Peter Reineker

Models and equilibrium properties of stiff molecular chains

The partition functions of discrete as well as continuous stiff molecular chains are calculated using the maximum entropy principle. The chain is described by mass points, and their connectivity is taken into account by harmonic constraints (flexible segments) in addition to the bending restrictions. For comparison and as a test of the formalism the freely rotating chain as well as the Kratky–Porod wormlike chain (rigid segments) are reexamined treating the bending restrictions as constraints. It is shown that the second moments for the chain of flexible segments agree exactly with those known from the freely rotating chain for the discrete as well as the continuous chain and for all stiffnesses. Moreover, the Green’s function for the continuous chain is determined, which allows to obtain any desired two point distribution function. The influence of various bending restrictions on equilibrium properties is discussed. Furthermore, a comparison to other existing models, especially the Harris and Hearst mode...

Forces affecting the substrate in resonant tapping force microscopy

We propose a simple model to describe the interaction of a forced cantilever oscillation with a specimen in a tapping-mode scanning force microscope experiment in order to make a rough estimation of the forces affecting the surface with each touch down of the tip. Assuming weak damping of the cantilever (quality factor of the cantilever between 100 and 1000) and of the surface, we can estimate the forces to be in the range of those in the contact mode. These forces can vary by orders of magnitude, e.g. 10-6 to 10-11 N. To reduce the interaction force we suggest scanning on the low-frequency side of the resonance frequency of the non-contact cantilever oscillation. Increasing the difference of phase between the non-contact oscillation of the cantilever in air and the oscillation during contact introduces strong variations of the force. The improvement in resolution which can be achieved for soft samples by using the tapping-mode system results from the elimination of shear forces and the possibility of minimizing the force on the surface by varying the set-point of the scanning amplitude. Forces on the substrate will be enhanced by a large substrate stiffness.

DYNAMIC STRUCTURE FACTOR OF SEMIFLEXIBLE MACROMOLECULES IN DILUTE SOLUTION

The dynamic structure factor for molecular chains with variable stiffness in a dilute solution is investigated. In the limit of small scattering vectors q only the overall translational motion of the macromolecules contributes to the dynamic structure factor. The translational diffusion coefficient D exhibits a chain length dependence D∼1/√L for flexible chains and D∼ln L/L+const/L for rodlike chains. For flexible chains there is an intermediate scattering vector regime in which the decay rate or spectral linewidth of the dynamic structure factor is proportional to q3 indicating that stretching modes are dominant. Such an intermediate scattering vector regime cannot be observed for semiflexible or rodlike chains. At large scattering vectors q/2p≳1.5, where 1/2p is the persistence length of the macromolecules, the chain stiffness becomes important for any kind of molecules, i.e., even for very flexible ones. The dynamic structure factor and the decay rate are compared with experimental results of quasielas...

Molecular dynamics simulation study of adsorption of polymer chains with variable degree of rigidity. I. Static properties

The adsorption of a single polymer chain onto a solid surface is investigated by molecular dynamics simulations. The chain is composed of mass points interacting via a truncated Lennard‐Jones potential, i.e., the excluded volume interaction is taken into account, and grafted to the surface with one end. The average adsorption degree is calculated for various chain lengths (N = 16, 32, 64, 128) and adsorption energies. In addition, the scaling behavior of the adsorption degree and the radius of gyration is investigated. The adsorption degree and the average length of loops and tails are obtained for chains of various stiffnesses. In this context, we find that stiffer chains adsorb more easily. Moreover, the distribution of the mass points perpendicular to the surface as well as the orientation of the bonds with respect to the surface is discussed for various adsorption energies and stiffnesses.

Dynamic properties of molecular chains with variable stiffness

The dynamics of a free‐draining chain of variable stiffness in a dilute solution is investigated. The chain is considered as a differentiable space curve with stretching and bending elasticity. Second moments, like the mean square end‐to‐end distance, the radius of gyration, and the pair correlation function of the equilibrium distribution exactly agree with those of the well‐known Kratky–Porod wormlike chain. The equation of motion of the chain is derived and solved by a normal mode analysis. In the limit of a flexible chain the model exhibits the well‐known Rouse dynamics, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the rotational motion in the latter limit is naturally obtained within the model. The relaxation times obtained by the model are compared with experimental transient birefringence and dynamic light scattering data. In addition, electric dichroism measurements are interpreted in terms of the model. All of these experiments are in good agreement ...

Aggregation and counterion condensation in solution of charged proteinlike copolymers: A molecular-dynamics study

We present the results of molecular dynamics simulations of charged proteinlike hydrophobic–hydrophilic (HP) copolymers with a fixed charge distribution under pure solvent conditions. The processes of coil-to-globule transition, aggregation of polymer globules, and counterion condensation are studied in detail as a function of temperature. Various static structure factors and pair correlation functions, that occur in polyelectrolyte solutions, are also analyzed. Our simulations show that the chains pass through strong conformational changes while changing temperature. We find three different temperature regimes which are characterized by a different behavior of Coulomb energy, chain sizes, and pair correlation functions. In the high-temperature regime, at the reduced temperature T>3.0, the chains have an extended conformation with many hydrophobic blobs. As temperature is decreased, one observes a counterion condensation and sharp decrease in chain size. In this regime, we observe a solution of nonaggrega...

Stoichiometric polyelectrolyte complexes of ionic block copolymers and oppositely charged polyions.

Micellization in dilute solutions of diblock copolymers with a polyelectrolyte and a hydrophilic nonionic blocks and oppositely charged polyions is studied using mean-field theory. In aqueous solutions the micelle core consists of the polyelectrolyte complex (PEC) while the corona is formed by hydrophilic blocks of the block copolymers. Describing PEC as a globule in the framework of the Lifshitz [Zh. Eksp. Teor. Fiz. 55, 2408 (1968)] globule theory we calculate the surface tension of the micellar core/solvent interface as a function of the polyion degree of ionization, solvent quality, and concentration of low-molecular-mass salt. The equilibrium aggregation number of starlike micelles formed by block copolymers and homopolymers of opposite charge at stoichiometric mixture compositions is found as a function of the system parameters. It is shown that micelles disintegrate upon addition of salt.

Integral equation theory for polyelectrolyte solutions containing counterions and coions

Integral equations for equilibrium correlation functions of a three-component polyelectrolyte solution (polyions, counterions, coions) are solved numerically. Various pair correlation functions and structure factors are investigated. It is shown that added salt screens the Coulomb interaction between the negatively charged polyions. The comparison of the calculated polyion–polyion partial structure factor with experimental results of light scattering experiments on tobacco mosaic virus in a solution with added salt exhibits good agreement. Moreover, the counterion condensation on rodlike polyions is studied by means of pair correlation functions.

Influence of stiffness on the dynamics of macromolecules in a melt

Analytical expressions are derived for the incoherent and coherent dynamic structure factor of macromolecules in a melt. In particular, the influence of chain stiffness on these quantities is investigated. For scattering vectors q πp/2 the incoherent dynamic structure factor is shown to be a universal function of only the combination q8/3tp1/3, reflecting the strong influence of the local chain stiffness on dynamical properties at small length scales. Moreover, the q dependence of both the full width at half maximum of the Fourier transformed incoherent dynamic structure factor and the initial decay rate of the coherent dynamic structure factor are calculated. The comparison of the theoretical results with quasielastic neutron scattering experiments of different polymers exhibits good agreement.

Exciton transport in dynamically disordered molecular aggregates: influence on optical line shapes

Abstract For Frenkel excitons moving on a linear trimer we investigate the influence of dynamic disorder on their optical line shapes. The dynamic disorder models the influence of vibrational degrees of freedom and is taken into account by fluctuations of the local excitation energy and of the transfer matrix element between neighbouring molecules. The fluctuations are represented by dichotomic Markov processes with coloured noise. We obtain a closed set of equations of motion for the correlation functions determining the optical line shape which is solved exactly as well as using various approximations. The line shapes are discussed for various sets of the model parameters. Furthermore we show that slower fluctuations need higher approximations in our factorization scheme. The limit of static fluctuations can only be covered by the full set of equations.