Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

Confined polyelectrolytes: The complexity of a simple system

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse‐grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut‐like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement. © 2015 Wiley Periodicals, Inc.     

Rheological properties of internal viscosity models with stress symmetry

Internal viscosity models (IVM) for dilute-solution polymer dynamics differ in how they define the deformational force F ^d which includes φ, the IV coefficient, and in how they treat polymer rotational velocity Ω. Here, the handling of angular momentum is shown to be crucial. A torque balance in simple shear flow at shear rate G leads to stress symmetry and specification of Ω(G) which differs greatly from the conventional Ω = G/2. This determines the G dependence of viscosity η and normal stress coefficient ζ. There are also implications of a transition in rotational behavior as φ approaches a critical value. Predictions of η(G), ζ(G), and η^*(ω) are presented for two versions of F^d : one derived recently by the authors and one being most commonly used at present. Limiting cases for high and low φ, and for high and low G and ω, are discussed. Some differences exist between predictions of the two F^d models, but these are surprisingly minor.     

Odd-even staggering in simple models of metal clusters

The odd-even staggering of free-electron metal clusters is studied using several simple models: Noninter-acting electrons in a rectangular box, triaxial harmonic oscillator, and Hückel model. Finite temperature effects are studied using the Monte Carlo method. All the models show qualitatively similar odd-even staggering. In the ground state the HOMO-LUMO gap is larger than the neighbouring energy gaps. The reduction of the odd-even staggering due to exchange and correlation is studied using the local-spin-density approximation.     

Electronic states of the benzene dimer: a simple case of complexity

Electronic structure calculations of the excited states of the benzene dimer using equation-of-motion coupled-cluster method are reported. The calculations reveal large density of electronic states, including multiple valence, Rydberg, and mixed Rydberg-valence states. The calculations of the oscillator strengths for the transitions between the excimer state (i.e., the lowest excited state of the dimer, 1(1)B(1g)) and other excited states allowed us to identify the target state responsible for the excimer absorption as the E(1u) state of a mixed Rydberg-valence character at 3.04 eV above the excimer (1(1)B(1g)). Although at D(6h) the 1(1)B(1g) → E(1u) transition is symmetry-forbidden, small geometric displacements (to D(2h)) that have a negligible effect on the excitation energy split this degenerate state into the dark (4B(3u)) and bright (4B(2u)) components (oscillator strength of 0.3 au). The excitation energy for this transition depends strongly on the dimer structure, which explains the broad character of the experimentally observed excimer absorption spectrum.     

Comparison of two models for local chain motion

A connection is presented between the Jones–Stockmayer solution to the three-bond-jump equation for local motion and the new correlation function developed by Hall and Helfand. Both correlation functions are based on a diffusional picture for cooperative local motions which allows for the development of a relationship between them. Numerical fits of the Hall–Helfand function to the Jones–Stockmayer function are also given for both the time and frequency domain; these numerical fits are consistent with the analyses of NMR data by both models. The fits and the analyses set a likely range for converting the correlation time of the three-bond jump to the correlation time for the cooperative transitions in the Hall–Helfand model.     

Polymer fracture—A simple model for chain scission

A simple model for calculating the fracture process for a single extended-chain molecule such as polyethylene is considered. The model consists of a chain of N coupled Morse oscillators. There exists a critical overall extension ΔL_c below which the fracture is energetically unfavorable but above which fracture is favored both energetically and kinetically. This elongation ΔL_c scales as N^1/2. For the critically stretched chain, the activation energy for rupture increases with N. Long chains must be stretched beyond this critical value to fail within experimentally meaningful times. Chains of all lengths subjected to the same force will fail with the same activation energy, provided this force is large enough to stretch each chain to ΔL > ΔL_c. Observed activation energies are less than 1/3D_e, where D_e is the bond energy.     

Statistical thermodynamics for chain molecules with simple RNA tertiary contacts

A statistical thermodynamic model is developed for chain molecules with simple RNA tertiary contacts. The model, which accounts for the excluded volume effect and the nonadditivity in the free energy, enables reliable predictions for the conformational entropy and partition function for simple tertiary folds. Illustrative applications are made to conformational transitions involving simple tertiary contacts. The model can predict the interplay between the secondary and the tertiary interactions in the conformational changes. Though the present form of the theory is tested and validated in a two-dimensional lattice model, the methodology, which is developed based on a general graphical representation for chain conformations, is applicable to any off-lattice chain representations. Moreover, the analytical formulation of the method makes possible the systematic development of the theory for more complex tertiary structures.     

Potential energy and trajectory calculations of bond-bond crossing in simple models

The possibility of bond-bond crossing has been investigated by means of ab-initio valence bond calculations of the energy barrier for the system H₂ + H₂⁺. A semiclassical treatment of the most favourable trajectories for the system H₂ + H₂ points out the feasibility of the process.     

Realistic parameters for simple models of the Belousov-Zhabotinsky reaction

We use experimental results to estimate the values of parameters of simple models describing the time evolution of the Belousov-Zhabotinsky reaction proceeding in droplets surrounded by hydrocarbons. The equations with fitted parameters correctly describe the period of oscillations for a large class of experimental conditions at which the reaction is performed.     

Polymer chain generation for coarse-grained models using radical-like polymerization

A versatile method is proposed to generate configurations of coarse-grained models for polymer melts. This method, largely inspired by chemical "radical polymerization," is divided in three stages: (i) nucleation of radicals (reacting molecules caching monomers), (ii) growth of chains within a solvent of monomers and (iii) termination: annihilation of radicals and removal of residual monomers. The main interest of this method is that relaxation is performed while chains are generated. Pure mono and polydisperse polymer melts are generated and compared to the configurations generated by the push off method from Auhl et al. [J. Chem. Phys. 119, 12718 (2003)]. A detailed study of the static properties (radius of gyration, mean square internal distance, entanglement length) confirms that the radical-like polymerization technique is suitable to generate equilibrated melts. Moreover, the method is flexible and can be adapted to generate nanostructured polymers, namely, diblock and triblock copolymers.     

Rheological properties of HyperMacs—long‐chain branched analogues of hyperbranched polymers

HyperMacs are long chain branched analogues of hyperbranched polymers, differing only in the sense that they have polymer chains, rather than monomers between branch points. Although the building blocks for HyperMacs and AB₂ macromonomers can be well defined in terms of molecular weight and polydispersity, the nature of the coupling strategy adopted for the synthesis of the HyperMacs results in branched polymers with a distribution of molecular weights and architectures. Melt rheology showed polystyrene HyperMacs to be thermorheologically simple, obeying William–Landel–Ferry behavior. Zero shear viscosities of the polymers were shown to increase with average molecular weight and the melts display shear‐thinning behavior. HyperMacs showed little evidence for relaxation by reptation and the rheological behavior agreed well with the Cayley tree model for hierarchical relaxation in tube models of branched polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2762–2769, 2007     

Electronic spectra of quasi-regular heterostructures: simple versus realistic models

The electronic spectra of quasi-regular systems are investigated via simple one-dimensional, one-band models and compared with those obtained by means of realistic empirical tight-binding models, particularly for the Fibonacci sequence case.     

A simple model of stiff and flexible polymer chain adsorption: the influence of the internal chain architecture

In this study, we investigated the process of random sequential adsorption of stiff and flexible polymer chains on a two-dimensional square lattice. The polymer chains were represented by sequence of lattice points forming needles, T shapes, and crosses as well as flexible linear chains and star-branched chains consisted of three and four arms. The Monte Carlo method was employed to generate the model systems. The percolation threshold and the jamming threshold were determined for all systems under consideration. The influence of the chain length and the chain architecture on both thresholds was calculated and discussed. The changes in the ordering of the system were also studied.