We present results from recent crystallization studies on marginal binary suspensions of colloidal particles. As small amounts of the second component are added, crystallization slows, and in some cases may cease altogether. The results support a growth mechanism whereby crystallization occurs in conjunction with a local fractionation process near the crystal-fluid interface, significantly altering the kinetics of crystallite nucleation and growth

Bryant, G

Martin, S

Van Megen, W

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Martin, S, Bryant, G and Van Megen, W 2004, 'Crystallization in polydisperse binary
colloidal suspensions', in N. Savvides (ed.) Proceedings of the 28th Annual
Condensed Matter and Materials Meeting, Wagga Wagga, Australia, 3-6 February
2004.
https://researchbank.rmit.edu.au/view/rmit:2420
Published Version
2004 Australian Institute of Physics Publications
 http://www.aip.org.au/wp-content/uploads/cmm/2004/p21.pdf
Please cite as: 
 
Martin, S, Bryant, G and Van Megen, W 2004 
'Crystallization in polydisperse binary colloidal suspensions' 
in N. Savvides (ed.) Proceedings of the 28th Annual Condensed Matter and Materials 
Meeting, Wagga Wagga, Australia, 3-6 February 2004. 
	
	
	
Crystallization in Polydisperse Binary Colloidal Suspensions 
 
S. Martina1 , G. Bryanta and W. van Megena 
 
a Department of Applied Physics, Royal Melbourne Institute of Technology, Victoria 3000, 
Australia. 
 
We present results from recent crystallization studies on marginal binary 
suspensions of colloidal particles. As small amounts of the second component 
are added, crystallization slows, and in some cases may cease altogether. The 
results support a growth mechanism whereby crystallization occurs in 
conjunction with a local fractionation process near the crystal-fluid interface, 
significantly altering the kinetics of crystallite nucleation and growth. 
 
1. Introduction 
 It is well known that single component hard spheres begin to crystallize at volume 
fractions beyond 0.494. Between 0.494 and 0.545 there is a crystal-fluid coexistence region, 
and above 0.545 the entire system will crystallize. The crystals take the form of close-packed 
hexagonal layers, and can be Face-Centered Cubic FCC (an ABCABC stacking sequence), 
Hexagonal Close Packed HCP (an ABAB stacking sequence), or random hexagonal close 
packed (RHCP), which consists of a mixture of FCC and HCP with random registration of 
planes. This latter form is observed experimentally in single component hard sphere colloidal 
systems crystallized from the melt [1, 2]. The application of shear can induce more FCC-like 
stacking [3], while some binary mixtures exhibit superlattice formation [4]. 
 However, colloidal particles are inherently polydisperse, and theory, simulation and 
experiment show that polydispersity causes a slowing in the crystallization process, and may 
be accompanied by local partitioning or segregation of particle sizes [5,6]. 
 We recently demonstrated [7, 8] that particles with a negatively skewed polydispersity 
can exhibit a smectic-like crystalline structure consisting of close-packed layers with no 
registration of planes. We also showed that for these particles, the onset of nucleation was 
delayed by up to an order of magnitude, and they displayed qualitatively different growth 
behaviour compared to particles with a more symmetric size distribution. We proposed a 
growth mechanism whereby local size-based fractionation of particles near the crystal-fluid 
interface accompanies growth. This completely alters the kinetics of crystal nucleation and 
growth, and becomes more significant as polydispersity or skewness increases. 
 In this paper marginal binary mixtures are used to further examine these ideas. 
 
2. Methods 
 The methods and analysis used here have been described in detail previously [7-11] and 
will be summarized only briefly. The particles behave as hard spheres in the suspending 
solvent, cis-decalin and are index matched to allow light scattering measurements [9]. 
 The mean particle radius and polydispersity were determined by light scattering [10]. 
Measurements of the crystal growth parameters were obtained from time resolved 
measurement of the Bragg reflections scattered from the growing crystallites, analogous to X-
ray powder crystallography [11]. The parameters measured from the main reflection are: the 
relative amount of crystal present in the sample, the crystallinity X(t), measured from the 
peak area; and the average crystallite size L(t), measured from the peak width. 
                                                 
1 Present address: Universität Konstanz, Fachbereich Physik, Fach M621, 78457 Konstanz, Germany. Electronic 
address: Stephen.Martin@uni-konstanz.de 
3. Results 
The structure factors as functions of volume fraction and composition are shown in 
figure 1. The single component samples (X1 and W1) exhibit quite different crystal structures 
– latex X exhibits the three peaks indicative of RHCP structure, while latex W (which has a 
polydispersity highly skewed towards smaller than average particles) shows a single peak at 
higher angles that is identified as being indicative of close-packed layers with no registration 
of planes [7].  
At a volume fraction of 0.53, the addition of small amounts of latex W (smaller 
particles), causes the peaks to broaden, implying smaller crystal sizes. However, the nature of 
the crystal packing (RHCP) does not change, even with 10% latex W. At higher volume 
fractions (0.54 and 0.55), the addition of even a small amount of latex W completely disrupts 
crystallization, and the samples remain amorphous over all time scales. The amorphous 
structure factors are, however, different from the initial metastable fluid, implying that there 
has been some structural rearrangement. 
By contrast, the addition of small amounts of the larger particles to latex W (W2) does 
not inhibit crystallization. The samples still crystallize, and in the case of a volume fraction of 
0.55, the crystallization is enhanced. 
 
Fig. 1. Structure factors of the metastable fluid, taken immediately following tumbling (red) 
and after crystallization ceased (black). Vertical axes are intensity (arb. units) and horizontal 
axes are angle. Data are shown for 3 different volume fractions, and 6 different compositions. 
 
 
   (a)         (b)
Fig. 2. (a) Log crystallinity vs. log time and (b) log average crystal size vs. log time. 
Figure 2 shows the amount of crystal X(t) and the average crystal size L(t) as functions 
of time for samples W1 (pure latex W) and W2 (latex W with 1% larger particles). At each 
volume fraction the presence of 1% of the second component significantly delays the onset 
and speed of crystal growth (fig. 2a – note the log scale). 
 Figure 2b shows the average crystal size as a function of log time, and in all cases it 
rises to a maximum, then either plateaus or falls. For both 0.54 and 0.55, the addition of the 
second component increases the value of the maximum average crystal size. The presence of 
the larger particles therefore encourages larger crystals, consistent with figure 1. 
 
4. Discussion and Conclusions 
Changing the shape of the particle size distributions through the production of marginal 
binary mixtures has confirmed our previous results on polydisperse single component 
colloidal suspensions [7,8]. In the early part of the crystallization process, a number of nuclei 
form and begin to grow. In order to grow from the polydisperse suspension, there must be a 
local fractionation process, excluding the smaller particles from the crystal. At some point, 
the excluded layer of particles becomes sufficiently large that movement of correctly sized 
particles onto the crystal becomes exceedingly slow, and further growth effectively stops. In 
order for the sample to approach equilibrium, new nuclei must form elsewhere and begin to 
grow. At this point, the measured average crystal size begins to drop due to new smaller 
crystallites forming. The addition of smaller than average particles to the distribution 
therefore slows and/or disrupts crystallization (figure 1). 
On the other hand, the addition of larger particles increases the distance between the 
planes and improves the ordering within the crystal lattice, allowing crystallization to proceed 
more easily (figure 2). A more extensive analysis of these results will be published elsewhere. 
 
Acknowledgments 
 This work was carried out with the help of the Australian Research Council, Grant No. 
A69701447. The authors would like to thank Phil Francis for technical support. 
 
References 
[1] P.N. Pusey, W. van Megen, P. Bartlett, B.J. Ackerson, J. G. Rarity and S.M.  
Underwood, Phys. Rev. Lett. 63, 2753 (1989). 
[2] P.N. Pusey, in Liquids, Freezing and the Glass Transition, edited by J.P. Hansen, D. 
Levesque, and J. Zinn-Justin (North Holland, Amsterdam. 1991) p. 763; P. Bartlett and 
W. van Megen, in Granular Matter. (Springer-Verlag, New York, 1994) p. 195. 
[3] An excellent recent review can be found in: V.C. Martelozzo, A.B. Schofield, W.C.K. 
Poon and P.N. Pusey, Phys. Rev. E 66, 0210408 (2002). 
[4] P. Bartlett, R.H. Ottewill and P.N. Pusey, J. Chem. Phys. 93, 1299 (1990); P. Bartlett, 
R.H. Ottewill and P.N. Pusey, Phys. Rev. Lett. 68, 3801 (1992). 
[5] D.A. Kofke and P.G. Bolhuis, Phys. Rev. E 59, 618 (1999). 
[6] P. Bartlett, J. Phys.: Cond. Matt. 12, A275 (2000); R.M.L. Evans and C.B. Holmes, 
Phys. Rev. E 64, 1404 (2001). 
[7] S. Martin, G. Bryant and W. van Megen, Phys. Rev. Lett. 90, 255702 (2003). 
[8]  S. Martin, G. Bryant and W. van Megen, Phys. Rev. E 67, 061405 (2003). 
[9] S.M. Underwood and W. van Megen, Coll. Polymer Sci. 274, 1072 (1996). 
[10] G. Bryant, S. Martin, B. Budi and W. van Megen, Langmuir 19, 616 (2003). 
[11] P. Francis P. et al., Rev. Sci. Instrum. 73, 3872 (2002). 


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Crystallization in polydisperse binary colloidal suspensions

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