КОЛЛОИДНЫМ ЖУРНАЛ, 2007, том 69, № 1, с. 33-42
МАТЕРИАЛЫ XIII МЕЖДУНАРОДНОЙ КОНФЕРЕНЦИИ "ПОВЕРХНОСТНЫЕ СИЛЫ"
УДК 541:182
NANOSIZE PRECURSORS AS BUILDING BLOCKS FOR MONODISPERSED COLLOIDS
© 2007 r. Egon Matijevic
Center for Advanced Materials Processing, Clarkson University Potsdam, NY 13699-5814, USA
Поступила в редакцию 29.06.2006 г.
It is shown that many monodispersed colloid particles, precipitated in homogeneous solutions, are formed by aggregation of nanosize subunits. A model is described that specifies conditions which may yield such spherical particles of narrow size distribution by interactions of precursor singlets. A good agreement was achieved for size selection of gold and cadmium sulfide dispersions. It is illustrated that particles of other shapes may also form by the aggregation mechanism, and the challenges facing attempts to quantity such processes are pointed out. Finally, examples are given of consequences caused by particles being composed of nanosubunits.
INTRODUCTION
The significance of the uniformity of the size and shape of finely dispersed matter in terms of their properties is now well recognized, especially with the recent focus on materials in the nanosize range. There is extensive literature that describes well defined inorganic and organic particles of simple or mixed chemical compositions, and of different shapes [1]. Many techniques have been developed to produce such "monodispersed" systems, based on chemical and physical processes. However, the method of choice is precipitation in homogeneous solutions, which offers by far the greatest versatility and, in many cases, advantageous simplicity in the synthetic procedures [2, 3]. In contrast, less well understood are the mechanisms by which such uniform particles are generated. The latter is not surprising, because the formation of a solid phase in a solution involves a number of stages, each of which is greatly affected by temperature and by the chemical composition and the concentration of all species in the reacting environment.
The scheme in Fig. 1 shows the sequence of essential events in the precipitation process leading to the formation of colloidal particles, the chemical and physical properties of which depend in a sensitive manner on each step. Obviously, there are two major paths that may yield monodispersed particles. Originally, the widely accepted way to achieve the size uniformity was to follow the left-hand side of the scheme by which particles are formed through attachment of solutes onto preferred nuclei. Accordingly, there should be a rapid burst of nuclei, which would be allowed to grow uniformly, as proposed by LaMer [4, 5]. While this kinetic explanation is appealing in principle, it is by no means as general as originally assumed to be.
In contrast, it has now been demonstrated in numerous cases that the formation of many, if not most colloids proceeds through a more complex process. The
stages up to nanosized particles may be the same, but instead for the growth to continue by diffusion of constituent species onto these precursors, these singlets aggregate to yield coarser dispersions, which are in most cases of broad size distributions. However, under certain conditions the products may consist of rather uniform larger particles. It is to be expected that the latter will be obtained under considerable constraints with respect to the experimental conditions. For this reason, it is not surprising to note the paucity of such systems produced before the middle of the last century.
This article describes a model which explains the mechanism by which uniform spherical particles may be generated by aggregation of nanosize subunits. Furthermore, the challenges are pointed out one faces in attempting to elucidate the processes and conditions that yield particles of other shapes, in order to make their formation predicable.
EXPERIMENTAL EVIDENCE
Figure 2 displays transmission electron micrographs (TEM) of (a) aluminum hydroxide and (b) zinc sulfide particles, both spherical of rather narrow size distribution. The aluminum hydroxide obtained by "forced hydrolysis", i.e. simply by aging an aqueous aluminum sulfate solution at 90°C [6], is amorphous - as one would expect.
The zinc sulfide particles were prepared by aging at room temperature an acidified solution of zinc nitrate and thioacetamide [7]. The significant difference from the previous example is that the XRD analysis of these solids exhibits the characteristic pattern of crystalline mineral sphalerite. This unexpected result triggered special interest, because it was not anticipated for spherical particles, obtained by precipitation in aqueous solutions, to be crystalline without calcination or some other post-treatments. Indeed, the X-ray analysis
Diffusional Growth
NANOSIZE PRIMARY PARTICLES
■î Aging, Recrystallization
Fig. 1. Stages in the precipitation of colloid particles in homogeneous solutions.
indicated that these ZnS spheres consisted of subunits of ~50 A in diameter. Afterwards, many different homogeneously prepared uniform spherical particles
(a) (b)
Al(OH)3 1 jam ZnS 0.5 jam
Fig. 2. Transmission electron micrographs (TEM) of (a) aluminum hydroxide [6] and (b) zinc sulfide [7] particles.
were found to be composed of nanosize precursors, as confirmed by X-ray analysis and by electron microscopy. A few such dispersions are as exemplified in Fig. 3 with gold [8], cadmium sulfide [9], tin oxide [10], and barium naproxenate [11].
MECHANISM OF FORMATION
The first question to be answered is how to explain the propensity of nanosize particles to aggregate rather then to continue to grow by diffusional transport. It is obvious that in the course of the precipitation process conditions, that kept these precursor singlets apart, must change to cause their loss of stability. In most of the studied inorganic systems this partial stability is due to electrostatic repulsion. Thus, during the particle formation the charge on the nanosized singlets must be either neutralized or shielded to eliminate repulsion. The former may take place, for example, if - due to chemical changes in the reacting solution - the pH is shifted towards the isoelectric point of the dispersed solids, rendering them unstable. In the second case the ionic strength may increase sufficiently, allowing for particles to aggregate.
Fig. 3. Scanning electron micrographs (SEM) of (a) gold, [8], (b) cadmium sulfide, [9], (c) tin oxide [10], and (d) barium naprox-enate [11] particles.
The next task is to establish conditions under which such aggregation can lead to size selection, i.e. to colloids of narrow size distribution. There is extensive literature dealing with aggregation processes. Usually, models of coagulation and nucleation have assumed diffusional transport and considered growth of particles and aggregates, either via microscopic nucleation processes [12, 13] or by particle-particle aggregation and aggregate-aggregate adhesion on encounters [14, 15]. Models of dilute systems typically produce size distributions that peak at small sizes, while larger aggregates normally result in size distributions that grow with time.
A different novel approach was developed by the author in collaboration with his colleagues V. Privman and D.V. Goia [16]. The main finding has been that the growth of the final particles by aggregation of singlets must be coupled with the rate of their formation. Numerical calculations indicated that if the concentration of singlets were constant, i.e., if they were continuously generated to compensate for their depletion due to aggregation, the resulting particles would be of broad size distribution peaked at small diameters. However, if the process is carried out to allow for the concentration of primary particles to decrease with time, size selection can be achieved.
To formulate the model it is assumed that the diffusion constant of singlets is larger than of the aggregates so that the attachment prevails. The standard rate equation then reads
^¡f = N_!- wSNS, for s > 1, (1)
where Ns(t) is the time dependent density of secondary particles containing s primary particles.
In normal approaches to aggregation the evolution of the population of singlets, which is not covered by Eq. (1), is obtained by the conservation of matter
N i (t) + £ jNj (t) = N i (0), (2)
j = 2
which assumes that at t = 0 there are only singlets.
Equations (1) and (2) need to be modified to conform by introducing a term that accounts for the rate p(t) at which primary particles are formed per unit volume. Consequently, the equation for N(t) is modified by replacing Eq. (2) with
Ni(t) = Jp(t')dt'- £ jNj(t), (3)
o j =2
Ns (1018 m-3)
80
t = 0.1 sec
o = 0.57 N/m
60
40
20
10 sec
0.3 0.4
Rs (pm)
Fig. 4. Distribution of the secondary gold particles by their sizes based on the described model [16].
with initial values of Ns(0) = 0 for all s = 1, 2, 3 from classical nucleation theory.
An expression for p(t) was developed which includes experimentally accessible parameters, as described in detail in Ref. [14],
P( t) =
3 2 n2 a3 oD c2 3 kT ln ( c / c 0 )
exp<
"ic 3 6 3
256n a o
27 (kT )3[ ln (c / c0 )]2
, (4)
Concentration 500
700
0. 0. 0.
1.
1.
1. 2. 2. Radius, pm
Fig. 5. Experimentally determined histograms of the size distribution of spherical CdS particles obtained by precipitation [17]. The theoretical curves are obtained by the numerical solution of the model described in [18]. The concentrations are given in arbitrary units.
dNs > 1 1
min(smax' s -1)
Y Y NN - N
/ , i m, s - m ' m ' s - m -''s
m =1
M
(5)
x
Y Y N
/ , J s, m y m;
where M = «> for smax > k > 1, and M = smax for k > smax> 1,
where c(t) is the concentration of solute, species (atoms, ions), which serve as monomers for primary particles nucleation, while c0 is its equilibrium saturation concentration. Finally, o is the effective surface tension of the singlets.
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