Crystal growth from colloidal spheres in suspension.

This invention relates to colloidal spheres in suspension, more particularly to a method of growing oriented colloidal crystals and devices produced thereby.

Colloidal spheres are uniformly sized and perfectly round particles, and are usually made out of materials such as polymers or ceramics. They can be made as hard or soft, solid or porous spheres. Colloidal spheres can be manufactured using methods such as emulsion polymerisation or that of using small seed particles made to grow uniformly. The spheres can pac to form a spatial array, termed a colloidal crystal, although this spatial array does not have long term order. A colloidal crystal can exist in free air or with the inter-sphere space filled with liquid such as that which is used as a suspension liquid.

Suspensions in a liquid of monosized spherical colloidal particles show a range of phase behaviour as the particle concentration is increased (P.N. Pusey and van hegen Nature 320 no. 6060 p3401986). If spheres whose interaction is steep and repulsive i.e. essentially hard sphere, are considered, then concentration of these spheres is expressed as volume fraction 9f, the fraction of the total volume of the suspension which is occupied by the particles.

For #40.49 the equilibrium state of the particles in suspension is fluid-like:- the particles are able to diffuse, in Brownian motion, throughout the suspension. For ,020.55 the equilibrium state is crystalline:- the particles are located at sites in an ordered spatial array. For 0.4yϊ f.S0.55 co-exis ting fluid- like and crystalline phases are found. For j2Ti0.58-0.6U the equilibrium state is still expected to be crystalline, the high viscosity of the suspension appears to hinder particle diffusion to the point where crystallisation is essentially suppressed and a glassy amorphous solid-like phase is formed.

Two crystallisation mechanisms have been found. The samples are mixed tho roughly and l ef t to s i t undis turbed. For 0.49^040.58 crystallisation is nucleated homogeneously at sites randomly-distributed throughout the sample and smal l compact crystal lites grow with ranao orientations. For .040.58 (i.e. near the glass transition) crystal lisation can be nucleated heterogeneously at the wal ls of the sample cel l and larger irregularly shaped crystallites grow inwards.

Three features of these crystals , formed spontaneous ly by bo th mechanisms , make them unsuitab l e f or materia l s applications :-

(i) The crystals contain a large number of stacking faults. Their structure is effectively a random mixture of face centred cubic (f.c.c. ) and hexagonal close packed (h.c.p. ) . (ii) The orientation of the crystallites is random. Ciii) Inevitably grain boundaries, with imperfect crystalline packing, occupy a significant fraction of the sample.

According to this invention, the above problems are solved by shearing a well mixed suspension of monosized colloidal spheres within a relatively narrow gap between two effectively parallel surfaces. This invention provides a method of growing oriented, essentially perfect, colloidal crystals, and devices produced by this method.

According to this invention a method of growing an oriented, essentially perfect, colloidal crystal comprises the sequential steps of:-

(i) preparing a well mixed suspension of monosized colloidal spheres with radii in the range of 0.1 microns to 1.0 microns having a volume fraction, jϊ, greater than 0.49 in a suitable carrier liquid,

(ii) inserting the colloidal suspension in a relatively narrow gap between two effectively parallel surfaces, and (iii) subjecting the surfaces to relative oscillating motion parallel to their surfaces, the relative motion having a frequency greater than that of the Brownian motion of the colloidal spheres and an amplitude approximately equal to that of the gap between the two surfaces.

Typical as supplied monosized colloidal sphere size distributions which are suitable for the invention method are those which are less than 5%.

The preferred minimum volume fraction of colloidal spheres is 0.55.

The relative motion of the plates is preferrably linear.

The two surfaces may be planar or concentrically cylindrical. Selection of a suitable carrier liquid for suspension may be characterised by the need for a liquid with a refractive index close to, but not exactly equal to that of the particles.

After oscillations sufficient to establish a substantially single * crystal structure, suitable sealing means may be applied to retain the carrier liquid in position between the surfaces. Alternatively, the carrier liquid may be exposed to a gel ling reagent so that it forms a stable gel matrix holding the colloid particles in the desired single crystal structure. A third al ternative is to let the liquid evaporate, if the co l loidal particles can form a self-supporting structure.

The amplitude of the applied oscillation is crucial for the formation of the colloidal single crystals. The perfect single crystal is obtained when this amplitude is roughly equal to the thickness of the gap between the two surfaces which are being sheared. This corresponds to an applied strain of about one: each particle moves in the shear f low over a dis tance equal to about one particle diameter relative to its neighbours in adjacent layers. With smaller amplitudes no crystallization is induced, whereas the structure created with oscil lations of greater amplitudes is more complicated.

The frequency of oscil lation is also important. The motion imposed by the applied oscillating shear must overcome the natural Brownian motion of the spheres. A Brownian relaxation time -• can be defined by:-

^ B = 1 ^{R3 (k}B^{T l ( 1}

where .-^ is the viscosity of the suspension measured at smal l shear rates, R is the radius of the particles, k is Boltz ann's

B constant and T is the absolute temperature. The condition for shear induced crystallization is:-

where A is a number of orαer 1.

The number of oscillations typically needed to produce oriented, essentially perfect, colloiαal crystals is between 100 and 1000. Typical gaps between plates vary between 50-1000 microns.

After growth of suitable colloidal crystals, light that is transmitted through the crystals becomes diffracted and concentrated in a few defined directions. These diffraction patterns show the colloidal spheres to be arranged during the oscillation in a flowing face centred cubic structure with one set of hexagonally packed planes parallel to the surfaces. When the shear is stopped at an appropriate point in the oscillation cycle a single f.c.c. crystal remains.

Typical applications of the oriented, essentially perfect, colloidal crystals are as notch or narrow band optical filters for laser safety goggles and other optical applications, use in the preparation of high strength ceramics with a high packing density, or other technological areas where essentially perfectly stacked ond oriented thin films are required such as for thin film dielectric materials. Where the colloidal crystals are needed for optical applications at least one of the effectively parallel surfaces must be optically transparent.

A notch optical filter may have a number (typically 10 to 100υ) layers of hexagonally-packed monosized colloidal spheres, stacked in such a way as to form a perfect crystal. When such a construction is illuminated perpendicularly with white light, that spectral component which satisfies the Bragg condition for ref lection by the layers of spheres wil l be strongly back-reflected. However light of other wavelengths will pass through the filter relatively unattenuated.

For particle layers spaced by a distance d, the condition for Bragg back-reflection is :-

2d = X _Q n^"1 (3)

where λ is the wavelength in vacuo of the reflected light and n the refractive index of the colloidal medium, where the colloidal medium is defined as the suspension of colloidal spheres in the carrier liquid. For a clo se-packed f.c.c. structure the relationship between the sphere radius R and the layer spacing is:-

d = i ΪT R = 1.633 (4)

Thus, (3) becomes j-

R = X o (3.27 n)^"1 (5)

For example, a filter blocking light of wavelength 500nm using colloidal spheres of refractive index 1.5 is obtained by using colloidal spheres of radius 102nm.

Reflection at angles other than the backward direction can also be effective. For example, with larger spheres of radius

R = 30ϋnm (and the refractive index of the carrier liquid is 1.5) ligh_t of waveleng_th 490nm will be diffracted in three beams at approximately 39 away from the (perpendicular) incident direction, thus still providing good filtration of transmitted light. _.However, this will be accompanied by other ref lections:- o = 738nm at an angle of about 70°, X o = 735nm at an angle of about 110 and λ = 668nm at an angle of about 121 . o

Nevertheless, the use of larger spheres (R = about 300nm as opposed to lOOnm for back reflection) could be advantageous for manufacturing processes. For example, it is easier to prepare the larger spheres to have a narrower size distribution which is required for crystallization.

The optimum number N of layers of colloidal spheres in a notch filter is determined by a compromise between two factors, the optical resolution of the filter and its attenuation. The width Δ of the spectral line removed by the filter is approximately defined as:

&>/ \ o N^_1 (6)

Thus 100 layers give a resolution λ /Δ of about 10 . The filter's attenuation depends largely on the optical inhomogeniety of the colloidal spheres.

Typical colloidal suspension materials for the construction of no_tch op_tical filters are charge-stabilized polymer colloidal spheres such as po lystyrene in water , sterical ly-stabilized polymer col loids such as polymethylmethacrylate (PMMA) in an organic carrier liquid or a mixture of organic liquids such as doαecane, decalin, tetralin, cyclohexane or carbon disulphide. Alternatively, colloidal spheres of materials such as silica, titania, alumina, or zirconia can be used as either charge- stabilized in water or sterically-stabilized in an organic liquid or a mixture of organic liquids such as dodecane, decalin, tetralin, cyclohexane or carbon disulphide.

This invention may also be applied to the manufacture of high strength ceramics. Colloidal spheres of ceramic materials such as silica, alumina, zirconia or titania which are charge- stabilized in water or sterically-stabilized in an organic liquid such as dodecane or cyclohexane are prepared in a concentrated suspension. In the current method of fabrication, this material is cast as a green body which is dried and sintered to form a final product. Two requirements for the green body for high strength ceramics are a high overall packing density of spheres, to minimise shrinkage on drying , and the absence of voids (or local regions of low packing density) which could form nucleii of weaknesses in the final sintered material. For the latter reason a polycrystalline green body is unsuitable because of the potentially weakening grain boundaries between crystallites. To avoid this an amorphous or glassy arrangement of spheres is currently preferred. However the maximum volume fraction j3 of compressed monosized spheres is about 0.64 (the random close packed density) whereas crys ta l l ine close packing has a significantly higher volume fraction of about 0.74. To use this invention a suspension of colloidal spheres of the ceramic material at a volume fraction of ^-aθ.6 is placed in a mould designed so that an oscillatory shear can be applied. After a sufficient number of shearing cycles the spheres are arranged spatially as a perfect f.c.c. crystal which is then be compressed to ^=^J0.74 before sintering. This process circumvents the difficulties in low overall and local packing densities described above. Ceramic sheets and pipes are proαuced by applying oscillating shear in a planar or cylindrical geometry respectively.

Specific applications of the invention will now be described by example only, with reference to the accompanying figures :-

Figure 1 is a schematic representation of the apparatus used to orientate essentially perfect colloidal crystals in a planar linear geometry.

Figure 2 is a schematic cross-section of a notch optical filter.

Figure 3 is a schematic plan view of the notch optical filter described in figure 2.

Figure 4 is a schematic cross-section of the apparatus used to orientate essentially perfect colloidal crystals in a cylindrical geometry.

As shown in figure 1, the invention is embodied by placing a well mixed colloidal suspension 1 between two f loat glass plates 2 and 3. The colloidal suspension 1 contains colloidal spheres of radius about lOOnm. The glass plates 2 and 3 are about 0.5mm to l.Omm thick. Spacers 4 are used to provide a gap between the two plates and this may be between 50 and 1000 microns. Linear lateral relative motion of plate 3 with respect to plate 2 is supplied by stepping motor 5 and linear translational device 6. The stepping motor and linear trans lational device provide accurate linear lateral oscillations which have a frequency greater than the Brownian motion of the co l loidal suspension spheres, and an amplitude approximately equal to the gap between plates 2 and 3.

In one example a colloidal suspension of silica spheres in water of volume fraction 0.57 was contained in a gap of 100 microns between glass plates 2 and 3. Stepping motor 5 and translational device 6 are used to lateral oscillation in plate 3 at an amplitude of about 100 microns and a frequency of 1Hz. After about 1000 cycles a crystalline layer is formed.

The apparatus described figure 2 may be used to produce essentially perfect, oriented colloidal crystal material which then becomes an integral part of a notch optical filter as shown in figures 2 and 3. Col loidal suspension 1 is a crystal line arrangement 11 of oriented, essentially perfect col loidal crystals due to alignment by precisely controlled relative motion as described by figure 1. In an alternative arrangement, either or both of plates 2 and 3 may be lens material with precise optical properties instead of float glass as described by figure 1. Af ter f orming a crystalline layer, an epoxy sealant 12 is used to seal the gap at the extreme edges of plates 2 and 3. As may be seen from the plan view in figure 3, the notch filter has plan dimensions of about 5cm by 5 cm. Cy lindrical geometries may al so be produced using the invention described. Figure 4 describes an apparatus where colloidal suspension 21 is enclosed between cylindrical plate 22 of thickness about 1mm and rod 23, which are concentric. Rod 23 is subjected to oscillating shear applied by stepping motor 24. There is a gap of about 50 microns to 1000 microns between cy lindrical plate 22 and rod 23. Osci l lation ampl itude is arranged to be approximately equal to the gap width.

The apparatus described by f igures 1 and 4 may be used f or producing high strength ceramic sheets and pipes where colloidal suspensions 1 and 21 are made up of material s such as charge- stabilized alumina in water at a volume fraction of about 0.6.