Copolymer equation, random

The systematic changes in the glass temperatures illustrated in Table 1 indicate quantitatively the changes in the composition within each phase. The random copolymer equation can be used to estimate the composition within each phase ... 

Where copolymer compositional heterogeneity was a problem, monomer charges and feed ratios were adjusted to produce constant composition homogeneous polymers. While the required composition for the monomer charge and feed ratios may be determined by a random process, it is much more convenient to use an integrated form of the copolymer equation to calculate these quantities (2). 

In random copolymers, there is a high degree of interaction between the different repeat units because they are held together chemically. The glass transition of a random copolymer consequently reflects the composition of the copolymer. Thus, the Tg of random copolymers can usually be represented as a monotonic function of composition by one of the various copolymer equations. Similarly, if blends of polymers are mixed at the segmental level, only one Tg should be evident, and a copolymer equation should be applicable. 

Equation (5.23) for the microhardness of the amorphous matrix of the MFC (Fig. 5.17(d)) is acceptable as it has been demonstrated (by Baltd Calleja et al, 1998) that the H values for completely amorphous copolymers (with random sequential order) obey the additivity law provided the Ha values for the respective homopolymers are used. In this way one obtains for the microhardness of... 

Equation (7.13) means that k /ki2 and k2i/k22 wiU be simultaneously either greater or less than unity or in other words, that both radicals prefer to react with the same monomer. Ail copolymers whose Vir2 product equals 1 are therefore called ideal copolymers or random copolymers. Most ionic copolymerizations are characterized by the ideal type of behavior. 

Case 2 q = Tj = 1. Under these conditions, the growing radicals cannot (fistinguish between the two monomers. The composition of the copolymer is the same as that of the feed and as we said above, the monomers are arranged randomly along the chain. The copolymer equation becomes ... 

Random copolymers will be formed, or course, if each radical attacks either monomer with equal facility k =kn, 22 = 21, f = f2 = I ) Free-radical copolymerization of ethylene and vinyl acetate is an example of such a system, but this is not a common case. Random monomer distributions are obtained more generally if fcn/A i2 is approximately equal to/t2i/ 22- That is to say,/ ] l/r2- This means that ku/k22 and 21/ 22 will be simultaneously either greater or less than unity or in other words, that both radicals prefer to react with the same monomer. If riT2 = 1, copolymer equation (7-13) reduces to... 

CCD describes the distribution of compositions of chains. It tells nothing about the distribution of monomers within each chain as noted. Particularly, it does not provide any information about the blockiness of the chains. For instance, is the polymer an alternating copolymer A random copolymer Are there long sequences of A monomer interspersed with sequences of B monomer The CSD describes the distribution of A (or B) sequence lengths within the polymer, independent of the question of on which chain each sequence resides. The CSD can be developed for monomer A and monomer B. There is no reason, in general, that the two should be the same. The CCD can be derived from Equations 16.11 and 16.12 as follows. The two equations in Equation 16.12 can be multiplied by g and sununed over all values of k to give ... 

The present study first examines the effect of comonomer content on the miscibility of random EO copolymers. The study is extended to test the miscibility of random EOs with OBCs of about the same molecular weight. The effect of blocky chain structure on the miscibility is discussed. The interaction parameter % for the blends of two random EO copolymers is calculated and tested for the copolymer equation. 

The interaction parameter between the ethylene (E) units and octene (O) units for a binary blend of two random copolymers can be obtained from the copolymer equation ... 

There are many examples known where a random copolymer Al, comprised of monomers 1 and 2, is miscible with a homopolymer B, comprised of monomer 3, even though neither homopolymer 1 or 2 is miscible with homopolymer 3, as illustrated by Table 2. The binary interaction model offers a relatively simple explanation for the increased likelihood of random copolymers forming miscible blends with other polymers. The overall interaction parameter for such blends can be shown (eg, by simplifying eq. 8) to have the form of equation 9 (133—134). 

Whereas random copolymers exhibit one T described by equation 38, block copolymers, because of this microphase separation, exhibit two glass-transition temperatures. The T of each block is close to, if not the same as, the homopolymer from which it was formed. Polymer properties are also affected by the arrangement of the blocks. This is shown for high styrene-containing or high molecular-weight styrene resias of various block arrangements ia Table 3. 

The glass transition temperature of a random copolymer usually falls between those of the corresponding homopolymers since the copolymers will tend to have intermediate chain stiffness and interchain attraction. Where these are the only important factors to be considered a linear relationship between Tg and copolymer composition is both reasonable to postulate and experimentally verifiable. One form of this relationship is given by the equation... 

Equations 22 and 23 can be solved numerically using the method described in Ref. 5. For oligomers, the probability generating functions are calculated by the appropriate sums. For random copolymers analytical expressions for and t can be written for a polymer or crosslinker using the appropriate Schulz-Zimm parameters (5) ... 

The component which brings about the depression in Tm may be a constituent of the polymer itself. In a copolymer consisting of A units which crystallize and B units which do not, with the two units occurring in random sequence along the chain, it is easy to show that the latter should depress the melting point of the former according to the equation... 

The use of simultaneous equations with at least three sets of experimental data can, however, be applied to Eq. (101) or (102) to yield M, MA and MB. This is especially useful, if the specific co-ordinates of the whole parabola cannot be realised experimentally as is often the case. The data159-1 in Table 14 relate to a random copolymer of styrene (A)/di-n-butyl itaconate (B) in which WA = 0.169. Solution of simultaneous equations [Eq. (101)] yields M = 67300, MA = 56800 and MB =64700. The compositional heterogeneity is such that the data conform to the required theoretical relationship149 ... 

The beads comprise an uncrosshnked propylene random copolymer having a melting point of at least 140C, as a base resin. The time required to attenuate an air pressure within the foamed beads applied by a pressurising treatment with air from 1.2 to 0.8 kgf/sq.cm.(G) under atmospheric pressure at 23C is at least 80 minutes and the CNl value of the foamed beads, which is defined by a given equation, is smaller than 3.80. 

A number of copolymers are formed employing vinyl chloride. Because of the presence of the comonomer, these copolymers are more flexible than PVC itself. Vinylite (Equation 6.59) is a random copolymer of vinyl chloride (87%) and vinyl acetate. While vinylite is not as strong as PVC, it is more easily processed. 

Preference for reaction with the unlike monomer occurs when ri is less than 1. When r and T2 are approximately equal to 1, the conditions are said to be ideal, with a random (not alternating) copolymer produced, in accordance with the Wall equation. Thus, a random copolymer (ideal copolymer) would be produced when chlorotrifluoroethylene is copolymerized with tetrafluoroethylene (Table 7.1). 

Describe by means of equations how random and block copolymers having the following compositions could be synthesized ... 

---