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Solvent Resistant Nanofiltration Membranes Prepared via Phase Inversion
Published in Stephen Gray, Toshinori Tsuru, Yoram Cohen, Woei-Jye Lau, Advanced Materials for Membrane Fabrication and Modification, 2018
Maarten Bastin, Ivo F.J. Vankelecom
Initially, a homogeneous polymer solution is prepared. This solution is thermodynamically stable and mostly located on the polymer/solvent axis of the diagram. However, it is possible to add a small portion of non-solvent directly to the initial polymer solution, while still keeping it in the stable monophasic region. This solution is then located in the region between the polymer/solvent axis, the solvent/non-solvent axis and the binodal. The binodal is defined as the curve where two distinct phases can co-exist (Jansen et al., 2005). It can be determined by cloudpoint measurements. These involve addition of non-solvent to a polymer/solvent solution untill turbidity in this solution remains permanently. Between the binodal and spinodal curve, a metastable region is present. In this region, the polymer solution is unstable but will not precipitate, unless well nucleated. When a polymer film is cast and immersed into the coagulation bath, the composition inside the film will change due to the increase in non-solvent concentration. As the cast film loses more and more solvent during the solvent/non-solvent exchange, a region is entered where the cast solution is thermodynamically unstable and it will spontaneously separate in two phases (Baker, 2004; Vandezande et al., 2008). The spinodal curve is the border between this unstable and metastable region, and can be determined by Pressure Pulsed Induced Critical Scattering (PPICS) (Wells et al., 1993) or by small angle neutron scattering (SANS) (Lefebvre et al., 2002).
Phase separation of active Brownian particles in two dimensions: anything for a quiet life
Published in Molecular Physics, 2021
Sophie Hermann, Daniel de las Heras, Matthias Schmidt
Active Brownian particles in steady state were considered in several different three-dimensional systems [23]: as an ideal gas, as Lennard–Jones swimmers under sedimentation and as Lennard–Jones particles in case of weak phase separation. Additionally two-dimensional particles with Weeks–Chandler–Anderson (WCA) interparticle pair interaction undergoing MIPS were investigated [23]. For active Lennard–Jones swimmers, the binodal is found to agree with simulation data. Here the interesting regime is that of low self-propulsion speeds, where activity competes with the entropy vs. energy balance of gas–liquid coexistence in equilibrium. However, for high strength of swimming as is relevant for WCA particles undergoing MIPS, the theory clearly overestimates the coexisting densities [23]. In simulations, the binodal is determined from the value of the orientationally averaged densities in the (gaseous or liquid) portion of a phase-separated system. Since the theoretical binodal is derived by the equal area Maxwell construction and therefore using the Gibbs–Duhem relation, it was proposed that this relation is not valid due to high anisotropy in the system. It was concluded that the consideration of interfacial contributions is necessary to determine coexistence densities. This situation is in contrast to equilibrium liquid-vapour phase separation. The approach of [23] has some similarities to the work of Takatori and Brady [18] and to that of Solon et al. [21], as these authors also introduce pressures and chemical potentials.
The use of solubility parameters and free energy theory for phase behaviour of polymer-modified bitumen: a review
Published in Road Materials and Pavement Design, 2021
Jiqing Zhu, Romain Balieu, Haopeng Wang
The phase diagram of a binary blend can be constructed by analysing its free energy. For a given blend, the free energy of the pure components keeps constant at a fixed temperature while the free energy of mixing forms a single or double well as shown in Figure 7(b). In the case of double well, the free energy curve has two minimum points and two inflection points. The minimum points decide the composition of the equilibrium phases (bitumen-rich phase and polymer-rich phase for PMB), due to the free energy minimisation. The location of binodal points at that temperature can thus be determined on the phase diagram. At the binodal points, a double tangent can be constructed to the free energy curve. This shows the homogenisation of chemical potential throughout the whole equilibrium system. The plot of all binodal points at different temperatures leads to the binodal curve on phase diagram of the blend (Figure 7). Similarly, the spinodal curve can be constructed by plotting all the inflection points of the free energy curves at different temperatures.