Bead, flexible

A flexible chain with rod-like side groups (Fig. 7c and the figure caption). For this model, it is natural to choose one rod as an elementary monomer then, the state of a monomer is defined by the co-ordinates of the origin of the rod x and by the unit vector specifying the orientation of the rod uf = (x, u), df = d3xdQ . To be definite, we assume that for this model (as well as for the model of beads ) flexible filaments connecting the monomers (i.e. rods) do not have the orientational memory. In this case, the kernel of the operator g is equal to the kernel (Eq. 

Figure 3.5 (a, b) Illustration of beads-and-springs models. Part (b) shows a two-bead flexible dumbbell. (From Larson 1988.)... 

Rubber-based adhesives provide softness and good low temperature flexibility (see Table 8). These properties make them the primary choice for the hinge application, which are two thin glue beads applied to the sides of the book block adjacent to the spine. These adhesive beads allow the book to open with the cover and help to protect the spine glue from stresses. Hinge glues have low if any wax, and are pressure sensitive. When used for the spine application, rubber-based adhesives require a water-based emulsion primer due to their short open time and thus low penetration of paper substrates. 

The radius of the beads and the interactions, Eqs. (8,9), have been chosen such that the chains may not intersect themselves or each other in the course of their movement within the box. Thus entanglement constraints are obeyed automatically and need not be enforced by extra (time consuming ) control. The chains are treated as fully flexible and a potential for bond angles is not considered, although an extension of the model to allow for semi-flexibihty of the chains is straightforward. 

The non-free draining character of flexible polymer chains was considered in the Zimm model [48], In this model, the effect of hydrodynamic interaction at the location of bead i is taken into account by an additional fluid velocity term vj ... 

The system used in the simulations usually consists of solid walls and lubricant molecules, but the specific arrangement of the system depends on the problem under investigation. In early studies, hard spherical molecules, interacting with each other through the Lennard-Jones (L-J) potential, were adopted to model the lubricant [27], but recently we tend to take more realistic models for describing the lubricant molecules. The alkane molecules with flexible linear chains [28,29] and bead-spring chains [7,30] are the examples for the most commonly used molecular architectures. The inter- and intra-molecular potentials, as well as the interactions between the lubricant molecule and solid wall, have to be properly defined in order to get reliable results. Readers who intend to learn more about the specific techniques of the simulations are referred to Refs. [27-29]. 

First approaches at modeling the viscoelasticity of polymer solutions on the basis of a molecular theory can be traced back to Rouse [33], who derived the so-called bead-spring model for flexible coiled polymers. It is assumed that the macromolecules can be treated as threads consisting of N beads freely jointed by (N-l) springs. Furthermore, it is considered that the solution is ideally dilute, so that intermolecular interactions can be neglected. 

To increase efficiency and ease of product separation from reaction mixtures, we also prepared styryl-substituted TADDOL-dendrimers that can act as crosslinkers in styrene suspension polymerizations, and thus lead to beads with intimately incorporated TADDOL sites [106,107]. Due to the presence of the con-formationally flexible dendritic spacers between the chiral ligand and the poly-... 

Real polymer processes involved in polymer crystallization are those at the crystal-melt or crystal-solution interfaces and inevitably 3D in nature. Before attacking our final target, the simulation of polymer crystallization from the melt, we studied crystallization of a single chain in a vacuum adsorption and folding at the growth front. The polymer molecule we considered was the same as described above a completely flexible chain composed of 500 or 1000 CH2 beads. We consider crystallization in a vacuum or in an extremely poor solvent condition. Here we took the detailed interaction between the chain molecule and the substrate atoms through Eqs. 8-10. 

Fig. 10 Equilibrium radius of gyration of a molecule plotted as a function of temperature the molecule is composed of 1000 beads. The radius of gyration shows a steep increase and a large fluctuation above 700 K. The insets show typical chain conformations at indicated temperatures. Note that the ideal random coil state of this fully flexible chain should have the mean-square radius of gyration R2 = 1000 x (1.54/3.92)2/6 = 25.7, the value is around 800 K...

Flexible force field models require 30 or more beads in Cartesian path integral descriptions to obtain converged intramolecular energies. Rigid water models require only about five beads due to the weaker intermolecular quantum effects. 

Formerly termed braced tread, rigid breaker or belted tyre. A pneumatic tyre in which the cords of the casing plies run directly across the tyre section from bead to bead, and not at an angle as in a cross-ply tyre the breaker in a radial-ply tyre is an inextensible band which runs circumferentially round the tyre between tread and casing. It is made up of layers of bias cut fabric set at discrete angles to confer the required stability in the tread but maintain the flexibility in the sidewall. 

Steel bead wires are used at the extremes of the reinforcing plies to ensure a complete seal to the rim. Many turns of small diameter wire are wrapped in a rubber-impregnated tape to form a flexible hoop of high strength. 

A basic theoretical model for flexible polymers is the Gaussian chain which assumes N ideal beads with intramolecular distance between them following a Gaussian distribution, so that the mean quadratic distance between two beads separated by n-1 ideal and not correlated bonds is given by [ 15,20]... 

In an early attempt to model the dynamics of the chromatin fiber, Ehrlich and Langowski [96] assumed a chain geometry similar to the one used later by Katritch et al. [89] nucleosomes were approximated as spherical beads and the linker DNA as a segmented flexible polymer with Debye-Huckel electrostatics. The interaction between nucleosomes was a steep repulsive Lennard-Jones type potential attractive interactions were not included. 

Unicellular foams are used for insulation, buoyancy, and flotation applications, while multicellular foams are used for upholstery, carpet backing, and laminated textiles. Expanded PS (Styrofoam), which is produced by the extrusion of PS beads containing a volatile liquid, is used to produce low-density moldings such as foamed drinking cups and insulation boards. Foamed products are also produced from PVC, LDPE, urea resins, ABS, and PU. PU foams are versatile materials, which range from hard (rigid) to soft (flexible). These are produced by the reaction of a polyol and a diisocyanate. 

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