Lattice base

Although this section has concentrated on MD, it should not be forgotten that lattice-based MC codes may be parallelized very efficiently for more infomration on parallel simulation methods see [220. 221. 222 and 223] and references therein. 

For structures with a high curvature (e.g., small micelles) or situations where orientational interactions become important (e.g., the gel phase of a membrane) lattice-based models might be inappropriate. Off-lattice models for amphiphiles, which are quite similar to their counterparts in polymeric systems, have been used to study the self-assembly into micelles [ ], or to explore the phase behaviour of Langmuir monolayers [ ] and bilayers. In those systems, various phases with a nematic ordering of the hydrophobic tails occur. 

Yet another common crystal lattice based on the simple cubic arrangement is known as the face-centered cubic structure. When four atoms form a square, there is open space at the center of the square. A fifth atom can fit into this space by moving the other four atoms away from one another. Stacking together two of these five-atom sets creates a cube. When we do this, additional atoms can be placed in the centers of the four faces along the sides of the cube, as Figure 11-28 shows. 

Figure 6.9 The five different surface lattices, base vectors of the real and reciprocal lattices, and the corresponding LEED patterns.

Giupponi and Buzza (2005) explored how the magnitude of the monomer-solvent interactions impacted the dendrimer stmcture using a lattice-based... 

Influence of Mean-Field-Lattice-Based Theory on the... 

Choudhury et al. [36] in their work on hydrogenated nitrile butadiene rubber (HNBR)-nanoclay systems showed the thermodynamic aspects of nanocomposite formation using the mean-field-lattice-based description of polymer melt intercalation, which was first proposed by Vaia and Giannelis [37]. Briefly, the free... 

Here Vi and v are the partial specific volumes of the polymer (/ = 2,4) and the solvent, respectively M is the molar weight of the solvent and Xu and 724 are the Flory-Huggins interaction parameters, quantifying the energy of interaction between unlike lattice-based polymer segments (%24) or between polymer segments and solvent molecules (%u). 

When we consider crystal structures we usually think of the pattern and symmetry of the packing of the atoms, ions, or molecules in building the lattice based on X-ray crystallography. However, detailed descriptions of crystals and their classification are much older. The seven systems of crystals and the 32 classes of crystal symmetry were recognized by 1830. The 14 Bravais Lattices were presented by A. Bravais in 1848. 

Density Functional Theory of Lattice Based Polymer 176 Adsorption... 

LATTICE BASED MOLECULAR THERMODYNAMIC MODEL OF POLYMER SYSTEMS... 

DENSITY FUNCTIONAL THEORY OF LATTICE BASED POLYMER ADSORPTION... 

J. A. Kulkarni and A. N. Bens, Lattice-based Simulation of Chain Conformation in Semicrystalline Polymers with Application to Flow Induced Crystallization, J. Non-Newt. Fluid Meek, 82, 331-336 (1999). 

So far, we have demonstrated that the MC simulation (lattice-based SRS model and off-lattice bead-spring model) results are in qualitative agreement with the experiments. A complementary approach is molecular dynamics (MD) simulation using the bead-spring model. Since MD study for PFPE is still the infant stage, we will discuss it only briefly. The equation of motion can be expressed in... 

The application of the lattice model to various systems requires a procedure to determine the lattice size and the chain bending energy, hence the number of segments and the chain stiffness in the lattice. Based on the equivalence between the contour length, volume, and gyration radius of a real polymer chain and that in the lattice model, the following equations were suggested 22... 

The formation and equilibrium structure of polymer layered silicate nanocomposites, in particular with organically modified layered silicates, has been shown to be a strong function of the nature of the polymer (polar or apolar), the charge carrying capacity of the layered silicate, as well as the chain length and structure of the cationic surfactant. However, both the polymer/silicate compatibility and hybrid equilibrium structure for these nanocomposites are observed to be independent of polymer molecular weight. The experimental results have been summarized by Vaia et al. and a lattice based mean field theory has been developed to explain these results [26]. 

The absence of a lattice-based mechanism, such as slip planes, does not necessarily preclude aU deformation in brittle materials. Plastic flow can proceed in other modes. For example, at temperatures of about 40 percent to 50 percent of their melting points, grain-boundary shding can become important. Grain-boundary sliding is beheved to be the major contributor to the superplasticity observed in some polycrystal-hne ceramics. 

Bravais lattice Classification of fourteen three-dimensional lattices based on primitive and nonprimitive unit cells. Named after Auguste Bravais, who first used them. 

Comparing the solubility behavior of a- and p-chitins (although the later exists in a crystalline-hydrated structure, which is much looser than that of the ot-chitin), p-chitin shows lower solubility due to the penetration of wafer between the chains of the lattice. Based upon chitin molecule-solvent conformation and solubility mechanisms, p-chitin starts gelling at a lower concentration than a-chitin. Table 2.6 illustrates the solubility of chifin and structurally related compounds in a saturated CaCl2 2H20-methanol solvent system. 

Figure 2.64 shows the electron wavefunctions in one imit cell of the system, illustrated by the density surface where the squared density has fallen to 0.05. It is seen that the "size" of the wavefunction parts surrounding Mg and H atoms is very similar, denouncing the common explanation of hydrogen absorption in metal lattices based on hydrogen being "such a small atom". 

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