Cahn’s linearized theory

The authors attempted to measure the intensities of light scattered from a NIPA gel during the phase separation induced by a change in temperature [23]. In this study, we examined the applicability of Cahn s linearized theory [24] to the spinodal decomposition of the geL... 

Besides the NIPA gel, we applied Cahn s linearized theory to a NNPA gel and determined the values of Dapp [25], which are presented in Fig. 21. The... 

Dynamical study of the phase transition of the gels in spinodal regimes was described. The evolution of intensity of light scattered from the gels indicated the applicability of Cahn s linearized theory to the phase transition. Our work offers a basis for the determination of diffusion coefficient of gels in their spinodal regimes. 

Late stage. The consequence of Cahn s linearized theory is that the growth of dominant concentration fluctuations is ruled by qm t°, i.e. it takes place with no change in the size. Experimental results show that this is fulfilled in the early... 

Fig. 19. From the intersections in this figure, the diffusion coefficients were determined and are presented in Fig. 20. By extrapolating the D pp value to the horizontal axis, the spinodal temperature can be determined. Applying this procedure, we could determine a spinodal temperature of 34.2 °C which was sHghtly higher than the phase transition temperature of 34 °C. Thus, it was verified that the initial sta of the phase separation with the NIPA gel was expressed by Cahn s linearized theory.

Cahn s linear theory for spinodal decomposition is difficult to test in mixtures of simple liquids, because phase separation occurs so rapidly that the range of validity of the linear theory is typically exceeded before data can be acquired. In polymeric mixtures, however, phase separation is much slower, and tests of the theory are easier. For polymers of not-too-... 

The application of the Cahn s linearized theory to polymer mixtures was first developed by de Gennes [40] and Pincus [41], based on the Flory-Huggins free energy expression. Subsequently, Binder [42] incorporated the concept of thermal noise, introduced earlier by Cook [75], into the polymer-based derivation. This theory implies an exponential growth of structure with time ... 

The Kinetics of Spinodal Decomposition. Cahn s kinetic theory of spinodal decomposition (2) was based on the diffuse interface theory of Cahn and Hilliard (13). By considering the local free energy a function of both composition and composition gradients, Cahn arrived at the following modified linearized diffusion equation (Equation 3) to describe the early stages of phase separation within the unstable region. In this equation, 2 is an Onsager-type... 

We can apply this theory to our case provided phase separation takes no more than 200-300 s (the first linear branch). In our case, during the reaction time when phase separation was observed, the composition of the system changes only slightly and can be considered as constant. This fact gives us the right to apply Cahn s theory for describing the phase separation in our system. However, we believe that Cahn s theory can also be formally applied to the second linear branches in Fig. 9. 

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