Potential energies, bead-spring model

Figure 27 A schematic of coarse-grained, bead-spring model with potential energies (PFPE).

Figure 1.41. Potential energies for the bead-spring model LJ1—Lennard-Jones potential LJ2—van der Waals potential EXP1, EXP2—short-range polar potential FENE—finitely extensible nonlinear elastic potential.

Another very important analytically solvable case is the harmonic oscillator. This term is used for a mechanical system in which potential energy depends quadratically on displacement from the equilibrium position. The harmonic oscillator is very important, as it is an interacting system (i.e., a system with nonzero potential energy), which admits an analytical solution. A diatomic molecule, linked by a chemical bond with potential energy described by Eq. (2), is a typical example that is reasonably well described by the harmonic oscillator model. A chain with harmonic potentials along its bonds (bead-spring model), often invoked in polymer theories such as the Rouse theory of viscoelasticity, can be described as a set of coupled harmonic oscillators. 

The Gaussian chain is often represented by a mechanical model (see Fig. 2.4) N + 1) beads are considered to be connected by a harmonic spring whose potential energy is given by... 

Let us consider a solution of long polymer chains (N—> ) adopting the simplest beads-and-springs chain model (Figure 12(b)). Two beads located at r, and q are interaaing with the effective potential energy (r,-r,) which includes... 

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