Amorphous limit

The hitherto undescribed y-dextrin appeared in the fractionation, although it was probably contaminated with other dextrins. Fractions 5 and e do not represent homogeneous materials most likely they are mixtures of the crystalline dextrins with amorphous limit dextrins (see Scheme III). 

Conformations of polymer chains in dilute solutions under theta conditions are essentially identical to the random coil conformations of chains in amorphous polymers [26], where the interactions of polymer chains with solvent molecules are replaced by interactions between polymer chains. The density and the refractive index in the amorphous limit of a polymer are therefore the appropriate values of pP and nP to use in calculating the specific refractive index increment via Equation 8.16. The correlation developed for V(298K) in Section 3.C was hence used to calculate pP, and the correlation developed in Section 8.C was used to calculate nP. 

Table 9.2. Experimental molar volumes V(exp) at 298K in cc/mole, predicted molar volumes V(pred) at 298K calculated by using equations 3.13 and 3.14, and experimental and predicted values of the molar polarization PLL in cc/mole, for 61 polymers. The calculations also utilize the experimental and fitted values of the dielectric constant, which are listed in Table 9.1. The V(exp) values listed for semicrystalline polymers are extrapolations to the amorphous limit. LL(exP) was not calculated for six polymers because V(exp) was not known.

Experimental refractive indices were used whenever available in these calculations. For semicrystalline polymers such as polyethylene, typical refractive indices of the semicrystalline specimens were used instead of taking the amorphous limit as was done whenever possible in Section 8.C. Whenever experimental refractive indices were not available, the best possible estimate was made for the refractive index, in most cases by using Equation 8.6. 

Even a small amount of crystallinity can cause a very significant increase in X. The thermal conductivity in the crystalline limit of a semicrystalline polymer can be many times larger than the thermal conductivity in the amorphous limit. The general fonn of the temperature dependence of X also changes with crystallinity. For example, X increases monotonically for amorphous polymers between T=1()()K and T=Tg. On the other hand, for highly crystalline... 

Poly(vinylidene chloride) (extrapolated to amorphous limit) 1.3 1.0... 

Typically one aims to predict the refractive index of the amorphous limit for a semicrystalline polymer. After that the effect of crystallinity may be calculated by using either 1 ll or Rqd combined with an estimate of the change in volume due to crystallization. A large collection of refractive index data on polymers may be found in Physical Properties of Polymers Handbook by the American Institute of Physics (22). A representative albeit necessarily short list is given below in Table 1. 

Pressure-area isotherms for many polymer films lack the well-defined phase regions shown in Fig. IV-16 such films give the appearance of being rather amorphous and plastic in nature. At low pressures, non-ideal-gas behavior is approached as seen in Fig. XV-1 for polyfmethyl acrylate) (PMA). The limiting slope is given by a viiial equation... 

N2 as adsorbate, was quite similar to that for N2 on a directly prepared and probably amorphous ice powder [35, 141], On the other hand, N2 adsorption on carbon with increasing thickness of preadsorbed methanol decreased steadily—no limiting isotherm was reached [139]. 

The practical adsorbents used in most gas phase appHcations are limited to the following types, classified by their amorphous or crystalline nature. 

The ions not only ate implanted in the surface, but cause considerable lattice damage displacing the host atoms. An amorphous layer maybe formed and the stmcture is not an equiUbtium one. Thus the solubility of the implanted ions may gteady exceed the solubility limit. AH of these effects combine to produce a hard case. 

Most Kaminsky catalysts contain only one type of active center. They produce ethylene—a-olefin copolymers with uniform compositional distributions and quite narrow MWDs which, at their limit, can be characterized by M.Jratios of about 2.0 and MFR of about 15. These features of the catalysts determine their first appHcations in the specialty resin area, to be used in the synthesis of either uniformly branched VLDPE resins or completely amorphous PE plastomers. Kaminsky catalysts have been gradually replacing Ziegler catalysts in the manufacture of certain commodity LLDPE products. They also faciUtate the copolymerization of ethylene with cycHc dienes such as cyclopentene and norhornene (33,34). These copolymers are compositionaHy uniform and can be used as LLDPE resins with special properties. Ethylene—norhornene copolymers are resistant to chemicals and heat, have high glass transitions, and very high transparency which makes them suitable for polymer optical fibers (34). 

Catalyst Development. Traditional slurry polypropylene homopolymer processes suffered from formation of excessive amounts of low grade amorphous polymer and catalyst residues. Introduction of catalysts with up to 30-fold higher activity together with better temperature control have almost eliminated these problems (7). Although low reactor volume and available heat-transfer surfaces ultimately limit further productivity increases, these limitations are less restrictive with the introduction of more finely suspended metallocene catalysts and the emergence of industrial gas-phase fluid-bed polymerization processes. 

The success has been primarily due to the developments that occurred in the eady 1970s (3) at the University of Dundee (United Kingdom) where it was demonstrated that a device-quaUty amorphous siUcon semiconductor (i -Si) could be produced with the following features low concentration of defects, high photosensitivity, abiUty to be doped, and no size limitation. 

There is another class of amorphous semiconductors based on chalcogens which predate the developments that have occurred in i -Si. Because their use has been limited, eg, to switching types of devices and optical memories, this discussion is restricted to the optoelectronic properties of i -Si-based alloys and their role in some appHcations. 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

Sihcate solutions of equivalent composition may exhibit different physical properties and chemical reactivities because of differences in the distributions of polymer sihcate species. This effect is keenly observed in commercial alkah sihcate solutions with compositions that he in the metastable region near the solubihty limit of amorphous sihca. Experimental studies have shown that the precipitation boundaries of sodium sihcate solutions expand as a function of time, depending on the concentration of metal salts (29,58). Apparently, the high viscosity of concentrated alkah sihcate solutions contributes to the slow approach to equihbrium. 

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