**Georgios Zamanakos, Nagarajan Vaidehi, Dan Mainz, Guofeng Wang,
Ryan Martin, Tahir Cagin and William Goddard III**

Materials and Process Simulation Center, Beckman Institute (139-74),

California Institute of Technology, Pasadena, California 91125

The full talk is available here.

You may also download the powerpoint version or the postscript version.

Dendrimers and hyperbranched polymers represent a novel
class of structurally controlled macromolecules derived from a branches-upon-branches
structural motif. They are well defined, highly branched macromolecules that
radiate from a central core. The Percec family of
dendrimers self-assemble into spherical supramolecular dendrimers that exhibit a
thermotropic cubic liquid-crystalline phase of *Pm3n * space
group. The Frechet dendrimers are stimuli responsive macromolecules based on linear,
star, and dendritic blocks. They respond to change in their
environment through changes in shape, size, or nature of their exposed surface
(e.g. hydrophilic or hydrophobic).

To predict the structures, organization, and properties of these systems strains the capacity of ordinary Molecular Dynamics. Thus, we have to develope and implement coarse-grained methods capable of accurate predictions while averaging over much of the detail in all-atom MD simulations.

The Frechet dendrimer consists of approximately 2,700 atoms and a good treatment of the solvent requires an additional 50,000 to 100,000 atoms. To coarsen the description, we combine two methods:

The Newton-Euler Inverse Mass Operator (NEIMO) technique for internal coordinate dynamics. This allows whole regions to be considered as rigid although coupled covalently to other regions that are allowed to undergo only torsional motions and coupled to other regions that are allowed full Cartesian flexibility. In this approach the forces are treated atomistically (fine grain) while the motions are considered coarse grain.

Continuum dielectric description of the solvent. This uses the electrostatic field of the solute to induce a set of reaction field charges (at the Poisson Boltzmann or Generalized Born level) to model the bulk solvent interaction of the solute.

These methods have been implemented in MPSim, the massively parallel MD code developed in MSC and preliminary results have been obtained.

**Figure 1**: Snapshots of the Frechet NEIMO/SGB simulation

The Percec Macromolecular system consists of a dendrimer with ~400 atoms
that leads to a conical shape and associates with 11 others to form a spherical aggregate
(~4700 atoms) that associates with other spheres to form a well-defined crystal with space
group *Pm3n*. This has 8 spheres per unit cell (one sphere each at the corner and center
of the cell) plus two on each face. This leads to ~38,000 atoms
per unit cell. To obtain a coarse grain description of this system, we
consider the energetics of a pair of spherical assemblies (9400 atoms total) as a function of
distance. We find a two-body potential that is quite flat near the bottom. This results from the
nature of the Percec dendrimer, which has 324 C_{12} alkyl tails on each sphere. At longer
distances these hair tend extend themselves to interleave with the hairs
of the adjacent sphere. For shorter distances, they tend to rearrange,
leading to somewhat similar binding energies. Finally for very short distances, steric interactions
lead to very repulsive potentials.

**Figure 2**: Dynamics of two Percec supramolecular dendrimers

The net result is a 2-body potential curve that is well
approximated by a flat bottom Morse potential. Using this form of the potential in MD calculations
(8 pseudo atoms per unit cell instead of 38,000), we melted and quenched
a 216-pseudoatom system and found a range of parameters that leads back
to the *Pn3m* space group observed by Percec.

**Figure 3**: Fitted flat-bottom Morse potential

Future work here will consider 3-body corrections to the 2-body interactions. Such corrections are important in obtaining quantitatively accurate coarse-grained descriptions of the Percec system.

ACKNOWLEDGEMENTS

This research was funded by ARO-MURI (Doug Kiserow) and by ARO-DURIP (Doug Kiserow).