Surface spinodal lines

Fig. 32. Phase diagram of the surface plotted in terms of the scaled variables h jy and g/y. For g/y < —2 one observes critical wetting and for g/y > —2 one observes first-order wetting. In the latter regime, mean field theory predicts melaslable wet and non-wet regions limited by the two surface spinodal lines ft, and ft( respectively. Also two quenching experiments arc indicated where starting at a rescaled time r = 0 from a stable state in the non-wet region one suddenly brings the system by a change of fti into the metastahle wet or unstable non-wet region, respectively. From Schmidt and Binder (1987).

Fig. 55. Surface phase diagram in the plane of variables g, and <)> for three values of g. The region where the surface is non-wet (at small gj is separated from the wet region by a phase boundary which describes the wetting transition. For > (second-order wetting) this is just the straight line giril = — g(l—) The region of first order wetting is shown for symmetrical mixtures with Na = NB = N = 10 and N = 100, respectively, and the first-order transitions are shown by dash-dotted curves. In this regime metastable wet and non wet phases are possible up to the stability limits ( surface spinodals ) denoted by dashed curves. Assuming that g, and g are essentially independent of temperature T, variation of T essentially means variation of <)>, . From Schmidt and Binder [125],...

If we imagine a line drawn on the primitive surface dividing all parts of the surface which are convex downwards in all directions from those which are concave downwards in one or both directions of principal curvature, this curve will have the equation (26), and is known as the spinodal carve. It divides the surface into two parts, which represent respectively states of stable and unstable equilibrium. For on one side A is positive, and on the other it is negative. If we assume that the tie-line of corresponding points on the connodal curve is ultimately tangent to that the direction of equations ... 

The boundary condition (16.64) is in effect a relation between X2 and Xq when T and p are given. This line separates unstable states from metastable states and must lie on the surface g(x2,x ) it is the spinodal curve in the sense of 8. The projection of this curve on the base is also termed the spinodal. 

In fig. 16.19 the line aKb represents the spinodal curve whose presence indicates the existence of a fold iii the surface g. Any system whose representative point is situated on the convex-concave surface is unstable and breaks into two stable phases, each of which will be represented by a point on the convex-convex surface. It can be shown... 

The boundary (line, surface, etc.) demarcating a metastable region from an unstable region in the phase space for a system is called the spinodal and is given by the equation... 

Figure 2. Ternary phase diagram illustrating compositional trajectories during asymmetric membrane formation. The solid line represents the binodal and the dashed line the spinodal. The initial casting solution composition is represented by I. The transient changes in concentration at the top surface are indicated by the top arrow emanating from I and ending in II. The changes at the bottom surface are indicated by the bottom arrow emanating from I and ending in III.

Figure 1.20. Surf2u e defined by Equation 1.2 34 to characterize the gas and liquid states of a onc-component system in the coordinates P V-T (a). Surface defined by Equation 1.2-33 for the crystal and liquid states (6). ACD is the binodal of liquid-vapour phase equilibria BCC is the spinodal of liquid-vapour phase transition Be and Ff are fragments of the binodal of the crystal-liquid phase equilibria Kj is the spinodal of the crystal-liquid phase transition GAD is the straight line of three-phase (vapour-liquid-crystal) equilibrium at the triple point (Skripov and Koverda, 1984)...

The common line of the hinodal and spinodal surfaces defines the critical state for a j/-componcnt system. 

The position of the line remains indefinite. This situation corresponds to the case where, because of enrichment of the surface layer in one component, the nearest layer is impoverished in this component. This profile may also be the result of the spinodal decomposition. 

Determination of the critical conditions alone qi. Td) suffices for estimating and provided the A G function of the system used is known. In the quasi-binary section TSX (Fig. 50) two lod can be drawn which are not dependent on the predse shape of the distribution, but are mere functions of its average molecular we%hts M and M, (75). The first is the spinodal, which is the intersection of TSX with the spinodal surface separating the unstable and meta-stable regions in the miscibility gap (Fig. 50). The spinodal is determined by alone (72, 13. 15) and passes through the critical point fixed by and M,. Hence, we can draw lines of constant and in the plane TSX. 

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