Composition for Random Copolymers

Copolymer composition can be calculated as a function of monomer composition when the polymer is formed by free radical polymerization in a CSTR (continuous stirred tank reactor). Consider two monomers 1 and 2 as starting materials for forming a copolymer with repeat units of 1 and 2. The initiation can be effected by thermal means or by using a peroxy initiator. 

The free radical species formed may be assumed to be highly reactive and can be assumed to be consumed as rapidly as they are formed. This is referred to as the quasi-steady-state assumption (QSSA). Thus  

Equation (10.8) is called the copolymerization composition equation. In a CSTR, the effluent concentration and the reactor concentration are the same. The reactor concentrations of monomers 1 and 2 are [MJ and [Mj], respectively. The polymer composition of monomer 1 repeat unit in the polymer F, can be seen to be 

Equation (10.9) gives the rate at which the monomer repeat unit 1 enters the copolymer compared with the rates at which both the monomer repeat units or rate at which all the monomer repeat units enter the backbone chain of the polymer. Equations (10.9) and (10.8) can be combined as 

FIGURE10.2 Copolymer composition as a function of monomer composition for SAN and AMS-AN copolymers. 

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Fig. 5.17 Plot of melting temperature against the melt composition for random copolymers of 3-hydroxy butyrate and 3-hydroxy valerate. (From Scandala, et al. (131))...

Fig. 5.18 Plot of melting temperature against melt composition for random copolymers of ethylene terephthalate and ethylene naphthalene 2,6-dicarboxylate for different crystallization procedures. A dynamic crystallized sample A annealed sample fiber sample,...

FIGURE 1.15 Tja and as functions of composition for random copolymers composed of two Class-I polymers. 

Shen et al. determined the BD/IP copolymerization parameters for the polymerization with the ternary catalyst system NdN/TIBA/EASC at 50 °C ted = 1.4 and np = 0.6 [92]. Over a wide range of BD/IP copolymer compositions the experimentally determined Tg values significantly deviate from the theoretical curve which was calculated by the Fox equation for random copolymers. Only for IP-contents < lOwt. % does the experimentally determined data coincide with the theoretical curve. Shen et al. also succeeded to synthesize block copolymers comprising poly(butadiene) and poly(isoprene) building blocks [92]. 

For polymers, DT is found to be virtually independent of chain length and chain branching, but it is strongly dependent on polymer and solvent composition [84]. For random copolymers, DT varies linearly with monomer composition block copolymers display more complex behavior [111,214]. For segregated block copolymers like micelles, DT seems to be determined by the monomers located in the outer region (see Fig. 18). For particles, DT appears to be both composition and size dependent [215]. 

Based on the pioneering work of Molau [64], it is evident that phase separation can occur in blends of two or more copolymers produced from the same monomers when the composition difference between the blend components exceeds some critical value. The mean field theory for random copolymer-copolymers blends has been applied to ES-ES blends differing in styrene content to determine the miscibility behavior of blends [65,66]. On the basis of the solubility parameter difference between PS and PE, it was predicted that the critical comonomer difference in styrene content at which phase separation occurs is about 10 wt% S for ESI with molecular weight around 105. DMS plots for ES73 and ES66 copolymers and their 1 1 blend are presented in Figure 26.8. 

Thus by the use of Wood s approximation we were able to construct a complete 7 /composition curve for the polyfisobutylene-co- -pinene) system. In view of the experimental difficulties in obtaining the Tg for poiy( -pinene), the accuracy of the dot is questionable beyond V2 = 63 volume% ie., above 63 volume% pinene in the copolymer. Howewr, in the range from 0 to 63 volume% /3-pinene, the curve is considered to be accurate and, importantly, reveals that useful rubbery poly(isobutylene-co-j3 pinene) could be made with up to about 28 vohime% pinene, re, to a Tg of —40 °C. In agreement with cnir spectroscopic and reactivity ratio studies, the (admittedly somewhat limited) applicability of Eq. (1) developed for random copolymers also suggests a statistically random copdymer structure for our poly(isobutylene-co- pinene) products. 

First, retention does not yield Dj directly, but rather the Soret coefficient, which is the ratio of to the ordinary diffusion coefficient (T>). Because compositional information is contained in alone, an independent measure of D must be available. Second, a general model for the dependence of on composition has not been established therefore, the dependence must be determined empirically for each polymer-solvent system. Fortunately, Dj is independent of molecular weight, and for certain copolymers, the dependence of Dj on chemical composition has been established. With random copolymers, for example, Dj is a weighted average of the Dj values for the corresponding homopolymers, where the weighting factors are the mole fractions of each component in the copolymers [9]. As a result, the composition of random copolymers can be determined by combining thermal FFF with any technique that measures D. 

The next step in the calculation of n(A) is the correlation of trimer peak intensities with the number of specific triads in the polymer. A parameter K can be assigned as a coefficient to express the relationship between the pyrolysis peak area and the triad number. These K values can be obtained by calibrating through copolymers with known composition. A random copolymer of known composition is the best choice in this case since it produces all trimer peaks allowing good calibration. For each trimer type, a simple relation of the type ... 

TABLE 8.4 Internal Pressure Parameter A/V and Characteristic Volume B for Random Copolymers with 50/50 mol% Composition and a Few Low-Molecular-Weight Liquids... 

If there are no heterointeractions in the coil expansion, the Mark-Houwink constants lie between those for the two homopolymers, although these constants are composition-dependent this can only apply to block copolymers. For random copolymers, heterointeractions affect the coil size in solution. 

It is now known that Dt does not depend on the MW but is related to the chemical nature of the polymer and solvent. This can be used to advantage to separate different polymers with the same diffusion coefficient and size, which cannot be achieved using SEC. It was found that for random copolymers Dt is hnearly related to the proportion of the amount of the two monomers present, providing a way of me-asiuing the composition of such copolymers. Further, for block copolymers, Dt apparently depends on the polymer block occupying the outer layer of the copolymer molecules. This could perhaps provide a method of studying the conformation of block copolymers in solution. 

For a block copolymer system where the differences in surface energy between the two components is less, wetting constraints can lead to surface heterogeneity (62). For the same composition, block copolymers, segregate more effectively to the surface than graft copoljuners, which in turn are more surface active than random copolymers, though problems with microphase separation are reduced for random copolymers (61). Other chain architectures have been investigated and also been shown to he surface active (67). 

Fig. 5.27 Melting temperature against composition for block copolymers of poly(ethylene terephthalate) with ethylene succinate(l) ethylene adipate(2) diethylene adipate(3) ethylene azelate(4) ethylene sebacate(5) ethylene phthalate(6) and ethylene isoph-thalate(7). For comparative purposes, data from random copolymers with ethylene adipate and with ethylene sebacate also are given. (From Kenney (189))...

The PL method has been used to investigate the influence of the composition of random copolymers on the IMM of the polymer chain 1 Methyl acrylate and methyl methacrylate (the chain mobilities of the corresponding polymers differ by two orders of magnitude), styrene and a-methylstyrene (the relaxation parameters of the corresponding polymers are very similar) and, finally, styrene and methyl methacrylate were chosen as components of the random copolymers. Anthracene-containing LM were used for all these copolymers. 

Fig. 4.5. Melting-temperature-composition relations for block copolymers of poly (ethylene terephthalate) with (1) ethylene succinate, (2) ethylene adipate, (3) diethylene adipate, (4) ethylene azelate, (5) ethylene sebacate, (6) ethylene phthalate, and (7) ethylene isophthalate. For comparative purposes data for random copolymers with ethylene adipate and with ethylene sebacate are also given. (Reproduced with permission from [16], copyright 1968, Polymer Engineering and Science.)...

The effects of varying composition in random copolymers can also be seen in isochronal or pseudoisochronal studies such as those in Fig. 12-3. Thus, Jenckel and Herwig found in copolymers of styrene and methyl acrylate that the maximum in tan 5 (measured in torsion at a frequency of 0.14 sec ) on the temperature scale shifted from about 20 to 110° with increasing proportions of styrene the sharpness of the maximum was not much affected. Similar progressive changes with composition have been described for random copolymers of styrene and a-methyl styrene and of methyl methacrylate and tri- -propyl tin methacry-... 

TLC has been used in the study of many homopolymers polystyrene, poly(methyl methacrylate), poly(ethylene oxide), polyisoprene, poly(vinyl acetate), poly(vinyl chloride) and polybutadiene. Their molecular weight, molecular-weight distributions, microstructure (stereo-regularity, isomerism and the content of polar end groups), isotope composition and branching have been studied. For copolymer characterisation (e.g. purity and compositional inhomogeneity), random copolymers such as styrene-methacrylate, and block copolymers such as styrene-butadiene, styrene-methyl methacrylate and styrene-ethylene oxide have been separated. A good review article on polymers... 

FIGURE 16.1 Copolymer composition. Instantaneous copolymer composition (Fj) as a function of monomer composition (/, ) for random copolymerization with r =l/r as indicated. This material is reprodnced with permission of John Wiley Sons, Inc from Billmeyer FW. Textbook of Polymer Science. 3rd ed. New York Wiley 1984. 

Figure4.9 Comparison of melting point versus composition relationships for random copolymers and polymer blends exhibiting isomorphic behavior...

The glass transition temperatures for random copolymers vary monotonically with composition between those of the homopolymers. They can be approximated fairly well from knowledge of the Tg values of the homopolymers, Tgj and with the empirical relation ... 

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