Confined geometries

Fig. 3. Schematics of magnetic confinement geometries (a) planar and (b) cylindrical geometries for magnetron sputtering sources (24) (c) open-ended...

Y. Rouault, A. Milchev. A Monte Carlo study of living polymers in confined geometries. Mol Theory and Simul 6 1177-1190, 1997. 

Although the properties of specific polymer/wall systems are no longer accessible, the various phase transitions of polymers in confined geometries can be treated (Fig. 1). For semi-infinite systems two distinct phase transitions occur for volume fraction 0 = 0 and chain length N oo, namely collapse in the bulk (at the theta-temperature 6 [26,27]) and adsorp-... 

For a recent review, see I. Teraoka. Polymer solutions in confining geometries. Prog Polym Sci 27 89-149, 1996. 

The model has been successfully used to describe wetting behavior of the microemulsion at the oil-water interface [12,18-20], to investigate a few ordered phases such as lamellar, double diamond, simple cubic, hexagonal, or crystals of spherical micelles [21,22], and to study the mixtures containing surfactant in confined geometry [23]. 

M. Schmidt. Freezing in Confined Geometry. Aachen Shaker-Verlag, 1997. 

Sect. 12 we describe the results of simulations of Gay-Berne molecules at interfaces and in confined geometries. 

If the confining geometry is known, the following boundary condition can be applied to determine the eigenvalues ... 

Very thin films exhibit special structure because of their confined geometry between substrate and surface. Their structure cannot be studied in a normal setup. In order to obtain enough photons on the detector, the X-ray beam must impinge on them under grazing incidence (Cf. Sects. 7.6.3.1,1.63.2, 8.8). This technique is suitably combined with microbeams. Current effort is focusing both on progress of the instrumentation and on the development of adapted analysis methods. 

Kalampounias, A. G., Yannopoulos, S. N., Steffen, W., Kirillova, L. I., Kirillov, S. A., Short-time dynamics of glass-forming liquids Phenyl salicylate (salol) in bulk liquid, dilute solution, and confining geometries, J. Chem. Phys., 118, 8340-8349 (2003). 

The mean-field SCFT neglects the fluctuation effects [131], which are considerably strong in the block copolymer melt near the order-disorder transition [132] (ODT). The fluctuation of the order parameter field can be included in the phase-diagram calculation as the one-loop corrections to the free-energy [37,128,133], or studied within the SCFT by analyzing stability of the ordered phases to anisotropic fluctuations [129]. The real space SCFT can also applied for a confined geometry systems [134], their dynamic development allows to study the phase-ordering kinetics [135]. 

Many techniques ideally suited for nanostructure characterization unfortunately depend also on the substrate properties. For example, the reflectivity and conductivity of a substrate play an important role in the successful execution of the instrumental method. Hence, substrate-independent techniques are needed so that structure and/or behavior of the material can be investigated in a confined geometry, decoupled from the potentially invasive effect of the substrate-mate-rial interface. 

In contrast to the mature instrumental techniques discussed above, a hitherto nonexistent class of techniques will require substantial development effort. The new instruments will be capable of measuring the thermal (e.g., glass transition temperatures for amorphous or semicrystalline polymers and melting temperatures for materials in the crystalline phase), chemical, and mechanical (e.g., viscoelastic) properties of nanoscale films in confined geometries, and their creation will require rethinking of conventional methods that are used for bulk measurements. 

The major problem with the application of the TNO multi-energy method is that the user must decide on the selection of a severity factor, based on the degree of confinement. Little guidance is provided for partial confinement geometries. Furthermore, it is not clear how the results from each blast strength should be combined. 

In this talk, we consider the TFD approach for free fields aiming to extend the Bogoliubov transformation to account also for spatial compactification effects. The main application of our general discussion is the Casimir effect for cartesian confining geometries at finite temperature. 

We have shown that generalizations of the TFD Bogoliubov transformation allow a calculation, in a very direct way, of the Casimir effect at finite temperature for cartesian confining geometries. This approach is applied to both bosonic and fermionic fields, making very clear the... 

Simulations of Supercooled Polymer Melts in the Bulk and in Confined Geometry. 

Rajalingam K, Bashir A, Badin M, Schroeder F, Hardman N, Strunskus T, Fischer RA, Woll C (2007) Chemistry in confined geometries reactions at an organic surface. ChemPhysChem 8 657-660... 

Wasan DT, Nikolov A (1999) Structural transitions in colloidal suspensions in confined films. In Manne S, Warr GG (eds) Supramolecular Structure in Confined Geometries. ACS Symp Ser 736. American Chemical Society, Washington, pp 40-53... 

The dynamics of the molecules adsorbed in confined geometry is one of the most common and important research subject which has received much attention in the past few decades. Owing to the large polarizability and the chemical inert nature of the monoatomic xenon, the l29Xe NMR chemical shift is very sensitive to its environment and thus provides an ideal probe for the investigation of the structure of porous materials [1]. There have been numerous publications in this area since the pioneering works by Ito and Fraissard [2] and by Ripmeester [3], and several reviews have been attributed to related subjects [4-7]. Recent developments of the mesoporous MCM-41 materials [8] have also drawn intense attention due... 

Finally, the difference of chirality enhancement in the N and SmC phases should be mentioned. As shown in Sect. 2.1, enhancement rate in SmC is about one order of magnitude larger than that in N. In the SmC chirality enhancement is attributed to two effects (1) the interaction between bent-core and chiral host molecules and (2) the coupling between ee, tilt, and spontaneous polarization. The latter effect is absent in the N phase and is an additional effect in SmC. Moreover, the chiral discrimination parameter AU is expected to be larger in SmC than in N because of a confined geometry, i.e., smectic layer. 

The present paper focuses on recent progress in experimental, theoretical, and experimental-simulational comparative studies of nanostructure formation in confined geometries that have led to the disclosure of novel fundamental insights. We review in particular the detailed results for the phase behavior and ordering... 

ABC terblock copolymers in confined geometries exhibit a higher versatility and complexity of phase behavior than do binary block copolymers, and this has only been partly explored so far [4, 18, 63],... 

Along with the surface interactions, the chain conformation that is imposed by the confined geometry and by the film preparation strongly affects the swelling behavior of polymer films [119, 169-171]. 

W/O microemulsions have been used in the preparation of nanopartides and for carrying out other reactions in highly confined geometries [234], As mentioned in Section 14.3 both nanoparticle suspensions and nanoemulsions have developed for use as drug-delivery agents. 

In this section, we will first give the theoretical basis for the understanding of transitions in confined geometries and then describe the different techniques based upon this phenomenon, in particular thermoporosimetry will be highlighted. 

---