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Figure 2. Two-dimensional diffraction data from 50:50 w/w PVC/PS blend particles produced from an 8 |im diameter droplet (left), and a 35 |im diameter droplet. (right).

Figure 2 shows examples of PVC/PS particles formed from an (a) 8 ^m diameter droplet, and (b) a 35 ^m diameter droplet of dilute ( 1% total polymer weight fraction) PVC/PS/THF solution. The size threshold (for this system) for producing homogeneous particles is about 10 pm. As shown in Figure 2-b, for larger droplets that have correspondingly longer drying times, we observed that the particles were inhomogeneous as evidenced by the absence of well defined (vertical) diffraction fringes. There is compelling evidence for material homogeneity at a molecular length scale for the particle represented in Figure 2-a: fringe uniformity, quantitative agreement with Mie calculations, and a refractive index (related to material dielectric constant) that is intermediate between the two pure materials.

Figure 3 shows time-resolved results of particle size and refractive index for a 2.4 ^m PVCPS (50:50 w/w) blend particle. Note that the particle continues to "dry" on a time-scale of several minutes, but remains homogeneous throughout the measurement sequence. The nominal index of pure THF is 1.41 and the measured (steady state) final index of the particle is 1 .527. These limiting values suggest that, for the first data point in

Figure 3, the particle is 22% by volume THF. Assuming that the last data point represents a fully dry particle (in good agreement with estimates based on refractive indices for pure PS and PVC), one would have expected a 60% decrease in particle size accompanying the loss of residual THF. This is clearly not observed, indicating that the particle has formed a fairly rigid matrix that compresses only slightly ( 3%) during the remainder of the observation time.

Figure 3, the particle is 22% by volume THF. Assuming that the last data point represents a fully dry particle (in good agreement with estimates based on refractive indices for pure PS and PVC), one would have expected a 60% decrease in particle size accompanying the loss of residual THF. This is clearly not observed, indicating that the particle has formed a fairly rigid matrix that compresses only slightly ( 3%) during the remainder of the observation time.

time past injection (seconds)

Figure 3. Particle size and refractive index (real and imaginary parts) for a PVC/PS composite particle (50:50 w/w) as a function of time past injection.

The data shown in Figure 3 also illustrates the 'tunable' nature of a material property in PVC/PS composite particles - namely the dielectric constant manifested in the refractive index. Both Re(n) and Im(n) for the polymer-blend microparticles are intermediate between the values determined for pure single-component particles (PVC: Re(n) = 1.4780, Im(n) = 10-3 ; PS: Re(n) = 1.5908, Im(n) = 2 x 10-5) and can be controlled by adjusting the weight fractions of polymers. Interestingly, the measured refractive index for composite particles are very close to estimates obtained from a simple mass-weighted average of the two species.

Domain Size 'Resolution' in 2-D Diffraction

We have recently shown that the presence of phase-separated structures in heterogeneous polymer-blend microparticles can be indicated qualitatively by a distortion in the two-dimensional diffraction pattern. The origin of fringe distortion from a multi phase composite particle can be understood as a result of refraction at the boundary between sub-domains of different polymers, which typically exhibit significant differences in refractive index. Thus, the presence of separate sub-domains introduces cumulative optical phase shifts and refraction resulting in a 'randomization' (distortion) in the internal electric field intensity distribution that is manifested as a distortion in the far-field diffraction pattern.

A critical question in the analysis of 2-D diffraction patterns from composite microparticles is what is the minimum domain size that can be detected with this technique. Light scattering and resolution analysis of Fabry-Perot interferometers suggest that refractive index discontinuities (phase-separated domains) with a length scale X/20 ( 25 - 30 nm), where X is the laser wavelength, are required tc produce a measurable distortion in the diffraction pattern. If true, this "resolution" is comparable to radii of gyration for most large molecular weight polymers, thus providing a method of looking "within" a composite particle and probing material homogeneity on a molecular scale. Here we examine in some detail the question of domain size and number density of phase-separated sub-domains within a host particle.

We have considered the issue of domain size resolution in 2-dimensional optical diffraction of polymer-blend and polymer-composite microparticles both experimentally and theoretically. The question can be phrased in two parts: (1) What is the smallest phase-separated sub-volume (domain) of the particle that will manifest its presence as a distortion in the 2-dimensional diffraction pattern? (2) What is the sensitivity to number density or relative weight fraction? That is, if two polymers phase-separate in a microparticle, at what relative weight fraction (or number density of phase-separated inclusions) will one to be able observe phase separation (0.1, 1, 10% etc.) as a distortion in 2-D diffraction patterns? These questions are not trivial to address by first-principles electrodynamics, although a perturbative volume-current method has recently been employed to simulate distortion of 2-D diffraction patterns from binary particles.33 These calculations suggest that, under the right experimental conditions, very low relative weight fractions (< 1%) are required to observe distortion, with domain size resolution on the order of 20 - 40 nm depending on the relative difference in refractive index between host and guest material.

Experimentally, we find good agreement between experiment and theory with respect to domain size but somewhat poorer agreement in number density (relative weight fraction) requirements for diffraction distortion. We examined diffraction from polyethylene glycol host particles doped with varying weight fractions of ceramic nanoparticles (A12O3, TiO2) and 14-nm latex beads. The A12O3 and TiO2 particles have nominal sizes of46 and 28 nm respectively (specified by manufacturer), but their refractive indices (1.57, and 2.1 respectively) are such that the two particles introduce approximately the same optical phase shift Figure 4 shows a surface plot of 2-D diffraction data from a PEG host particle (7.5 ^m diameter) doped with 46-nm AUO3 particles at a 14:1 relative weight ratio. The intensity oscillations along the polar angles (left abscissa) are the signature of material inhomogeneity. Similar results were obtained for TiO2. The dopant ceramic particles do indeed produce measurable distortion in the diffraction patterns (quantitatively described by Fourier transform of individual diffraction fringes), but only at relative weight fractions > 5%. Interestingly (see subsection 4.1.4), addition of 14-nm latex beads to PEG host particles did not result in distortion of the diffraction pattern at relative weight fractions up to 50%, but do significantly modify the refractive index.

Figure 4. Surface plot representation of 2-D diffraction data from a PEG/A12O3 (46 nm nom. diameter) composite particle in a 14:l relative weight ratio. The x and y cooordinates are pixel numbers corresponding to azimuthal and polar scattering angles respectively. The host particle diameter is 7.5 |xm. The intensity oscillations along each diffraction fringe signal material inhomogeneity.

Figure 4. Surface plot representation of 2-D diffraction data from a PEG/A12O3 (46 nm nom. diameter) composite particle in a 14:l relative weight ratio. The x and y cooordinates are pixel numbers corresponding to azimuthal and polar scattering angles respectively. The host particle diameter is 7.5 |xm. The intensity oscillations along each diffraction fringe signal material inhomogeneity.

Formation of homogeneous polymer-blend composites from bulk-immiscible co-dissolved components using droplet techniques has two requirements. First, solvent evaporation must occur on a relatively time scale compared to polymer translational diffusion. Second, the polymer mobility must be low enough so that, once the solvent has evaporated, the polymers cannot overcome the surface energy barrier and phase-separate. We have shown definitively the effects of droplet size and solvent evaporation, and the second requirement is almost always satisfied even for modest molecular weight polymers. In order to explore effects of polymer mobility in more detail, we looked at composite particles of PEG oligomers (MW 200, 400, 1000, and 3400) with medium molecular weight (14 k) atactic polyvinyl alcohol (PVA). This system allows us to systematically examine the phase separation behavior where one component (PEG) has substantially different viscosities (specified as 4.3, 7.3, and 90 cStokes at room temperature for PEG [200], PEG [400], and PEG [3400] respectively). All of the polymers examined in this study ,we probed at temperatures above the glass transition. The glass transition temperatures for PEG(400) and PEG(3400) are 205o and 232o K respectively.1 - we did not find data for PEG(200) but expect it to be less than or approximately equal to that of PEG(400). So in the absence of deep evaporative cooling (which we have no evidence of) all the polymers studied are above their respective Tg

We observed that the higher molecular weight PEG polymer-blend particles were homogeneous as determined from bright-field microscopy, optical diffraction and fluorescence imaging. Blend-particles prepared with the 200-molecular weight PEG were observed to form sphere-within-a-sphere particles with a PVA central core. On a time scale of about 10 minutes, the composite particle undergoes phase separation into an inhomogeneous particle as evidenced by fringe distortion. Interestingly, the structure in the 2D diffraction data for this system is much different than those observed for large phase-separated PVC/PS particles that presumably coalesce into sub-micron spheroidal domains.34 Based on fluorescence imaging data, 35the PEG[200]/PVA[ 14k] particle forms spherically symmetric (sphere-within-a-sphere) heterogeneous structures, which should also (but does not) produce well-defined diffraction fringe36 37 38.

Our interpretation of this observation is that diffusional motion of the PVA core in the PEG host particle, combined with rotational diffusion of the particle breaks the spherical symmetry and thereby introduces distortion in the diffraction pattern. This observation is entirely consistent with our model of polymer-composite formation where heterogeneous particles may be formed provided that the mobility of one of the polymers is low enough to overcome the surface energy barrier. Composite particles formed from the higher molecular weight PEG (>1000) form homogeneous blend particles with PVA. The time scale for transitions from a homogeneous to inhomogeneous particle provides an estimate (at least to an order of magnitude) of the diffusion coefficient of the light component within the particle. This is a number that can be connected directly to molecular dynamics simulations. By equating the average diffusion distance r = (6Dt)1/2 to the particle radius (6 ^m) and using a value of t = 10 minutes (600 s), we estimate a value of D = 10-10 cm2/s, which is consistent with recent molecular modeling results (see the following section). Composite particles formed from the higher molecular weight PEG (>1000) form homogeneous composite particles with PVA.

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