Lamellae surface

Polymer crystals most commonly take the form of folded-chain lamellae. Figure 3 sketches single polymer crystals grown from dilute solution and illustrates two possible modes of chain re-entry. Similar stmctures exist in bulk-crystallized polymers, although the lamellae are usually thicker. Individual lamellae are held together by tie molecules that pass irregularly between lamellae. This explains why it is difficult to obtain a completely crystalline polymer. Tie molecules and material in the folds at the lamellae surfaces cannot readily fit into a lattice. 

Thirdly, (Type C) oil will enter the surface of foam lamellae and then spread over the lamellae surfaces if both E and S are greater than zero. This latter behavior, typically, will destabilize the foam. 

The presence of mixed surfactant adsorption seems to be a factor in obtaining films with very viscous surfaces [411]. For example, in some cases the addition of a small amount of non-ionic surfactant to a solution of anionic surfactant can enhance foam stability due to the formation of a viscous surface layer, which is possibly a liquid crystalline surface phase in equilibrium with a bulk isotropic solution phase [25,110], In general, some very stable foams can be formed from systems in which a liquid crystal phase is present at lamella surfaces and in equilibrium with an isotropic interior liquid. If only the liquid crystal phase is present, stable foams are not produced. In this connection foam phase diagrams may be used to delineate compositions that will produce stable foams [25,110],... 

Foams, in the form of froths, are intimately involved and critical to the success of many mineral-separation processes (Chapter 10). Foams may also be applied or encountered at all stages in the petroleum recovery and processing industry (oil-well drilling, reservoir injection, oil-well production and process-plant foams). A class of enhanced oil recovery process involves injecting a gas in the form of a foam. Suitable foams can be formulated for injection with air/nitrogen, natural gas, carbon dioxide, or steam [3,5]. In a thermal process, when a steam foam contacts residual crude oil, there is a tendency to condense and create W/O emulsions. Or, in a non-thermal process, the foam may emulsify the oil itself (now as an O/W emulsion) which is then drawn up into the foam structure the oil droplets eventually penetrate the lamella surfaces, destroying the foam [3], See Chapter 11. 

Akelah et al. [64] reported the expansion of the d,J0 spacing in MMT in the amine terminated butadiene/acrylonitrile-montmorillonite system (ATBN-MMT) to 14 A (Fig. 3) and of the span between the lamella surface to 5 A, implying horizontal packing of the polymer molecule as shown in Fig. 3. In their patent work, which covered every possible class of polymers, a Toyota group of re-... 

Similar to the WAXS pole figures, with SAXS one can obtain the orientation distribution of the normals onto the lamella surfaces. The measurements are based on the same instrumental technique, but with conventional X-ray sources the acquisition of one single SAXS pattern needs as much as several hours or days. Therefore the acquisition of a complete SAXS pole figure would require a tremendous amount of time and has never been carried out. The availability of S.R. reduces the required time to a few hours. 

Figure 11. A simplified illustration of the surface and zeta potentials for a charged foam lamella surface. (Reproduced from reference 57. Copyright 1975 Butterworth.)...

Type C. If both and S are positive, then the oil will be drawn through and then spread as a film along the lamellae surfaces. This behavior leads to lamellae ruptures. 

It is well known that banding is the result of the cooperative twisting of the lamellae during growth. Although such twisting has been associated with internal stresses produced on the lamellae surfaces, the reason for its occurrence is still controversial (Lotz and Cheng 2005). It has also been reported in case of polymer... 

Another such example is the connection between interface stresses and crystal lattice distortion, and lamellar twisting. The latter phenomenon requires two additional ingredients, in addition to the interface stresses Firstly, the interface stresses must occur asymmetrically at the two opposite lamella surfaces [56,57], which can not be achieved in our simulations by construction of the simulation cell. Reasons for such asymmetries have to be found on different grounds. Secondly, lamellar twisting can only be predicted if also the material properties of the crystalline lamellae are incorporated, either based on experimental [58,59] or simulated data [60]. 

The block copolymers formed by lamella surface modification would be expected to be less crystallizable than the parent polymer. It is possible that crystallization with the same lamellar thickness as obtained for the parent polymer could occur. However, thinner and thicker lamellas would only form with difficulty, due to the chemical modification of the preexisting surfaces. However, the domain structure reported for ABA and AB type block copolymers are not expected in the (AB)n type, discussed herein. 

Thereby, (j) is the volume fraction of polymer in solution (as aggregates), Vc is the fraction of the crystallizable segment in the polymer, R is the lateral dimension of the lamellae (discs) and D x) denotes the Dawson function. The second term in Eq.5 arises from the polymeric structure of the brush (the "blob" scattering). P(Q) is the form factor of the density profile perpendicular to the lamellae surface including the contrast factors of the core and the brush parts and the density profiles of the polymer volume fraction. The form factor of an infinitely large plate of the thickness d considering a simple rectangular density profile is... 

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