Blend solutions entangled

In Chapter 3, we used the Rouse model for a polymer chain to study the diffusion motion and the time-correlation function of the end-to-end vector. The Rouse model was first developed to describe polymer viscoelastic behavior in a dilute solution. In spite of its original intention, the theory successfully interprets the viscoelastic behavior of the entanglement-free poljuner melt or blend-solution system. The Rouse theory, developed on the Gaussian chain model, effectively simplifies the complexity associated with the large number of intra-molecular degrees of freedom and describes the slow dynamic viscoelastic behavior — slower than the motion of a single Rouse segment. 

M/Me- Thus, the line shape of the relaxation modulus G t) changes with concentration. As showm below, the viscoelastic behavior of the entangled component in the concentrated blend solution is well described by Eq. (9.19) with the entanglement molecular weight Me replaced by M, which is given by Eq. (11.4). This means that G t) is universal among monodisperse melt systems and blend solution systems, as all the G t) curves are described by... 

As discussed above, the entanglement molecular weight M in a concentrated blend solution is given by Eq. (11.4). If the concentration is smaller than the critical concentration Wc, defined by... 

As the molecular weight of the solvent component (component one) in the blend solution is raised above the entanglement molecular weight Me, the viscoelastic behavior of the blend system (the system with Mw2 > >... 

Consider the blend-solution system whose universal viscoelastic behavior has been extensively studied in Chapter 11. Here we replace the weight fraction Wi of the solvent component by (f>. Then for the blend solution we have the entanglement molecular weight ... 

Corresponding to Eq. (13.4), the number of entanglement strands per cubed entanglement distance for the blend solution is now defined by... 

When short Mg chains are introduced into a sample of entangled Ml - chains with a voliune fraction < ) of long chains such as (j) Ml > Mg, the blend can be viewed as a concentrated solution of the long chains, or in other words, the Mg component is acting as a solvent at least in the terminal zone of relaxation of the long chains. 

All the masses lie below Mg in the literatru e, the Rouse description of the relaxation modes of non-entangled melts or solutions is also used for polydisperse samples by means of a linear blending law. In order to consider the free voltune variations of each mass in the blend, the relaxation times have to be shifted by a factor X which is the ratio of the monomeric fiiction coefficients of the blend Cob and of each species (Co)-... 

Polymers can also form gels, such as gelatin, as a solid suspension. Entangled polymer chains trap solvent. Some polymer mixtures form solid-insolid solutions, such as poly(ethylene) and poly(propylene) blends in clothing fabrics. Polymers can also be surfactants, such as starch with hydrophilic and hydrophobic segments. 

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