Short-range Contact Interaction Research Articles

Folding of polymer chains with short-range binormal interactions

We study the structure of chains which have anisotropic short-range contact interactions that depend on the alignment of the binormal vectors of chain segments. This represents a crude model of hydrogen bonding or 'stacking' interactions out of the plane of curvature. The polymers are treated as ribbon-like semi-flexible chains, where the plane of the ribbon is determined by the local binormal. We show that with dipole–dipole interactions between the binormals of contacting chain segments, mean-field theory predicts a first-order transition to a binormally aligned state. We describe the onset of this transition as a function of the temperature-dependent parameters that govern the chain stiffness and the strength of the binormal interaction, as well as the binormal alignment's coupling to chain collapse. We also examine a metastable state governing the folding kinetics. Finally, we discuss the possible mesoscopic structure of the aligned phase, and application of our model to secondary structure motifs like β-sheets and α-helices, as well as composite structures like β-(amyloid) fibrils.

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^{\nu}(\log N)^{\gamma}$ where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterize the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings, by a direct numerical minimization of the variational energy for chains of increasing size $2^4<N<2^{15}$. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length $2^4<N<2^{10}$. The non universal behavior of the exponent $ \gamma$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ dimension. Particular attention is devoted to the homopolymer chain problem, when short range contact interactions are present.

Intramolecular chiral discrimination between meso and d, l isomers

The problem of short-range (contact) interactions between chiral molecules is modelled by that of intramolecular interaction within a molecule formed by combining chiral moieties. The example used is 2,3-dicyanobutane in its active and meso isomers. The energy difference between the two conformational minima, which is the analogue of the intermolecular discrimination energy, is found by ab initio molecular orbital calculations to be 3.1 kJ mol -1 in favour of the meso species. A simpler calculation with the help of a pairwise additivity scheme (see Craig, Radom &amp; Stiles 1975, preceding paper) gives 2.9 k J mol -1 . These discriminations are much greater than any found previously for dispersive and electrostatic forces, but on account of the stronger binding of the chiral moieties are expected to be greater than in intermolecular contacts.

Nuclear electron double resonance in liquids

In this contribution we hope to illustrate with preliminary measurements some of the ways in which nuclear-electron double resonance experiments can yield information of value to the chemist. The magnetic coupling between a paramagnetic electron of spin S and a nucleus of spin I may be described (Abragam 1961) by the spin Hamiltonian H s, I = γ e γ n I [3r(S. r)/ r 5 – S/ r 3 + 16 π /3 S| ψ e (0)| 2 ], where γ e , γ n are the electron and nuclear gyromagnetic ratios respectively, r is the vector radius joining I and S and | ψ e (0)| 2 is a measure of the overlap between the electron and nuclear wave functions. The first two terms describe the magnetic dipole-dipole interaction dominant at large interspin distances, and the third covers any short-range scalar or contact interactions. In non-viscous solutions of free radicals the rapid relative motion of the spins causes the Hamiltonian to become time dependent. If the motion is quite random the dipolar terms become entirely time dependent and are significant only in electron-nucleus relaxation phenomena. The scalar term, on the other hand, may not be completely averaged and can thus cause both relaxation phenomena and paramagnetic shifts in the nuclear resonance spectrum of the solvent (Bloembergen 1957). Thus the dynamic parts of both the scalar and the dipolar interactions are effective in producing mutual relaxation of the spins. Just which of the possible two spin processes is the most effective can be found by expanding the time-dependent Hamiltonian from equation (1) into its component spin operators and finding their relative spectral densities (Abragam 1955,1961). The dipole-dipole part of the Hamiltonian then becomes H d.d ( t ) = [ J 1 S z I z + J 2 {S + I_ + S_I + } + J 3 { S z I + + I z S + } ( A ) ( B ) ( C ) + J 3 { S z I_ + I z S_} + J 4 {S + I + } + J 4 {S_I_}] σ 1 /&lt; r 3 SI &gt;, ( D ) ( E ) ( F ) and the scalar part becomes H sc . ( t ) = [ J 5 S z I z + J 6 {S + I_ + S_I + }] σ 2 | ψ e (0)| 2 , where &lt; r 3 SI &gt; is the mean value of the cube of the electron-nuclear distance, σ1 and σ2 are proportionality constants, the J ’s are the spectral densities, S z , I z are the z components of the spin operators and S + I + ; S_I_ are the raising and lowering operators for the electron and nuclear spins respectively. For a white spectrum of relative motions between the spins, terms E and F are not the most important for dipolar coupling. This leads to the established reversal of nuclear polarization in Overhauser experiments between nuclei with positive magnetic moments and electrons (Richards &amp; White 1962 a, b ). Under the same conditions a dominant scalar coupling leads to an enhancement of the nuclear polarization because of its different relaxation operators.