Microphase separation thermodynamics

Microdomain stmcture is a consequence of microphase separation. It is associated with processability and performance of block copolymer as TPE, pressure sensitive adhesive, etc. The size of the domain decreases as temperature increases [184,185]. At processing temperature they are in a disordered state, melt viscosity becomes low with great advantage in processability. At service temperamre, they are in ordered state and the dispersed domain of plastic blocks acts as reinforcing filler for the matrix polymer [186]. This transition is a thermodynamic transition and is controlled by counterbalanced physical factors, e.g., energetics and entropy. 

Blockcopolymer microphase separation [9] Depending on the length of chemically different blocks of monomers in a block copolymer, ordered nanostructures can be obtained in bulk samples and thin films. The film morphology can differ significantly from the bulk morphology, but because the structure is determined by the pair-pair interaction of monomers and/or an interface, and it is a thermodynamically stable structure, it is classified as self-assembly. 

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 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. 

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-... 

Several additional phases are observed experimentally, but are not thermodynamically stable [13]. Moreover, the synthetic nature of the copolymers implies some heterogeneity in the polymer structure and molecular weight distribution. An excellent review has recently been published [97], and the main conclusion is that the polydispersity index (PDI) influences all aspects of the self-assembly. For example, upon an increase of the PDI of one block, the lattice constant of an ordered structure or the size of microphase-separated domains increases, interfacial thickness increases, and phase transitions may be induced. In addition, macrophase-separation may occur as the PDI is increased at certain compositions and segregation strengths. 

Thin films of block copolymers are likely to find many applications as nanostructured materials, due to the ability to tailor nanoscale dot and stripe patterns. Theory for microphase separation in thin films, especially the effect of confinement on structure orientation is now quite advanced. " Models for the effect of confinement on thermodynamics have also been developed, although this aspect has attracted less attention. 

Rgure 8.5 Representative polymer-polymer phase behaviour with different molecular architectures. Microphase separation (a) results when thermodynamically incompatible linear homopolymers are mixed. The covalent bond between blocks in a diblock copolymer leads to microphase segregation (c). A mixed architecture of linear homopolymers and the corresponding diblock copolymer produces a surfactant-like stabilized intermediate-scale phase separation (b). 

Some phase diagrams of low-polydispersity amphiphilic block copolymers, exhibit areas of coexistence over a relatively wide range of composition (see Fig. 4) [32]. This is probably due to kinetic inertia or to the fact that at the borderline between two thermodynamically stable phases the energetic differences between two structures are marginal. Swelling these coexisting phases with a siliceous precursor affords a microphase-separated siliceous phase, which has the same structure as the binary mixture consisting of water and amphiphilic... 

Thermodynamic incompatibility of the A and B block segments of amorphous AB and ABA block copolymers involves microphase separation at a critical micelle concentration (I, 2). The micelles formed at this concentration are essentially maintained through the solvent evaporation process to produce the domain structures observed in solid state (2, 3, 4). The shape and size of the micelles, and consequently of the domains, depend on the incompatibility, molecular weight, and fractional composition of the block copolymers and on the casting solvent and the temperature (3-10). 

The thermodynamic properties of block copolymers in disordered state, have been studied by Leibler [1980]. Using the random phase approximation [de Gennes, 1979], the author developed a relation between the segmental density correlation function and the scattering vector. An order parameter, related to the reduced segmental density, was introduced. In the disordered state, this order parameter is zero whereas for the ordered phase, it is a periodic non zero-function. Leibler s demonstrated that the critical condition for microphase separation in di-block copolymers... 

---