Dispersion, of distribution

At low-conversion copolymerization in classical systems, the composition of macromolecules X whose value enters in expression (Eq. 69) does not depend on their length l, and thus the weight composition distribution / ( ) (Eq. 1) equals 5(f -X°) where X° = jt(x°). Hence, according to the theory, copolymers prepared in classical systems will be in asymptotic limit (/) -> oo monodisperse in composition. In the next approximation in small parameter 1/(1), where (/) denotes the average chemical size of macromolecules, the weight composition distribution will have a finite width. However, its dispersion specified by formula (Eq. 13) upon the replacement in it of l by (l) will be substantially less than the dispersion of distribution (Eq. 69)... 

SEA should be determined, mainly, by the A-mode aerosol. The latter is characterized by substantially constant size distributions for weak dust loads Tm < 0.4 M-m, a = 2.2 for moderate and heavy dust loads rm = 0.45 Hm, tJ = 2.1 (rm is the mean radius of particles in the number lognormal distribution cH the dispersion of distribution). 

The approximate equations (3.77, 80) account for the paths of the mean values and dispersion of distributions as long as the latter do not divide out into multi-modal distributions. 

At higher flow rates the dispersion of the tracer and the lower limit for time resolution of the concentration versus time distribution limits the accuracy to better than dt2%. 

In the next several sections, the theoretical distributions and tests of significance will be examined beginning with Student s distribution or t test. If the data contained only random (or chance) errors, the cumulative estimates x and 5- would gradually approach the limits p and cr. The distribution of results would be normally distributed with mean p and standard deviation cr. Were the true mean of the infinite population known, it would also have some symmetrical type of distribution centered around p. However, it would be expected that the dispersion or spread of this dispersion about the mean would depend on the sample size. 

Rosin sizing usually involves the addition of dilute aqueous solutions or dispersions of rosin soap size and alum to a pulp slurry (44—46). Although beater addition of either coreactant is permissable, addition of both before final pulp refining is unwise because subsequently exposed ceUulose surfaces may not be properly sized. The size and alum should be added sufficiendy eady to provide uniform distribution in the slurry, and adequate time for the formation and retention of aluminum resinates, commonly referred to as size precipitate. Free rosin emulsion sizes, however, do not react to a significant degree with alum in the pulp slurry, and addition of a cationic starch or resin is recommended to maximize retention of size to fiber. Subsequent reaction with aluminum occurs principally in the machine drier sections (47). 

Suspension Polymerization. At very low levels of stabilizer, eg, 0.1 wt %, the polymer does not form a creamy dispersion that stays indefinitely suspended in the aqueous phase but forms small beads that setde and may be easily separated by filtration (qv) (69). This suspension or pearl polymerization process has been used to prepare polymers for adhesive and coating appHcations and for conversion to poly(vinyl alcohol). Products in bead form are available from several commercial suppHers of PVAc resins. Suspension polymerizations are carried out with monomer-soluble initiators predominantly, with low levels of stabilizers. Suspension copolymerization processes for the production of vinyl acetate—ethylene bead products have been described and the properties of the copolymers determined (70). Continuous tubular polymerization of vinyl acetate in suspension (71,72) yields stable dispersions of beads with narrow particle size distributions at high yields. 

Another parameter is called the standard deviation, which is designated as O. The square of the standard deviation is used frequently and is called the popular variance, O". Basically, the standard deviation is a quantity which measures the spread or dispersion of the distribution from its mean [L. If the spread is broad, then the standard deviation will be larger than if it were more constrained. 

Although it is entirely possible for erosion-corrosion to occur in the absence of entrained particulate, it is common to find erosion-corrosion accelerated by a dilute dispersion of fine particulate matter (sand, silt, gas bubbles) entrained in the fluid. The character of the particulate, and even the fluid itself, substantially influences the effect. Eight major characteristics are influential particle shape, particle size, particle density, particle hardness, particle size distribution, angle of impact, impact velocity, and fluid viscosity. 

The horizontal dispersion of a plume has been modeled by the use of expanding cells well mixed vertically, with the chemistry calculated for each cell (31). The resulting simulation of transformation of NO to NO2 in a power plant plume by infusion of atmospheric ozone is a peaked distribution of NO2 that resembles a plume of the primary pollutants, SO2 and NO. The ozone distribution shows depletion across the plume, with maximum depletion in the center at 20 min travel time from the source, but relatively uniform ozone concentrations back to initial levels at travel distances 1 h from the source. 

At the effective stack height, the dispersion of the pollutants are assumed to spread out as a Gaussian distribution. The basic dispersion equation considers... 

Flow behavior of the polymer blends is determined by their structure, which is governed by the degree of dispersion of the component and by the mode of their distribution. For blends having identical compositions, it is possible to produce systems in which one and the same component may be either a dispersion medium or a dispersed phase [1]. This behavior of the polyblend systems depends on various parameters, the most important of which is the blending sequence. It is, therefore, difficult to obtain a uniform composition property relationship for the polymer blends even though the composition remains identical. 

Air and spent catalyst distribution. Modifications to the air and spent catalyst distributors permit uniform dispersion of air and spent catalyst into the regenerator. Improvements are lower carbon on the catalyst and less catalyst sintering. The benefits are a cleaner and higher-activity catalyst, which results in more liquid products and less coke and gas. 

It has been suggested that the role of nickel (as NiAlj) is to provide sites of low hydrogen overvoltage, where cathodically liberated hydrogen may be liberated without disrupting the protective oxide . The distribution of such sites is apparently critical however, since high corrosion resistance is associated with a fine dispersion of the second phase, while the electronic conductivity of the film is probably also important . 

The important thing is that in all works where the uniformity of filler distribution in the matrix has been studied (cf., e.g. [316, 317]) a better dispersion of the filler has been reported for PFCM than could be achieved in the case of mechanical mixing of ingredients even if carried out in a solvent. 

Third, a complicated question on the role of the dispersion of particles dimensions of particles dimensions is of independent value it is known that the viscosity of equi-concentrated dispersions of even spherical particles depends on the fact if spheres of one dimension or mixtures of different fractions were used in the experiments and here in all the cases the transition from monodisperse particles to wide distributions leads to a considerable decrease in viscosity [21] (which, certainly, is of theoretical and enormous practical interest as well). 

A comment should be made on the dispersity of star polymers. If the arms each have a most probable distribution 2), dispersity of the star... 

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