, the tetramer units can stack on top of each other or edge-to-edge, and further studies with local probes, like NMR, EXAFS, or PDF, are required to unambiguously determine the atomic connectivity of the cyclic tetramer building blocks. A recent PDF study of the zirconyl nitrate suggested a model with edgeto-edge connectivity to describe the data for untreated precursor solutions,32 while a SAXS study of the same precursor at various pH conditions suggested stacking of cyclic tetramer units.33 For the zirconium acetate no such studies have yet been reported. It should be noted that polymerization occurs even at room temperature but that it proceeds very slowly; zirconium acetate stored for many months could therefore result in more extended oligomers than reported here. The growth rate, however, increases drastically upon even moderate heating, and even a temperature a few degrees above room temperature could easily induce more significant chain growth. Information about the extended lengths is limited by the q-range, here Lmax ≅ 2π/qmin ≅ 400 Å, and also by the clustering of the chains. In general for SAXS instruments the transversal correlation length can also be a limiting factor,34 but in the present study the qmin is the limiting factor. Upon heating of the most concentrated solutions the chain lengths rapidly increase beyond this limit; although the data clearly show chains with lengths beyond the limiting value, the modeling is not sensitive to the actual length of the chains, and the lengths are simply determined to be >400 Å.
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: +45 87 15 59 03. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The Carlsberg Foundation is acknowledged for funding of the rheometer. HB and JSP thank the Danish Research Council for Independent Research for funding. MB thanks the Villum Foundation for funding. Center for Materials Crystallography is a Center of Excellence funded by the Danish National Research Foundation (DNRF93).
■
REFERENCES
(1) Bocanegra-Bernal, M. H.; De la Torre, S. D. Phase Transitions in Zirconium Dioxide and Related Materials for High Performance Engineering Ceramics. J. Mater. Sci. 2002, 37, 4947−4971. (2) Bremholm, M.; Becker-Christensen, J.; Iversen, B. High-Pressure, High-Temperature Formation of Phase-Pure Monoclinic Zirconia Nanocrystals Studied by Time-Resolved in situ Synchrotron X-Ray Diffraction. Adv. Mater. 2009, 21, 3572−3575. (3) Singhal, A.; Toth, L. M.; Lin, J. S.; Affholter, K. Zirconium(IV) Tetramer/Octamer Hydrolysis Equilibrium in Aqueous Hydrochloric Acid Solution. J. Am. Chem. Soc. 1996, 118, 11529−11534. (4) Singhal, A.; Toth, L. M.; Beaucage, G.; Lin, J. S.; Peterson, J. Growth and Structure of Zirconium Hydrous Polymers in Aqueous solutions. J. Colloid Interface Sci. 1997, 194, 470−481. (5) Mak, T. C. W. Refinement of Crystal Structure of Zirconyl Chloride Octahydrate. Can. J. Chem. 1968, 46, 3491−3497. (6) Cölfen, H.; Schnablegger, H.; Fischer, A.; Jentoft, F. C.; Weinberg, G.; Schlogl, R. Particle Growth Kinetics in Zirconium Sulfate Aqueous Solutions Followed by Dynamic Light Scattering and Analytical Ultracentrifugation: Implications for Thin Film Deposition. Langmuir 2002, 18, 3500−3509. (7) Alcock, C. B.; Jacob, K. T.; Zador, S. Zirconium Physicochemical Properties of Its Compounds and Alloys 0.1. Thermochemical Properties. At. Energy Rev. 1976, 7−65. (8) Geiculescu, A. C.; Rack, H. J. X-Ray Sscattering Studies of Polymeric Zirconium Species in aqueous xerogels. J. Non-Cryst. Solids 2002, 306 (1), 30−41. (9) Geiculescu, A. C.; Rack, H. J. Atomic-Scale Structure of WaterBased Zirconia Xerogels by X-Ray Diffraction. J. Sol-Gel Sci. Technol. 2001, 20, 13−26.
■
CONCLUSIONS Modeling of time-resolved SAXS experiments at 85 °C demonstrates that aqueous zirconium acetate forms linear oligomer units with a radius of 4.9 ± 0.9 Å independent of concentration. The oligomers are already present in the untreated solution with a length of 100 ± 15 Å and unambiguously shows that zirconium acetate forms neither individual tetramers units nor sheet-like assemblies as suggested 12666
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
Article
The Journal of Physical Chemistry C
(31) Zimm, B. H. The Scattering of Light and the Radial Distribution Function of High Polymer Solutions. J. Chem. Phys. 1948, 16, 1093− 1098. (32) Tyrsted, C.; Lock, N.; Jensen, K. M. O.; Christensen, M.; Bojesen, E. D.; Emerich, H.; Vaughan, G.; Billinge, S. J. L.; Iversen, B. B. Evolution of Atomic Structure during Nanoparticle Formation. IUCr J. 2014, 1, 165−71. (33) Gossard, A.; Toquer, G.; Grandjean, S.; Grandjean, A. Coupling Between SAXS and Raman Spectroscopy Applied to the Gelation of Colloidal Zirconium Oxy-Hydroxide Systems. J. Sol-Gel Sci. Technol. 2014, 71, 571−579. (34) Pauw, B. R. Everything SAXS: Small-Angle Scattering Pattern Collection and Correction. J. Phys.: Condens. Matter 2013, 25, 383201.
(10) Berry, F. J.; Skinner, S. J.; Bell, I. M.; Clark, R. J. H.; Ponton, C. B. The Influence of pH on Zirconia Formed from Zirconium(IV) Acetate Solution: Characterization by X-Ray Powder Diffraction and Raman Spectroscopy. J. Solid State Chem. 1999, 145, 394−400. (11) Kanazhevskii, V. V.; Novgorodov, B. N.; Shmachkova, V. P.; Kotsarenko, N. S.; Kriventsov, V. V.; Kochubey, D. I. Structure of Zirconium Complexes in Aqueous Solutions. Mendeleev Commun. 2001, 211−212. (12) Chaumont, D.; Craievich, A.; Zarzycki, J. In A SAXS Study of the Formation of ZrO2 Sols and Gels, 6th International Workshop on Glasses and Ceramics from Gels, Seville, Spain, Oct 06−11; Elsevier Science Bv: Seville, Spain, 1991; pp 127−134. (13) Riello, P.; Minesso, A.; Craievich, A.; Benedetti, A. Synchrotron SAXS Study of the Mechanisms of Aggregation of Sulfate Zirconia Sols. J. Phys. Chem. B 2003, 107, 3390−3399. (14) Clearfield, A. Structural Aspects of Zirconium Chemistry. Rev. Pure Appl. Chem. 1964, 14, 91−108. (15) Clearfield, A. The Mechanism of Hydrolytic Polymerization of Zirconyl Solutions. J. Mater. Res. 1990, 5, 161−162. (16) Gebauer, D.; Kellermeier, M.; Gale, J. D.; Bergstrom, L.; Cölfen, H. Pre-Nucleation Clusters as Solute Precursors in Crystallisation. Chem. Soc. Rev. 2014, 43, 2348−2371. (17) Olliges-Stadler, I.; Rossell, M. D.; Suess, M. J.; Ludi, B.; Bunk, O.; Pedersen, J. S.; Birkedal, H.; Niederberger, M. A Comprehensive Study of the Crystallization Mechanism Involved in the Nonaqueous Formation of Tungstite. Nanoscale 2013, 5, 8517−8525. (18) Jensen, G. V.; Bremholm, M.; Lock, N.; Deen, G. R.; Jensen, T. R.; Iversen, B. B.; Niederberger, M.; Pedersen, J. S.; Birkedal, H. Anisotropic Crystal Growth Kinetics of Anatase TiO2 Nanoparticles Synthesized in a Nonaqueous Medium. Chem. Mater. 2010, 22, 6044− 6055. (19) Pedersen, J. S. A Flux- and Background-Optimized Version of the NanoSTAR Small-Angle X-Ray Scattering Camera for Solution Scattering. J. Appl. Crystallogr. 2004, 37, 369−380. (20) Mezger, T. G. The Rheology Handbook, 2nd ed.; Vincentz Network: Hannover, 2006. (21) Higgings, J. S.; Benoit, B. C. Polymers and Neutron Scattering; Oxford University Press - Clarendon Press: Oxford, 1997. (22) Pedersen, J. S. Analysis of Small-Angle Scattering Data from Colloids and Polymer Solutions: Modeling and Least-Squares Fitting. Adv. Colloid Interface Sci. 1997, 70, 171−210. (23) Pedersen, J. S.; Schurtenberger, P. Cross-Section Structure of Cylindrical and Polymer-Like Micelles from Small-Angle Scattering Data 0.1. Test of Analysis Methods. J. Appl. Crystallogr. 1996, 29, 646− 661. (24) Cannavacciuolo, L.; Pedersen, J. S.; Schurtenberger, P. Monte Carlo Simulation Study of Concentration Effects and Scattering Functions for Polyelectrolyte Wormlike Micelles. Langmuir 2002, 18, 2922−2932. (25) Jerke, G.; Pedersen, J. S.; Egelhaaf, S. U.; Schurtenberger, P. Static Sstructure Factor of Polymerlike Micelles: Overall Dimension, Flexibility, and Local Properties of Lecithin Reverse Micelles in Deuterated Isooctane. Phys. Rev. E 1997, 56, 5772−5788. (26) Pedersen, J. S.; Schurtenberger, P. Scattering Functions of Semiflexible Polymers with and without Excluded Volume Effects. Macromolecules 1996, 29, 7602−7612. (27) Cates, M. E. Reptation of Living Polymers - Dynamics of Entangled Polymers in the Presence of Reversible Chain-Scission Reactions. Macromolecules 1987, 20, 2289−2296. (28) Derjaguin, B.; Landau, L. Theory of the Stability of Strongly Charged Lyophobic Sols and of the Adhesion of Strongly Charged Particles in Solutions of Electrolytes. Acta Phys. Chem. URSS 1941, 14, 633−662. (29) Verwey, E. J. W.; Overbeek, J. T. G. Theory of the stability of lyophobic colloids; Elsevier: Amsterdam, 1948. (30) Israelachvili, J. N. Intermolecular and Surface Forces, 3rd ed.; Academic Press: New York, 2011. 12667
DOI: 10.1021/acs.jpcc.5b00698 J. Phys. Chem. C 2015, 119, 12660−12667
