Chain stretching, block copolymers

Figure 9.29 Schematic illustration of expanding nanopores in block copolymer nanodomains and elastic forces acting on the pores. Pressure in the pores expands the pores, stretches block copolymer domains in the peripheral direction, and compresses block copolymer chains in the radial direction. If the number of chains per pore does not change, then the elastic force of a block copolymer balloon resists being expanded and limits the size of pores.

Here, the chains are expected to be stretched, as indicated by the 2/3-power dependence of L on N, but less strongly than in solvent. The experimental evidence available to examine this argument is discussed in the section on block copolymer melts. 

Experimentally, the stretching of block copolymer chains has been addressed in two ways by measuring L as a function of N, and by measuring the components of Rg of the block chains both parallel and perpendicular to the interface. The domain dimensions have been studied most extensively for styrene-isoprene and styrene-butadiene block copolymers X-ray and neutron scattering are the methods of choice. The predicted SSL scaling of L N2/3 has been reported for spheres, cylinders and lamellae [99,102-106], but not in all cases. For example, Bates et al. found N0 37 for styrene-butadiene spheres [100], and Hadziioannou and Skoulios observed N0 79 for styrene-isoprene lamellae [107], In the sphere case, kinetic limitations to equilibration were felt to be an important factor [100],... 

It is important to define clearly the characteristic features of block copolymer micelles. We mentioned above that the insoluble blocks formed a micellar core surrounded by a corona. Depending on the composition of the starting block copolymer, two limiting structures can be drawn (1) starlike micelles with a small core compared to the corona and (2) crew-cut micelles with a large core and highly stretched coronal chains. Both situations are schematically depicted in Fig. 2. 

A simple scaling model of block copolymer micelles was derived by de Gennes (1978). He obtained scaling relations assuming uniformly stretched chains for the core radius, RB, of micelles with association number p.This model can be viewed as a development of the Alexander de Gennes theory (Alexander 1977 de Gennes 1976,1980) for polymer brushes at a planar interface, where the density profile normal to the interface is a step function. In the limit of short coronal (A) chains (crew-cut micelles) de Gennes (1978) predicted... 

Computer simulations of a range of properties of block copolymer micelles have been performed by Mattice and co-workers.These simulations have been based on bead models for copolymer chains on a cubic lattice. Types of allowed moves for bead chains are illustrated in Fig. 3.27. The formation of micelles by diblock copolymers under weak segregation conditions was simulated with pairwise interactions between A and B beads and between the A bead and vacant sites occupied by solvent, S (Wang et al. 19936). This leads to the formation of micelles with a B core. The cmc was found to depend strongly on fVB and % = x.w = %AS. In the range 3 < (xlz)N < 6, where z is the lattice constant, the cmc was found to be exponentially dependent onIt was found than in the micelles the insoluble block is slightly collapsed, and that the soluble block becomes stretched as Na increases, with [Pg.178]

These results imply that homopolymer PS is not always miscible with the PS blocks of the copolymer, i.e. confinement of PS to an interface in a block copolymer can lead to immiscibility with homopolymer PS (Hashimoto et al. 1990). This has been interpreted in terms of the enthalpic and entropic contributions to the free energy (Hasegawa and Hashimoto 1996). For a < 1 uniform solubilization increases the translational entropy of the homopolymer, but chain stretching in the homopolymer and in the PS chain of the diblock leads to a decrease in conformational entropy. At the same time, the lateral swelling of microdomains leads... 

Fig. 6.9 Schematic showing the effect of addition of low-molecular-weight homopolymer on block copolymer chain configuration (Hasegawa and Hashimoto 1996). (a) A symmetric diblock forms a lamellar phase, (b) On addition of homopolymer, swelling induced by solubilized homopolymer causes stretching of the corresponding block chain/and or contraction of the other block, resulting in a decrease in conformational entropy, (c) Alternatively, a curved interface is formed to attain a uniform packing density.

Fig. 13 Effect of an electric field on the lamellar distance of a block copolymer solution, (a) 2D scattering pattern of a 50 wt% solution of SI51 dissolved in THF for different electric field strengths, (b) Dependence of the lamellar distance d of parallel (filled circles) and perpendicular (open circles) aligned lamellae, with respect to the electric field lines, on the electric field strength for the same solution, (c) Proposed chain stretching effect for lamellae aligned parallel to the field lines. Adapted with permission from Nature Materials [57]. Copyright (2008) Nature Publishing Group...

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