Interfacial curvatures

The results for different domain spacings are summarized in Table 3. It is obvious that cyclic block copolymers exhibit smaller domain spacings compared to their linear analogues, which is due to an entropically less favourable situation and an increased interfacial curvature. 

C. SOIL DROPLET REMOVED BY ROLL-UP) SOIL/BATH INTERFACIAL CURVATURE, J>0, -80"... 

R. Strey Microemulsion, Microstructure and Interfacial Curvature. Colloid Polym. Sci. 272, 1005 (1994). 

The surface energy per area, 7, has the same units as a force per length and for some interfacial geometries can lead to an interfacial net force that is balanced by a difference in pressure between the two adjacent phases. If 7 is isotropic, this pressure difference is directly proportional to the interfacial curvature through the the Gibbs-Thomson equation (see Sections C.2.1 and C.4.1),... 

Similar calculations were also performed in the strong segregation limit. In this case, the two-phase and disordered homogeneous regions were found to be smaller, and the phase boundaries were more vertical (see Fig. 6.49) (Shi and Noolandi 1995). This phase diagram was interpreted on the basis of interfacial curvature. If the diblocks are completely segregated, the phase boundaries are determined by the total composition / (=

phase boundaries are parallel to this line (dashed line sloping to the left in Fig. 6.49) ( one-component approximation ). This explains the approximately parallel... 

Tarahovsky YS, Koynova R, MacDonald RC (2004) DNA release from lipoplexes by anionic lipids correlation with lipid mesomorphism, interfacial curvature, and membrane fusion. Biophys J 87 1054—1064... 

The intrinsic 3D interfacial curvature in compositionally asymmetric block copolymers provides extra degrees of freedom for the phase behavior in hexagonally structured microdomains. It is now well established that confinement of a cylinderforming block copolymer to a thickness other than the characteristic structure dimension in bulk, together with surface fields, can cause the microstructure to deviate from that of the corresponding bulk material. Surface structures in Fig. 1 are examples of simulated [57-59] and experimentally observed morphologies [40, 49, 60-62] that are formed in thin films of bulk cylinder-forming block copolymers. 

Fig. 28. Schematic diagram to show how interfacial curvature in a smectic phase can lead to the formation of a columnar phase.

A final remark concerns the effect of interfacial curvature. Above we have considered the surface to be flat, i.e., its radius of curvature is supposed to be large with respect to the thickness of the adsorbed layer. Some adsorption studies, however, deal with colloidal particles which are too small to fulfil this condition. Intuitively, one would expect different adsorbed amounts on a strongly convex surface, since the curvature changes the lateral repulsion. Others have argued that also the thickness could be different. Very few studies have dealt explicitly with these effects -2 3 4)... 

In fact, the molecular shape determines only the local shape of the interface, i.e. the interfacial curvatures. This can be demonstrated using simple equations from differential geometry describing the area of parallel surfaces. (Parallel surfaces are discussed in section 1.13.) If we trace out surface patcties that are parallel to a patch of area [Pg.145]

These equations (4.3 and 4.11) uniquely determine the interfacial curvatures... 

The dominant contribution to the free energy of lengthy (rubbery) polymer chains is entropy. This is known to accoimt for rubber elasticity, which can be satisfactorily modelled by the entropy of the cross-linked pol3rmer chains alone. A simple illustrative model of copolymer self-assembly can be developed by extending rubber elasticity theory to include bending as well as stretching deformations, to calculate chain entropy as a function of interfacial curvatures in diblock aggregates. 

Note that Co is the equilibrium concentration associated with a flat interface, B is a constant term, the two jump terms correspond to the jump in the Eshelby tensor across the interface and the final term corresponds to the Gibbs-Thomson term and depends upon the interfacial curvature k. 

Polyhedral gas cells produced on aging thin flat walls are produced with junction points of the interconnecting channels (plateau borders). Due to the interfacial curvature, the pressure is lower and the film is thicker in the plateau border. A capillary suction effect of the liquid occurs from the centre of the film to its periphery. 

---