Binary polymer blends volume fraction

Consider a binary polymer blend (A and B components) of gaussian chains with degrees of polymerization NA, NB, volume fractions <(>A, 4>B, and monomeric volumes vA, vB, respectively. When the blend is a homogeneous phase mixture,... 

Consider a binary polymer blend [43] of deuterated polystyrene, PSD, (Mw = 1.95 x 10s g/mole, Mw/Mn = 1.02) and poly(vinyl methyl ether), PVME, (Mw = 1.59 x 10s g/mole, Mw/M = 1.3) with a composition of 48.4% PSD (volume fraction). SANS data were taken at various temperatures ranging from ambient to 160°C. De Gennes s RPA formula ... 

Fig. 1. Temperature T vs volume fraction phase diagram of a binary polymer blend. Solid line denotes the coexistence curve (binodal) while the me dashed line marks the spinodal line. Binodal connects with spinodal at the critical point (( )c> Tc)...

Sanchez and Lacombe supposed that in a binary polymer blend, free volume occupied Nq lattice sites, and the bulk polymer density p = NKN + Nq), where N = ILNiri and r, was the chain length of /th fraction, then they developed the lattice fluid theory to calculate Helmholtz free energy (Sanchez and Lacombe 1974 Sanchez 1978), as given by... 

Once the binary interaction parameters for the blend system are known, EOS theory can be used to predict phase separation behavior. Lower critical solution temperature (LCST) is the temperature above which a miscible system becomes immiscible. Upper critical solution temperature (UCST) is the temperature above which an immiscible polymer blend system becomes miscible. Some polymer-polymer systems exhibit either LCST or UCST or both or neither. Another set of phase separation can be obtained as shown in the copolymer-homopolymer example in Section 3.2 by varying the blend volume fraction. The Gibbs free energy of mixing per unit volume for a binary system of two polymers can be written as... 

A lot of literature exists concerning the formation of co-continuous phase morphologies in uncompatibilized binary polymer blends. In general, the blend component with the lowest viscosity and highest volume fiaction forms the continuous phase, while the blend component with the highest viscosity and lowest volume faction forms the dispersed phase. The continuity of one phase within the other at low volume fractions depends on the... 

The percolation threshold can be further reduced, and conductivity increased, if one makes use of the concept of double percolation, first theoretically studied by Levon, Margolina, and Patashinsky [164], and experimentally observed by Sumita and coworkers [161], as well as other researchers [157, 158, 162] for the dispersion of carbon black in binary polymer blends. To obtain double percolation, one needs to have a ternary system, with two phase-separating polymers and conducting filler with strong affinity to one of the polymers (we denote it as A, and the second polymer as B). Then, the system could be conducting if (i) filler loading in the A-domain is above percolation threshold and (ii) the volume fraction of the filled A-domains is above... 

The values of the equilibrium melting temperature T, determined from Eq. (3), decrease in a continuous way with increasing PMMA content (Fig, 6). The depression observed for the equilibrium melting temperature of pure PEO, AT = T° - T j (where T° refers to pure PEO) has then been related to the volume fraction of the non-crystallizing polymer according to the equation derived by Nishi and Wang for compatible binary blends ... 

Fig. 10.26 Schematic illustration of types of possible polymer blend phase diagrams, for binary blends where additional complications that can be introduced by competing processes (such as crystallization of a component) are absent. The coefficients di and d2 refer to a general functional form (as a function of temperature and component volume fractions) of the binary interaction parameter that quantifies deviations from ideal mixing (Courtesy Online resources)...

Fig.2. Variations in relative free energies of mixing in a binary blend of polymers A and B with degrees of polymerization of, respectively, with volume fraction of polymer A for different values of the interaction parameter (a) 0, (b) 0.00105, (c) 0.0013, (d) 0.0020...

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