Homopolymer solutions

To summarize the results of NSE investigations on dilute homopolymer solutions, the following conclusions have to be drawn ... 

Now, let us discuss why those chains with a high content of hydrophobic MACA form smaller aggregates. Picarra and Martinho [143] showed that in the phase separation of a thin-layer dilute homopolymer solution on the surface, the collision would not be effective as long as the collision (or contact) time (rc) is shorter than the time (re) needed to establish a permanent chain entanglement between two approaching aggregates. Quantitatively, Tanaka [144] showed that rc and re could be roughly characterized as... 

In this paper, we have reviewed some recent applications of the HPTMC method. We have attempted to demonstrate its versatility and usefulness with examples for Lennard-Jones fluids, asymmetric electrolytes, homopolymer solutions and blends, block copolymer and random copolymer solutions, semiflexible polymer solutions, and mixtures. For these systems, the proposed method can be orders of magnitude more efficient than traditional grand canonical or Gibbs ensemble simulation techniques. More importantly, the new method is remarkably simple and can be incorporated into existing simulation codes with minor modifications. We expect it to find widespread use in the simulation of complex, many-molecule systems. 

X10 Xiong, X., Eckelt, J., Zhang, L., and Wolf, B.A., Thermodynamics of block copolymer solutions as compared with the corresponding homopolymer solutions Experiment and theory (exp. data by J. Eckelt and B. A. WoU), Macromolecules, 42, 8398, 2009. 

A numerical calculation needs knowledge of the solvent activity of die corresponding homopolymer solution at the same equilibrium concentration (here characterized by the value of the Flory-Huggins %-function) and the assumption of a deformation model that provides values of the factors A and B. There is an extensive literature for statistical thermodynamic models which provide, for example, Flory A = 1 and B = 0.5 Hermans A = 1 and B = 1 James and Guttf or Edwards and Freed A = 0.5 and B = 0. A detailed explanation was given recently by Heinrich et al. ... 

While these equations are often used indiscriminately for homopolymer solutions and for copolymers, it can be shown that sequence distributions of copolymers, given by the reactivity ratios rj and r2 of Sect. 3.4.1, can affect the glass transition. Different chain stiffness can result for other reactivity ratios at the same overall concentration. 

For homopolymer solutions these assumption lead to the well-known Huggins-X-parameter concept. The residual part of the change in the Gibbs free energy of mixing, Ag reads (if only one solvent A is assumed to be present in the mixture)... 

For calculating the spinodal curve and the critical point, there are two possible ways in the framework of continuous thermodynamics. The most general one is the application of the stability theory of continuous thermodynamics [45-47]. The other way is based on a power series expansion of the phase equilibrium conditions at the critical point. Following the second procedure. Sole et al. [48] studied multiple critical points in homopolymer solutions. However, in the case of divariate distribution functions the method by Sole has to be modified as outlined in the text below. 

Figure 3 illustrates the relationship between steady shear viscosity and shear rate for PBTA homopolymer solutions in NMP/4% LiCl with various concentrations. This figure clearly revels the shear-thinning effect for isotropic (C C r) solutions and anisotropic (C > Ccj-) solutions with the most shear rate region. Meanwhile, a Newtonian plateau appears in a low shear rate region for anisotropic solutions, especially for C = 6 wt% and C = 6.5 wt%. Furthermore, the experimental data could be fitted with theoretical non-Newtonian fluid model. Among which, power-law model was applied for isotropic solutions and Carreau model (22) for anisotropic solutions, as shown below ... 

In the case of copolymer solutions, the melting temperature also depends on interactions between the different monomeric imits and the solvent. Considering the case in which the crystalline phase is pure (i.e., only monomeric units of a single type crystallize and no solvent is present in the lattice), the decrease in the melting temperature can be derived in a similar manner as for the homopolymer solution case using the Flory-Huggins theory with an appropriate modification [15]. To take into accoimt the interactions between both comonomers and solvent, the net interaction parameter for binary copolymers should be calculated as follows ... 

The solvent-polymer interaction parameters were calculated from vapor pressure data of aqueous homopolymer solutions [25], using the Flory-Huggins expression [26] x//=6 ln/)//) —ln(l — 0) —(1 — l/N)0, where p is the vapor pressure and 6 is the polymer volume fraction. The chain length N was determined using 13/3 (EO) or 30/9 (PO) monomers per bead. This gives for the interaction parameters X s=l-4, Xi>s=l-7 (here S denotes solvent). For the EO-PO interaction parameter from group contribution methods [27] we estimated xep = 3.0. 

The second experiment that was performed consisted of mixing the three components (diblock copolymer solution, homopolymer solution and protein solution) in three different ways, and following the light scattering intensity and hydrodynamic radius as a function of time [50]. For system A, it was found that, independently of the way of mixing, the same light scattering intensity and hydro-dynamic radius were found after 1 day. For system B, the intensity remained different for different preparation methods over a period of at least 10 days. The hydrodynamic radius remained the same from the start of the experiment. 

A third class of new polymer integral equation theories have been proposed by Kierlik and Rosinberg. Their work is an extension of a density functional theory of inhomogeneous polyatomic fluids to treat the homogeneous phase. The Wertheim thermodynamic pertubation theory of polymerization is employed in an essential manner. Applications to calculate the intermolecular structure of rather short homopolymer solutions and melts have been made. Good results are found for short chains at high densities, but the authors comment that their earlier theory appears to be unsuited for long chains at low to moderate (semidilute) densities. ... 

In conclusion of this section, it is worthwhile noting that the interrelation of the system-specific parameters established for homopolymer solutions (cf. Fig. 5) also holds tme for all copolymer solutions studied here (as demonstrated in Figure 15 of [25]). 

Fig. 21 Composition dependence of the Flory-Huggins interaction parameter for the solutions of a diblock copolymer of styrene and butadiene solid line) in THF at 55°C. The information for the corresponding homopolymer solutions dotted lines) refers to 55°C for PB, and to 60°C for PS [58]...

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