Body centered cubic microdomains

Figure 5.19 Small-angle neutron scattering intensity obtained with a styrene-butadiene diblock copolymer having spherical butadiene microdomains. The peaks at very small q are due to a body-centered cubic lattice structure of ordered microdomains. The solid curve is the calculated intensity of independent scattering from solid spheres of mean radius 124 A. (From Bates etal.34)...

The development of patterns is not necessarily a manifestation of a nonequilibrium process. A spatially non-uniform state can correspond to the minimum of the free-energy functional of a system in thermodynamic equihbrium, as Abrikosov vortex lattices, stripe ferromagnetic phases and periodic diblock-copolymer phases mentioned above. In the latter, a hnear chain molecule of a diblock-copolymer consists of two blocks, say, A and B. Above the critical temperature Tc, there is a mixture of both types of blocks. Below Tc, the copolymer melt undergoes phase separation that leads to the formation of A-rich and B-rich microdomains. In the bulk, these microdomains typically have the shape of lamellae, hexagonally ordered cylinders or body-centered cubic (bee) ordered spheres. On the surface, one again observes stripes or hexagonally ordered spots. 

An isothermal morphology diagram of poly(styrene-fe/oc -butadiene) is shown in Fig. 19 as a function of molecular weight and copolymer composition the classic morphologies include spherical microdomains (0< a<0.15) packed in a body-centered cubic lattice, hexagonally packed cylindrical microdomains (0.15 <( a-0-3), and alternating lamellae of approximately symmetric diblocks (0.3 <0 -0-5). Sever-... 

Block copolymers consisting of immiscible block chains form microdomains on the order of 10 nm at temperatures below the order-disorder transition temperature (Toq ), because of a chemical junction between the constituent blocks (/). One of the most fascinating features of block copolymers is their ability to self-assemble into various microdomains, such as body-centered cubic spheres (BCC), hexagonally packed cylindo s (HEX) and lamellae layers depending on the volume fraction of one block as well as temperature. It is known today that besides these classical structures, a complex structure, e.g. Gyroid (laid), was found for some block copolymers (2). 

At temperatures at 138.2 and 118.7°C (profiles c and d) the higho -ordo scattering maxima were observed at the positions of -Jl and >/3 relative to that of the first-order scattering maximum, q . Detailed analyses of them indicates the formation of spherical microdomains packed in a body-centered cubic lattice (denoted as bcc-sphere) [19]. Leibler s theory [8] predicts that the disordered state is transformed into the bcc-sphere when the intention parameter between the constituents, x, is increased. In this sense the structure at 157.7 and 177.4°C (profiles a and b) is expected to exhibit the disordered state since x between PS and PI, Xsi decreases with increasing temperature. However die profiles a and b show evidence of the microdomains (possibly spherical microdomains) as mentioned before. Thus we... 

Gallot and Diao [5] and Gallot and Hassan [15] have carried out studies on the phase behavior of lipopeptides by X-ray diffraction studies. Dry lipopeptides of Gly, Ala, Sar, Ser, Tyr, Lys, Glu, and derivatives with alkyl chains containing 12-18 carbon atoms were dissolved in water at concentrated conditions. The solutions exhibited microdomains of lamellar, hexagonal, and body-centered cubic mesophases. This polymorphism was found to require a minimum hydrophilicity for the amino acids. 

Figure 18.2 Molecular packing models for (a) disordered state and (b) ordered state, and (c) models of five equilibrium microdomain morphologies for AB diblock copolymers. L lamellae, F Fddd network, G double-gyroid networks, C hexagonally packed cylinders, S body-centered-cubic spheres.

The bulk properties of microphase-separated diblock copolymers are well understood. Studies show that the relative volume fraction of each component of a microphase separated copolymer essentially determines the structure that it exhibits,If the average volume fraction of one of the blocks of the copolymer chain is between 0.4 and 0.6 then the equilibrium structure is comprised of alternating lamellae of each component. When the volume fraction of the minor component is less than 0.2 it forms spherical microdomains, exhibiting a body-centered cubic structure, in a matrix of the major component. The minor component forms cylindrical microdomains which exhibit a hexagonal close-packed (hep) structure in the major component of its volume fraction is between 0.2 and 0.4. It has recently been shown that these cylindrically shaped microdomains form a structure which exhibits a double diamond-like symmetry when the volume fraction of the minor component lies in the narrow regime between those which predict the formation of the lamellar and the cylindrical microdomains arranged in a hep structure.The size of the microphase separated domains is determined by the total length of the copolymer chain. 

Leibler [13] developed a statistical thermodynamic theory for the microphase separation of an AB-type diblock copolymer on the basis of random phase approximation (RPA) [43], The Leibler theory predicts the spinodal temperature (7].) and Todt of microphase-separated AB-type diblock copolymers, as well as the type of microdomain structure (body-centered cubic, hexagonally packed cylinders or lamellae). This theory is believed to be valid for WSL, whereas the H-W theory is only valid for SSL due to its use of NIA. 

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