Binary Diffusion in Polymer Blends

Binary Diffusion in Polymer Blends Upon integration ... 

This is a three-part book with the first part devoted to polymer blends, the second to copolymers and glass transition tanperatme and to reversible polymerization. Separate chapters are devoted to blends Chapter 1, Introduction to Polymer Blends Chapter 2, Equations of State Theories for polymers Chapter 3, Binary Interaction Model Chapter 4, Keesome Forces and Group Solubility Parameter Approach Chapter 5, Phase Behavior Chapter 6, Partially Miscible Blends. The second group of chapters discusses copolymers Chapter 7, Polymer Nanocomposites Chapter 8, Polymer Alloys Chapter 9, Binary Diffusion in Polymer Blends Chapter 10, Copolymer Composition Chapter 11, Sequence Distribution of Copolymers Chapter 12, Reversible Polymerization. 

TDGL is a microscale method for simulating the structural evolution of phase-separation in polymer blends and block copolymers. It is based on the Cahn-Hilliard-Cook (CHC) nonlinear diffusion equation for a binary blend and falls under the more general phase-field and... 

First we treat diffusion processes within the homogeneous phase. The presence of a temperature gradient in binary fluid mixtures and polymer blends requires an extension of Fick s diffusion laws, since the mass is not only driven by a concentration but also by a temperature gradient [76] ... 

The feasibility of diffuse reflectance NIR, Fourier transform mid-IR and FT-Raman spectroscopy in combination with multivariate data analysis for in/ on-line compositional analysis of binary polymer blends found in household and industrial recyclates has been reported [121, 122]. In addition, a thorough chemometric analysis of the Raman spectral data was performed. 

Subramanian, G., and Shanbhag, S., 2008c. Self-diffusion in binary blends of cyclic and linear polymers. Macromolecules, 41(19) 7239-7242. 

Amerongen [34a] has an early review on curative migration in het-erophasic elastomer blends based on optical and radiochemical analyses. A later, more detailed work by Gardiner [34b-d] used optical analysis to study curative diffusion across the boundaries of elastomer blends consisting of binary combination of polymers of CllR, HR, EPDM, CR, SBR, BR, and NR. Gardiner measured a diffusion gradient for the concentration change as a function of distance and time. His measurements for the diffusion of accelerator and sulfur from HR to other elastomers are listed in Table IV. 

One criterion to distinguish the miscibility of blends is the glass transition temperature (Tg) that can be measured with different calorimetric methods [95]. Tg is the characteristic transition of the amorphous phase in polymers. Below Tg, polymer chains are fixed by intermolecular interactions, no diffusion is possible, and the polymer is rigid. At temperatures higher than Tg, kinetic forces are stronger than molecular interactions and polymer chain diffusion is likely. In binary or multi-component miscible one-phase systems, macromolecules are statistically distributed on a molecular level. Therefore, only one glass transition occurs, which normally lies between the glass transition temperatures of the pure components. 

The application of the dynamic SCF theory [97] or EPD [29,31,109] to the collective dynamics of concentration fluctuations and the relation between the dynamics of collective concentration fluctuations and the single chain dynamics is an additional, practically important aspect. We have merely illustrated the simplest possible case—the early stages of spontaneous phase separation within purely diffusive dynamics. In applications the hydrodynamic effects [110,111], shear and viscoelasticity [112] might become important. Even deceptively simple situations—like nucleation phenomena in binary polymer blends—still pose challenging questions [113]. Also the assumption of local equilibrium for the chain conformations, which allows us to use the SCE free energy functional, has to be questioned critically. Methods have been devised to incorporate some of these complications [76,96,99, 111, 112] but the development in this area is still in its early stages. 

In this chapter, attention will be focused on applications of the Cahn-Hilliard equation on the numerical simulation of an inhomogeneous polymer blend. The numerical model of a binary polymer system and a polymer-polymer-solvent system will be reviewed as examples to illustrate the application of such modeling methodologies. Attention will be paid in particular to a diffusion-controlled system with no mechanical flow, and the effects of substrate patterning will be taken into consideration to highlight the influences of external attraction during the phase separation of polymer blends. The results of the numerical simulation will then be verified using realistic experimental results, on a quantitative basis. 

When investigating a binary polymer blend system, if the polymer mixture is quenched into an immiscible state then the stable blend will separate into A-rich and B-rich domains, and coarsen with time. In the present study, the system was assumed to be diffusion-controlled and there was no predominant dynamic mass flow. Rather, the composition profile was determined by the free energy minimization, as stated above. 

The numerical modeling methods for polymer blends have been reviewed in this chapter, with different categories such as volume-of-fluid, molecular dynamics and diffusion-controlled methods being introduced. Use of the Cahn-Hilliard method was emphasized for binary and ternary polymer systems with no obvious mechanical flux, while specific factors such as elastic energy and functionalized substrate were considered for purposes of comparison. The diffusion-controlled model described, using the Cahn-Hilliard equation as the constitutive equation, can be used to depict the gradient of the interface as well as the composition profile of partially miscible blends hence, it is feasible to implement this equation in a polymer blend system. It should be noted that although these examples do not consider mechanical flux, additional constitutive equations (e.g., Navier-Stokes) can easily be added to this diffusion-controlled model. 

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