Article

.THETA. State, Transition Curves, and Conformational Properties of Cyclic Chains

Macromolecules 04/2002; DOI: 10.1021/ma00111a019
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    ABSTRACT: It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness epsilon(b). In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as epsilon(b) is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system's phase diagram at zero force is obtained. Depending on epsilon(b) and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of epsilon(b) the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.
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    ABSTRACT: By use of an intramolecular criterion, i.e., the direct proportionality between mean square dimension and chain length, theta conditions for linear chains and ring shaped polymers are evaluated for several types of cubic lattice chains (simple cubic, body centered cubic, and face centered cubic). The properties of the rings are evaluated for the same thermodynamic conditions under which they are prepared thus allowing for a natural amount of knots which have been identified by use of Alexander polynomials. For the limit of infinite chain lengths the same theta parameter is found for linear chains and rings. On the contrary, a significant theta point depression occurs due to an additional excluded volume effect if unknots are exclusively regarded. Parameters characteristic of the shape of rings and chains under theta conditions extrapolated to infinite chain length fairly well coincide with respective data for random walks. Mean square dimensions (characteristic of the size) of theta systems are slightly in excess as compared to nonreversal random walks due to the necessity of avoiding overlaps on a local scale. Furthermore athermal systems are studied as well for comparison; mean square dimensions are described by use of scaling relations with proper short chain corrections, shape parameters are given in the limit of infinite chain length.
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