Homopolymer-Copolymer Mixtures

It seems plausible that fluctuations affect the Lifshitz point. If the lamellar distance is large enough that the interfaces between A and B sheets can bend around, the lamellae may rupture and form a globally disordered structure. A Ginzburg analysis reveals that the upper critical dimension of isotropic Lifshitz points is as high as 8 (see also Sect. 4.1). Unfortunately, the lower critical dimension of isotropic Lifshitz points is not known [ 102], 

Indeed, the experimentally observed phase behavior differs substantially from the mean-field phase diagram. An example is shown in Fig. 6. The Lifshitz point is destroyed, the three phase coexistence region between the 

In order to study this effect, Diichs et al. have performed field-theoretic Monte Carlo simulations of the system of Fig. 5 [80,83,104], in two dimensions. (For the reasons explained in Sect. 4.4.2, most of these simulations were carried out in the EP approximation). Some characteristic snapshots were already shown in Fig. 4. Here we show another series of snapshots at = 12.5 for increasing homopolymer concentrations (Fig. 8). For all these points, the self-consistent field theory would predict an ordered lamellar phase. In the 

The phase transition can be identified by defining appropriate order parameters. We use anisotropy parameters, which are defined in terms of the Fourier transform F q) of images as those shown in Fig. 8  

F q) is zero for isotropic (disordered) configurations and non-zero for anisotropic (lamellar) configurations. The anisotropy information can be condensed into a single dimensionless parameter 

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We now consider the random copolymer model in the presence of solvent— that is, for a copolymer volume fraction p0 < 1. We are not aware of previous work on this model in the literature, but will briefly discuss below the link to models of homopolymer/copolymer mixtures [57]. The excess free energy (86) then depends on two moment densities, rather than just one as in all previous examples. For simplicity, we restrict ourselves to the case of a neutral solvent that does not in itself induce phase separation this corresponds to X = 0, making the excess free energy... 

M. Muller and M. Schick (1996) Bulk and interfacial thermodynamics of a symmetric, ternary homopolymer-copolymer mixture A Monte Carlo study. J. Chem. Phys. 105, pp. 8885-8901... 

Free volume effects cause g to depend strongly on concentration. More than one L,/L2-critical point and two extremes in spinodals may occur easily. As was shown in the MFLG approach we have for a homopolymer/copolymer mixture under pressure ... 

Since the amphiphilic nature is essential for the phase behaviour, systems of small molecules (e.g., lipid water mixtures) and polymeric systems (e.g., homopolymer copolymer blends) share many connnon features. 

Many commercially important polymers are actually mixtures of two or more polymer components that differ from one another in composition (for copolymers) or in microstructure (for homopolymers). Such mixtures may be the deliberate result of polymer blending, polymer synthesis, or the presence of different types of initiators or catalytic sites that produce different polymer chains. The ung spectral data of the whole polymer in such systems would include contributions from all its components, and as such should be treated with care. 

A number of classes of polymer blends containing block copolymers have been studied. Namely, binary blends of a block copolymer with a homopolymer, ternary mixtures of a block copolymer with two homopolymers and blends of two block copolymers. Experimental and theoretical studies of all these mixtures are the subject of Chapter 6. 

Procedure 3 Oxidation of MPP with Redissolved DPP Homopolymer. A mixture of 7.3 grams of MPP and 9.8 grams of DPP homopolymer was oxidized for 15 minutes at 30°C, as described in the previous examples, yielding 86% of copolymer, with an intrinsic viscosity of 0.48 dl/g. 

Gel permeation chromatography (GPC) of poly(methyl methacrylate) and cellulose nitrate showed elution volume peaks at 62.5 ml for PMMA and at 87.5 for cellulose nitrate (Figure 5), due to their difference in molecular weight. A mixture of poly(methyl methacrylate) and cellulose nitrate of the same ratio as that of the graft copolymer was recorded and two peaks in elution volume at almost identical positions were observed. This shows that the constituent homopolymers retain their identity in a physical mixture. The isolated graft copolymer showed a single peak in elution volume at 80.0 ml. The second peak in elution volume is absent in spite of poly(methyl methacrylate) attached to cellulose nitrate as revealed by infrared spectrum. Hence, these results indicate that GPC can be used as a technique to differentiate between homopolymer, physical mixture, and graft copolymer. 

Appendix A Multicomponent Random Phase Approximation for Homopolymer and Copolymer Mixtures... 

Consider a polymer system consisting of n components. These could be homopolymer mixtures or homopolymer and copolymer mixtures. In order to simplify the calculations, we consider that at least one of the components (that we call matrix component) is a homopolymer. The formalism presented here is a straightforward extension of the two-component case in an n-vector and nxn matrix notation [13] ... 

This generalization of de Gennes formula to multicomponent homopolymer and copolymer blends can describe a wide variety of situations. After a slight generalization (described in Appendix B) it can also, describe the case of pure copolymer mixtures whereby a copolymer has to be shared between M and R. Using Appendix A, one could obtain this limit (pure copolymer mixtures) by... 

Table III shows the increase of molecular weight of BCMO polymerization with conversion, although the polymer tends to precipitate. The monomer reactivity ratios of DOL-BCMO copolymerization were previously determined as rx (DOL) = 0.65 0.05, r2 (BCMO) = 1.5 0.1 at 0°C. by BF3 Et20 (8). Table IV shows a preparation of block copolymer of DOL, St, and BCMO. In the first step we polymerized DOL and St in the second step we added BCMO to this living system. The copolymer obtained showed an increase of molecular weight, and considerable BCMO was incorporated in the copolymer still remaining soluble in ethylene dichloride. The solubility behavior together with the increase of molecular weight with addition of BCMO shows that this polymer consists of block sequences of DOL-St and (St)-DOL-BCMO. This we call block and random copolymer of DOL-St—BCMO. We can deny the presence of BCMO, St, or DOL homopolymers in this system, but some chain-breaking reactions are unavoidable, leading to copolymer mixtures. Thus, the principle of formation of block copolymers by cationic system is partly substantiated.

For the case of homopolyisoprene/styrene-isoprene copolymer mixtures [364], it was shown that the miscibility increases in the order four-arm star-block < triblock < diblock. Increased incompatibility was observed in the pair poly(isoprene-g-styrene)/polyisoprene [365] even when the molecular weight of the homopolymer was much lower than the PI segment length between junction points of the graft copolymers. 

Witt [1959] studied under vacuum gamma-radi-ation-induced crosslinking in butadiene-styrene copolymers, homopolymers and mixtures of these homopolymers, (Table 11.9). The behavior of the styrene units in the copolymers and in the physical mixtures, was different. Gel fraction measurements showed that in the copolymer, the styrene units did inhibit the crosslinking of the polybutadiene. However, there was no evidence of such inhibition in the mill- and latex-prepared physical mixtures of the two homopolymers. 

The polycondensation of difunctional oligomers leads to the preparation of well-defined polymer structures. Monomers in this type of reactions must be soluble in the reaction mixture and stable when the reaction is carried out in the melt, which is the case for some aromatic polymers prepared by polycondensation [22]. As previously described, polycondensation can occur with monomers bearing the same or a different functional group at both ends of the molecule. When one of the reactive functional groups is a hydroxyl moiety, several types of materials can be prepared, such as polyethers, polyesters, and polyurethanes, independently if they are used to form homopolymers, copolymers, or hyperbranched polymers. 

The polymers were formed by condensation of 4,4dihydroxy-benzene and 2,2 -dimethyl-4,4 dihydroxyazoxybenzene with various diacid chlorides acting as flexible spacer groups Polydisperse homopolymers and copolymers, sharp fractions of homopolymers and mixtures of polydisperse polymers with a low mass mesogen were investigated. Supercooling at the mesophase-isotropic and solid-mesophase transitions, sharpness of the nematic-isotropic transition (range of N+I biphase), polymer crystallization from the mesophase melt, and enhancement of crystallinity upon addition of a low mass nematic, were studied. 

Figure 1. GPC curves of graft copolymer, styrene homopolymer, a mixture of graft copolymer and homopolymer, and trunk polymer(EVNB) in the graft copolymerization of styrene onto ethylene-vinyl p-nitrobenzoate copolymer.

We only mention, that for homopolymer-block copolymer mixtures RPA predicts that the wavelength of lamellar ordering may diverge at particular points... 

This portion of the chapter can be summarized by noting that there is a substantial body of evidence demonstrating that formal phase-equilibrium thermodynamics can be successfully applied to the fusion of homopolymers, copolymers, and polymer-diluent mixtures. This conclusion has many far-reaching consequences. It has also been found that the same principles of phase equilibrium can be applied to the analysis of the influence of hydrostratic pressure and various types of deformation on the process of fusion [11], However, equilibrium conditions are rarely obtained in crystalline polymer systems. Usually, one is dealing with a metastable state, in which the crystallization is not complete and the crystallite sizes are restricted. Consequently, the actual molecular stmcture and related morphology that is involved determines properties. Information that leads to an understanding of the structure in the crystalline state comes from studying the kinetics and mechanism of crystallization. This is the subject matter of the next section. 

Lyatskaya J, Balazs AC (1996) Using copolymer mixtures to eompatibilize immiscible homopolymer bltaids. Macnnnolecules 29 7581-7587... 

When racemic 3,7-dimethyloctene-l and 3-methylpentene-l were polymerized respectively with (s)-3-methylpentene-l and (r)-3,7-di-methyloctene-1 177), the optical activity and the IR analysis of the copolymer fractions demonstrated that copolymerization takes place predominantly between the optically active monomer and the monomer in the racemic mixture having the same chirality, the other antipode giving the homopolymer. Copolymer formation in these cases was detected by the IR method, using the ratio of the absorbances of the 763 cm" band (ethyl group mode in 3-methylpentene-l units) and those of the 732 cm tard [(CHjla rocking mode of the 3,7-dimethyloctene-l units] as a qualitative measure of the copolymer composition. 

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