Bead model

The hierarchy of models is complemented by a variety of methods and tecluiiques. Mesoscopic models tliat incorporate some fluid-like packing (e.g., spring-bead models for polymer solutions) are investigated by Monte Carlo... 

Hongmei Jian. A Combined Wormlike-Chain and Bead Model for Dynamic Simulations of Long DNA. PhD thesis. New York University, Department of Physics, New York, New York, October 1997. 

The bead model for polymer simulations. The heads may he connected by stiff rods or by harmonic springs. 

In vivo spectra of complexed tin on Pseudomonas 244 are essentially Identical to those of the glass bead model system, exhibiting an emission maxlmvm at 475 nm. A lower Intensity residual peak at 550 nm In Figure 4 Is due to uncomplexed flavonol, which was not completely removed from the cell membrane despite multiple washings. 

Bueche (16,152) had earlier proposed a related theory based on a spring-bead model (springs with a rubberlikc elasticity spring constant coupled in a linear chain by beads whose friction factor supplies the viscous resistance). This theory as extended by Fox and co-workers (28,153) gives... 

Fig. 3.1 Bead-spring-bead model of a Gaussian chain as assumed in tbe Rouse model. Tbe beads are connected by entropic springs and are subject to a frictional force where v is the bead velocity and fo the bead friction coefficient...

This agrees with all previous results as far as the first term is concerned. The second constant term 0.3863 is very close to Broersma s 0.38 (73) and to the value 0.392 obtained by Broomfield et al. (76) from their shell-model theory, which is essentially a limiting case of the Kikwood-Riseman theory (77) for the bead model of flexible chains. However, these values are about 0.3 smaller than the corresponding term in Eq. (D-5). This implies that if the ellipsoid model and the continuous string model are applied to the same experimental data for as a function of M, the former should lead to a d value which is about i.35 times larger than that obtained by the latter. On the other hand, both models should give an identical value for ML. 

Systematic departures from the Zimm moduli are observed at high frequencies (93, 117). These deviations appear to stem from the expected inadequacies of spring-bead models when the driving frequency approaches the frequency of the primitive backbone motions. The effects are attributed to a local resistance to the articulations of the chain which are required to bring about configurational... 

Spring-bead models relate frictional force to the relative velocity of the medium at the point of interaction. The entanglement friction coefficient above is defined in terms of the relative velocity of the passing chain. Since the coupling point lies, on the average, midway between the centers of the two molecules involved, the macroscopic shear rate must be doubled when applying the result to a spring-bead model. Substitution of 2 CE for Con in the Rouse expression for viscosity yields... 

Internal viscosity (Section 4) provides another possible source of shear-rate dependence. For sufficiently rapid disturbances, a spring-bead model with internal viscosity acts like a rigid body for sufficiently slow disturbances it is flexible and indefinitely extensible. The analytical difficulties for coupled, non-linear spring-bead systems are equally severe in linear spring-bead systems with internal viscosity. Even the elastic dumbbell with internal viscosity has only been solved exactly in the limit of small e (559), where e is the ratio of internal friction coefficient to molecular (external) friction coefficient Co n. For this case, the viscosity decreases with shear rate. 

Verdier,P.H., Stockmayer, W.H. Monte Carlo calculations on the dynamics of polymers in dilute solution. J. Chem. Phys. 36, 227-235 (1962). See also Verdier,P.H. Monte Carlo studies of lattice-model polymer chains. 1. Correlation functions in the statistical-bead model. J. Chem. Phys. 45,2118-2121 (1966). 

Model networks, synthesized by endlinking processes, contain few structural defects and are close to ideality. Spring-suspended bead models seem to fit adequately with the structural data obtained on labelled model networks and with the swelling and uniaxial deformation behavior of these networks. (67 refs.)... 

Similar results26, yielding even better accuracy have been obtained with swollen networks, submitted to an extension A. Further experimental work is necessary to settle this point. Nevertheless the increase of d with Ax is a further argument in favor of the spring-suspended beads model for the networks obtained by endlinking processes, as it is a direct proof of the proportionality between the macroscopic deformation and the deformation of the individual structural elements in the network, when it is submitted to a stress. 

Computer simulations of a range of properties of block copolymer micelles have been performed by Mattice and co-workers.These simulations have been based on bead models for copolymer chains on a cubic lattice. Types of allowed moves for bead chains are illustrated in Fig. 3.27. The formation of micelles by diblock copolymers under weak segregation conditions was simulated with pairwise interactions between A and B beads and between the A bead and vacant sites occupied by solvent, S (Wang et al. 19936). This leads to the formation of micelles with a B core. The cmc was found to depend strongly on fVB and % = x.w = %AS. In the range 3 < (xlz)N < 6, where z is the lattice constant, the cmc was found to be exponentially dependent onIt was found than in the micelles the insoluble block is slightly collapsed, and that the soluble block becomes stretched as Na increases, with [Pg.178]

All this analysis will be based on the mathematically most simple spring and bead model. Standard two parameter theory is based on the continuous chain model, which can be derived from our model by a not quite trivial limiting process. The derivation stresses that, standard two parameter theory is expected to hold only close to the (9-temperature, In this context we also exhibit the relation of polymer theory to a special quantum held theory. 

Figure 11.1 Atomic resolution structure of yeast tRNAPhe (PDB accession code 1TRA), rendered as black sticks and reconstructed density (red transparent surface). The reconstructed density was generated from the filtered consensus bead model by smoothing with a Gaussian kernel. Figure adapted from Lipfert ct al. (2007b).

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