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

Macromolecules 04/2002; DOI: 10.1021/ma00111a019
  • Source
    [Show abstract] [Hide abstract]
    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.
    The Journal of Chemical Physics 04/2008; 128(12):124905. · 3.12 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this article, the conformational properties and elastic behaviors of ring polymers in the process of tensile elongation are investigated with the Monte Carlo method and the bond fluctuation model. The ratio of the mean-square diameter to the mean-square radius of gyration increases with the elongation ratio, λ, and the instantaneous shape of ring polymers is more symmetric than that of linear chains in the process of tensile elongation. Here for ring polymers rather than the mean-square end-to-end distance for linear polymers is defined as the average of squared distances between two segments separated by N/2 bonds, where N represents the total number of bonds. Local quantities, that is, the mean-square bond length and the mean bond angle <θ> increase with λ, especially for short ring chains. The and have the same relationship with the chain length, N, that is, ∼ N1.130±0.020 and ∼ N1.160±0.013 for a different λ. Some thermodynamics properties are also addressed here. The average energy per bond decreases with λ and the average Helmholtz free energy and elastic force f increase with λ, especially for short ring chains. Comparisons with linear chains are also made. These investigations may provide insight into the elastic behaviors of ring polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 223–232, 2005
    Journal of Polymer Science Part B Polymer Physics 01/2005; 43(2):223 - 232. · 2.22 Impact Factor
  • [Show abstract] [Hide abstract]
    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.
    The Journal of Chemical Physics 11/2011; 135(18):184906. · 3.12 Impact Factor