Polystyrene latex distributions

Segment density profiles and hydrodynamic thickness measurements have been made for polyethylene oxides adsorbed on polystyrene latex. Comparison with theoretical models shows that the hydro-dynamic thickness is determined by polymer segments (tails) at the extremity of the distribution. It is also concluded that the sensitivity of the s.a.n.s. experiment precludes the measurement of segments in this region and that the experimental segment density profiles are essentially dominated by loops and trains. 

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

Earlier work (3) has shown that cleaned monodisperse polystyrene latexes stabilized with surface sulfate (and perhaps a few hydroxyl) groups an be used as model colloids. For example, the distribution of H ions in the electric double layer as determined by conductometric titration has been correlated with the particle diameter determined by ultracentrifugation (3). The conductometric titration gives two measures of the concentration of H+ ions the initial conductance of the latex and the amount of base required for neutralization. The number of H+ ions determined by conductance is always smaller than the number determined by titration. This difference is attributed to the distribution of the H+ ions in the electric double layer those closest to the particle surface contribute least to the overall conductance. This distribution is expressed as the apparent degree of dissociation a, which is defined as the ratio H+ ions... 

The mixture was sonicated to eliminate aggregates. A polystyrene latex with a broad distribution was obtained from Kodak. This distribution had been characterized previously by electron microscopy, ultra centrifuge and Coulter counter. A monodlsperse, surfactant free, sulfated, polystyrene standard and a mixture of 10 such monodlsperse standards were purchased from Interfaclal Dynamics Corporation. A polyvinyl chloride latex with a broad distribution was donated by B. F. Goodrich. This sample had been characterized by Joyce Loebl disc centrifuge. These samples were diluted to 0.01% solids and sonicated to eliminate aggregates. 

The raw data trace for a mixture of 6 standard polystyrene latex microspheres is shown in Figure 2. This separation was done in 20 minutes at 10,450 rpm. While particle size data in the first few minutes is difficult to quantitate accurately with the DCP, this separation demonstrates the resolution capability of the instrument. Figures 3-7 show typical raw data, and number, surface and weight differential and cumulative distribution plots produced by the data system along with the corresponding report. 

Figure 5. Particle size distribution of a mixture of polystyrene latexes with nominal diameters of 0.804 and 1.09 pm obtained by disk centrifugation at 4000 rpm in a 1/4% sucrose gradient.

Narrow particle fractions approaching a monodisperse distribution are particularly easy to treat and characterize when the above equations are applied to experimental data. Figure 2 shows an example of the elution profile (fractogram) obtained by running a mixture of four samples of "monodisperse" polystyrene latex beads. It is clear from the figure that a rather precise value of retention volume Vr can be identified with each bead size. With Vr known, it is easy to obtain R and X from Equation 5 and thence particle diameter d from Equation 4. This operation, as noted, yields diameters accurate to approximately 1-3%. 

Figure 8.6. Separation of polystyrene latex beads of four different diameters (indicated in the figure) by a disc centrifuge operated at 3586 rpm. (From ref. 44. Reprinted with permission from R. M. Holsworth, T. Provder, and J. J. Stansbrey, in T. Provder, Ed., Particle Size Distribution, ACS Symposium Series No. 332, American Chemical Society, Washington, DC, 1987, Chapter 13. Copyright 1987 American Chemical Society.)...

As pointed out in Chapter 8, the forces of centrifugation are too weak to influence the distribution of small molecules. The molecular weight M of species must be 106 in order to generate the necessary force in SdFFF. However for M > 106, there are many important separation problems involving polymers, biological macromolecules (such as DNAs), subcellular particles, emulsions, and a great variety of natural and industrial colloids. SdFFF has been applied to many such systems [10-12,16]. An example of the separation of colloidal polystyrene latex microspheres is shown in Figure 9.9,. 

Many papers report the fractionation of polystyrene latexes or mixtures thereof, as such commonly available spherical latex standards are an ideal system to test FFF setups or evaluations (for an example, see [362,401]). Recent coupling of Fl-FFF to MALLS enables a very high precision in particle size determinations. One example is shown in Fig. 31, where two Duke standard latex batches of a nominal size of 100 nm were investigated by Fl-FFF/M ALLS, underlining both separation power and resolution. Using traditional techniques such as photon correlation spectroscopy (PCS) and classic Fl-FFF detection, these samples seem to be identical. However, with Fl-FFF/MALLS, the batches could be separated as two discrete size distributions with a peak size that differed by 3 nm. However, it is not stated if a precise temperature control was maintained so that, critically considered, the observed differences could also have their origin in slight temperature... 

Fig. 34.A Correction for zone broadening of a model fractogram. a represents the original curve and the corrected one whereas b is the uncorrected fractogram. Reproduced from [460] with kind permission of the American Chemical Society. B Comparison of differential particle size distributions of narrowly distributed polystyrene latex standards derived by MALLS and Fl-FFF without correction for zone broadening. Reproduced from [461] with kind permission of Academic Press...

Polystyrene Latex (PSL) Bead Solution Filtration Experiments were conducted to obtain filter retention, flow rate, and Ap data for a DI water based PSL bead mix solution prepared using particles ranging from bead diameters of 0.772 to 20 pm. It is a common practice to use PSL bead challenge solutions (created by mixing different size PSL bead standards in specific volumetric ratio to simulate slurry-like particle size distribution for the bead mix solution) to obtain relative quantitative retention data for various filters. These solutions are expected to retain stable PSD and provide more consistent information compared to real CMP slurries, which may change particle characteristics over time. 

A method for on-line monitoring of particle size distribution and volume fraction in real time using frequency domain photon migration measurements (FDPM) has been described. In FDPM the time dependence of the propagation of multiply scattered light provides measurement of particle size distribution and volume fraction. The technique has been applied to a polystyrene latex and a titanium dioxide sluny at volume concentrations in the range 0.3 to 1% [341]. 

This form is employed in aero.sol technology to characterize panicles that are nearly monodisperse such as the polystyrene latex spheres used in laboratory. studies and in instrument calibration. The value of dp can be calculated using the moment equation (1.15). In integrating, it is necessary to set a lower limit airfj, 0 and to assume that the distribution... 

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