Homopolymers theory

The extreme sensitivity of the crystallization isotherms to small amounts of irregular structure is demonstrated in Fig. 10.7 for Wb = 0.01. Although deviations from Eq. (9.31a) are not observed until 1 — 0 0.6, a small but significant departure from the homopolymer theory develops as the level of crystallinity increases... 

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

The basic features of folding can be understood in tenns of two fundamental equilibrium temperatures that detennine tire phases of tire system [7]. At sufficiently high temperatures (JcT greater tlian all tire attractive interactions) tire shape of tire polypeptide chain can be described as a random coil and hence its behaviour is tire same as a self-avoiding walk. As tire temperature is lowered one expects a transition at7 = Tq to a compact phase. This transition is very much in tire spirit of tire collapse transition familiar in tire theory of homopolymers [10]. The number of compact... 

The principal monomer is acrylamide [79-06-17, where R = H and R = NH2, made by the hydrolysis of acrylonitrile. The homopolymer [9003-05-8] of acrylamide, which in theory has no electrical charge, has some use as a flocculant however, the majority of acrylamide-based flocculants are copolymers with acryHc monomers containing charged functional groups, such as those shown in Figure 1, or polymers containing functional groups formed by modification of acrylamide homopolymers or copolymers (Fig. 2). The chemistry of polyacrylamides has been reviewed by several authors (18—20) (see... 

The desorption and termination constants were calculated for a copolymer from the corresponding homopolymer constants as discussed in Nomura and Fujita (12.) The homopolymer desorption coefficients were calculated from the appropriate chain transfer constants and radical diffusivities in the aqueous and polymer phases using an extension of the desorption theory developed by Nomura and Fujita (12.). The homopolymer termination constants were corrected for the Trommsdorff effect by using the Friis and Hamielec (12) correlation. 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

The theoretical and (model) experimental work referred to above has largely been concerned with linear homopolymers adsorbed on regular surfaces. However, there is a vast literature of experimental studies on more complex systems. Unfortunately, in many cases the systems are either ill-defined and/or only adsorption isotherms have been established for drawing general conclusions or comparison with theory such studies are of little use. On the theoretical side, clearly the work needs to be extended towards these more complex systems. In particular, developments are required in the following areas (starts have already been made in some cases) ... 

It is considered that, if ideal, optically active poly(alkyl(aryl)silane) homopolymer and copolymer systems could be obtained which had stiffer main-chain structures with longer persistence lengths, it should be possible to clarify the relationship between the gabs value and the chiral molar composition. The magnitude of the chirality of the polyisocyanates allowed precise correlations with the cooperativity models.18q In the theory of the cooperative helical order in polyisocyanates, the polymers are characterized by the chiral order parameter M, which is the fraction of the main chain twisting in one helical sense minus the fraction of the main chain twisting in the opposing sense. This order parameter is equal to the optical activity normalized by the value for an entirely one-handed helical polymer. The theory predicts... 

Fig. 9 Inverse of the crystallization half-time as a function of isothermal crystallization temperature for PCL11 homopolymer and for the PCL block of the indicated copolymers. All experiments were performed after the PPDX block had been previously crystallized until saturation. Solid lines are fits to the Lauritzen and Hoffman theory. (From [103]. Reproduced with permission of the Royal Society of Chemistry)...

Polydispersity of the molecular weight is not so well described by the DE approach, even qualitatively. In reptation theory the blend of two compatible homopolymers A and B of different molecular weights is given by... 

As pointed out above, the RPA theory predicts that the dynamics of the respective homopolymers should be observed at high Q in the Rouse regime. While the experiment shows that the predicted Q dependencies are reproduced well by the data, the absolute values for the observed relaxation rates disagree with the predictions (see Table 6.2). In particular the observed Rouse factors for PE are considerably smaller than predicted, (Wf )expt=2xl0 s" compared to Wf pa=3.8x 10 A s at T=473 K. At low Q values, the two blocks display the same single chain dynamics. 

Table 6.2 Experimental Rouse rates (Wi ) for the pure homopolymers and for the hlock-copolymer melts obtained from the high Q behaviour of JXQ) compared to the predictions of the RPA theory. Values of are given in 10s ...

The relative retention a=k/ki is a measure of the separation selectivity for two compounds i and j with retention factors ki and kj, respectively, differing by one repeat structural unit, An=l.p in Equation 5.16 is the end-group contribution to the retention factor. The conventional theory describes adequately the retention of oligomers and lower homopolymers and copolymers up to the molar masses 10,000-30,000Da for higher polymers the accuracy of the determination of retention model parameters is too low [95]. 

As is well known from free radical copolymerization theory, the composition of the copolymers will depend only on the propagation reaction. The relative ability of monomer to add to a growing chain is influenced by the nature of the last chain unit and by the relative concentration. Generally, chain transfer to monomer by polymer radicals will occur to an appreciable extent, and the final product will be made up of homopolymers, multisegment block copolymers, and branched and grafted structures. In the presence of two or more monomers,... 

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