Bead-rod chain

In the model of Agarwal and Khakhar [57] the polymer molecules are taken to be bead-rod chains with the hydrodynamic forces concentrated at the beads. The chains may bend about a bead, and a spring force acts to restore the chain to is equilibrium conformation, which is a straight chain. The connecting rods are inextensible. The system is confined to a plane, and the chains diffuse due to Brownian forces resisted by hydrodynamic forces. Hydrodynamic forces resulting from an imposed shear flow deform and orient the molecules. Two chains may react and combine to form a longer chain if the chain ends approach to within the capture radius (a) and if the angle between the chains is less than the critical value (0 ). The reaction is assumed to be very fast (kfj k j ) so that every collision that satisfies the above criteria results in... 

Equation (11) indicates that the drag force alcmg a bead-rod chain has a parabolic distribution with the maximum force at the midpoint (12). Substituting Stake s law into (12) yields the full expression of [Pg.156]

In 1944 Kramers [1] published a phase-space kinetic theory for the steady-state potential flow of monodisperse dilute polymer systems in which the polymer molecule is modeled as a freely jointed bead-rod chain. Subsequent scholars developed kinetic theories for shearing flows of monodisperse dilute polymer solutions Kirkwood [2] for freely rotating bead-rod chains with equilibnum-averaged hydrodynamic interaction. Rouse [3] and Zimm [4] for freely jointed bead-spring chains, and others. These theories were all formulated m the configuration space of a single polymer chain. 

The ability to fluorescently tag individual DNA molecules and visualize their dynamics in these flows can considerably enhance the information we obtain from these flows. Numerous single molecule visualization experiments have already led to significant advancements in our understanding of polymer chain dynamics in viscous flows. In addition, these experiments have recently been combined with Brownian dynamics simulations, which simulate the motion of bead-rod chains in viscous flows and can quantitatively predict the chain conformation for given flow conditions. This powerful combination has allowed for the validation of detailed molecular scale physics, as well as the development of new physical insights. These conclusions are described in a recent review [10] we summarize a few of the salient conclusions here. 

Liu, S., Ashok, B., and Muthukumar, M., 2004. Brownian dynamics simulations of bead-rod-chain in sinqtle shear flow and elongational flow. Polymer, 45, 1383-1389. 

Petera, D. and Muthukumar, M., 1999. Brownian dynamics simulation of bead-rod chains under shear with hydrodynamic interaction, J. Chem. Phys., Ill, 7614-7623. 

Fig. 7.11 Phase diagrams for a symmetrical off-lattice mixture with Na = Ng = N = 20, where both components are modeled as bead-rod chains, and all nonbonded beads interact with standard Lennard-Jones potentials which are truncated at 2.5b), and data are shown for a bulk system (full dots) and thin films with repulsive walls for thickness IO.Sct (squares) and 5cr (triangles). Lines represent a fit according to xi - xic oc (T- (From Kumar et...

The freely jointed bead-rod chain (Kramers model) is of interest because it has a large number of internal degrees of freedom and is also finitely extensible. Many equilibrium properties have been... 

In addition to the Curtiss-Bird theory for Kramers bead-rod chains, a simpler theory for FENE dumbbells has also been worked out and compared with experimental data. The simplicity of this model enables one to see the structure of the theory without the mathematical complications. 

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