Chava Brender

Monte Carlo study of polyelectrolyte behavior. I. Technique

A dynamic Monte Carlo method for the relaxation of a polyion in the presence of its counter ions is reported. A lattice model incorporating long range interaction of a Coulombic and excluded volume nature is considered. Results are listed for the configurational energy 〈UNI/NIkT〉, as well as the mean square end‐to‐end distance 〈R2N〉, and the mean square radius of gyration 〈S2N〉, for short chains.

Monte Carlo study of polyelectrolyte behavior. II.

A Monte Carlo simulation of an isolated polyelectrolyte chain in the presence of its counter ions without added salt is reported. Configurational properties such as the mean square end‐to‐end distance 〈R2N〉, the mean square radius of gyration 〈S2N〉, and the mean reduced electrostatic energy 〈UNI/NIkT〉, were studied as a function of the ionic strength of the solution, C; and the % charge of the chain. System behavior is classified into three regions: I: κ−1≪〈S2N〉1/2; II: κ−1∼1/2<S2N〉1/2; III: κ−1≫〈S2N 〉1/2, where κ−1 is the Debye–Huckel radius describing the scale of order of interionic interactions. In region I, the polyelectrolyte behaves configurationally as a random coil and the system is describable electrically as a simple electrolyte. In region II, the polyelectrolyte undergoes a conformational transition and the system electrically deviates notably from simple electrolyte behavior. In region III, the polyelectrolyte behaves configurationally as a rod and the system is characterized electrically by ...

A Monte Carlo off‐lattice method: The slithering snake in a continuum

An off‐lattice Monte Carlo simulation of a polymer chain using the slithering snake method is introduced. The mean square end‐to‐end distance is calculated and compared with previous studies. Results indicate that small angular deviations from the tetrahedral lattice models produce large conformational change in the polymer chain.

Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

Self‐avoiding walks on the simple cubic lattice of lengths up to 11 steps were exactly enumerated. The mean square end‐to‐end distance and its mean square components were recorded as a function of the span separation along one principle Cartesian axis. The molecular weight dependence for narrow spans (thin slabs—up to two lattice spacings) obeys that of a two‐dimensional walk as conjectured by Wall et al. As the slab thickness increases, one encounters a dimensionality transition in the behavior of the mean separations which is compared with similar transitions observed for the self‐avoiding walk in the presence of one interacting barrier. For thick slabs the behavior is three dimensional.

Coil to rod transitions in Monte Carlo simulations of a short polyelectrolyte. III. Contact as a new type of bond

In previous articles we introduced a new thermal effect which causes a fully charged chain to unfold under cooling. In this article we develop a new method to monitor the progress of the unfolding process. A new order parameter is suggested and an attempt is made to define a new kind of what we call statistical–physical bond.

Coil to rod transitions in Monte Carlo simulations of a short polyelectrolyte. I. New thermal and screening effects

A Monte Carlo simulation of a single short polyelectrolyte chain immersed in a dielectric continuum solvent with screened Coulombic interactions is described. Two main effects are involved in the coil→rod conformational transitions that have been observed when the temperature is decreased: a new thermal effect and a screening effect. The pure thermal effect is resolved by simulating a bare fully ionized polyion with Coulombic interactions at various T. With decreasing T, the radius of gyration exhibits a crossover from a self‐avoiding walk configuration to a rod‐like shape. This phenomenon is explained by fundamental thermodynamic considerations. The screening effect at various temperatures, has been investigated for several ‘‘salt’’ concentrations using a screened Coulomb potential instead of a pure Coulomb one. Configurational properties such as the mean square end‐to‐end distance 〈R2〉, the mean square radius of gyration 〈S2〉, the average of the ratio of the means 〈S2〉/〈R2〉, the mean reduced electrostat...

Coil to rod transitions in Monte Carlo simulations of a short polyelectrolyte. II. Natural screening and a new thermal effect

A new thermal effect appears in a Monte Carlo simulation of a system of a single short polyelectrolyte chain together with counter ions in a dielectric continuum solvent. Interactions are taken to be Coulombic and the behavior at various temperatures is investigated. A ‘‘natural’’ screening effect is compared to the Debye–Huckel screening effect which was described in a previous article. Great differences between these effects are observed at 0<C<1 M, indicating the existence of counter ion condensation near the polyion, thus creating two kinds of concentrations: that in the bulk and that in the vicinity of the polyion.

The average number of kinks of a short polyelectrolyte chain : a Monte Carlo study

An interesting connection between the mean straight length 〈ls〉 and the defined average number of kinks 〈nkink〉 in a polyelectrolyte chain configuration is found and described. 〈nkink〉 is found to be the dominant parameter throughout the entire range of the Bjerrum length λ and very sensitive to salt concentration. Identification of λm where (nkink values for various chain lengths coincide, as a percolation threshold is suggested. Considering the kink as a bond, it is found to be much more significant than the contacts described in a previous article as a new type of bonds. It is shown that the family of the physical statistical bonds includes not only contacts but also kinks. The kink fraction in a chain and the effective screening of 〈nkink〉 are defined and described for various values of λ. Through the use of these new parameters, pronounced size effects appear clearly. A connection between polymer systems and molecular cluster systems is proposed.

Monte Carlo lattice simulation of a simple electrolyte

Monte Carlo simulations are reported for the primitive electrolyte model of Card and Valleau [Ref.4(a)]. (AIP)

Polymers confined to thin slabs: Scaling law

A scaling method is applied to a polymer in a thin slab of thickness L. The results indicate that the component of the mean square end‐to‐end distance, in the direction parallel to the slab plane, <R2y(L)≳, behaves asymptotically as <R2y(L)≳∼L−1/4 N3/2. Results from data on self‐avoiding walks generated on the SC and FCC lattices verify the scaling law.