Flexible polymers phase diagram

To study the nature of this rapid polymer transport in detail, this section will be concerned with a series of experimental measurements on one particular system, namely a solution of dextran T10 (N5W 10 ) with a uniform concentration of 135 kg m-3 and an imposed gradient of a linear, flexible polyvinylpyrrolidone) (NTn 3 x 10s) (PVP 360). This gradient initially extended from 5 kg m3 to zero concentration. The choice of using the polymers at this concentration was based upon our earlier work441 in which it was shown that nearly maximal transport rates of PVP 360 occur in such a system. This system will be referred to as the standard system. The phase diagram of this PVP 360/dextran T10 mixture clearly demonstrates that the transport experiments were performed within the one-phase region 47). 

Fig. 7. Phase diagram for a binary blend mixture of a flexible (A component) and a rigid (B component) polymers with NA = 200, N = 800, vA = vB = 1, and W B/kBTxAB = 0.4 as predicted by the RPA...

Now let us discuss the applicability of the results obtained for other models of semiflexible macromolecules. It is clear that the qualitative form of the phase diagram does not depend on the model adopted. The low-temperature behavior of the phase diagram is independent of the flexibility distribution along the chain contour as well, since at low temperatures the two coexisting phases are very dilute, nearly ideal solution and the dense phase composed of practically completely stretched chains. The high temperature behavior is also universal (see Sect. 3.2). So, some unessential dependence of the parameters of the phase diagram on the chosen polymer chain model (with the same p) can be expected only in the intermediate temperature range, i.e. in the vicinity of the triple point. 

Fig. 12. Phase diagram for semiflexible polymer and fully flexible polymer. Circles are results for flexible polymers, and diamonds are results for semiflexible polymers. Both systems have a chain length n = 100. The bending energy penalty for the semiflexible polymer is = 5.

Fig. 14. Liquid-liquid phase diagram for a mixture of semiflexible and flexible polymers at constant pressure. The chain lengths of both species are n = 200.

Figure 14 shows the phase diagram of a flexible-semiflexible polymer blend at a constant pressure. Theoretical calculations and experimental results show that such mixtures can exhibit an isotropic-isotropic and isotropic-nematic phase separation. Our calculations are able to capture the isotropic-isotropic phase separation and serve to show that the origin of such a transition can be purely entropic. 

A model presented by Wang Warner (1987) quantitatively describes the statistical mechanics of side chain nematic polymers with a semi-flexible backbone and stiff mesogenic side chains. In general, side chains and backbones have different orders, the former denoted by Sa and the latter denoted by Sb, respectively. The phase types, phase diagrams and backbone conformations in each phase is dependent on the competition of side chains of various lengths, x, and backbone of various stiffness, g. Mesogenic... 

Comparison of the phase diagrams plotted in Fig. 14 of poly(5- [ -[4 -4"-cyano-phenyl)phenoxy]alkyl]carbonyl]bicy-clo[2.2.1]hept-2-ene]s [189] and poly(n-[(4 -(4"-cyanophenyl)phenoxy)alkyl]vinyl ethers [122-127, 212, 213] which contain a single mesogen per repeat unit demonstrates that the glass transition temperature decreases as the flexibility of the polymer backbone increases from polynorbornene to poly(vinyl ether), whereas the isotropiza-tion temperature increases. In addition to revealing additional mesophases at lower temperatures, this increase in polymer flexibility enables the poly(vinyl ether)s to form more ordered mesophases. That is, poly(5- [ -[4 -(4"-cyanophenyl)phenoxy]al-kyl]carbonyl ]bicyclo[2.2.1 ]-hept-2-ene ]... 

Dubault, A., Casagrande, C., and Veyesie, M., Flexible polymers in nematic solvents phase diagrams in dilute regime. Mol. Cryst. Liq. Cryst., 72,189-194 (1982). 

Figure 9.2 3 A section of a schematic phase diagram starting from the left at the pure flexible polymer with its melting temperature flexible- Mole fraction of the liquid crystalline component X. increases towards the right. An LC phase or phases exist to the right of flicUmif (According to [58] with permission of The American Chemical Society.)...

Fig. 2 Schematic phase diagram of a single flexible polymer chain in the thermodynamic limit (Af —> Qo) as a function of temperature T and range of attractive monomer-monomer interaction X. For 2 > At, there occurs a transition at T = 6 X) from the swollen coil to the collapsed fluid globule. At TcystCiV = < ) the globule crystalhzes. Due to slow crystallization kinetics, this transition may be undercooled and at FcystW the collapsed globule freezes into a glassy slate. Since it was assumed that the transition lines vary linearly with the interaction volume A, A rather than A has been chosen as an abscissa variable. Adapted from Binder et al. [4]...

Here we outline how these more highly ordered phases can be accounted for in the phase diagram of mixtures of rod-like colloids and flexible polymers using FVT and follow the work of Bolhuis et al. [46]. The FVT requires the pressure, the chemical potential of the hard spherocylinder (HSC) reference system, and the free volume fraction (cf. (6.40) and (6.41)) as input. The computer simulations presented in [2, 4] contain the necessary information on the pressure and chemical potential of the HSC reference system and in [46] the free volume fraction was obtained using the Widom insertion method [47]. In this method one attempts to insert the polymers (represented by phs with diameter cr) at random positions in the simulation box. The fraction of insertions that does not result in an overlap corresponds to the free volume fraction. The free volume fraction measured in this way at different volume fractions of the HSC was fitted to a functional form similar to the SPT expression for the free volume fraction and used in (6.40) and (6.41). In Fig. 6.21 we present the simulation results for L/D = 5 and q= 1.0, q = 0.65 and = 0.15 obtained in [46] using the method outline above. In the upper graph of Fig. 6.21 q = 1) we compare the results for the Ii—12 transition... 

Polymers show reversible cloud points with no hysteresis Tcp of these polymers depends on chemical composition and can be adjusted between 20 phase diagram Typically Tg < 0°C longer flexible PEO side chains decrease Tg [516]... 

Another example of the phase behavior of asymmetric molecules is given in Fig. 3.22 for aqueous solutions of hydroxypropyl cellulose.(97) The phase diagram for this system shows all of the major features expected from the Rory theory for an asymmetric polymer solute. The slight tilting of the narrow biphasic region could possibly be attributed to some molecular flexibility as well as anisotropic interac-tion.(98) The phase diagram for the ternary system, polymer and two solvents, for poly(p-phenylene terephthalamide) also shows the major features expected from theory. (99)... 

---