Results

Figure 1 shows a family of 2-D slices (Re(n) varied and Im(n) fixed) of a typical error surface obtained from data acquired for a PEG particle. The three independent factors that define the scattering pattern - size, Re(n), and Im(n) - are systematically varied to find the best possible match to the experimental data by locating the minimum in a 4-dimensional error function. From exhaustive analysis of these error surfaces from many different sized particles, we find absolute size uncertainties to be between 2 and 5 nanometers, and the uncertainty in Re(n) to be between 10-3 and 5 x 10-4 For materials with a low molar absorptivity (typical of most dielectric liquids), Im(n) is correspondingly small - on the order of 10-5 to 10-7 At these values, there is very little (if any) effect on the match to data by varying Im(n). For many polymers (polyvinyl chlorides for example) however, this is not the case and Im(n) can be as large as 10-3 At this order of magnitude, Im(n) does indeed influence the Mie analysis of the data.

A key issue in forming homogeneous composites from co-dissolved bulk-immiscible polymers from solution is that the droplet evaporation rate must be fast compared with the polymer self-organization time scale. Since the time scale for solvent evaporation is proportional to 1/(r3/2) r is the droplet radius, the most obvious way to satisfy this condition is to make droplets smaller - an option which is nontrivial experimentally." Alternatively, one can modify the atmosphere around the droplet (temperature, different bath gases, etc.) to accelerate particle drying.'' As part of our effort in developing single-molecule isolation and manipulation methodologies in droplet streams, we have been able to produce (water) droplets as small as 2 - 3 microns in diameter with 1% size dispersity. For a 3-^m (nom.) droplet, approximately 95% of the initial droplet volume is lost due to evaporation in about 5 ms. The diffusion coefficient of a free polymer molecule in solution with molecular weight of say, 104 is on the order of 10-9cm2/sec. In this case, diffusional motion of the polymer center-of-mass is negligible (<r> 30 nm ) on the time scale of solvent evaporation.

Material Properties and Particle Dynamics

Another important aspect of our approach is the ability to obtain very precise information on the refractive index which provides a way of characterizing material properties and particle dynamics that is not possible with conventional microscopy techniques. One can, for example, directly measure kinetics of particle drying by monitoring the refractive index change as the solvent evaporates. In general, we find that the particle drying kinetics have two distinct solvent evaporation regimes. When the droplet is first ejected, the size decreases rapidly with most of the solvent evaporation taking place within the first 10 to 100 milliseconds. This is followed by a much slower ("wet particle") evaporation regime where the particle continues to lose solvent on a time scale of several minutes (dependent on size). Interestingly, in the slow-evaporation regime, we generally observe that the volume change expected from solvent loss (assuming an ideal solution) is not accompanied by the expected corresponding change in particle size.

Put another way, we observe a much smaller change in size than would be expected from the change in refractive index (solvent loss) if the particle were able to respond to solvent removal in the same way as an ideal solution. This suggests that, in most cases, the polymers form a semi-rigid matrix through which trapped residual solvent escapes by diffusion.

We examined two bulk-immiscible polymers (polystyrene and polyvinyl chloride) that are soluble in THF.14 We have not characterized evaporation rates of pure THF droplets, but estimate on the basis of vapor pressure differences relative to water, that evaporation is roughly a factor of 5 more rapid (for a given droplet size). To provide some kind of relative time scale, a water droplet with an initial diameter of 10-pm will evaporate to 1 ^m diameter in about 5 ms in a dry Argon atmosphere.16

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