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Thermodynamics of Polymer Mixtures
Published in Timothy P. Lodge, Paul C. Hiemenz, Polymer Chemistry, 2020
Timothy P. Lodge, Paul C. Hiemenz
Spinodal decomposition occurs when a homogeneous (single phase) mixture is thrust into the unstable region of a phase diagram. The resulting morphology is a complex bicontinuous structure that finds interesting and useful applications. Certain membranes (e.g., reverse osmosis) are produced this way using polymer–solvent mixtures. Your CEO wants to make money in the membrane business using excess company capacity to make M = 2 × 105 g/mol poly(vinyl acetate) membranes. Choose a solvent and specify the composition range that can be used for this purpose if the phase separation temperature is 27 °C. (Hint: Place the critical temperature at about 100 °C by choosing an appropriate solvent. You may blend two solvents and assume that the associated solubility parameter and molar volume are simple averages, provided the solvents don't phase separate. Table 7.1 may be helpful.)
Mechanism and Kinetics of Phase Separation in Polymer Solutions and Blends
Published in Yuri S. Lipatov, Anatoly E. Nesterov, Thermodynamics of Polymer Blends, 2020
Yuri S. Lipatov, Anatoly E. Nesterov
In a number of articles, it was established188–193 that the processes of microphase separation in IPNs proceed according to the spinodal mechanism. For a number of systems (network polymers on the basis of oligoisoprene dihydrazide and epoxy oligomers, styrene-divinyl benzene copolymer-PBMA, and others), from an analysis of their structure, it follows that, due to microphase separation, a periodic structure appears during curing. This periodicity is largely preserved until the end of microphase separation. Since the heterogeneity microregions is very different in their composition than for pure components, it is possible that phase separation in such systems initiates and proceeds in the regions of unstable states (inside a spinodal) and it is subject to spinodal decomposition peculiarities.193
Diffusion
Published in Harshad K. D. H. Bhadeshia, Theory of Transformations in Steels, 2021
Darken's experiment [120, 121] proved that diffusion can occur against a concentration gradient; carbon initially distributed uniformly migrated across a diffusion couple from a silicon-rich to a silicon-poor steel. In spinodal decomposition, a chemically uniform solution can become spontaneously inhomogeneous as diffusion enhances concentration gradients. Artificially created multilayered structures also exhibit this uphill diffusion[122]. Consequently, the forces that drive diffusion are best described in terms of gradients of free energy rather than concentration [123, 124].
Finite size effect on the existence of the liquid–vapour spinodal curve
Published in Molecular Physics, 2022
Enrique Díaz-Herrera, Eduardo Cerón-García, Anthony Bryan Gutiérrez, Gustavo A. Chapela
Spinodal decomposition is a very fast picosecond process, by which a fluid located in the unstable region separates itself, via diffusion, into two phases in equilibrium. For this work, the two phases are liquid and vapour [13,14]. Mayer et al. [15] gave a theoretical account of the interfacial tension effect in two-dimensional systems and in 1979 Evans et al. [16] developed the Cahn–Hilliard equations for a single Lennard-Jones (LJ) component fluid in the liquid–vapour unstable region.
Immiscibility regions in iron based ferritic solid solutions and their relevance to thermodynamics and kinetics of nitriding
Published in Philosophical Magazine, 2019
Figure 1 shows the much enhanced amplitude in composition fluctuation required for the equilibrium nitride precipitation by classical nucleation (class (i) alloys), as compared to the much smaller amplitude in case of class (ii) alloys (also by classical nucleation) and infinitesimal amplitude in class (iii) alloys (by spinodal decomposition). This difference in the kinetic barrier for further phase transformation among the three classes actually explains the observed distinct N uptake kinetics in systems with and without miscibility gaps. In case of the class (i) alloys (Fe-Al and Fe-Si alloys, Figure 3) which do not have a region of immiscibility, N content in the work piece cannot be increased in the ferrite matrix beyond the low paraequilibrium solubility limit (about 0.5 at %), until the equilibrium precipitates nucleate. Due to the much higher amplitude of compositional fluctuation necessary in these alloys (Figure 1), this nucleation requires long range diffusion of the substitutional alloying elements, thus making the N absorption kinetics to in turn depend on the substitutional element diffusion. On the other hand, decomposition of the N supersaturated solid solution within the region of immiscibility in case of Fe-Ti, Fe-Cr and Fe-V alloys requires only short range diffusion of the substitutional elements due to the relatively smaller amplitude in compositional fluctuations. Also, as mentioned earlier due to the mechanism of precipitation from supersaturated solutions, with compositions lying between the binodal and spinodal limits (i.e. corresponding to class (ii)) being different from both the classical nucleation (class (i)) and spinodal decomposition (class (iii)) [19], faster kinetics is expected. Therefore, N uptake beyond the paraequilibrium N solubility limit of the alloys having a region of immiscibility does not depend on substitutional element diffusion, and its kinetics can be explained to be practically governed by N diffusion alone.
Fracture mechanisms of spinodal alloys
Published in Philosophical Magazine, 2018
Arpan Das, Chandra Bhanu Basak
Spinodal strengthening is an emerging method by which the strength of alloys can be enhanced or modified. This technique is well established and understood in the metallurgical research community. This is a mechanism where a solution of two or more components can divide into clear phases with completely different alloying compositions and physical properties. More precisely, it refers to a process in which a supersaturated solid solution decomposes into solute-rich and solute-depleted regions (equilibrium phases) when it is aged at elevated temperature [18–25]. Spinodal decomposition takes place when there is no thermodynamic barrier to decomposition and completely by diffusion process. Hence, this process is treated purely thermodynamical as diffusion problem, and many of the characteristics of such decomposition can be deduced by the analytical solution to general diffusion equation [18–25]. Phase separation due to such decomposition is clearly defined and occurs uniformly throughout the material microstructure not just at discrete nucleation sites. As a result, a modulated structure nucleates within the solid and subsequent ageing treatment results in the formation of ordered structures. The strain field generation around the modulated structure produced by this method along with the ordered structure impedes the dislocation motion and, thereby, causes hardening in the material [24,25]. The modulated and ordered structures are finely dispersed microstructures (nano-scale) and cannot be resolved simply by optical imaging techniques. The evolution of such microstructure with spinodals results in the variation of material properties of the alloy, such as strength, hardness, magnetism, fracture toughness and ductility. A diagram of the spinodal can be seen from Figure 1. The mechanism is clearly understood by simple thermodynamics. A concentration gradient causes uphill and downhill diffusion otherwise; the acts as driving force for diffusion to occur [47].