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Behind the decomposition of matter: What makes liquid mixtures separate naturally?
In the field of materials science, "spontaneous phase separation" is a fascinating phenomenon. In particular, the "spinodal decomposition" mechanism is a thermodynamic phase behavior that allows a pure phase to spontaneously separate into two phases without a nucleation process. When decomposition occurs, there are no thermodynamic barriers to phase separation, so no nucleation events caused by thermodynamic fluctuations are required to trigger phase separation.
This phenomenon is commonly seen in mixtures of metals or polymers, which separate into two coexisting phases, each rich in one component and relatively poor in the other.
Spinodal decomposition is different from the traditional nucleation and growth process. In the latter, the system must take time to overcome the nucleation barrier, but spinodal decomposition is characterized by the absence of such barriers. Once a small fluctuation occurs, those gradually growing fluctuations are immediately amplified. At the same time, the two phases of spin odal decomposition grow uniformly throughout the system, while nucleation begins at a limited number of points.
Thermodynamic basis of spinodal decomposition
Spinodal decomposition occurs when a homogeneous phase becomes thermodynamically unstable. In this case, the unstable phase is located at the maximum of the free energy. In contrast, nucleation and growth processes occur when the homogeneous phase is held in a local minimum of free energy. Here, the other two-phase system has lower free energy, but the homogeneous phase has some resistance to smaller fluctuations. According to the definition of J. Willard Gibbs, a stable phase must be able to resist small changes and remain stable.
Historical BackgroundIn the early 1940s, Bradley reported the observation of sidebands in the X-ray diffraction patterns of Cu-Ni-Fe alloys. Subsequently, further studies by Daniel and Lipson showed that these side frequencies could be explained by periodic modulation of the components along the [100] direction. The study showed that the wavelength of this composition modulation was about 100 angstroms (10 nanometers). The occurrence of this phenomenon suggests that upward diffusion or a negative diffusion coefficient occurs in the initially homogeneous alloy.
The earliest work explaining this periodicity was proposed by Mats Hillert in his 1955 doctoral dissertation at MIT, who derived a flux equation for one-dimensional diffusion that included the effect of the interface energy on The influence of phase and component interactions.
Hillert's research laid the foundation for a more flexible continuum model later developed by John W. Cahn and John Hilliard, which took into account the effects of compatible strain and gradient energy. This is particularly important in the decomposition morphology of anisotropic materials.
Cahn–Hilliard model and spinodal decomposition
The Cahn-Hilliard equation is an effective formula for describing small fluctuations in free energy. When evaluating small amplitude fluctuations, its free energy can be approximated as an unfolding concentrated around the concentration gradient. This approach allows us to use a quadratic expression to describe the change in free energy.
The form of this equation is:
F = ∫ [fb + κ (∇c)^2] dVwherefbis the free energy per unit volume of the homogeneous solution , whileκis a parameter that controls the free energy cost of concentration changes.
When we wish to study the stability of a system, for example in technical analysis involving small fluctuations, we need to assess the changes in free energy that these concentration fluctuations can bring. According to the Cahn-Hilliard theory, spinodal decomposition occurs when the free energy change is negative, and perturbations with low wave vectors become spontaneously unstable.
Dynamics of spinodal decomposition
The dynamics of spinodal decomposition can be modeled by an extended diffusion equation. The equation is expressed as: ∂c/∂t = M ∇^2μ, where μ represents the chemical potential and M is the flow rate. The equation is based on the positive definition of the flow rate and interprets it as the ratio of the flux to the local gradient of the chemical potential.
Combining all the above information, spinodal decomposition is an extremely important phenomenon that exists widely in many materials such as metals and polymers. Scientists continue to explore this mechanism in order to gain a deeper understanding in material design and performance improvement.
So, have you ever wondered how spin-odal decomposition might affect the properties and applications of materials in future materials science?
