Thermodynamics of Block Copolymers

This chapter deals almost exclusively with neat, or pure, diblock copolymer melts. Polymer blends are discussed in Chapter 9, micellar solutions in Chapter 12, and stabilized suspensions in Chapter 6. In the following, Section 13.2 briefly reviews the thermodynamics of block copolymers, and Section 13.3 describes the rheological properties and flow alignment of lamellae, cylinders, and sphere-forming mesophases of block copolymers. More thorough reviews of the thermodynamics and dynamics of block copolymers in the liquid state have been written by Bates and Fredrickson (1990 Fredrickson and Bates 1996). The processing of block copolymers and mechanical properties of the solid-state structures formed by them are covered in Folkes (1985). Biological applications are discussed in Alexandridis (1996). 

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Uk, ---,Uk comprising Zc1,...,/cM 1 units, respectively [14]. Generating functions of such correlators play a key role in the theory of microphase separation and in the statistical thermodynamics of block copolymers [3]. 

The dynamics of block copolymers melts are as intriguing as their thermodynamics leading to complex linear viscoelastic behaviour and anisotropic diffusion processes. The non-linear viscoelastic behaviour is even richer, and the study of the effect of external fields (shear, electric. ..) on the alignment and orientation of ordered structures in block copolymer melts is still in its infancy. Furthermore, these fields can influence the thermodynamics of block copolymer melts, as recent work has shown that phase transition lines shift depending on the applied shear. The theoretical understanding of dynamic processes in block copolymer melts is much less advanced than that for thermodynamics, and promises to be a particularly active area of research in the coming years. 

The fascinating thermodynamics of block copolymers that results from microphase separation are the subject of the parts 2.2,2.3, and 2.4 of Chapter 2. Part 2.4 is concerned with the complex kinetic processes that accompany phase transitions, and the dynamic processes controlled by the structure of the block copolymer melt. 

A review of the thermodynamics of block copolymer melts prior to the discovery of complex phases was presented by Bates and Fredrickson (1990). Ryan and Hamley (1997) have recently reviewed the morphology of block copolymers containing a glassy component, in the melt and glassy states, and a discussion of complex phases is included. Fredrickson and Bates (1996) and Colby (1996) have reviewed the dynamics of block copolymer melts, of which the former is a par-... 

Recently, a theoretical description of microphase separation in block copolymer by Semonov has assumed significant chain stretching [185]. This work demonstrated that this assumption simplifies the description of the thermodynamics of block copolymers un-... 

SCFT today is one of the most commonly used tools in polymer science. SCFT is based on de Gennes-Edwards description of a polymer molecule as a flexible Gaussian chain combined with the Flory-Huggins "local" treatment of intermolecular interactions. Applications of SCFT include thermodynamics of block copolymers (Bates and Fredrickson, 1999 Matsen and Bates, 1996), adsorption of polymer chains on solid surfaces (Scheutjens and Fleer, 1979,1980), and calculation of interfacial tension in binary polymer blends compatibilized by block copolymers (Lyatskaya et al., 1996), among others. 

X10 Xiong, X., Eckelt, J., Zhang, L., and Wolf, B.A., Thermodynamics of block copolymer solutions as compared with the corresponding homopolymer solutions Experiment and theory (exp. data by J. Eckelt and B. A. WoU), Macromolecules, 42, 8398, 2009. 

As in the case of macrophase separation, the two competing terms of enthalpic and entropic nature govern the thermodynamics of block copolymers. Similar to binary polymer bends the phase behavior of diblock copolymer melts is primarily controlled by the segregation strength and the volume fractions /a and /b = 1 - /a of the two blocks. Being covalently bonded, repulsive blocks are prevented from separating on a macroscopic level. Hence, the segregation into A- and B-rich domains... 

These questions are discussed in the sections after the next one, where first some theoretical basics are given to imderstand the thermodynamics of block copolymers. 

The statistical thermodynamics of block copolymer adsorption was considered elsewhere.Many theories attempt to characterize adsorption by smface density, block segment distribution profile, and the thickness of adsorbed layer. As a rule, an adsorbed diblock copolymer has one block adsorbed on the surface in a rather flat conformation, whereas the other block, having a lower surface activity, forms dangling tails. Because of their freely dangling blocks, adsorbed diblock copolymers are often interpenetrated. The adsorption of block copolymers leads to the segregation of blocks in the adsorption layer. It was found that both kinetic and equilibrium features of the block copolymer adsorption are intimately related to the phase behavior of the block copolymer solution. In particular, a very strong increase in the adsorbed amount is observed when the system approaches the phase boundary. As a consequence, a partial phase separation phenomenon may proceed in the surface zone. 

Lin CC, Jonnalagadda SV, Kesani PK, Dai HJ, Balsara NP (1994) Effect of molecular structure on the thermodynamics of block copolymer melts. Macromolecules 27 7769-7780... 

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