Disordered/ordered

The entropically driven disorder-order transition in hard-sphere fluids was originally discovered in computer simulations [58, 59]. The development of colloidal suspensions behaving as hard spheres (i.e., having negligible Hamaker constants, see Section VI-3) provided the means to experimentally verify the transition. Experimental data on the nucleation of hard-sphere colloidal crystals [60] allows one to extract the hard-sphere solid-liquid interfacial tension, 7 = 0.55 0.02k T/o, where a is the hard-sphere diameter [61]. This value agrees well with that found from density functional theory, 7 = 0.6 0.02k r/a 2 [21] (Section IX-2A). 

Magnussen O M, Hageboeck J, Hotios J and Behm R J 1992 In s/fu scanning tunneiing microscopy observations of a disorder-order phase transition in hydrogensuiphate adiayers on Au(111) Faraday Discuss. 94 329-38... 

On warming to 300 K, the adlayer undergoes a disorder-order transition the Os states present at 120 K, together with the surface copper atoms, are highly mobile and can be considered to resemble a two-dimensional gas which at 300 K transforms into a structurally well-ordered immobile oxide adlayer.22 This is very similar to the model proposed from spectroscopic (XPS) studies and based on chemical reactivity evidence (see Chapter 2). 

As the temperature is decreased, the chains become increasingly rigid zc then approaches 1 if we assume that there is only one fully ordered crystalline structure and Zconf for the liquid becomes smaller than 1. This means that, at this level of approximation, the disordered state becomes less favorable than the crystalline ground state. A first-order disorder-order phase transition is expected to occur under these conditions. Flory interpreted this phase transition as the spontaneous crystallization of bulk semiflexible polymers [12], However, since the intermolecular anisotropic repulsion essential in the Onsager model is not considered in the calculation, only the short-range intramolecular interaction is responsible for this phase transition. 

Figure 12 Snapshots of the surface during anion adsorption for the model without second neighbor shell interaction. Before the disorder-order transition (left panel) there is no ordering during the disorder-order transition ( /2 x /l) islands grow (not shown) after the disorder-order transition large islands dominate (right panel). The ( f% x /7) unit cell is indicated in the right panel...

In ordered alloys there is the question of whether disorder-order transition occurs by homogeneous ordering reaction or by nucleation and... 

An important step in developing the mean-field concept was done by Landau [8, 10]. Without discussing the relation between such fundamental quantities as disorder-order transitions and symmetry lowering, we just want to note here that his theory is based on thermodynamics and the derivation of the temperature dependence of the order parameter via the thermodynamic potential minimization (e.g., the free energy A(r),T)) which is a function of the order parameter. It is assumed that the function A(rj,T) is analytical in the parameter 77 and thus near the phase transition point could be expanded into the series in 77 usually it is a polynomial expansion with temperature-dependent coefficients. Despite the fact that such a thermodynamical approach differs from the original molecular field theory, they are quite similar conceptually. In particular, the r.h.s. of the equation of state for the pressure of gases or liquids and the external field in ferromagnetics, respectively, have the same polynomial form. 

Gast and co-workers (Gast 1996 McConnell et al. 1993,1995) have used SAXS to probe ordered micellar structures in PS-PI block copolymers dissolved in decane, which is a preferential solvent for PI. They determined the form factor of a range of diblocks by performing SAXS in dilute solution (McConnell et al. 1993). The same diblocks in more concentrated solutions were found to form cubic micellar structures, and the gelation (micellar disorder-order) transition on increasing concentration was determined. Remarkably, both BCC and FCC struc-... 

Another type of phase transition is called a lambda transition, because a graph of heat capacity versus temperature for this type of transition resembles the Greek letter X, as shown in Fig. 4. This type of transition is usually associated with a change from an ordered state to a state with some disorder (order-disorder... 

Another most interesting phenomenon has been observed by Mikami et al.31> The ethanol molecules exhibit orientational disorder over three different sites in the high-spin phase, but orient themselves more and more in one of the three sites with decreasing temperature. The variation with temperature of the orientational ground state population seems to be strongly correlated with the temperature dependent spin transition. The authors therefore suggest that the disorder-order transition of the ethanol molecule triggers the spin state transition. 

Interaction, Disorder-Order and Order-Disorder Transitions... 

Macromolecular conformations and reversible order-disorder and disorder-order transitions are highly sensitive to solvent, temperature, pressure, pH, water activity, and metal ions. Polyanions are distinguished from neutral molecules by their sensitivity to electrolytes. Whereas synthetic polymers do not normally dissolve or disperse spontaneously, some polysaccharides may do so in water (hydration), given their strong hydrophilicity. 

Xanthan-locust bean gum gelation is a lock-and-key mechanism that guar gum does not fit (Rocks, 1971). Brownsey et al. (1988) came upon evidence of the denaturation (disorder-order transition) of the xanthan helix, and of binding of the stereochemically compatible cellulose chains. Having studied a series of stereochemically compatible synergistic and non-synergistic blends of xanthan and other gums, Morris (1992) concluded that denaturation of the xanthan helix was necessary. 

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