Transition, first-order copolymer

Mech nic lProperties. Extensive Hsts of the physical properties of FEP copolymers are given in References 58—63. Mechanical properties are shown in Table 3. Most of the important properties of FEP are similar to those of PTFE the main difference is the lower continuous service temperature of 204°C of FEP compared to that of 260°C of PTFE. The flexibiUty at low temperatures and the low coefficients of friction and stabiUty at high temperatures are relatively independent of fabrication conditions. Unlike PTFE, FEP resins do not exhibit a marked change in volume at room temperature, because they do not have a first-order transition at 19°C. They ate usehil above —267°C and are highly flexible above —79°C (64). 

Fig. 35 Phase diagrams AB miktoarm-star copolymers for n = 2, n = 3, n = 4 and n = 5. mean-field critical point through which system can transition from disordered state to Lam phase via continuous, second-order phase transition. All other phase transitions are first-order. From [112]. Copyright 2004 American Chemical Society...

Fig. 68 Comparison of temperature-dependent intensity of first-order Bragg peak for bare matrix copolymer (A) containing 0.5 wt% nanocomposites with plate-like (V), spherical (o) and rod-like ( ) geometry. Data are vertically shifted for clarity. Inset dependence of ODT temperature on dimensionality of fillers (spherical 0, rod-like 1, plate-like 2). Vertical bars width of phase transition region. Pure block copolymer is denoted matrix . From [215]. Copyright 2003 American Chemical Society...

These concentration fluctuations are pivotal to the phase transitions in block copolymer melts and are dynamic in nature. They lead to a renormahzation of the relevant interaction parameters and are thought to be responsible for the induction of the first-order nature of the phase transition [264,265]. Such fluctuations are better studied in dynamic experiments. Thus, one can observe an increasing interest in diblock copolymer dynamics. These dynamic properties are being analysed through experimental, theoretical [266,267] and computer simulation approaches [268,269] with the aim of determining the main featirres of diblock copolymer dynamics in comparison to homopolymer dynamics. There are three main issues ... 

The resulting phase diagram for diblock copolymers is shown in Fig. 2.40.The theory predicts that microphase separation occurs to a body-centred cubic structure for all compositions except where a direct second-order transition to a lamellar structure is predicted. First-order transitions to hex and lam phases are expected on further lowering the temperature for asymmetric diblocks. 

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.

The effect of constraints introduced by confining diblock copolymers between two solid surfaces was examined by Lambooy et al. (1994) and Russell et al. (1995). They studied a symmetric PS-PMMA diblock sandwiched between a silicon substrate, and silicon oxide evaporated onto the top (homopolymer PMMA) surface. Neutron reflectivity showed that lamellae formed parallel to the solid interfaces with PMMA at both surfaces. The period of the confined multilayers deviated from the bulk period in a cyclic manner as a function of the confined film thickness, as illustrated in Fig. 2.60. First-order transitions were observed at t d0 = (n + j)d0, where t is the film thickness and d0 is the bulk lamellar period, between expanded states with n layers and states with (n + 1) layers where d was contracted. Finally, the deviation from the bulk lamellar spacing was found to decrease with increasing film thickness (Lambooy et al. 1994 Russell et al. 1995). These experimental results are complemented by the phenomenologi-... 

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

In their statistical model for microphase separation of block copolymers, Leary and Williams (43) proposed the concept of a separation temperature Ts. It is defined as the temperature at which a first-order transition occurs when the domain structure is at equilibrium with a homogeneous melt, i.e.,... 

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...

Fig. 12. Schematic variation of the order parameter profile /(z) of a symmetric (f=l/2) diblock copolymer melt as a function of the distance z from a wall situated at z=0. It is assumed that the wall attracts preferentially species A. Case (a) refers to the case % %v where non-linear effects are still negligible, correlation length and wavelength X are then of the same order of magnitude, and it is also assumed that the surface "field" Hj is so weak that at the surface it only induces an order parameter 0.2 n if mb is the order parameter amplitude that appears for %=%t at the first-order transition in the bulk. Case (b) refers to a case where % is only slightly smaller than %t, such that an ordered "wetting layer" of thickness 1 [Eq. (76)] much larger than the interfacial thickness which is of the same order as [Eq. (74)] is stabilized by the wall, while the bulk is still disordered. The envelope (denoted as m(z) in the figure) of the order parameter profile is then essentially identical to an interfacial profile between the coexisting ordered phase at T=Tt for (zl). The quantitative form of this profile [234] is shown in Fig. 13. From Binder [6]...

This wetting picture (Fig. 12 [6]) of surface-induced ordering in block copolymer melts has been considered recently by Milner and Morse [60]. They considered the transition from the state of weak surface-induced order (Fig. 12a) to the case of strong-surface induced order (Fig. 12b) and pointed out that typically a first-order transition may occur between these states, in analogy to the "prewetting transition" first proposed by Cahn [226] (Fig. 14a). This prewetting-type first-order transition may persist in a thin film (Fig. 14b), but it ends in a triple point where the surface excess ( ) is still finite, of course, since no diver-... 

Although the gross shape of the phase envelope predicted by the mean-field theory, as well as the regions of lamellar and hexagonal phases, are more or less in agreement with experiments on diblock copolymers (see Fig. 13-4), the predictions of the theory near the critical point at / = 0.5, /(V = 10.5 are incorrect. Fredrickson and Helfand (1987) showed that the second-order transition predicted by the mean-field theory is corrected to SL first-order transition when the effects of fluctuations on the free energy are accounted for using a so-called Brazovskii Hamiltonian (Brazovskii 1975). 

The simulation techniques presented above can be applied to all first order phase transitions provided that an appropriate order parameter is identified. For vapor-liquid equilibria, where the two coexisting phases of the fluid have the a similar structure, the density (a thermodynamic property) was an appropriate order parameter. More generally, the order parameter must clearly distinguish any coexisting phases from each other. Examples of suitable order parameters include the scalar order parameter for study of nematic-isotropic transitions in liquid crystals [87], a density-based order parameter for block copolymer systems [88], or a bond order parameter for study of crystallization [89]. Having specified a suitable order parameter, we now show how the EXEDOS technique introduced earlier can be used to obtain in a particularly effective manner for simulations of crystallization [33]. The Landau free energy of the system A( ) can then be related to P,g p( ((/"))... 

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