Physical characteristic, linear

Olig omerization and Polymerization. Siace an aHyl radical is stable, linear a-olefins are not readily polymerized by free-radical processes such as those employed ia the polymerization of styrene. However, ia the presence of Ziegler-Natta catalysts, these a-olefins can be smoothly converted to copolymers of various descriptions. Addition of higher olefins during polymerization of ethylene is commonly practiced to yield finished polymers with improved physical characteristics. 

Among the physical characteristics of these nonlinear condensation polymerizations, the occurrence of a sharp gel point is of foremost significance. At the gel point, which occurs at a well-defined stage in the course of the polymerization, the condensate transforms suddenly from a viscous liquid to an elastic gel. Prior to the gel point, all of the polymer is soluble in suitable solvents, and it is fusible also. Beyond the gel point, it is no longer fusible to a liquid nor is it entirely soluble in solvents. Linear polymers, on the other hand, remain soluble in suitable solvents and fusible to liquids as well (unless the melting point is above the temperature of thermal decomposition), regardless of the extent of condensation. 

The gel point is defined as the point at which the entire solid mass becomes interconnected. The physical characteristics of the gel network depends upon the size of particles and extent of cross-linking prior to gelation. Acid-catalysis leads to a more polymeric form of gel with linear chains as intermediates. Base-catalysis yields colloidal gels where gelation occurs by cross-linking of the colloidal particles. 

Model 1 is linear in the coefficients, and model 2 is nonlinear in the coefficients. The mathematical structure of model 2 has a fundamental basis that takes into account the physical characteristics of the particulate matter, including particle size and electrical properties, but we do not have the space to derive the equation here. 

The side groups and the repeating structure of the side groups change the chemical and physical properties of the polymer, and this defines the chemical and physical characteristics of the different polypeptide molecules. Not all natural macromolecules, however, are polymers. For example, insulin is a natural macromolecule with a molecular weight of 5733 kg/kg-mol. Insulin has long linear chains that are connected by 21 sulfur crosslinks. When it is decomposed 51 residual molecules result. Insulin is not a polymer because it does not have repeating units of monomers. 

Consider a GC capillary column where the length, diameter and thickness of the film of the stationary phase could all be modified (one factor at a time and without adjustment of the apparatus physical characteristics, such as temperature and pressure, yet maintaining a flow such that the linear velocity of the gas remains the same). 

To estimate the time at which steady-state conditions are expected, the required penetration distance is set equal to the largest characteristic length over which diffusion can take place in the system. If L is the characteristic linear dimension of a body, steady state may be expected to apply at times r L2/Dmm, where Dmin is the smallest value of the diffusivity in the body. Of course, there are many physical situations where steady-state conditions will never arise, such as when the boundary conditions are time dependent or the system is infinite or semi-infinite. 

At least for a first approach, the active component in the strain-stress relation may be treated in a simple manner. For some strain emax the active stress aa is maximum, and on both sides the stress decreases almost linearly with e — emax. Moreover, the stress is proportional to the muscle tone xjr. By numerically integrating the passive and active contributions across the arteriolar wall, one can establish a relation among the equilibrium pressure Peq, the normalized radius r, and the activation level xjr [19]. This relation is based solely on the physical characteristics of the vessel wall. However, computation of the relation for every time step of the simulation model is time-consuming. To speed up the process we have used the following analytic approximation [12] ... 

Besides the outstanding chemical characteristics of certain mesoscopic structures, they also possess a number of surprising physical characteristics. Typical examples are the initiation of premelting near dislocations, twin boundaries or grain boundaries (e g. Raterron et al. 1999, Jamnik and Maier 1997) and the movement of twin boundaries under external stress which leads to non-linear strain-stress relationships. It is the purpose of this review to focus on some of the characteristic features of mesocopic structures and to illustrate the generic results for the case of ferroeleastic twin patterns (Salje 1993). 

The characteristics of disperse systems (see Section 1.1.2) are determined by geometrical parameters, i.e. linear dimensions, projection areas, surfaces, volumes, and, sometimes, angular dimensions. In addition, other physical characteristics, which do not directly represent particle size, may be used for the determination of these parameters. In such cases, a mathematical conversion into the desired geometrical dimension takes place. The term particle size analysis defines the experimental determination of particle characteristics and the statistical treatment of results. 

These anionic ring opening polymerizations are usually carried out either in bulk or in solution. A host of catalyst types are active. For synthetic references using specific catalysts, the reader is referred to several excellent sources (4,7,31,32). Representative catalysts include hydroxides, alcoholates, phenolates, silanolates, siloxanolates, mercaptides of the alkali metals, organolithium and potassium compounds, and quaternary ammonium and phosphonium bases and their silanolates and siloxanolates. Some physical characteristics of linear oligomers are given in Table 5 (10). 

TABLE 5. SOME PHYSICAL CHARACTERISTICS OF LINEAR OLIGOMERS... 

Mineral hydrocarbon waxes are a heterogeneous group of substances consisting of mixtures of different-sized hydrocarbon molecules, which may include saturated and/or unsaturated hydrocarbons these may be linear, branched or cyclic. The relative proportions of these different hydrocarbon molecules varies widely and is best defined on the basis of their physical characteristics, such as viscosity and density, rather than on the basis of their precise chemical identity. 

Very slow linear flow velocities characteristic of deep groundwater aquifers extend from meters per year and up. Such slow velocities are generally derived from model calculations based on the known physical characteristics of the... 

A curious aspect of these new types of reactions is that, polyethylene, which cannot be stereospecific because it has no substituents on the C atomE also shows increased crystallinity, higher density and melting point, and better physical characteristics when prepared with the same imtiation systems as used for isotactic polymers. In this case the improved properties are attributed to the fact that this polyethylene is a truly linear molecule, while ordinary polyethylene contains short side chains whidi inhibit crystallization. 

Polarimetry is a powerful method for studying solar-system bodies. It has allowed the determination of such parameters as the complex refractive index of particles in planetary atmospheres, the size distribution functions of these particles, the methane concentrations, the atmospheric pressure values above the cloud layers, etc. Independent spectral analyses of linear P) and circular (V) polarization observational data also may facilitate the determination of physical characteristics of particles at different heights in a planetary atmosphere. Polarimetiy enables us to make qualitative conclusions about... 

Algebraic expressions are used to reduce a population of particles with a wide size distribution to a single value. The expression relies on a physical characteristic of the population or a combination of characteristics—number, length (or some linear dimension representing the particle) area, mass, or volume, assuming that the particle density is invariant with volume. 

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