Microphase-separation transition

Ordered Microphase - separation transition Rheometer 1 Disordered ii.v4 um... 

Block copolymers have peculiar characteristics due to the coexistence of two or several different parts of different chemical compositions within a chain. They can undergo microphase separation transitions from a homogenous phase to a variety of spatially periodic structures [176]. A distinction should be made between star copolymers, where each arm is composed by two or more blocks, and miktoarm polymers, formed by homopolymer arms of different chemical compositions. Floudas et al. [177] recently performed an extensive study of four-... 

Lee KM, Han CD. Microphase separation transition and rheology of side-chain liquid-crystalline block copolymers. Macromolecules 2002b 35 3145-3156. 

Heteropolymers can self-assemble into highly ordered patterns of microstructures, both in solution and in bulk. This subject has been reviewed extensively [1,123-127]. The driving force for structure formation in such systems is competing interactions, i.e., the attraction between one of the monomer species and the repulsion between the others, on the one hand, and covalent bonding of units within the same macromolecule, on the other hand. The latter factor prevents the separation of the system into homogeneous macroscopic phases, which can, under specific conditions, stabilize some types of microdomain structures. Usually, such a phenomenon is treated as microphase separation transition, MIST, or order-disorder transition, ODT. 

Adams JL, Graessley WM et al (1994) Rheology and the microphase separation transition in styrene-isoprene block copolymers. Macromolecules 27 6026-6032... 

Fig. 39a. Chemical architecture of a diblock copolymer. A diblock copolymer consists of a polymerized sequence of A monomers (A-Block) covalently attached to a similar sequence of B-monomers. b The microphase separation transition occurs when a compositionally disordered melt of copolymers (right side) transforms to a spatially periodic compositionally inhomogeneous phase (left side) on lowering the temperature. For nearly symmetric copolymers (composition f near fas 1/2) the ordered phase has the lamellar structure shown. From Fredrickson and Binder [61]...

Summary of Leiblers RPA Theory of the Microphase Separation Transition... 

Fig. 43a. Neutron small angle scattering intensity I(q) plotted vs q for three temperatures T above Tmst (main graph), for a polyethylenepropylene(PEP) — polyethylethylene(PEE) diblock copolymer, with f = 0.55, molecular weight Mw — 57.500, polydispersity index Mw/Mn = 1.05. The microphase separation transition occurs for Tmst = 125°C. For further explanations cl Textb Inverse peak intensity I (q ) dotted vs inverse temperature.The full curve is a one-para meter fit to the theoty of Fredrickson and Helfand [58], while Leibler s [43] prediction for the intensity at the transition is marked as mean field theory . From Bates et al. [317]...

Fried H, Binder K (1991) The microphase separation transition in symmetric diblock copolymer melts A Monte Carlo study. J Chem Phys 94(15) 8349-8366... 

To study microphase separation transition (MST), we next consider the correlation function of concentration fluctuations, whose Fourier components give the intensity of scattered waves. We have polydisperse clusters whose polydispersity is controlled by the temperature T and the composition 4>. 

However, when the numbers of A- and B-chains are comparable, F Q) exhibits a maximum at finite Q. Sufficiently many copolymers are produced to form a microphase. In this case the instability condition is first fulfilled at this wavenumber as the temperature is lowered, which indicates that the microphase separation transition (MST) takes place before SP. The condition for this situation to be realized is given by... 

In a similar way, we can study the mixed linear association of R A2) molecules and R B2 ones. The sequence distribution along an associated chain can be alternative, sequential, or statistically random, depending upon the strength of association constants. All these associated chains, or rings, are block copolymers if the primary molecules are polymers, so that they undergo microphase separation transition as well as macroscopic phase separation. This problem of competing micro- and macrophase separation in associating polymers is one of the important unsolved problems to be studied. 

Fig. 6.5 Phase diagrams of side-chain association. The binodal (solid line), the spinodals (borderline of the gray areas), microphase separation transition Une (broken line), critical solution points (white circles), and Lifshitz points (black circles) are shown. The homogeneous mixture region, microphase region, and the macroscopicaUy unstable region are indicated by H, M, and U, respectively. Parameters are fixed at wa = 1000, f = 200, = 10, A.q = 1.0, and tjfi = 1.0. The...

The WSL approach for the description of the order-disorder transition, ie, the transition between the microphase-separated block copolymer and the disordered melt, where the two blocks mix with each other, has been developed (74,88,89) using the random phase approximation. This transition is ofl en called the microphase separation transition (MST), and Toot is the temperature at which the order-disorder transition occurs. In this picture the system is described by a so-called order parameter, which is related to the space-dependent volume fraction or segment density of one of the components, say, component A. Again, the system is considered to be incompressible. The order parameter is then given by the deviation of the local segment density from the mean composition value. 

The transition between the ordered, microdomain structure and the disordered, homogeneous structure, induced by temperature change, can be oberserved by rheological measurement or by small-angle scattering. The transition, often called the order-disorder transition or microphase separation transition, resembles the solid-liquid transition, and should be of a first order according to the theory of Leib-ler, but experimentally its character has not yet been established clearly. 

The transition from a disordered phase (D) to a microphase is often referred to as the microphase separation transition, or MST. A variety of domain structures occurs, which can form either ordered or disordered arrays. In most cases, the material within each domain is amorphous, but it can sometimes be crystalline. The simplest structure consists of alternating layers, or lamellae. This is shown schematically for both amorphous and semicrystallizable copolymers in Figure 2. The phase behavior is relatively simple for diblock copolymers, but can be far richer for triblocks. 

The structure of the simulated block copolymer systems has been characterized in detail [38-40]. Temperature dependencies of various structural parameters have shown that all of them change in a characteristic way in correspondence to Tqdt- The microphase separation in the diblock copolymer system is accompanied by chain extension. The chains of the diblock copolymer start to extend at a temperature well above that of the transition to the strongly segregated regime. This extension of chains is related also to an increase of local orientation correlations, which appear well above the transition temperature. On the other hand, the global orientation correlation factor remains zero at temperature above the microphase separation transition and jumps to a finite value at the transition. 

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