Polymer blends models

Sundaraj, U., Dori, Y., and Macosko, C. W., Sheet formation in immiscible polymer blends model experiments on an initial blend morphology. Polymer 36,1957-1968 (1995). Swanson, P. D., and Ottino, J. M., A comparative computational and experimental study of chaotic mixing of viscous fluids, J. Fluid Mech. 213, 227-249 (1990). 

It is usually difficult to isolate and characterize a copolymer from a melt-processed polymer blend. Model studies of copolymer formation between immiscible polymers have been performed either in solution (where there is unlimited interfacial volume for reaction) or using hot-pressed films of the polymers (where the interfacial volume for reaction is strictly controlled at a fixed phase interface). Model smdies using low molecular weight analogs of the reactive polymers are useful but their applicability to high molecular weight reacting systems is limited. 

Leroy, E., Alegria, A., and Colmenero, J. 2003. Segmental dynamics in miscible polymer blends Modeling the combined effects of chain connectivity and concentration fluctuations. Macromolecules 36 7280-7288. 

Ajji, A. and Choplin, L. (1991) Rheology and dynamics near phase separation in a polymer blend model and scaling analysis. Macromolecules, 24 (18), 5221-5223. 

Simdararaj, U., Dori, Y, and Macosko, C.W. (1995) Sheet formation in immiscible polymer blends model experiments on initial blend morphology. Polymer, 36, 1957. 

Table 12.1 Theoretical models to explain the viscoelastic behavior of polymer and polymer blends. Model Equation Reference...

Up to now, the study about phase-separation theory is mainly focused on amorphous/amorphous polymer blend and crystalline/amorphous polymer blend models. There is still lack of systemically theoretical guidance and support for crystalline/crystalline polymer blend models. Therefore, the establishment of the phase-separation theory... 

B.5 Diffusivity of a Polymer Blend. Model a polymer blend by a lattice of rectangular parallelepipeds (Bar-rer and Petropoulos, 1961) suspended in a polymer matrix. Figure 4.24. Using geometrical arguments and Fick s first law, calculate the blend diffusivity, Dbiend, as a function of the diffusivities of both phases and geometrical constants. Simplify the expression for the cases of (a) impermeable dispersed phase, (b) dispersion of platelets, and (c) extremely permeable dispersed phase in the form of platelets. 

Muller M 1999 Misoibility behavior and single ohain properties in polymer blends a bond fluotuation model study Macromol. Theory Simul. 8 343... 

Flory-Huggins Theory. The simplest quantitative model foi that iacludes the most essential elements needed foi polymer blends is... 

Sjoerdsma S.D., Bleijenberg A.C.A.M., and Heikens D., The Poisson ratio of polymer blend, effects of adhesion and correlation with the Kemer packed grain model. Polymer, 22, 619, 1981. 

Flory-Huggins model for polymer solutions, based on statistical thermodynamics, is often used for illustrating the behavior of polymer blends [6,7]. The expression for the free energy change... 

Huneault, M. A., Shi, Z. H., and Utracki, L. A., Development of polymer blend morphology during compounding in a twin-screw extruder. Part IV A new computational model with coalescence. Polym. Eng. Sci. 35(1), 115-127 (1995). 

Core damage frequency (CDF), for nuclear power facilities, 17 540 Coreless induction furnaces, 12 309-311 Core level electron energy loss spectroscopy (CEELS), 24 74 Coremans, Paul, 11 398 Core-shell model, 14 464 Core-shell particles, in polymer blends, 20 354-355... 

Equity capital cost, 9 542 Equivalent box model (EBM) for polymer blends, 20 344 volume fraction calculation in, 20 345-346... 

In order to illustrate the utility of model parameter interpretation, a data set containing NIR transmission spectra of a series of polymer films will be used [85]. In this example, films were extruded from seven different polymer blends, each of which was formulated using a different ratio of high-density polyethylene (HDPE) and low-density polyethylene (LDPE) where the blend compositions were 0, 2.5, 5,10, 25, 50 and 100% HDPE. NIR spectra were then obtained for four or five replicate film samples at each blend composition. Figure 12.18 shows the NIR spectra that were obtained. 

Other models are based upon the immiscibility of polymer blends described above, and they model the system as Newtonian drops of the dispersed polymer with concentration (pi in a Newtonian medium of the second polymer with concentration (p2 = — (pi. There exists some concentration, cpu = cp2i — 1, at which phase inversion takes place that is, at snfficiently high concentration, the droplet phase suddenly becomes continuous, and the second phase forms droplets. The phase inversion concentration has been shown to correlate with the viscosity ratio, A. = r i/r 2, and the intrinsic viscosity for at least a dozen polymer alloys and blends ... 

Theoretically miscible polymer blends will show Tg values that are intermediate between those of the parent polymers. They follow such models as the Fox or Gordon-Taylor relationships (18,19). However, in the case of HPL/PVA blends, the Tg data did not follow any of these well known models, and Tg values above those of the parent polymers were observed (10). The quotient of the experimental blend-Ttf divided by the predicted (Fox) Tg consistently rose above 1.00 for blends exceeding 5% HPL content (10). This indicates molecular interactions between HPL and PVA. An... 

Bogue,D.C., Masuda,T., Einaga,Y., Onogi,S, A constitutive model for molecular weight and concentration effects in polymer blends. Polymer J. (Japan) 1,563-572 (1970). 

The miscibility behaviour of polymer systems has been studied extensively, and experimental data and thermodynamic models have been generated for (co)polymer solutions and for polymer blends. 

EOS models were derived for polymer blends that gave the first evidence of the severe pressure - dependence of the phase behaviour of such blends [41,42], First, experimental data under pressure were presented for the mixture of poly(ethyl acetate) and polyfvinylidene fluoride) [9], and later for in several other systems [27,43,44,45], However, the direction of the shift in cloud-point temperature with pressure proved to be system-dependent. In addition, the phase behaviour of mixtures containing random copolymers strongly depends on the exact chemical composition of both copolymers. In the production of reactor blends or copolymers a small variation of the reactor feed or process variables, such as temperature and pressure, may lead to demixing of the copolymer solution (or the blend) in the reactor. Fig. 9.7-1 shows some data collected in a laser-light-scattering autoclave on the blend PMMA/SAN [46],... 

Application of the dual mode sorption and diffusion models to homogeneous polymer blend-gas systems 26,65) and filled polymers 66) has also been reported. 

Flory-Huggins Theory. The simplest quantitative model for AGmx that includes the most essential elements needed for polymer blends is the Flory-Huggins theory, originally developed for polymer solutions (3,4). It assumes the only contribution to the entropy of mixing is combinatorial in origin and is given by equation 3, for a unit volume of a mixture of polymers A. and B. Here, pt and... 

Permeability measurements for polymer blends prepared by mixing different latices have been reported by Peterson (14). Interpreting transport data for such heterogeneous systems as polymer blends is extremely difficult, however (3, 9,15). The main purpose of the present investigation is, therefore, to study the applicability of gas permeation measurements to characterize polymer blends and not to evaluate the different theoretical models for the permeation process in heterogeneous polymer systems. 

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