Liquid-like order

Recently the wall-PRISM theory has been used to investigate the forces between hydrophobic surfaces immersed in polyelectrolyte solutions [98], Polyelectrolyte solutions display strong peaks at low wavevectors in the static structure factor, which is a manifestation of liquid-like order on long lengths-cales. Consequently, the force between surfaces confining polyelectrolyte solutions is an oscillatory function of their separation. The wall-PRISM theory predicts oscillatory forces in salt-free solutions with a period of oscillation that scales with concentration as p 1/3 and p 1/2 in dilute and semidilute solutions, respectively. This behavior is explained in terms of liquid-like ordering in the bulk solution which results in liquid-like layering when the solution is confined between surfaces. In the presence of added salt the theory predicts the possibility of a predominantly attractive force under some conditions. These predictions are in accord with available experiments [99,100]. 

Recent work has supported early observations (e.g. Aggarwal 1976 Hashimoto et al. 1983) of a liquid micellar phase between the BCC micelle phase and the disordered phase. A representative TEM image from a spherical micellar liquid phase is shown in Fig. 2.18. Kinning and Thomas (1984) analysed SANS data obtained by Berney et al. (1982) on PS-PB diblocks and PS/PS-PB blends where the minority (PB) component formed spherical micelles with only liquid-like ordering. The Percus-Yevick model for liquids of hard spheres was used to obtain the interparticle contribution to the scattered intensity (Kinning and Thomas 1984). The ordering of an asymmetric PS-PI diblock was observed by Harkless... 

Polyelectrolyte solutions exhibit liquid-like order in dilute solutions which diminishes at high concentrations (cf. Figure 8 [23, 24, 26-28]. At infinite dilution gmm(r) has a value close to zero at small separations and... 

The liquid-like order present in the pair correlation function manifests itself as a peak in the static structure factor (S(q)). The scaling of the position qm of this maximum with the density has attracted much attention in the literature [40, 51-53]. Scaling arguments suggest [35, 42, 49, 51] that qm obeys the relation qm p1/3 for dilute solutions and qm pv/(3v 1) for semidilute solutions. Here v is the scaling exponent for the end-to-end distance, i.e., RE hT. The overlap threshold concentration is estimated as p N1 3v. As a conse-... 

Behavior that is intermediate between that of a solid and that of a liquid is perhaps not surprising for a block copolymer with hexagonally ordered cylinders, since such a material has solid-like order in the two directions perpendicular to the cylinders and liquid-like order parallel to the cylinders. Similar behavior is observed in lamellar block copolymers, which has solid-like order in the direction normal to the lamellae and has liquid-like order in the other two directions. For lamellar block copolymers, solid-like behavior at low frequencies typically arises from the disrupting effect of defects, such as those present in smectic liquid crystals (see Section 10.4.8). 

Fig. 11 The dynamic structure factor C(, r) of polybutadiene star 12880 (nominally f = 128, Ma = 80kgmol ) in cyclohexane at ci = 0.016gmL and q = 0.035nm , along with the fit (solid line) from the ILT analysis. The corresponding relaxation distribution function L(ln(T)) (shown here for f i and q = 0.023gmL ) embraces the cooperative diffusion (1), the collective apparent diffusion (2), and the self-diffusion (3). The slowing-down of the middle structural mode (2) and the increase of its intensity with q are shown in the upper inset whereas the lower cartoon illustrates the liquid-like ordering [43,189]. The core regions are drawn out of scale (larger) for clarity...

The star-like micellar interactions lead to liquid-like ordering at volume fraction 0 0 as seen in the 5(7) of Fig. 12b (0 = 0.072) [55]. Except for the very low-q region, all main features of S q), i.e., peak positions and heights, are indentical in multiarm stars of the same f. Above 0, the transition to a bcc polycrystalline structure is evidenced by tlie Bragg peaks, the height (exceeding 2.8) of the first peak of S q) and the 2D SANS pattern [54]. 

For M = Co and Zn, the structures are of the same type, but the alkyl chains (n = 9-17) are perpendicular to the ionic layers with intercalation of chains between successive layers in the low-temperature, solid phase (Figure 68b). However, in these cases, the coordination about the metal is tetrahedral so that extended anions are not formed and the chains of successive layers are able to intercalate. Note that the liquid-like order of the alkyl chains in the high-temperature phase of all these compounds has been proved by X-ray diffraction and infrared studies. Similar pohmiorphic behavior was observed for a series of bis(alkylammonium) tetrabromozincates ( = 10-16). It was shown by X-ray diffraction and infrared, NMR, and NQR techniques that the transition from the ordered solid to the disordered solid is accompanied by a conformational... 

Faunce, C. A. and Paradies, H. H. (2008). Observations of liquid like order of chaiged rodlike lipid A-diphosphate assemblies at pH 8.5. J. Chem. Phys. 128,065105-065113. 

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