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Coalescence Control of Elastomer Clusters by Fixed Surface Charges Cornelius Gauer, Hua Wu, and Massimo Morbidelli* Institute for Chemical and Bioengineering, Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland ReceiVed: July 31, 2009; ReVised Manuscript ReceiVed: December 14, 2009
We studied the coalescence behavior of a fluorinated elastomer colloid, stabilized by fixed surface charges, with a glass transition temperature of about -20 °C, as a function of temperature under diffusion-limited cluster-cluster aggregation (DLCA) conditions. We first measured the aggregation kinetics by in situ dynamic light scattering and then simulated it through the Smoluchowski approach (i.e., population balance equations) using the only unknown parameter, the fractal dimension Df of the clusters, as the fit parameter. It was found that the estimated Df value increased as the temperature increased, starting from 1.7 at 25 °C and reaching the upper limit of 3.0 for T g 55 °C. These results indicate that the coalescence extent increases as the temperature increases. Such temperature-dependent coalescence behavior cannot be explained by thermodynamic considerations, and it must be related to a certain kinetic resistance. We explain this effect by considering the resistance of the fixed charges to relocation on the particle surface, which decreases as the temperature increases. 1. Introduction Elastomers, when produced by emulsion polymerization, are in the form of soft colloidal particles dispersed in water. In contrast to rigid colloidal particles (e.g., many inorganic oxides and metals), soft elastomer particles can deform or even fuse upon physical contact as a result of polymer-chain interdiffusion, leading to so-called coalescence.1,2 Recently,3,4 we have studied the aggregation behavior of two elastomer colloids with the same polymer composition but with one stabilized by ionic surfactants and the other stabilized by fixed charges originating from the polymer-chain end groups. It was found that, at 25 °C, which is sufficiently above the glass transition temperature of the elastomers to ensure adequate polymer flowability, complete cluster coalescence occurred during aggregation only for surfactant-stabilized particles, whereas particles carrying fixed charges formed fractal clusters with a fractal dimension of Df ) 1.7 under diffusion-limited cluster-cluster aggregation (DLCA) conditions and Df ) 2.1 in the reaction-limited cluster-cluster aggregation (RLCA) regime. This indicates that the coalescence of elastomer particles can be controlled by acting on their surface properties. This finding is explored more deeply in this work, where we investigate how temperature can affect such coalescence behavior during aggregation for an elastomer colloid stabilized by fixed charges. We performed the aggregation under DLCA conditions and measured the time evolution of the average hydrodynamic radius in situ using dynamic light scattering. We chose the DLCA limit for studying the particle coalescence because the time evolution of the measured cluster size in this case is determined uniquely by the Df value of the clusters.5,6 In particular, numerous studies6–22 have verified that DLCA kinetics follows a power law with a scaling exponent equal to 1/Df, which allows for the estimatation of the value of Df and, thus, for the quantification of the extent of cluster coalescence. * To whom correspondence should be addressed. E-mail: morbidelli@ chem.ethz.ch. Tel.: 0041-44-6323034.
In practice, however, the power-law regime cannot always be reached because of limitations, such as large sizes of the primary particles, high polymer densities, and so on, that constrain the upper limit of the cluster size above which sedimentation becomes effective. Thus, we proposed to simulate the measured aggregation kinetics by applying the Smoluchowski kinetic approach, based on population balance equations (PBE), using the only unknown parameter, Df, as the free parameter for the fit. In this way, we did not need to monitor the kinetics until reaching the power-law regime. In fact, the proposed approach was used recently23 to investigate the effect of the tetrafluoroethylene (TFE) fraction, copolymerized within fluorinated elastomer particles, on the coalescence behavior of the particles. It was found that the thus-obtained fractal dimension Df was well correlated with the TFE fraction inside the particles, with a value equal to 3.0 in the absence of TFE and 1.7 when 75% TFE was present in the particles. The former indicates full coalescence of particles during aggregation, and the latter, negligible coalescence. 2. Theoretical Background: The PBE Modeling Approach At low particle concentrations, the time evolution of the cluster mass distribution (CMD), Ni(t), can be modeled by the Smoluchowski kinetic approach.24 Irreversible sticking of colliding particles is regarded as a second-order process, so that the corresponding mass or PBE can be formulated in discrete form as24–27 ∞ i-1 dNi(t) 1 Ki,jNi(t) Nj(t) + K N (t) Nj(t) )dt 2 j)1 i-j,j i-j j)1
∑
∑
(1) where Ki,j is the rate constant or kernel, for which the typical expression under DLCA conditions can be written as25,26,28–32
10.1021/jp907348e 2010 American Chemical Society Published on Web 01/07/2010
Coalescence Control of Elastomer Clusters
Ki,j )
KB (i1/Df + j1/Df)(i-1/Df + j-1/Df) W 4
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(2)
In eq 2, KB ) 8kT/(3µl), where kT is the thermal energy and µl is the dynamic viscosity of the liquid dispersant, is the Smoluchowski rate constant. The quantity W in eq 2 is the Fuchs stability ratio, which, under DLCA conditions, is basically a constant, having a value of approximately 212,28,29,33–39 and accounting for reduced aggregation efficiency mainly due to hydrodynamic resistance upon particle encounter.30,40 Df in eq 2 denotes the fractal dimension, which defines the sizes of the two colliding clusters (Ri ∝ i1/Df) and, thus, their diffusion coefficients and collision cross section.5,26,41–43 In our previous studies,3,4,20,44–46 we exploited this fact by introducing the dimensionless time, τ, and dimensionless CMD, Xi,29,44 as follows
τ)
8kTN1,0 t 3µlW
(3)
Ni N1,0
(4)
Xi )
where N1,0 ) 3φ/(4πRp3) is the initial number concentration of primary particles. In this case, the PBE (eq 1) reduces to the dimensionless form ∞ i-1 dXi 1 βi,jXiXj + β X X )dτ 2 j)1 i-j,j i-j j j)1
∑
∑
(5)
and the kernel (eq 2) reduces to
βi,j )
(i1/Df + j1/Df)(i-1/Df + j-1/Df) 4
(6)
In this way, the evolution of Xi in τ is a function of only Df. The numerical procedure used to solve the PBE (eq 5) to obtain Xi has been described elsewhere.4,44 The kinetic data used to quantify the coalescence extent in this study are the time evolutions of the average hydrodynamic radius, 〈Rh〉, measured in situ by dynamic light scattering (DLS) at a fixed angle, θ, or scattering vector, q. The relation between the measured values of 〈Rh〉 and the dimensionless CMD, Xi computed from eq 5, is given by47
〈Rh〉 )
∑ Xii2Pi(q) ∑ Xii2Pi(q)Rh,i-1
(7)
where Pi(q) and Rh,i are the form factor and the effective hydrodynamic radius, respectively, of a cluster with mass i. In the case of complete coalescence (Df ) 3), a cluster becomes a spherical particle; in this case, Pi(q) is calculated according to Lorenz-Mie theory,48 using the subroutine developed by Wiscombe,49 and Rh,i ) i1/3Rp. In the case of fractal clusters (Df < 3), Pi(q) ) P1(q) × Si(q), where P1(q) is the primary particle form factor, given by the Rayleigh-Debye-Gans (RDG) expression48,50
[
P1(q) ) 9
sin(qRp) - (qRp) cos(qRp) (qRp)3
]
2
(8)
and Si(q) is the structure factor, computed using the Fisher-Burford expression51,52
(
Si(q) ) 1 +
2 2q2Rg,i 3Df
)
-Df/2
(9)
with Rg,i being the radius of gyration of the cluster with mass i. Both the hydrodynamic and gyration radii, Rh,i and Rg,i, respectively, are calculated based on Df as described in the literature.53,54 It should be noted from eqs 5-9 that, if various DLCA processes produce clusters of the same structure (Df value), independent of the particle composition, size, concentration, and coagulant type, all of the kinetic data (e.g., time evolutions of the average hydrodynamic radius) collapse onto a single mastercurve when they are plotted in terms of the dimensionless time τ. On the other hand, if the kinetic data of different DLCA processes cannot be merged onto a single curve, this must be related to differences in the Df values. It is this feature that motivated us to use DLCA conditions to investigate the coalescence behavior of elastomer particles. In particular, we first measured the DLCA kinetics and then applied the PBE modeling approach to simulate the measured kinetics using Df as the fit parameter. The obtained Df value reflects the coalescence extent. 3. Experiments 3.1. Investigated Colloid. The colloid of interest was an aqueous dispersion of fluorinated elastomer particles, synthesized by surfactant-free emulsion polymerization and provided by Solvay Solexis (Bollate, Italy). The particles were stabilized purely by fixed negative charges originating from dissociation of polymer-chain end groups. The effective surface charge density estimated from fitting the measured values of the Fuchs stability ratio was 0.32 sites/nm2.4 The isoelectric point, determined by a Zetasizer Nano instrument (Malvern Instruments, Malvern, U.K.) using HNO3, was below pH 1. The mean radius of the primary particles was Rp ) 115 nm. The glass transition point of the elastomer phase was at about -20 °C, the refractive index was 1.37, and the density was about 1.8 kg/L. More details about the colloid can be found in our previous work.4 It has been found4 that the particles fuse easily when they are dried at 25 °C (latex film formation). This fact indicates that contacting elastomer particles can coalesce completely, which can be supported from a thermodynamic point of view. 3.2. DLCA Experiments. All aggregation experiments were conducted at temperatures between 25 and 70 °C. To guarantee DLCA conditions, coagulant concentrations were chosen well above the critical coagulant concentration (CCC) for the onset of DLCA.4 In particular, we chose 2.0 mol/L for nitric acid (HNO3), 2.0 and 5.1 mol/L for sodium chloride (NaCl), and 1.0 and 2.5 mol/L for magnesium sulfate (MgSO4). Deionized water for dilution was purified through a Millipore Simpak 2 column and filtered through 0.1 µm Acrodisc syringe filters (Pall, Portsmouth, U.K.) to remove any potential dust. The experiments were started by pouring 4 parts prediluted coagulant into 1 part prediluted colloid to obtain a particle volume fraction of φ ) 5.0 × 10-5. After a few seconds equilibration time, the aggregating system (50 mL) was portioned into two glass vials.
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One vial was used for particle size measurement by DLS and the second was stored upside down. The vials were turned and exchanged for measurement every 10-20 min. Such a procedure was necessary to prevent particle sedimentation, which was possible because of the rather high polymer density with respect to water. For all experiments at different temperatures, the aggregating colloids were stored in a thermostat, and the chamber of the light scattering device was heated at the same temperature by a circuit with an external thermostat. The reported time evolutions of the average hydrodynamic radius are averages from at least three runs each. The DLS measurements were carried out at an angle of θ ) 90°, on a BI-200SM goniometer system (Brookhaven Instruments, Holtsville, NY), equipped with a solid-state Ventus LP532 laser (Laser Quantum, Stockport, U.K.) with a wavelength of λ0 ) 532 nm. The corresponding scattering vector is defined by q ) 4πn0/λ0 × sin(θ/2), where n0 represents the refractive index of the continuous phase. Note that, in converting the measured average diffusivity 〈D〉 to the average hydrodynamic radius by the Stokes-Einstein relation47,50,55
〈Rh〉 )
kT 6πµ1〈D〉
(10)
the variations in the dispersant viscosity µl due to the rather high concentrations of the electrolytes must be taken into account, as estimated based on available literature information.56 4. Results and Discussion 4.1. Role of Temperature in Particle Coalescence. We first compare the time evolutions of the average hydrodynamic radius, 〈Rh〉, measured at two temperatures, T ) 25 and 70 °C, for the cases where HNO3, NaCl, and MgSO4 were used as coagulants, as shown in parts a-c, respectively, of Figure 1. It can be seen that, in all cases, 〈Rh〉 initially evolves faster at 70 °C than at 25 °C. Such behavior can be expected when one considers that the dispersant viscosities are reduced with increasing temperature; see Table 1. Then, after a certain aggregation time, crossover occurs; that is, the 〈Rh〉 evolution becomes faster at 25 °C than at 70 °C. As discussed in the Theoretical Background section, this is obviously related to the difference in the cluster structures at the two temperatures. Before addressing the problem of cluster structure variation with temperature, let us investigate whether the coagulant type affects the cluster structure. This can be done by plotting the kinetic data in Figure 1 as a function of the dimensionless time τ, defined in eq 3, as given in Figure 2 (symbols). In this way, one can eliminate the effects of variations in temperature, viscosity (which depends on both temperature and coagulant type), and initial particle concentration (N1,0). As mentioned in the Theoretical Background section, W under DLCA conditions is basically a constant. Its value is typically between 1 and 3,4 which is generally due to the viscous resistance when clusters approach, although additional interactions (e.g., hydration forces) can also play a role. Thus, for the calculation of τ, we have tuned the W values around 2 (see Table 1) to achieve the best overlapping of the kinetic data. In addition, the involved minor tuning eventually also accounts for all inaccuracies in the measurements and parameter evaluations. It should be noted that such variations in W shift only the position of the kinetic curve but not its shape. The latter is determined by the cluster structure (Df) and the aggregation mechanism (i.e., DLCA or RLCA). In fact, it is well-known44–46,57 that, under RLCA, even
Figure 1. Time evolutions of the average hydrodynamic radius, 〈Rh〉, measured under DLCA conditions at two temperatures, T ) 25 °C (filled symbols) and 70 °C (open symbols), using the coagulants (a) HNO3, (b) NaCl, and (c) MgSO4. Particle volume fraction φ ) 5.0 × 10-5.
Figure 2. Replotting of the 〈Rh〉 data in Figure 1 as a function of the dimensionless time τ, defined by eq 3. The solid curves are the PBE simulations with Df ) 1.7 and 3.0 at T ) 25 and 70 °C, respectively.
if the W values differ by orders of magnitude, when the kinetic data measured under different conditions are plotted against the dimensionless time, they all collapse onto a single master-curve. Figure 2 shows that all of the kinetic data measured using the
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TABLE 1: Absolute Dynamic Dispersant Viscosities with Respect to the Coagulant Concentration, Estimated from Reference 56, and W Values Used for the Calculation of τ (Eq 3) T ) 25 °C HNO3, 2.0 mol/L NaCl, 2.0 mol/L NaCl, 5.1 mol/L MgSO4, 1.0 mol/L NaOH, 6.1 mol/L NaOH, 8.4 mol/L NaOH, 10.0 mol/L
T ) 70 °C
µl (mPa s)
W
µl (mPa s)
W
0.94 1.09 1.72 4.1 -
2.0 1.8 2.6 1.4 -
0.43 0.49 0.77 0.78 1.3 2.1 2.6
1.6 1.5 2.0 2.7 1.4 1.7 2.0
different coagulants collapsed onto a single master-curve for T ) 25 °C and onto another one for T ) 70 °C. This clearly indicates that the cluster structure was independent of the coagulant type but dependent on the aggregation temperature. Let us now apply the PBE approach to simulate the two sets of kinetic data in Figure 2, using Df as the only fit parameter. The PBE solutions are shown in Figure 2 by the solid curves, and the obtained values for Df are 1.7 and 3.0 at 25 and 70 °C, respectively. The former is well in the range of the Df values for DLCA clusters of rigid particles, indicating that, for the DLCA carried out at T ) 25 °C, the elastomer particles behaved as if they were rigid particles with negligible coalescence. Instead, at T ) 70 °C, the obtained value of Df ) 3.0 reveals that the DLCA clusters were practically spherical particles; in other words, complete coalescence occurred in this case. Because the reliability of the structure information obtained from PBE solutions was confirmed by cryogenic scanning electron microscopy (cryo-SEM) image analysis in related work,4,23 further validation of the structure is not provided in the present article. From the results at 25 and 70 °C in Figure 2, one would naturally ask what would happen if the DLCA experiments were carried out at intermediate temperatures. To explore the transition between the two extremes, we performed the DLCA experiments using HNO3 (2.0 mol/L) as the coagulant at four additional temperatures: 40, 50, 55, and 60 °C. The results are reported in Figure 3, again as a function of the dimensionless time τ, together with those from Figure 2. Then, we simulated all of the kinetic curves using the PBE approach to obtain the Df values. The PBE solutions (solid curves in Figure 3) are in good agreement with the experiments, and the obtained values for Df are 1.7, 2.4, 2.5, and 3.0 for T ) 25, 40, 50, and g55
°C, respectively. These results suggest a gradual change in the cluster structure from typical DLCA fractals to sphere-like particles with a critical temperature of 55 °C, above which complete coalescence occurs. 4.2. Temperature-Dependent Coalescence Resistance. The fractal clusters with Df ) 1.7 at 25 °C were already observed in our previous work,4 and negligible coalescence of the elastomer particles in this case was explained by the resistance of the fixed surface charges against relocation upon particle deformation. This explanation is supported by the fact that the particles can completely coalesce (film formation) at 25 °C upon drying, as observed through conventional SEM images.4 Moreover, film formation was also observed during cluster sedimentation. This indicates that the barrier against coalescence is rather weak with respect to capillary or compression forces. Now, the complete coalescence at 70 °C further confirms that such resistance is rather weak and decreases as the temperature increases. We believe that this is related to the fact that, as the temperature increases, the flexibility of the end-group chains increases and the viscosity of the elastomer decreases, both of which favor the relocation of the fixed charges, thus facilitating coalescence. To support the above explanation, let us perform a simple thermodynamic analysis of the energy balance for the coalescence of two contacting primary particles. Without entropic contribution, the change in free energy upon coalescence is given by
∆G ) γ(S2 - 2S1) + (Uel,2 - 2Uel,1)
where S1 and S2 are the surface areas of the primary particle and the coalesced doublet, respectively, and Uel,1 and Uel,2 are the corresponding electrostatic energies. For the particledispersant surface tension, γ, we can take the value for a polytetrafluoroethylene (PTFE)-water interface,58 namely, 50 × 10-3 J/m2, thereby neglecting any contribution of the charged surface groups. Then, we obtain γ(S2 - 2S1) ≈ -4 × 10-15 J for the change in surface energy. Approximate values for the electrostatic energies of the particle surface can be obtained by integrating59
Uel,i ) Si
∫ σ(ψs) dψs
(12)
In the limit of low surface potential and high electrolyte concentration, as under the present DLCA conditions, the linear approximation for the relation between the surface potential, ψs, and the surface charge density, σ, can be applied, namely, σ ) ε0εrκψs,60 where ε0εr is the permittivity and κ is the Debye-Hu¨ckel parameter, accounting for ionic strength. Then, with the σ expression from eq 12, we obtain
Uel,i ) Siε0εrκψs2 /2
Figure 3. Experimental 〈Rh〉 evolutions (symbols) as a function of the dimensionless time τ, using 2.0 mol/L HNO3 at different aggregation temperatures. The solid curves are the PBE simulations with Df ) 1.7, 2.4, 2.5, and 3.0, for T ) 25, 40, 50, and g55 °C, respectively.
(11)
(13)
Considering the case of using NaCl (2.0 mol/L) as the coagulant, for which σ1 ) -40 mC/m2 (and σ2 ) -50.4 mC/m2),4 it follows that the gain of electrostatic energy from doublet coalescence is Uel,2 - 2Uel,1 ≈ 3 × 10-17 J, which is 2 orders of magnitude smaller than the energy loss due to the surface reduction (approximately -4 × 10-15 J), leading to a strongly negative ∆G value. This shows that coalescence is always preferred from a thermodynamic point of view, and with this regard, no significant temperature effect
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Figure 4. 〈Rh〉 evolutions as a function of the dimensionless time τ, measured using NaOH as the coagulant, at two temperatures (T ) 25 and 70 °C) and three NaOH concentrations. The solid curves are the PBE simulations with Df ) 1.7 at both 6.1 mol/L NaOH and T ) 25 °C and 10.0 mol/L NaOH and T ) 70 °C, and with Df ) 2.7 at 8.4 mol/L NaOH and T ) 70 °C.
should be observed. This further supports the conclusion that the coalescence process is kinetically controlled. 4.3. Abnormal Aggregation Behavior with NaOH. The above experimental results demonstrate that the cluster structures, though depending on temperature, are independent of the coagulant type. However, among the three coagulants, there is no basic coagulant. To determine whether the same conclusion can be applied to basic coagulants, we performed the aggregation experiments using sodium hydroxide (NaOH) as the coagulant. We first determined the CCC for NaOH, which is 1.5 mol/L, and then ran the DLCA experiments at a NaOH concentration of 6.1 mol/L at 25 and 70 °C. The corresponding results are displayed in Figure 4 as a function of τ, with the filled boxes representing T ) 25 °C and the open stars representing T ) 70 °C. At T ) 25 °C, the experimental data are well simulated by the PBE using Df ) 1.7, which is the same value as obtained for the other three types of coagulants in Figure 2, confirming that, in this case, the cluster structure is independent of the coagulant type. At T ) 70 °C, however, the aggregation kinetics with NaOH in Figure 4 is completely different from that found for the other three coagulants in Figure 2. After the initial growth, 〈Rh〉 basically no longerr evolves with time, indicating the occurrence of some restabilization. This is most probably due to the fact that the employed coagulant concentration was insufficient to keep the aggregation in the DLCA regime throughout the entire time interval, because of charge accumulation as a result of surface reduction from coalescence. An analogous example is the aggregation observed using NaCl as the coagulant at 2.0 mol/L and T ) 70 °C, as shown in Figure 5 (open circles). When this is compared with the aggregation at the same temperature but at a higher NaCl concentration of 5.1 mol/L (open triangles in Figure 5), it is seen that, initially, the two sets of results follow the same curve, and then the 〈Rh〉 evolution becomes slower in the case of 2.0 mol/L NaCl than in the case of 5.1 mol/L. Because the predicted value is Df ) 3.0 (i.e., complete coalescence occurs) in the case of 5.1 mol/L, the decrease in the 〈Rh〉 evolution rate in the case of 2.0 mol/L NaCl (CCC ) 1.3 mol/L) is basically related to restabilization of the system in the course of aggregation and cluster coalescence. When restabilization occurs, the aggregation process changes from initially DLCA to RLCA (reaction-limited cluster-cluster aggregation) kinetics. As demonstrated in our previous work,3 the kinetic data under RLCA conditions are interaction-specific
Gauer et al.
Figure 5. Different 〈Rh〉 evolutions as a function of τ, measured at T ) 70 °C with NaCl as the coagulant at two concentrations. The solid curve is the PBE simulation with Df ) 3.0 for the case of 5.1 mol/L NaCl. The slowing in the 〈Rh〉 evolution in the case of 2.0 mol/L NaCl clearly indicates the occurrence of restabilization.
and do not collapse onto a single master-curve. In fact, the 〈Rh〉 curve in Figure 4 for 6.1 mol/L NaOH does not have the same shape as that in Figure 5 for 2.0 mol/L NaCl. Because the observed restabilization disappears when the NaCl concentration increases from 2.0 to 5.1 mol/L, it is worth investigating whether this is the case for NaOH as well. Thus, we carried out the aggregation at two higher NaOH concentrations, 8.4 and 10.0 mol/L, again at T ) 70 °C. The results are also shown in Figure 4. It is interesting to find that the 〈Rh〉 growth rate increases as the NaOH concentration increases. When the two 〈Rh〉 curves are simulated using the PBE, we obtain Df ) 2.7 and 1.7 for the NaOH concentrations of 8.4 and 10.0 mol/L, respectively. Thus, as the NaOH concentration increased, the restabilization phenomenon indeed disappeared, but in this case, the coalescence extent also decreased, until reaching the limit of the DLCA fractal-cluster regime. This behavior is specific for NaOH and its complete explanation requires a detailed understanding of the interactions between the particle surface functional groups and NaOH in solution, which is currently not available. However, the above results indicate that, for the given elastomer particles, NaOH acts as a special coagulant: by changing its concentration, one can tune the structure of the clusters formed during the DLCA process. 5. Conclusions The coalescence behavior of a fluorinated elastomer colloid, stabilized by fixed surface charges, with a glass transition temperature of about -20 °C has been studied in the diffusion-limited cluster-cluster aggregation (DLCA) regime, in the temperature range from 25 to 70 °C, using different electrolytes as coagulants. In particular, we first measured the time evolutions of the average hydrodynamic radius, 〈Rh〉, by in situ dynamic light scattering. Then, the obtained kinetic data were simulated by the Smoluchowski kinetic approach, based on the PBE, using the only unknown parameter, the fractal dimension Df of the clusters, as the fit parameter. The estimated Df value is correlated to the coalescence extent of the particles during aggregation. It was found that, at T ) 25 °C, all of the DLCA kinetic data obtained using HNO3, NaCl, NaOH, and MgSO4 as the coagulants, when plotted as a function of a properly defined dimensionless time, collapsed onto a single master-curve. When the master-curve was simulated by the PBE, we obtained the value Df ) 1.7, a typical value for DLCA clusters of rigid particles. This indicates that, at 25 °C, the elastomer particles
Coalescence Control of Elastomer Clusters behave like rigid particles, with negligible coalescence, independent of the type of coagulant used for the aggregation. However, as the aggregation temperature increased, the estimated Df value from the DLCA kinetic data increased and reached the upper limit of 3.0 for T g 55 °C. This result indicates that T ) 55 °C represents the critical temperature above which complete coalescence between particles occurs during aggregation, so that sphere-like clusters are formed. Such temperature-dependent coalescence behavior cannot be explained by thermodynamic considerations because the free energy change upon particle coalescence is always negative. Thus, it must be related to a certain kinetic resistance. We explain this by considering the fact that the particles are stabilized purely by fixed charges originating from the polymerchain end groups. These fixed charges, upon contact during coalescence, repel each other and need to be relocated, but because of both a certain resistance from the bulk polymer phase and the rigidity of the polymer chains, such relocation is difficult at T ) 25 °C. However, as the temperature increases, the flexibility of the end-group chains increases, and the viscosity of the polymer phase decreases, both of which favor the relocation of the fixed charges, thus facilitating coalescence. In addition, when NaOH was used as the coagulant, a peculiar behavior was observed. At T ) 70 °C, the coalescence extent of particles during aggregation was found to depend on the NaOH concentration, allowing even clusters with Df ) 1.7 to be generated. This phenomenon, although difficult to explain, can provide a tool for controlling the cluster structure of coalescing systems with fixed charges, at least of the type considered in this work. Acknowledgment. Discussions with Marco Lattuada significantly improved this article. Latex supplied by Solvay Solexis and funding from the Swiss National Science Foundation (Grant 200020-126487/1) are gratefully acknowledged. Note Added after ASAP Publication. This paper was published on the Web on January 7, 2010, before all corrections were made. The corrected version was reposted on January 11, 2010. References and Notes (1) Mazur, S. Coalescence of Polymer Particles. In Polymer Powder Technology; Narkis, M., Rosenzweig, N., Eds.; Wiley: Chichester, U.K., 1995. (2) Keddie, J. L. Mater. Sci. Eng. R 1997, 21, 101–170. (3) Gauer, C.; Jia, Z.; Wu, H.; Morbidelli, M. Langmuir 2009, 25, 9703–9713. (4) Gauer, C.; Wu, H.; Morbidelli, M. Langmuir 2009, 25, 12073– 12083. (5) Meakin, P. AdV. Colloid Interface Sci. 1988, 28, 249–331. (6) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Klein, R.; Ball, R. C.; Meakin, P. J. Phys.-Condens. Mater. 1990, 2, 3093–3113. (7) Weitz, D. A.; Oliveria, M. Phys. ReV. Lett. 1984, 52, 1433–1436. (8) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. ReV. Lett. 1984, 53, 1657–1660. (9) Aubert, C.; Cannell, D. S. Phys. ReV. Lett. 1986, 56, 738–741. (10) Bolle, G.; Cametti, C.; Codastefano, P.; Tartaglia, P. Phys. ReV. A 1987, 35, 837–841. (11) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360–362. (12) Midmore, B. R. J. Chem. Soc., Faraday Trans. 1990, 86, 3763– 3768. (13) Martin, J. E.; Wilcoxon, J. P.; Schaefer, D.; Odinek, J. Phys. ReV. A 1990, 41, 4379–4391. (14) Carpineti, M.; Ferri, F.; Giglio, M.; Paganini, E.; Perini, U. Phys. ReV. A 1990, 42, 7347–7354. (15) Shih, W. Y.; Liu, J.; Shih, W.-H.; Aksay, I. A. J. Stat. Phys. 1991, 62, 961–984. (16) Zhou, Z.; Chu, B. J. Colloid Interface Sci. 1991, 143, 356–365. (17) Burns, J. L.; Yan, Y. D.; Jameson, G. J.; Biggs, S. Langmuir 1997, 13, 6413–6420.
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