Collect. Czech. Chem. Commun. 1994, 59, 2166-2189

Tethered Chains in Concave Volumes. A Monte Carlo Study

Karel Procházka and Zuzana Limpouchová

Department of Physical and Macromolecular Chemistry, Charles University, 128 40 Prague 2, Czech Republic


Monte Carlo study of tethered chain conformations in spherical cavities was performed in a relatively broad range of average segment densities (i.e. numbers of tethered chains with increasing length in the sphere). Simulations were performed on a tetrahedral lattice using (i) an equilibrated self-avoiding walk for systems containing a single tethered chain with increasing length, and (ii) a simultaneous self-avoiding walk of many tethered chains in the spherical cavity together with equilibration of the system which was performed by a modified algorithm similar to that of Siepmann and Frenkel. Only a geometric excluded volume effect of segments was considered (i.e. the prohibition principle of a double occupancy of one lattice site by two different segments). Various distribution functions (e.g. distribution of the end-to-end and the end-to-gravity center distances and their orientations with respect either to the radial direction, or to the direction of the first-to-second segment connection, etc.) were calculated and the effect of increasing average segment density in the sphere on conformational characteristics of individual chains was studied. It was found that conformational and orientational properties of relatively short tethered chains are only little affected by increasing segment density (i.e. by the number of chains in the spherical cavity), whereas arrangements of long tethered chains are significantly influenced by the density of the system.