Symmetric diblock copolymers

NSE measurements at zero average contrast conditions on a symmetric diblock copolymer of H-PS and D-PS dissolved in an appropriate mixture of proto-nated and deuterated benzene are reported [171,172]. The measurements were performed at different concentrations c > c. For comparison, the interdiffusion of a corresponding blend of H-PS and D-PS homopolymers dissolved in deuterated benzene was studied, too [171]. Owing to the relatively low molecular masses, only the regime Q1/2 < 1 was accessible, and the internal modes could not be probed. 

A phase diagram of the symmetric PS-fc-PI blended with PS homopolymer of shorter chain lengths was constructed by Bodycomb et al. [ 174]. The effect of blend composition on the ODT is shown in Fig. 56 along with the results of mean-field calculations. In analogy to MFT the addition of homopolymer decreases the ODT temperature for the nearly symmetric diblock copolymer. 

A variant of the zero average contrast method has been applied on a solution of a symmetric diblock copolymer of dPS and hPS in benzene [331]. The dynamic scattering of multicomponent solutions in the framework of the RPA approximation [324] yields the sum of two decay modes, which are represented by exponentials valid in the short time limit. For a symmetric diblock the results for the observable scattering intensity yields conditions for the cancellation of either of these modes. In particular the zero average contrast condition, i.e. a solvent scattering length density that equals the average of both... 

Smith AP, Douglas JF, Meredith JC et al. (2001) High-throughput characterization of pattern formation in symmetric diblock copolymer films. J Polym Sci Part B Polym Phys 39 2141-2158... 

Fig. 6 Illustration of surface energy effects on the self-assembly of thin films of volume symmetric diblock copolymer (a). Sections b and c show surface-parallel block domains orientation that occur when one block preferentially wets the substrate. Symmetric wetting (b) occurs when the substrate and free surface favor interactions with one block B, which is more hydrophobic. Asymmetric wetting (c) occurs when blocks A and B are favored by the substrate and free surface, respectively. For some systems, a neutral substrate surface energy, which favors neither block, results in a self-assembled domains oriented perpendicular to the film plane (d). Lo is the equilibrium length-scale of pattern formation in the diblock system...

Fig. 2.44 Phase diagram for a conformationally-symmetric diblock copolymer, calculated using self-consistent mean field theory. Regions of stability of disordered, lamellar, gyroid, hexagonal, BCC and close-packed spherical (CPS), phases are indicated (Matsen and Schick 1994 ). All phase transitions are first order, except for the critical point which is marked by a dot.

Fig. 2.48 Self-diffusion of nearly symmetric diblock copolymers measured using forced Rayleigh scattering (Dalvi et al. 1993). (a) Diffusivities, D, for the lower molecular weight PS-PVP sample, which is disordered at these temperatures, have been scaled down by a factor of 0.48, assumming Rouse dynamics (b) D for the lower molecular weight symmetric PEP-PEE diblock copolymer have been scaled down by a factor of 0.40, assuming reptation dynamics. The solid line indicates a fit of the standard Williams-Landel-Ferry (WLF) temperature dependence to the data for the lower molecular weight sample. Values of M are in g mol1.

Fig. 2.59 Neutron reflectivity profiles for a PS-riPMMA symmetric diblock copolymer (Mw = 29.7kgmor ) film of total thickness 5232 A (Menelle et al. 1992). Experiments were performed on samples annealed at the temperatures shown. The solid lines were computed using the scattering length density profiles shown in the insets, which show that the surface induces lamellar order even above the bulk ODT 157 8°C (the air-polymer interface is located at z - 0). 

Xu T, Hawker CJ, Russell TP (2003) Interfacial energy effects on the electric field alignment of symmetric diblock copolymers. Macromolecules 36(16) 6178-6182... 

Fig. 10. Schematic phase diagram of a semi-infinite block copolymer melt for the special case of a perfectly neutral surface (Hj=0). Variables chosen are the surface interaction enhancement parameter (-a) and the temperature T rescaled by chain length (assuming X l/T the ordinate hence is proportional to %c/%). While according to the Leibler [197] mean-field theory a symmetric diblock copolymer transforms from the disordered phase (DIS) at Tcb oc n in a second-order transition to the lamellar phase (LAM), according to the theory of Fredrickson and Helfand [210] the transition is of first-order and depressed by a relative amount of order N 1/3. In the second-order case, the surface orders before the bulk at a transition temperature T (oc l / ) as soon as a is negative [216], and the enhancement...

In this section, we consider confined symmetric diblock copolymers in the limit %N—>°o then the lamellar phase consists of a sequence of essentially pure A domains and pure B domains, separated by sharp interfaces (of width... 

Fig. 32. Period X of dPS-PMMA symmetric diblock copolymers relative to the period X0 in the bulk, plotted as a function of the film thickness D in units of 0. The solid line in the figure shows what would be expected if the period X varied linearly with D/X0 between (n-- 2)Xq and (n+l/2)X0, n =1,2,... From Lambooy et al. [112]...

Figure 13.10 Phase diagram for a conformationally symmetric diblock copolymer predicted by the mean-field theory, showing the regions where the equilibrium phases are disordered (DIS), lamellar (L), gy-roid (Gi33(])s hexagonal cylindrical (H), BCC cubic (i2im3m)> close-packed spheres (CPS, which is either face-centered cubic or hexagonally close-packed). (Reprinted with permission from Matsen and Bates, Macromolecules 29 1091. Copyright 1996, American Chemical Society.)...

In a large part of what we have discussed above, we considered binary polymer mixtures. However, the situation is somewhat different, if instead of polymer blends, thin films of block copolymers are investigated. Due to the molecular connectivity of the different blocks, the inherent length scale is now determined by the size of the molecules. Early experiments focussed on the thin film morphology in symmetric diblock copolymers, where surface interactions tend to orient the block copolymer lamellae parallel to the boundary surfaces. In contrast to most bulk specimens, the planar interfaces lead to the formation... 

Fig. 31. jc vs. 2 for interfaces between PMMA and PPO reinforced by ( ) 1400-1400 PS-PMMA symmetric diblock copolymers and ( ) 560-1650-625 PS-b-PB-PMMA triblock copolymers. Data from [64]... 

First experiments which focused on the variation of the conformational properties have been performed by Brown et al. [240], who studied the role of the interactions between matrix and brush polymers (enthalpy driven brush swelling, see Eq. 59). They used a series of polystyrene (PS)-poly(methyl methacrylate) (PMMA) symmetric diblock copolymers with different blocks labeled by deuterium, placed at the interface between PMMA and poly(2,6-dimethylphenylene oxide) (PPO) homopolymers. A double brush layer was created with PMMA blocks dangling into (neutral) PMMA homopolymer and PS blocks immersed in favorably interacting PPO melt (x=Xps/ppo<0)- The SIMS profiles obtained showed that the PS side of the block copolymer is stretched by at least a factor of 2 with respect to the PMMA side. 

Fig. 46a-c. t ree energy density fL(A) of a symmetrical diblock copolymer melt plotted vs the amplitude A of a concentration wave with q = q. Above the critical point(a) onlyA = 0 is stable, while at the critical point (b) the curvature of the effective potential at A = 0 vanishes, and (c) below the critical point two symmetrical minima occur, corresponding to the stable lamellar phase. From Fredrickson and Binder [61]. 

Fig. 48a. Normalized inverse scattering intensity NS l(q, e) observed in the Monte Carlo simulation of a block copolymer model on the simple cubic lattice (see Fig. 44) plotted vs the normalized inverse temperature eN. b Reciprocal structure factor S (q ) -l(cxrcfes, left scale) and q ( squares, right scale) plotted vs temperature for a nearly symmetric diblock copolymer of polystyrene/poly (cis— 1,4) isoprene (Mw = 15 700). Filled symbols refer to cooling, open symbols to heating runs. The straight tine indicates the extrapolation to a spinodal temperature (T,) that occurs above the actual transition temperature (Tmst). where the data show a jump. From Stuhn et al. [323],...

Holyst and Schick [339] study the phase diagram and scattering of AB symmetric diblock copolymers diluted with A and B homopolymers (in equal concentrations) having the same chain length NA = NB = N as the copolymers. Constructing a Landau expansion, they show that the wave vector q vanishes at a critical copolymer concentration ordering transition there as that of a Lifshitz tricritical point, where the disordered phase, lamellar phase, A-rich and B-rich separated phases can coexist. The critical behavior near this point is expected to deviate strongly from mean field theory [339]. 

Fig. 49a. A representative configuration of block copolymers on the lattice (For clarity a square lattice is shown, while all work refers to a simple cubic lattice). Three symmetric diblock copolymers are shown, each of chain length N = 10. The two monomeric species are labeled A-type (full dots) and B-type (open dots). The vacancies are not shown explicitly, but are assumed to reside on each lattice site left unoccupied by either of the two species of monomer. A volume fraction of < >v = 0.2 is used, since experience with blends [107] has shown that such a system behaves like a very dense melt. The energy contributions eAA, eBB and eAB are shown, b Examples of typical slithering-snake [298,299] motion monomer situated at point labelled by 5 is removed, and one of sites 1,2,3 is randomly chosen for occupation. Note that unlike Refs. [298,299] also the junction point needs to be displaced accordingly, as shown in the figure. For the reverse process, monomer at 3 is removed and the sites 4,5,6 are considered for attachment (of course, a move to site 6 is rejected due to excluded volume constraints), c Interchange of A-Block and B-Block of a diblock copolymer chain. From Fried and Binder [325],...

Recently, another theoretical expression for A/ was derived for symmetric diblock copolymer with = Ng = N/2 in a lamellar morphology [Spontak and Zielinski, 1993] ... 

FIGURE 11.9 Phase diagram for conformationally symmetric diblock-copolymer melts showing regions of stability for the disordered (D), lamellar (L), gyroid (G), hexagonal (H), and cubic (C) phases. Dashed lines denote extrapolated phase boundaries and the dot marks the critical point. (Adapted from Matsen, M.W. and Schick, M., Phys. Rev. Lett., 72, 2660, 1994. With permission from the American Physical Society.)... 

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