Dispersions process

Dispersion Processing. A commercial aqueous dispersion of Teflon PEA 335 contains more than 50 wt % PEA particles, about 5 wt % surfactants and fillers. This dispersion is processed by the same technique as for PTEE dispersion. It is used for coating various surfaces, including metal, glass, and glass fabrics. A thin layer of Teflon PEA coating can also serve as an adhesive layer for PTEE topcoat. 

In the post-dispersion process, the soHd phenoHc resin is added to a mixture of water, cosolvent, and dispersant at high shear mixing, possibly with heating. The cosolvent, frequently an alcohol or glycol ether, and heat soften the resin and permit small particles to form. On cooling, the resin particles, stabilized by dispersant and perhaps thickener, harden and resist settling and agglomeration. Both resole and novolak resins have been made by this process (25). 

Sedimentation (qv) techniques, whether based on gravitational forces or centrifugation, derive the particle size from the measured travel rates of particles in a Hquid. Before the particle analysis is carried out, the sample is usually dispersed in a medium to break down granules, agglomerates, and aggregates. The dispersion process might involve a simple stirring of the powder into a Hquid, but the use of an ultrasonic dispersion is preferred. 

The dead point is the position of the peak maximum of an unretained solute. It is not the initial part of the dead volume peak as this represents a retarded portion of the peak that is caused by dispersion processes. The importance of employing the peak maximum for such measurements as dead volume and retention volume will be discussed in later chapters of the book that deal with peak dispersion. 

The different dispersion processes (1, 2, 3,...) that occur in a column will now be considered theoretically, their individual contributions to the variance per unit length of the column (Hi, H2, H3...) evaluated and then summed to provide an expression for the total variance per unit length of the column (H), i.e.,... 

The theory that results from the investigation of the dynamics of solute distribution between the two phases of a chromatographic system and which allows the different dispersion processes to be qualitatively and quantitatively specified has been designated the Rate Theory. However, historically, the Rate Theory was never developed as such, but evolved over more than a decade from the work of a number of physical chemists and chemical engineers, such as those mentioned in chapter 1. 

Various mathematical concepts and techniques have been used to derive the functions that describe the different types of dispersion and to simplify further development of the rate theory two of these procedures will be discussed in some detail. The two processes are, firstly, the Random Walk Concept [1] which was introduced to the rate theory by Giddings [2] and, secondly, the mathematics of diffusion which is both critical in the study of dispersion due to longitudinal diffusion and that due to solute mass transfer between the two phases. The random walk model allows the relatively simple derivation of the variance contributions from two of the dispersion processes that occur in the column and, so, this model will be the first to be discussed. 

Equation (1) can be used in a general way to determine the variance resulting from the different dispersion processes that occur in an LC column. However, although the application of equation (1) to physical chemical processes may be simple, there is often a problem in identifying the average step and, sometimes, the total number of steps associated with the particular process being considered. To illustrate the use of the Random Walk model, equation (1) will be first applied to the problem of radial dispersion that occurs when a sample is placed on a packed LC column in the manner of Horne et al. [3]. 

This example of the use of the Random Walk model illustrates the procedure that must be followed to relate the variance of a random process to the step width and step frequency. The model will also be used to derive an expression for other dispersion processes that take place in a column. 

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

In summary, equation (13) accurately describes longitudinal dispersion in the stationary phase of capillary columns, but it will only be significant compared with other dispersion mechanisms in LC capillary columns, should they ever become generally practical and available. Dispersion due to longitudinal diffusion in the stationary phase in packed columns is not significant due to the discontinuous nature of the stationary phase and, compared to other dispersion processes, can be ignored in practice. 

The resistance to the mass transfer term for the stationary phase will now be considered in isolation. The experimentally observed plate height (variance per unit length) resulting from a particular dispersion process [e.g., (hs), the resistance to... 

It is seen that the two curves are quite different and, if the results are fitted to the HETP equation, only the data obtained by using the exit velocity gives correct and realistic values for the individual dispersion processes. This point is emphasized by the graphs shown in Figure 5 where the HETP curve obtained by using average velocity data are deconvoluted into the individual contributions from the different dispersion processes. 

Figure 5 shows that using average velocity data the extracted value for the multi-path term is negative, which is physically impossible, and, furthermore, for a capillary column should be zero or close to zero. In contrast, the extracted values for the different dispersion processes obtained from data involving the exit velocity give small positive, but realistic values for the multi-path term. 

The curve in Figure IB is probably more useful from a practical point of view. Although the standard deviations of any dispersion process are not additive, they do give a better impression of the actual dispersion that a connecting tube alone can cause. It is clear that a tube 10 cm long and 0.012 cm I.D. can cause dispersion resulting in a peak with a standard deviation of 4 pi. Now, a peak with a standard deviation of 4 pi would have a base width of 16 pi and, in practice, many short... 

The problem is made more difficult because these different dispersion processes are interactive and the extent to which one process affects the peak shape is modified by the presence of another. It follows if the processes that causes dispersion in mass overload are not random, but interactive, the normal procedures for mathematically analyzing peak dispersion can not be applied. These complex interacting effects can, however, be demonstrated experimentally, if not by rigorous theoretical treatment, and examples of mass overload were included in the work of Scott and Kucera [1]. The authors employed the same chromatographic system that they used to examine volume overload, but they employed two mobile phases of different polarity. In the first experiments, the mobile phase n-heptane was used and the sample volume was kept constant at 200 pi. The masses of naphthalene and anthracene were kept... 

A tertiary amine such as triethylamine is then added to the isocyanate-terminated prepolymer (containing carboxylic acid groups). The tertiary amine reacts with the pendant carboxylic acid groups, forming a carboxylic acid salt. The presence of this salt, together with adequate stirring, allows the dispersion of the prepolymer in water by the so-called melt dispersion process [57]. 

The Dispersion Process. The calculation methods to predict ambient pollutant concentrations are based on a two-step process for dispersion. First, the pollutant gases from a stack rise as a result of their own conditions of release, and then they are dispersed approximately in accordance with a Gaussian or normal distribution. 

Both aggregation inefficiency (Adler, 1981) and particle disruption (Hartel and Randolph, 1986) increase with particle size. These dispersive processes can counteract the positive effect of aggregation thereby imposing agglomerate particle size limitations and may give rise to apparent size-independence. 

Experiments to Study Deflagration of Fuel-Air Clouds after a Dispersion Process... 

Assuming there are (p) non-interacting, random dispersive processes occurring in the chromatographic system, then any process (q) acting... 

Equation (1) is the algebraic expression of the principle of the summation of variances. If the individual dispersion processes that take place in a column can be identified, and the variance that results... 

It is generally accepted that the maximum increase in band width that can be tolerated due to any extraneous dispersion process is a 5% increase in standard deviation (or a 10% increase in peak variance). 

Van Deemter considered peak dispersion results from four spreading processes that take place in a column, namely, the Multi-Path Effect, Longitudinal Diffusion, Resistance to Mass Transfer in the Mobile Phase and Resistance to Mass Transfer in the Stationary Phase. Each one of these dispersion processes will now be considered separately... 

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