Symmetric polymer blend

For the simple example of a symmetric polymer blend with Aa — Ab = A . 

For a symmetric polymer blend Nfi, = NB = N), the whole phase diagram is symmetric (see Fig. 4.8) with the critical composition... 

Estimate the size of the critical region near the critical point in a symmetric polymer blend by comparing the mean-square composition fluctuations with the square of the difference in volume fractions of the... 

Detailed (mean field) analytical calculations were performed by Tang et al. [219] to evaluate the shift in the critical temperature TCD of a thin film as a function of D. They considered a symmetric polymer blend confined by neutral... 

Another way of thinking about this result draws on the notion we introduced in section 5.1 that the concentration perturbation introduced by the surface decays to the bulk over a distance characterised by the bulk correlation length. For a system such as a symmetrical polymer blend, for which the correlation length is a weak function of the concentration, this leads to an exponential adsorption profile... 

For a symmetric polymer blend, two components share the same molecular weights, i.e., r =V2 = r, and the critical point becomes... 

Why do diblock copolymers ( 10.5) contain the larger critical segregation strength than the symmetric polymer blends (=2)7... 

Fig. 11.3 Comparisons of phase diagrams of symmetric polymer blends (same chain lengths 32 monomers, only one component crystallizable) obtained from simulations (data point with the same labeled sequences as the solid lines) and from mean-field theory (solid lines for binodals, and dashed lines for liquid-solid coexistence lines) in the cubic lattice space 32. The x-axis is the volume fraction of crystallizable comptment, and the y-axis is the reduced temperature. The data labeled near the solid lines are the reduced eneigy parameter B/Ec, and all the cinves have EpIEc = 1 (Ma et al. 2007) (Reprinted with permission)...

Fig. 11.7 Theoretical melting points versus volume fractions of crystallizable polymers in homogeneous symmetric polymer blends with chain length 16 monomers, showing melting point risen-up on dilution under the immiscible thermodynamic ctmditions. The mixing inteiactimi parameters BjEc are labeled near the curves, and EpjEc = 1. The arrow is drawn to guide the eyes (Ma et al. 2008) (Reprinted with permission)...

Symmetric polymer blends do not exist in reality. A host erf asymmetries are present in real chemical alloys of interest These include attractive potential asymmetries (present even for isotopic blends) and specific interactions, molecular weight asymmetries and polydispersity, and single chain structural differences between the blend components (e.g., monomer shape and volume, backbone stiffness, and tacticity). Realistic accounting for most of these effects would seem to require an off-lattice description which includes local interchain density and concentration correlations, and compressibility effects [1, 2, 63, 66, 67, 80]. 

Fig. 3.33. Spinodal decomposition initiated by a jump from the one-phase region (Nx = 1) to the two-phase region (Nx = 2.5). Model calculation for a symmetric polymer blend (Na = Nb = N,Ra = Rb = R) on the basis of Eqs. (3.189),(3.181),(3.165). The numbers represent units of time [23]...

Figure 3.3 Phase diagram of a binary symmetric polymer blend with low critical solution temperature.

For a symmetric polymer blend, Na = Nb = N, the equations above lead to a critical point given by relation... 

Huang, C., Olvera de la Cruz, M., and Swift, B.W. (1995) Phase separation of ternary mixtures Symmetric polymer blends. Macromolecules, 28, 7996-8005. 

For symmetrical polymer blends (as well as weakly asymmetrical ones) the problem of hydrodynamical slowing down of long wavelength concentration fluctuations can be elegantly avoided by carrying out the simulation in the semi-grand-canonical ensemble rather than the canonical ensemble only the total number of chains n = is fixed, while the ratio... 

A schematic phase diagram of a symmetrical binary mixture is shown in Fig. 1 in a temperature versus composition representation. A symmetric polymer blend is characterized by two polymer components of the same molar volume and, therefore, with a 50% critical composition. Within mean field approximation the binodal and spinodal phase boundaries of a binary (A/B) incompressible polymer mixture are described by the Gibbs free energy of mixing AG according to... 

For a symmetric polymer blend phase separation occurs already for x > Xait — 2/iV 1... 

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