Copolymer theory

Helfand E., Block copolymer theory. I. Statistical thermodynamics of the microphases, ACS Poly. Prep., 14, 970, 1973. 

Helfand E. and Wasserman Z.R., Block copolymers theory. 6. Cyfindrical domain. Macromolecules, 13, 994, 1980. 

Matson M.W. and Bates E.S., Unifying weak- and strong-segregation block copolymer theories. Macromolecules, 29, 1091, 1996. 

Helfand E (1975) Block copolymer theory. HI. Statistical mechanics of the microdomain structure. Macromolecules 8 552-556... 

Helfand E, Wasserman ZR (1976) Block copolymer theory. 4. Narrow interphase approximation. Macromolecules 9 879-888... 

Fredrickson GH, Bates FS (1996) Dynamics of block copolymers theory and experiment. Annu Rev Mater Sci 26 501-550... 

To predict the course of a copolymerization we need to be able to express the composition of a copolymer in terms of the concentrations of the monomers in the reaction mixture and some ready measure of the relative reactivities of these monomers. The utility of such a model can be tested by comparing experimental and estimated compositions of copolymers formed from given monomer concentrations. Asa general rule in science, the preferred model is the simplest one which fits the facts. For chain-growth copolymerizations, this turns out to be the simple copolymer model, which was the earliest useful theory in this connection [1,21. All other relations which have been proposed include more parameters than the simple copolymer model. We focus here on the simple copolymer theory because the basic concepts of copolymerization are most easily understood in this framework and because it is consistent with most copolymer composition and sequence distribution data. 

Deviations from the behavior of the simple copolymer model have been noted for various systems and have prompted the development of alternative models, all of which use more parameters than the two reactivity ratios in Eq. (7-1. ). Such models will often fit particular sets of copolymerization data better than the simple copolymer model. It appears in retrospect, however, that many of the apparent deviations from this model may be accounted for by large uncertainties in reactivity ratio values. The inadequacy of the simple copolymer theory can be established only if deviations between calculated and observed copolymer compositions arc shown to be systematic as the feed composition or monomer dilution is varied. Random errors do not necessarily show that the basic model is inapplicable. 

Obviously many variables were not investigated, such as the effect of the type of nonionic surfactant, broader ranges of surfactant concentration, and broader ranges of monomer concentration. However, the results of this work are sufiBcient to demonstrate that the block copolymer architecture can be modified in MHAP by modifying the anionic surfactant concentration and type. These results have supported but not proved the block copolymer theory for this type of polymer-surfactant system. This model system is also a simple means of studying some aspects of mixed surfactant systems, an area of much current interest (e.g., ref 37). 

Weyersberg A, Vilgis TA (1993) Phase transitions in diblock copolymers Theory and Monte Carlo simulations. Phys Rev E 48(l) 377-390... 

Self-Assembled Structures of Amphiphilic Ionic Block Copolymers Theory, Self-Consistent Field Modeling and Experiment... 

Matsen MW, Bates FS (1996) Unifying Weak-and Strong-segregation Block Copolymer Theories. Macromolecules 29 1091-1098 and Matsen MW, Bates FS (1997) Block Copolymer Microstructures in the Intermediate-segregation Regime. J Chem Phys 106 2436-2448. 

C. Electrothermodynamics of Microphase-Separated Block Copolymers—Theory... 

Although the possibility of the order-disorder transition was recognized in most of the block copolymer theories, it is Leibler who has expressedly addressed this problem. He derived the free energy of a block copolymer system in a series expanded in powers of the order parameter j denoting the deviation of the local density from the mean. The coefficients of this expansion up to the fourth ordef term were evaluated by a method which is a generalization of the random phase approximation method described above (Equation (16) was, in fact, derived as the second order term in the... 

The amount of 1,4-1,2-1,4 sequences in polybutadienes can be estimated from the amounts of the different ozonolysis products (Table 5.5) if one considers the amount of 1,4 structure not detected. Because the ozonolysis technique cleaves the centre of a butadiene monomer unit, one-half of a 1,4 unit remains attached to each end of a block of 1,2 units after ozonolysis these structures do not elute from the gas chromatographic column. Using random copolymer theory, the maximum amounts of these undetected 1,4 structures can then be calculated. Tanaka and coworkers [28] also discussed the determination by ozonolysis of 1,2 butadiene units in polybutadiene. 

More than a quarter of a century being elapsed since the copolymerization equation was first proposed, all aspects of copolymer theory have been largely studied, both theoretically and experimentally, and very exhaustive information on copolymer microstructure can be now obtained on the basis of a few well-established and widely used quantities. The number of these quantities depends on the complexity of the mechanisms acting in copolymerization. If the copolymerization equation is put in the usual form... 

X for this system was essentially negligible however, at higher temperatures X became negative. This was attributed to the copolymer effect rather than the existence of specific interactions. The poly butadienes were treated as random copolymers of 1,4- and 1,2-addition units, and there are deuterated and hydrogenous homologues in the mixture, i.e. there are four different types of monomer segment. A, B,C and D. Using the copolymer theory of ten Brinke et al. [30], then % can be written as ... 

Matsen M and Bates F S (1996) Unifying Weak- and Strong-Segregation Block Copolymer Theories, Macromolecules 29 1091-1098, and references therein. Ginzburg V V, Bicerano J, Christenson C P, Schrock A K and Patashinski A Z (2007) Theoretical Modeling of the Relationship Between Young s Modulus and Formulation Variables for Segmented Polyurethanes, J Polym Sci Part B Polym Phys 45 2123-2135. 

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