Order-disorder transition diblock copolymers

Gehlsen MD, Almdal K et al (1992) Order-disorder transition - diblock versus triblock copolymers. Macromolecules 25 939-943... 

FIGURE 5.17 Temperature versus G —the shear storage modulus at a frequency of 1.6 Hz for diblock copolymer poly(ethylene propylene)-poly(ethylethylene) (PEP-PEE). The order-disorder transition (ODT) calculated to be 291°C 1°C. (From Rosedale, J.H. and Bates, F.S., Macromolecules, 23, 2329, 1990. With permission of American Chemical Society.)... 

LeiblerL., Theory of microphase separation in block copolymers. Macromolecules, 13, 1602, 1980. Eoerster S., Khandpur A.K., Zhao J., Bates E.S., Hamley I.W., Ryan A.J., and Bras W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules, 21, 6922, 1994. 

Diblock copolymers represent an important and interesting class of polymeric materials, and are being studied at present by quite a large number of research groups. Most of the scientific interest has been devoted to static properties and to the identification of the relevant parameters controlhng thermodynamic properties and thus morphologies [257-260]. All these studies have allowed for improvements to the random phase approximation (RPA) theory first developed by Leibler [261]. In particular, the role of the concentration fluctuations, which occur and accompany the order-disorder transition, is studied [262,263]. 

Fig. 6.3 Schematic phase diagram for lamellar PS-PB diblocks in PS homopolymer (volume fraction 0h). where the homopolymer Mv is comparable to that of the PS block (Jeon and Roe 1994). L is a lamellar phase, I, and I2 are disordered phases, M may correspond to microphase-separated copolymer micelles in a homopolymer matrix. Point A is the order-disorder transition.The horizontal lines BCD and EFG are lines where three phases coexist at a fixed temperature and are lines of peritectic points. The lines BE and EH denote the limit of solubility of the PS in the copolymer as a function of temperature.

Fig. 6.36 Phase diagram calculated using SCFT for a blend of a symmetric diblock with a homopolymer with fl = 1 (see Fig. 6.32 for a blend with a diblock with / = 0.45) as a function of the copolymer volume fraction

Hashimoto T et al (1999) The effect of temperature gradient on the microdomain orientation of diblock copolymers undergoing an order-disorder transition. Macromolecules 32(3) 952-954... 

Khandpur AK, Forster S et al (1995) Polyisoprene-polystyrene diblock copolymer phase diagram near the order-disorder transition. Macromolecules 28 8796-8806... 

Figure 13.4 Phase diagram of a PS-PI diblock copolymer showing regions of BCC spheres (Im3m), hexagonal cylinders (HEX), laid gyroid, hexagonally perforated lamellae (HPL), lamellar (LAM), and disordered phases /pi is the volume fraction of polyisoprene. The dot-dash line represents the mean-field order-disorder transition based on the formula x = 71.4/T — 0.0857 with reference segment volume v — 144 A. (Reprinted with permission from Khandpur et al.. Macromolecules 28 8796. Copyright 1995, American Chemical Society.)...

Figure 13.15 Reduced storage modulus versus reduced frequency arco for a lamellae-forming polystyrene-polyisoprene diblock copolymer (M = 22,000) at temperatures above the order-disorder transition temperature Todt = 152°C, and quenched to temperatures below it. The disordered samples show terminal behavior, and the ordered (but unoriented) ones show nonterminal behavior. (Reprinted with permission from Patel et al.. Macromolecules 28 4313. Copyright 1995, American Chemical...

Fig. 3. Computer simulation results using a time-dependent Ginzburg-Landau approach, showing the microstructural evolution after a temperature jump from the lamellar phase to the hexagonal cylinder phase for a moderately asymmetric diblock copolymer. The time units are arbitrary. (Reprinted with permission from Polymer 39, S. Y. Qi and Z.-G. Zheng, Weakly segregated block copolymers Anisotropic fluctuations and kinetics of order-order and order-disorder transitions, 4639-4648, copyright 1998, with permission of Excerpta Medica Inc.)...

In contrast to the situation found for dilute solutions, the behavior of nonlinear block copolymers in the solid state seems to have attracted great attention. Many theoretical publications appeared in recent years, dealing mainly with the phase behavior of star-block, simple graft and comb copolymers. Issues like the nature of the phase diagram and the order-disorder transition have been studied in considerable detail. The compatibilizing effects of complex copolymers, in comparison to simple diblock copolymers, were also investigated. 

Figure 12 Equilibrium order-disorder transition and spinodal of the disordered state as a function of shear rate D, as predicted by Eqs. (61) and (62), respectively. The data points are experimental results for a nearly symmetrical diblock copolymer melt [147]. Data points given by open and full circles were obtained at fixed temperature T by varying A while those represented by open and full triangles were determined by varying temperature at fixed share rate. (Redrawn from Ref. 147.)...

The simplest case of a block copolymer is a diblock consisting of two covalently bonded polymers with chemically distinct repeat units A and B. If A and B are incompatible, below the order-disorder transition at Todt microphase separation is obtained into, for example, a spherical, cylindrical, or lamellar phase. The phase behavior depends on the relative volume fraction of A and B and on the magnitude of the product xabN, where xab is the Flory-Huggins interaction parameter between the two polymers, and N the total degree of polymerization [7]. We can write... 

Fig. 15 Mean-field phase diagram of supramolecular diblock copolymer model with equivalent block lengths. Labeled phases are Dis (hranogeneous disordered), Lam (lamellar), and 2 phase (coexisting A-rich and B-rich homogtaieons phases). The values of N indicate the diblock copolymer length. Solid dots denote Ltfshitz points (LS). The horizontal dashed line on the l denotes 1//N = 1/4, the macrophase separation transition for a binary blend of polymers. The horizontal dashed line on the right signifies 1//A1 = 0.095, the order-disorder transition for a symmetric diblock copolymer. Reprinted with permission from [97]. Copyright 2007 American Chemical Society...

Tsori, Y., Andelman, D. Diblock copolymer ordering induced by patterned surfaces above the order-disorder transition. Macromolecules 34, 2719 (2001)... 

In the case of diblock copolymer melts, which are the simplest model system for the elucidation of structure formation processes involving BCPs in nanoporous hard templates, only the two immiscible blocks have to be considered as components. Self-consistent field methods were applied to study the morphologies of liquid diblock copolymer/homopolymer mixtures that were considered as a model system for triblock copolymers in sol solutions [182], of pure diblock copolymer melts [200-202], and of order-disorder transitions in diblock copolymer melts [203]. For example, Li et al. found for a model diblock copolymer that forms cylinders in the bulk... 

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