Poly from theory

The rate of hydrolysis of the partially ethoxylated polymer was retarded, although not to the extent calculated from theory (Fig. 25), suggesting some contribution to the rate of chain scission by an uncatalyzed process. End-capping poly (glycolic acid-co-lactic acid) has a similar effect on the rate of hydrolysis of this polyester (100). 

All SiC poly types have the valence band maximum at the zone centre but the conduction band minimum is polytype dependent. The indirect bandgaps increase with polytype hexagonality from 2.39 eV for 3C-SiC to 3.33 eV for 2H-SiC. In 3C-SiC, isolated silicon and carbon vacancies and a divacancy complex of carbon and silicon sites produce states in the forbidden gap but antisite defects do not. Theoretical values for the energy gap in 2H-SiC do not correspond to the experimental values. The valence band offset between 3C- and 2H-SiC is found to be 0.13 eV. Relatively little work has been carried out on the other poly types. Theory and experiment are also at variance for the energy gap of 4H- and 6H-SiC polytypes. 

One potential area of application that has direct impact in polymer chemistry is the characterization of copolymers. The quantitative analysis of copolymer composition by MALDI has been demonstrated in a limited number of systems, though with varying degrees of success. For example. Abate et al showed that the relative amounts of hydroxybutyrate and hydroxyvalerate in a random copolymer, poly(P-hydroxybutyrate-co-P-hydroxyvalerate), when determined by MALDI, agree with those expected from theory [174]. Wilczek-Vera et al. have shown that for diblock... 

Another example of the phase behavior of asymmetric molecules is given in Fig. 3.22 for aqueous solutions of hydroxypropyl cellulose.(97) The phase diagram for this system shows all of the major features expected from the Rory theory for an asymmetric polymer solute. The slight tilting of the narrow biphasic region could possibly be attributed to some molecular flexibility as well as anisotropic interac-tion.(98) The phase diagram for the ternary system, polymer and two solvents, for poly(p-phenylene terephthalamide) also shows the major features expected from theory. (99)... 

Fig. 9.20 Plots of crystallinity levels as functions of molecular weight, (a) Linear polyethylene fractions (34) (b) poly(ethylene oxide) fractions (49). Pseudoequilibrium level of crystallinity that is attained A crystallinity levels at which deviations occur from theory Goler-Sachs Avrami o. Dashed curve represents ratio of crystallinity level at which deviation occurs to that actually attained.

Most of the reactions with which organic chemists are concerned involve poly-atomic molecules, and occur in solution at temperatures not far removed from the ambient. There is not at present the faintest possibility of chemical theory predicting the absolute rates of such processes. 

Blends of poly(vinyl chloride) (PVC) and a-methylstyrene—acrylonitrile copolymers (a-MSAN) exhibit a miscibiUty window that stems from an LCST-type phase diagram. Figure 3 shows how the phase-separation temperature of 50% PVC blends varies with the AN content of the copolymer (96). This behavior can be described by an appropriate equation-of-state theory and interaction energy of the form given by equation 9. 

It is also possible to prepare them from amino acids by the self-condensation reaction (3.12). The PAs (AABB) can be prepared from diamines and diacids by hydrolytic polymerization [see (3.12)]. The polyamides can also be prepared from other starting materials, such as esters, acid chlorides, isocyanates, silylated amines, and nitrils. The reactive acid chlorides are employed in the synthesis of wholly aromatic polyamides, such as poly(p-phenyleneterephthalamide) in (3.4). The molecular weight distribution (Mw/Mn) of these polymers follows the classical theory of molecular weight distribution and is nearly always in the region of 2. In some cases, such as PA-6,6, chain branching can take place and then the Mw/Mn ratio is higher. 

Subsequent work by Johansson and Lofroth [183] compared this result with those obtained from Brownian dynamics simulation of hard-sphere diffusion in polymer networks of wormlike chains. They concluded that their theory gave excellent agreement for small particles. For larger particles, the theory predicted a faster diffusion than was observed. They have also compared the diffusion coefficients from Eq. (73) to the experimental values [182] for diffusion of poly(ethylene glycol) in k-carrageenan gels and solutions. It was found that their theory can successfully predict the diffusion of solutes in both flexible and stiff polymer systems. Equation (73) is an example of the so-called stretched exponential function discussed further later. 

Figure 9 The equations of motion (TF theory) correlate swelling of poly(A-isopropyl acrylamide) caused by an increase in temperature from 10 to 25°C. D = 2.5 X 10 7 cm2/s L0 = 1.5 mm. (Adapted from Ref. 84.)...

Figure 14 The free volume theory of Yasuda and coworkers holds for the diffusion of acetaminophen in swollen 10 X 4 poly(lV-isopropyl acrylamide) gel. (Adapted from Ref. 176.)...

Although being qualitatively in agreement with experimental results, disagreements between experiment and theory remain. Besides the composition, /a, and the total degree of polymerization, N, all theoretical works refer to the segmental interaction parameter x This parameter can be estimated from a relationship to the solubility parameters. The ODT as a thermodynamic measure of the incompatibility was used to compare a set of symmetrically composed diblock copolymers from different hydrocarbons, polydimethyl-siloxane and poly(ethylene oxide) (PEO) [33]. While the behaviour of hydrocarbon diblock copolymers was successfully described by a consistent set of solubility parameters, this procedure failed for systems containing PEO. The... 

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