Article

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

Macromolecules 04/2002; DOI: 10.1021/ma00111a019

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**ABSTRACT:**We have used molecular dynamics methods to investigate the effects of cyclic chain architecture on the properties of dilute solutions. In order to include solvent effects in estimating these properties, we use a van der Waals scaling factor determined for each solvent by matching to the theta condition. We predict that the theta temperature (theta) of cyclic PE (c-PE) is ~10% lower than for the linear case (l-PE). This can be compared to the experimental results for polystyrene (PS), where theta for cyclic PS is 2% lower. For conditions corresponding to n-pentane solvent, we predict that <R<sub>g</sub><sup>2</sup>>cyclic/<R<sub>g</sub><sup>2</sup>>linear is 0.59 for all temperatures above 350 K. The deviation from the ratio of 0.50–0.53 expected from analytic theory is due to the competition between chain stiffness and excluded volume effects. To calculate the intrinsic viscosity of c-PE and l-PE we extended the Bloomfield–Zimm type theory to include chain stiffness corrections. We find that for the theta temperature, the ratio of viscosities for c-PE and l-PE is 0.71, which is 7% higher than the value of 0.66 from the freely jointed chain model. This difference is caused by the larger value of <R<sub>g</sub><sup>2</sup>>cyclic/<R<sub>g</sub><sup>2</sup>>linear from the simulations.The Journal of Chemical Physics 01/2003; · 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, 2005Journal 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

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