Drastic Variation of the Microstructure Formation in a Charged Sphere

DOI: 10.1021/cg9015806

Drastic Variation of the Microstructure Formation in a Charged Sphere Colloidal Model System by Adding Merely Tiny Amounts of Larger Particles

2010, Vol. 10 2258–2266

Andreas Engelbrecht and Hans Joachim Sch€ ope* Institut f€ ur Physik, Johannes Gutenberg-Universit€ at Mainz, Staudingerweg 7, 55128 Mainz, Germany Received December 16, 2009; Revised Manuscript Received February 26, 2010

ABSTRACT: We have investigated the changes of the crystallization scenario in charged sphere colloidal suspensions upon adding tiny amounts of a second, larger and higher charged particle species (size ratio 4.3, charge ratio 1.6). For even minute amounts of added particles, less than 1%, the whole crystallization behavior changes dramatically and for this reason the resulting microstructure of the solidified material. Both nucleation and growth of crystals slow down drastically and considerably coarsen the resulting microstructure. We show that this is related to a considerable decrease of the kinetic prefactors of both nucleation and growth, while at the same time the nucleation barrier height shows only a moderate 5% increase.

Introduction A complete understanding of the crystallization process is one of the long-standing problems in condensed matter physics, and remains of intense research interest. In the classical picture of crystallization, three processes can be discriminated: crystal nucleation, growth, and ripening. The extensive control of these processes is highly needed to adjust the microstructure of the arising material in a precise way giving the possibility to create new materials with desired properties.1,2 In the classical nucleation theory (CNT),3,4 the nucleation rate density depends exponentially on the ratio between some intrinsic energy scale and the thermal energy J = J0 exp (-ΔG*/kBT), where the height of the nucleation rate barrier ΔG* = 16πγ3/3(nΔμ)2 is given by surface tension γ of the critical nucleus and the “undercooling” Δμ. The kinetic prefactor J0 ∼ KþZ is mainly given by the Zeldovich factor Z and the particle attachment rate Kþ. The absolute nucleation rate density can be modified either by varying the nucleation barrier height or by modifying the rate of particle attachment to the crystal liquid interface. The same applies for crystal growth in the reaction controlled limit described by Wilson and Frenkel.3,4 Although the classical theories have existed for almost 100 years, the experimental determination of crystal nucleation and crystal growth is still a great challenge. A great deal of progress in understanding the solidification process has been made in recent years using colloidal suspensions as model systems studying crystallization and vitrification.5-8 Because of their large size, both the dynamics and kinetics of these systems are experimentally much more accessible than is the case for atomic and molecular systems. Close analogies to atomic systems are observed which can be exploited to address questions not accessible in atomic solidification. Under equilibrium conditions, colloidal crystals are formed in suspensions of spherical particles if the particle concentration is higher than a certain freezing volume fraction. The colloidal particles are either stabilized by sterical stabilization, or by electrostatic repulsion. The latter can be *To whom correspondence should be addressed. E-mail: jschoepe@ uni-mainz.de. pubs.acs.org/crystal

Published on Web 03/24/2010

well described in terms of a screened Coulomb potential. Because of the long-range nature of the screened Coulomb interaction, colloidal crystals with bcc structure may form in suspensions of highly charged spherical particles at very low particle concentrations (particle number density n = 1017-1018m-3, volume fraction φ = 0.01-0.1%), if the concentration c of the screening electrolyte is kept at or below the micromolar level.9 The pair energy in monodisperse charged colloidal systems of radius a and effective charge Z* can be written on the mean field level as VðrÞ ¼

ðZ eÞ2 expðKaÞ 2 expð - KrÞ r 4πε0 εr 1 þ Ka

ð1Þ

with the screening parameter κ calculated via K2 ¼

e2 ðnZ þ nsalt Þ ε0 εr k B T

ð2Þ

where ε0εr is the dielectric permittivity of the suspension, kBT is the thermal energy, and nsalt = 2000NAc is the number density of monovalent background electrolyte of concentration c with NA being Avogadro’s number. The interaction is very sensitive to the screening electrolyte and the particle concentration. Crystallization can also be observed in binary mixtures of colloidal model systems. Using the correct size ratio alarge/ asmall and mixing ratio nlarge/nsmall, crystal superstructures can be prepared in hard sphere (HS) suspensions. Otherwise, complete vitrification or phase separation in a one-component crystal phase and a fluid/glassy phase is obtained.10,11 Binary charged sphere (CS) mixtures crystallize building superstructures or substitutional crystals as a function of size and charge ratio Z*large/Z*small and amount of added electrolyte.12-15 The crystallization kinetics in one-component colloidal systems was studied quite often,6,8,16-19 while binary systems were investigated only occasionally. In colloidal HS, the addition of slightly larger and smaller particles was investigated:20,21 adding only small amounts of a second larger or smaller component slows down the kinetics r 2010 American Chemical Society

Article

Crystal Growth & Design, Vol. 10, No. 5, 2010

and modifies the crystallization scenario. Interestingly, in these studies the average crystal size was reduced. In colloidal CS of small size and charge ratio,22 it was observed that at a specific mixing ratio corresponding to an enhanced crystal stability the crystallization kinetics was also modified. Here increased limiting growth velocities were found. In another case, at size and charge ratios closer to unity,23 it was observed that nucleation in a 1:1 mixture was slightly accelerated. In a third study on a system of intermediate size and charge ratio, it was observed that growth was considerably slowed.24 Comprehensive measurements comprising a detailed analysis of both nucleation and growth in binary colloidal model systems still have to be performed. The situation is quite similar for the case of heterogeneous nucleation. While homogeneous nucleation was investigated in a number of studies, little is known about heterogeneous nucleation.7 Wall crystals originated by heterogeneous nucleation at the container walls dominate the crystallization scenario in CS at low metastability close to the phase boundary.22,25,26 In combination with unidirectional shear oriented wall crystals can be prepared.27,28 While growth of these crystals is well understood much less is known about their nucleation kinetics.29 Classical theory3,4 predicts a decrease of the nucleation energy barrier in the case of heterogeneous nucleation, while a substrate is present. Heterogeneous nucleation can be induced by either container walls or additional particles acting as seeds. The latter combines bidisperse systems and the study of heterogeneous nucleation. Crystallization in HS close to large spherical impurities was investigated using simulations30 and confocal microscopy.31 While simulations predict a decrease of the nucleation barrier height with increasing diameter of the seed particle, in the experiment heterogeneous nucleation was only observed on seeds with varying curvature where flat surface regions could be found. There are no other experimental investigations present. The systematic determination of heterogeneous nucleation rate densities and the comparison with homogeneous nucleation is still highly desired. With the present study, we address some of the open questions for a binary charged sphere mixture. We performed a crystallization kinetics study adding small amounts of significantly larger and higher charged particles (supposed to work as seeds) to a well characterized charged sphere model system. For just a tiny amount of added particles, less than 1%, the whole crystallization behavior changes dramatically and consequently drastically alters the resulting microstructure of the solidified material. Experimental Section All measurements were performed using two kinds of highly charged spherical particles. The majority component consists of a polystyrene-poly n-butylacrylamide copolymer (a kind gift of BASF Ludwigshafen, Pn-BAPS70; lot no. GK0748). These particles are quite small (diameter 2aPn-BAPS70 = 70 nm, refractive index νPn-BAPS = 1.59) and have an effective charge Z*Pn-BAPS70 = 325 ( 10 obtained by elasticity measurements.32 Under fully deionized conditions, the equilibrium phase boundary is at nfreezing = 1.8 μm-3. Above the freezing transition, the system crystallizes forming bcc crystals. Dyneon perfluor-alkoxylalkan 6902 particles (a kind gift of Dyneon Gendorf, PFA300, lot no. 34C 6003) were used as a second particle species in this experiment. The PFA-particles are larger in size 2aPFA = 300 nm as well as having a higher effective charge of Z*PFA = 530 ( 11. The refractive index of PFA (νPFA =1.36) is well matched to the refractive index of water, which yields the PFA particles to be almost invisible. Therefore, an addition of PFA particles to the suspension does not result in a significantly higher turbidity even for high PFA concentrations.

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Samples were conditioned in a closed system under inert gas atmosphere.14 Gas tight tubes connect several devices including a reservoir to add water, electrolyte, or further particles, an ion exchange column filled with mixed bed ion-exchange resin (Amberlite, Carl Roth, D), a conductivity-meter, and different optical cells: For static light scattering cylindrical cells of 10 mm diameter were used, while for microscopy flat rectangular cells of 10 2 mm2 and 10 1 mm2 cross section were used. All optical cell types are made of quartz glass. During preparation, the suspension is driven through the circuit by a peristaltic pump. In this way, it is kept in a shear molten state until the shear is stopped. Then the particles of the suspension readily start to form crystals, if the particle number density exceeds the freezing concentration nfreezing. Complete crystallization is observed above the melting concentration nmelting. The obtained coexistence region for the Pn-BAPS70 is very narrow: under fully deionized conditions, we obtain nfreezing= 1.8 μm-3 and nmelting= 2 μm-3. The deionization process can be monitored in situ via conductivity measurements, which allows the performance of the experiments under controlled deionized conditions. Thereby typical residual ionic impurity concentrations are on the order of the ion product of water. Further details on the preparation have been given elsewhere.33 The particle number density n was determined by static light scattering. For this purpose, we used a homemade high precision light scattering setup.34 Further details are given elsewhere.34 Growth of heterogeneous nucleated wall crystals was studied by Bragg microscopy using a CMOS-camera (SMX-M73, EHD, D) on a microscope stage (Stemi SV 6, Zeiss, D). Here the sample is illuminated with white light under an angle Θ to obtain a Bragg reflection in the direction of the observing microscope objective. Crystals were observable if oriented properly to fulfill the Bragg condition. Crystals of identical color correspond to identical structure and orientation. Further details of this method have been described at length in one of our previous papers.35 Nucleation, crystal growth, and crystal morphology in the bulk were determined by polarization microscopy. Further details of the applied method and data analysis are given elsewhere.36 During conditioning, the suspension is continuously cycled through the tubing system and kept in a shear molten state. Resolidification after abortion of shear is monitored in a flat flow through optical cell of rectangular cross section (1 10 mm2, Hellma, D). The cell was mounted on the stage of a polarization microscope (Laborlux 12, Leitz, D) equipped with a low resolution objective. For time-resolved measurements, images were recorded by a CMOS-camera (SMXM73, EHD, D) and saved on a computer as bitmap data for later image analysis. For the microstructure analysis, we alternatively used a CCD-camera (Micropublisher 3.3, Qimaging, CA) with deeper colors for better differentiation between individual crystals in the polycrystal. Under crossed polarizers the shear molten fluid appears as almost black background, because the fluid does not influence the polarization direction of the transmitted light, and the amount of depolarized light scattering is small due to very low shape polydispersity. On the other hand, crystals of charged sphere colloidal particles show Bragg-scattering for visible light, because typical distances in these crystals are on the order of the wavelength of visible light. If a crystal scatters light under any Bragg condition, the scattered light will be polarized. The lack of this polarization fraction in the transmitted light for that reason leads to a change in the polarization direction as well. The crystal appears in a bright color depending on the fulfilled Bragg condition and hence the orientation of that crystal. We can distinguish crystals from the remaining melt by color. This allows us to count their total number and determine their lateral size for any time after cessation of the shear. As we are working with low magnification objectives, the minimum detectable crystal size is on the order of 10 μm, which is slightly larger than the critical size of nucleus in a system of CS.37,38 At the detection limit, the occurring crystals show a roughly spherical shape. Immediately after complete solidification of the melt to avoid any distortions of the results by crystal ripening, an analysis of the crystal size was performed by compiling the crystal size distribution. A mosaic-like structure with crystallites in different colors due to different crystal orientations can be obtained with an objective of narrow depths of field and can be interpreted using image analysis.

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Engelbrecht and Sch€ ope

Figure 1. (a) Crystal growth velocities of heterogeneous nucleated wall crystals as a function of rescaled energy density under fully deionized conditions. The data can be described by a fit to the Wilson-Frenkel law. (b) Difference in the chemical potential between the metastable melt and the crystal as a function of the particle number density under fully deionized conditions.

Figure 2. Polarization micrographs closely after solidification for increasing amounts of PFA particles nPFA/nPn-BAPS70 from left to right. The picture size is 1.46 1.94 mm2. The experiments were performed for a particle number density nPn-BAPS70 = 24.9 μm-3 of the majority particle species Pn-BAPS70. In this area of concentration, homogeneous nucleation is the dominant process, while the heterogeneous nucleation at the wall is suppressed. Additionally, the crystal size in a pure suspension of Pn-BAPS70 in this region of particle number densities allows us to resolve single crystallites and to determine their size after solidification as well as to analyze a sufficiently high number of crystallites at once in order to obtain crystal size distributions. Suspension of PFA particles was added to achieve an amount from nPFA = 5 1015 m-3 up to 1.5 1017 m-3 in the binary mixture, corresponding to a particle number density ratio of 0.02% up to 0.7% PFA particles to Pn-BAPS70 particles.

Results and Discussion A. Determination of Supersaturation by Crystal Growth Measurements. Following W€ urth et al.,26 we determined the chemical potential difference Δμ between the supersaturated melt and the formed crystal from growth measurements on heterogeneously nucleated wall crystals. Since growth velocities are on the order of some μm s-1, this is conveniently studied by Bragg microscopy as described above. We measured growth velocities for particle number densities n from close above freezing at 1.8 μm-3 up to 21.0 μm-3 for PnBAPS70. At higher particle number densities, the growth of the wall crystal is already at the early stage constrained by

homogeneously nucleated crystals near the wall; therefore, homogeneous nucleation becomes the dominating process with increasing n. The growth velocity increases with increasing n to a limiting value of v¥ = 13.54 ( 0.14 μm s-1 (Figure 1a) and can be well described by a Wilson-Frenkel law: v = v¥ (1 - exp(-Δμ/ kBT)). The limiting growth velocity is given by v¥ = DdI/l2, where D is an appropriate diffusion coefficient, dI is the thickness of the interfacial region, and l is the mean distance between a particle in the fluid to its place of destination in the crystal. Expressing Δμ in terms of a rescaled energy density Δμ = BΠ* with Π* = (Π - ΠF)/ΠF gives us the possibility to determine Δμ (Figure 1) F denotes freezing.26 The energy density is given as Π = RnV(dNN), with R being the particle coordination number, V(dNN) is the interaction energy at nearest neighbor distance. This approach considers both the direct linear density dependence of Δμ and the pair interaction energy V(r). We obtain B = 1.01 ( 0.04kBT. B. Nucleation, Crystal Growth, and Microstructure Formation by Adding Tiny Amounts of a Second Component with a Larger Radius and Charge. The crystallization kinetics and the crystal morphology were determined using polarization microscopy. Immediately after complete crystallization, the pure Pn-BAPS70 suspension forms a polycrystal made of fine crystallites of irregular shape and with straight facets

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Figure 3. (a) Crystal size distribution for different amounts of PFA particles. The counts are normalized to 1 at the maximum of the distribution. The width of the bins is 20 μm for 0-0.3% and 50 μm for 0.4-0.7% content of PFA particles. (b) Normalized crystal size distribution, crystal size normalized by the average size ; each curve is shifted by 0.75 for clarity.

(Figure 2). Individual crystals appear in different colors, while the grain boundaries are difficult to identify. By adding PFA particles, the crystal size increases up to a point where just a few crystals appear in the observed volume. At the highest PFA particle concentration, the micrograph displays crystals with rounded facets. The thickness of the grain boundaries is increased significantly and can be easily identified as pronounced dark regions. To obtain statistically significant crystal size distributions, we analyzed on average about 250 crystallites in each sample. The 2D projected area of the faceted crystals is determined via software (Image Pro Plus 5.0, Media Cybernetics, US). To extract the crystal size L, we assume the crystals to be of spherical shape, so we get Li = 2Ai1/2/π1/2 with Ai the obtained area of a single crystal. The results are shown in the histograms of Figure 3. Here the number of counted crystallites is set to 1 at the maximum of each distribution. As can be seen easily, the maximum shifts almost by a factor of 3 toward bigger crystallites, while the width is also increasing. The shapes of the distributions for larger additions of PFA particles stay nearly unaffected as can be seen in Figure 3b, where the normalized number is plotted against the normalized crystal size L/, whereas for the lowest amount of added PFA particles a few larger crystals are present modifying the shape of the distribution. In order to obtain time-resolved nucleation rate densities for different particle number densities of the second component nPFA of the mixture, the solidification of the undercooled melt was observed by time-resolved polarization microscopy. The number of newly appearing crystals in the polarization micrographs was counted individually for each frame in five up to eight iterations of the experiment and averaged over the number of iterations. We determined the average number of new crystals mi(t) showing up at frame i, which corresponds to the time t = iΔt with t = 0 being the time of cessation of shear. The time steps were chosen to be Δt = 0.2 s, but had to be increased to 0.5 s in the case of 0.7% PFA content for statistical reasons. From video microscopy, the time-dependent nucleation rate Γ(t) can be obtained. We further require the nucleation rate

densities given by J = Γ(t)/VF(t), the number of appearing crystals per time and free remaining volume. The free volume VF(t) cannot be measured directly; therefore, we calculate the free volume with a model described in detail in ref 36. We express the relative free volume by F(t) = VF(t)/V0 with V0 being the free volume at t = 0, which is equal to the total observed volume in the flow through the cell. With increasing time, the free volume shrinks due to growth of both wall crystal and newly nucleated bulk crystals. The volume of the bulk crystals - not yet intersecting - is given by VB(t)=Σi mi(4/3)πv3(t - τi)3 with the number of nucleated crystals mi at time τi and v the corresponding growth velocity. The Avrami theory39 already accounts for the overlap of bulk crystals at later times during solidification. This leads to the expression F(t) = exp(-VB(t)/V0), which encounters the problem of ignoring the growth of the wall crystal. If this is also considered the relative free volume is given by the following expression:36 V0 - 2Ad0 - 2AvW t FðtÞ ¼ V0 - 2Ad0 0 1 j X 4π m i ðR0 þvðt - τi ÞÞ3 A exp@ 3 i ¼1 V0 - 2Ad0 - 2AvW τi ð3Þ Here a finite size of the bulk crystals R0 is included because appearing crystals can be distinguished from the melt not until they have grown up to a radius of R0 ≈ 10 μm, which is the value we use for the following calculations. Furthermore, the wall crystal grows with the velocity vW and could have a finite size d0 at t = 0 depending on shear and metastability.25 The growth velocity for crystals in the bulk can be extracted directly from the image sequences. For a series of time steps, the diameters of individual crystallites were determined. Thereby, only crystals were selected that did not interfere with other crystallites during growth. The resulting linear increase of the radius is the average radial growth velocity of different crystallographic directions. The

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determination was averaged over several different crystallites during different solidifications. The result is presented in Figure 7b. The wall crystal growth velocity cannot be observed directly in this setup, so we use the results obtained by Bragg microscopy. We here use the free relative volume F(t) for the case of d0 = 0 for simplicity reasons. An example for the nucleation rate Γ(t) and the corresponding relative free volume at 0.04% PFA content is given in Figure 4. The free volume decreases almost linearly at early times, while solely growth at the wall diminishes the free volume. With the onset of bulk nucleation the free volume begins to shrink more rapidly and ultimately runs down to zero at complete solidification. Bulk nucleation starts when about 10% of the sample is crystallized and vanishes when about 40% are crystallized. Only for the samples with the highest concentration of PFA particles F(t) already decreases significantly in the induction period of homogeneous nucleation and therefore has a significant effect on the nucleation rate density. With the nucleation rates measured and the free volume calculated, we compute the time-dependent nucleation rate densities for all measured samples. The time traces of the nucleation rate densities for increasing amounts of the second component are shown in Figure 5. The nucleation scenarios with and without addition of PFA particles are remarkably different. After a finite induc-

Figure 4. Example of the nucleation rate at 0.04% PFA content and the evolution of the relative free volume F(t) = VF(t)/V0.


tion time, the nucleation rate density increases fast to its maximum value. For small or no addition of the PFA component, the rate density decreases shortly after that and only a peak is observed. At around 0.1% addition of PFA particles the shape of the peak begins to flatten out. Instead of a sharp maximum a plateau with almost constant nucleation rate density can be observed. In particular, the data of the fast nucleating samples show a time trace of the nucleation rate density indicating transient nucleation. Kashchiev discussed the transient effects in crystal nucleation in detail.40 He obtained a simple expression for the timedependent nucleation rate density: 2 0 !13 ¥ 2 X m t m A5 ð4Þ ð - 1Þ exp JðtÞ ¼ JSS 41 þ 2@ ti m ¼1 where ti is the induction time of the nucleation process and JSS the steady-state nucleation rate density. Our data can be described using Kashchiev’s theory of transient nucleation, but the fitting procedure is very sensitive to the selected data interval leading to a large systematic error in both fitting parameter. In particular, the induction time displayed a huge scatter, while reasonable data could be obtained for the nucleation rate density. Another approach describing crystal nucleation is the assumption of a time-independent nucleation rate density which is fulfilled for our slowly crystallizing samples. Therefore, we determined the nucleation rate densities by applying a reformulation of Avrami’s model, in which an estimate for the steady-state nucleation rate density is given by the simple expression: JAvrami = βvF4/3, with β = 1.158 being a geometrical factor, v the growth velocity, and F = -3 the crystallite density. This evaluation scheme was already applied to colloids by Aastuen et al.41 The growth velocity of homogeneous nucleated crystals was determined in the timeresolved polarization microscopy measurements, whereas the average crystal sizes were taken from the crystal size distributions. In Figure 6, the results of these determinations are plotted in comparison with the maximum Jmax and mean value of the time-resolved J from the video microscopy and the steady-state nucleation rate densities JSS,Kashchiev obtained by the fitting of Kashchiev’s theory. The four different nucleation rate densities display different absolute values but show a qualitatively similar behavior (Figure 6a): the nucleation rate density decreases by about 1

Figure 5. (a) Time resolved nucleation rate densities for a series of increasing nPFA smoothed over five points. (b, c) Fit of Kashchiev’s theory describing transient nucleation to the data with no and maximum amount of PFA particles.

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In the case of charged colloidal systems, the nucleation energy barrier ΔG* is given by 16πγ3 ð6Þ ΔG ¼ 3ðnΔμÞ2 In Figure 6b we show the comparison of the time averaged nucleation rate densities of the pure Pn-BAPS70 suspension and for the suspension with increasing amount of added PFA particles as a function of chemical potential difference. The behavior of the pure suspension can be well described using CNT fitting the following expression to the data set ! rffiffiffiffiffiffiffiffiffi γ 16πγ3 L 4=3 ð7Þ D n exp J ¼A kB T S 3kB TðnΔμÞ2

Figure 6. (a) Comparison of the maximum values of the timeresolved nucleation rate density Jmax with its mean values , J calculated with Avrami model JAvrami and J from Kashchiev model for transient nucleation JSS,Kashchiev. Error for , Jmax, JAvrami are about 10-30%. Errors for JSS,Kashchiev from transient nucleation as indicated by error bars. (b) Averaged nucleation rate density as a function of the difference in the chemical potential for the pure Pn-BAPS70 suspension (open stars) and for increasing amount of added PFA particles (red points). The data of the pure suspension can be described by a fit based on CNT.37

order of magnitude with an increasing amount of PFA particles. This is also highlighted in Figure 6b, where we plot the mean nucleation rate densities as a function of metastability. As all mixtures have the same phase boundaries as the pure Pn-BAPS70 suspension, we used the result shown in Figure 1b to determine the metastability for all our samples. Furthermore, in Figure 6a there is a pronounced dip in J adding the smallest amount of larger particles. Because of the averaged nucleation rate densities having the smallest error (about 15%) and to stay consistent with our previous work, we will use for further analysis. Wette and Sch€ ope applied the CNT to charged sphere colloids and calculated the nucleation rate density with an explicitly derived kinetic prefactor J0:37 2=3 rffiffiffiffiffiffiffiffiffi 4 γ - 1=3 J ¼ 12 π DL n4=3 expð - ΔG=kB TÞ ð5Þ 3 kB T S where DSL is the long time self-diffusion coefficient and γ is the macroscopic surface tension.

with the fitting parameters A and γ using a constant diffusion coefficient. The nucleation rate density displays a low decrease with decreasing meta stability, whereas the nucleation rate densities adding PFA particles show a much steeper slope: There is a significantly increasing spread with an increasing amount of the second larger and higher charged particle species. Analyzing the characteristic times extracted from the timeresolved nucleation rate densities and the crystal growth velocity of homogeneous nucleated crystals as function of PFA particle concentration, we observe a dramatic slowing down of the crystallization process (Figure 7). The induction times are getting slightly larger (factor 2), whereas the end time of observed nucleation is strongly shifted to longer times (factor 17). Interestingly, the strongest increase is observed adding the smallest amount of larger particles. The orientationally averaged crystal growth velocity of the bulk crystals is larger than the limiting growth velocity in the (110) direction measured for the wall crystals by about 20%. This is in quantitative agreement with previous observations.26 With an increasing amount of added PFA particles the latter quantity displays a nearly linear decrease: crystal growth slows down by more than 50% and drops well below the wall crystal growth velocities of the pure Pn-BAPS70 at the same metastability. As in the saturation limit of the WF growth law, the undercooling does not change the growth velocity, and the observed changes are attributed to changes of the kinetic prefactor of the WF-law. C. Determination of Surface Tension and Nucleation Energy Barrier by Means of CNT. One possibility to analyze the data in terms of CNT is to use the numerical expression given by eq 5 to calculate the surface tension. With a known diffusion coefficient DSL, it is possible to solve eq 5 for γ as the only remained unknown physical quantity. Since we did not obtain long time self-diffusion coefficients directly by dynamic light scattering experiments, we have to make some assumptions about it. The long time self-diffusion coefficient at freezing is given by DSL ≈ 0.1DSS as shown experimentally and in simulations42 with DSS ≈ D0 = kBT/6πηa the StokesEinstein diffusion coefficient and η the viscosity of the dispersing agent. Former studies on the self-diffusion coefficient43 lead to the result of a nearly linear decrease with increasing particle concentration. Systematic measurements in the metastable fluid using dynamic light scattering (DLS) are still missing because the metastable state only exists for a very short time (seconds) before crystallization occurs, making a determination of DSL using DLS impossible. Following classical theory of nucleation and reaction controlled growth,3,4,44,45 the single particle attachment during

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Figure 7. (a) Induction times and the time span between the first appearance of crystals and the last observed nucleation event as a function of the particle number ratio and metastability. (b) The averaged growth velocities of bulk crystals as a function of the particle number density ratio and metastability. The pure suspension displays a constant growth velocity as a function of Δμ as indicated by the dashed line.

nucleation and growth follows the same mechanism. As the limiting crystal growth velocity of the WF-law is connected with the long time self-diffusion coefficient (see above), we approximated the long time self-diffusion coefficient in the case of the used mixture by the following expression: vðnPFA Þ ð8Þ DLS 0:1D0 vðnPFA ¼ 0Þ We used the decreasing ratio of the growth velocities between the pure suspension and the mixture (see Figure 7) as a measurement for the observed slowing down of the kinetics while increasing the concentration of larger particles. Using this approximation for the long time self-diffusion coefficient, we are able to solve eq 5 numerically obtaining surface tensions γ and nucleation energy barriers ΔG*. Plotting the surface tension as a function of the chemical potential difference, we get a linear increase of the surface tension (Figure 8). Both slope and absolute values are very similar for the pure and the contaminated samples. This behavior was also observed in previous nucleation studies of charged sphere colloids.37,46 Calculating the ratio of the nucleation barrier height of the mixture and the pure suspension ΔG*(nPFA)/ΔG*(nPFA = 0), we notice an increase of the nucleation barrier height of approximately 5% due to the increased surface tension. Such a small modification of the nucleation barrier height hardly affects the absolute value of the nucleation rate density. The main effect of the strong decrease in J is primarily caused by the strong slowing down of the kinetics describing the particle attachment to the crystal-fluid interface. D. Discussion. At this point, it is useful to briefly summarize our main findings. We did systematic measurements in a

charged colloidal model system adding small amounts of second larger and higher charged component. Using microscopy, we got direct access to the time-resolved nucleation rate densities, to the crystal growth as well as to the crystal size distributions. With an increasing amount of the second component, we observe a pronounced slowing down of the whole crystallization process. While the induction time is only increasing by a couple of seconds, the whole time span of the nucleation process is strongly elongated and the crystal growth velocities decrease significantly. Such a strong decrease in the growth velocity was preliminary observed by Stipp.24 Further, we observe a decrease of the maximum as well as of the mean nucleation rate density ; the values calculated by applying Avrami’s model and by Kashchiev’s model show a similar behavior. For an addition between 0.1 and 0.7% PFA particles, the nucleation process is strongly modified: the time trace changes from a peaked nucleation rate density to a situation with a rather long constant nucleation rate density. In addition, the nucleation barrier height derived using a data analysis based on CNT is slightly increasing. The change in the crystallization kinetics results in a completely different microstructure after complete solidification of the shear molten suspension. Starting from a mosaic-like structure of fine crystallites (narrow distribution in L around = 140 μm), the microstructure can be modified to a state with just a few crystals in the observed volume ( = 375 μm) and pronounced dark (fluid ordered) grain boundaries simply by adjusting the parameter nPFA. For very small amounts of the second component rare big crystallites are found, which may be a hint of seed-induced nucleation. A further

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Figure 8. (a) Comparison of the surface tensions of the critical nuclei of the pure Pn-BAPS70 suspension (black squares) and for an increasing amount of added PFA particles (red points) as a function of the chemical potential difference. (b) Relative change of the nucleation barrier height as a function of added PFA-particles. Table 1. Particles Radius a, Effective Charge from Elasticity Measurements Z*, Screening Parameter κ, Single Particle Potential at the Averaged Particle Distance dAVG, “Effective Hard Sphere Radius” a þ κ-1 a Z* κ Φ (dAVG) a þ κ-1

Dyneon PFA

Pn-BAPS70

ratio

150 nm 530 1.52 107 m-1 0.00089 V 216 nm

35 nm 325 1.17 107 m-1 0.00062 V 120 nm

4.3 1.6 1.3 1.4 1.8

observation of this behavior is needed to make conclusions on this subject. Simulations for hard sphere colloids by Cacciuto, Auer, and Frenkel30 show that an addition of a second component results in a decreased nucleation energy and therefore catalyzes the nucleation in the system, if the radius of added particles is at least five times larger. Therefore, there should be a boost in the nucleation rate density due to the reduced nucleation energy barrier, if the added PFA-particles would induce heterogeneous nucleation. We rather find the nucleation rates decrease by adding more and more larger and higher charged spherical particles, so an addition of these particles causes an inhibition of the total number of nucleation events. Our particles used have a radius ratio of 4.3 in combination with a charge ratio of 1.6, which obviously does not fulfill the requirements for a reduced nucleation energy barrier in a system of charged spheres; we rather find the ΔG* becoming larger with an increasing ratio of PFA particles. In Table 1, we list several parameters characterizing our mixture at a particle concentration of n = 24.9 μm-3. Because of the “softness” of the charge sphere interaction, the asymmetry of the used mixture is much smaller than the radius and charge ratio suggests. The ratio of the particle potential at the averaged particle distance is only 1.4. If we consider a þ κ-1 as a measure for an effective hard sphere radius, we gain a ratio of 1.8, considerably lower than 5, which may explain why we see no increase in nucleation. However, our obtained results likely compare to experimental studies in colloidal hard spheres. Martin, Bryant, and

van Megen21 investigated the crystallization kinetics in colloidal hard spheres adding a small amount (1%) of slightly larger particles (size ratio 1.22). They observed a significant slowing down of the fluid to crystal conversion, and an increased averaged crystal size compared to the pure system. They explain their findings in the framework of local fractionation during crystallization.47 The slowing down of the crystallization process observed in our experiment might be caused by the same mechanism. In particular, the observation that the amount of grain boundaries increases by increasing the number of larger particles and that the grain boundaries do not have a color contrast in polarization microscopy suggests that the larger invisible PFA particles are fractionated out. Conclusion Adding small amounts of larger and higher charged particles to a colloidal suspension of charged spheres does not significantly modify the nucleation barrier height but has an enormous effect on the kinetics of nucleation and growth. In particular, the nucleation kinetics is most affected which is mainly caused by a variation of the kinetic prefactor of crystal nucleation. The slowing down of the kinetics is possibly due to particle fractionation during crystallization. This effect can be used to tune the microstructure formation in a very effective way. Acknowledgment. We are indebted to the BASF Luwigshafen and Dyneon Gendorf for the kind gift of particle samples. We are pleased to thank T. Palberg and P. Wette for helpful discussions. We gratefully acknowledge the financial support of the DFG (SPP1296, SFB-TR6 D1).

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Drastic Variation of the Microstructure Formation in a Charged Sphere

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