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Non-linear dynamics of spinodal decomposition in multi-component polymer systems. I. General approach

100%
Prostomolotova E.
Open Physics
|
2007
|
vol. 5
|
issue 1
35-48
EN
Spinodal decomposition of multi-component systems is analyzed within the framework of a new approach focusing on the description of this dynamic process in terms of the Langevin equation for the one-time structure factor S(q, t) treated as an independent dynamic object. We apply this approach, in particular, to multi-component incompressible polymer systems (binary polymer solutions, ternary polymer blends etc.). The dynamic equation describing the simultaneous relaxation of both the order parameters (component concentrations) and the matrix of the component-component dynamic correlation functions ∥S ij(q, t)∥, including the explicit expression for the corresponding effective kinetic coefficients, is derived.
2
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Magnetic properties of the mixed spin-5/2 and spin-3/2 Blume-Capel Ising system on the two-fold Cayley tree

64%
Yessoufou R., Amoussa S., Hontinfinde F.
Open Physics
|
2009
|
vol. 7
|
issue 3
555-567
EN
We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ1 and Δ2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D A = Δ1/J,D B = Δ2/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D A or D B increases. The first-order transitions only exist for some appropriate non-zero values of D A and/or D B. The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β 0 of the model is estimated and found to be ¼ at small values of D A = D B = D and β 0 = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.
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