Ideal Polymer Chain Research Articles

Self-segregation in chemical reactions, diffusion in a catalytic environment and an ideal polymer near a defect

We study a family of equivalent continuum models in one dimension. All these models map onto a single equation and include simple chemical reactions, diffusion in presence of a trap or a source and an ideal polymer chain near an attractive or repulsive site. We have obtained analytical results for the survival probability, total growth rate, statistical properties of nearest-neighbour distribution between a trap and unreacted particle and mean-squared displacement of the polymer chain. Our results are compared with the known asymptotic results in the theory of discrete random walks on a lattice in presence of a defect.

The static scattering function and optical birefringence of a deformed, ideal polymer chain

An exact formula is derived for the van Hove static scattering function of an ideal chain under traction. Results obtained from this formula are applied to the description of affinely deformed elastomers. Calculations are performed for two models of polymeric chains with the aim of establishing connections between the models and experimentally observable characteristics of macroscopic samples.

An ideal polymer chain in arbitrary dimensions near an attractive site

We study a lattice model of an ideal (no self-exclusion) polymer chain in d dimensions in the presence of an attractive site. For very long chains, we calculate analytically, for all dimensions, the partition function, the average energy per monomer unit and the probability distribution of the end-to-end length of the chain. For d⩾3, the system undergoes a phase transition from the low-temperature adsorbed phase to a high-temperature extended phase. This transition is continuous for d⩽4 and first order for d > 4. We determine the finite-size scaling functions near the transition for all d≠4, there is no scaling from due to the existence of logarithmic corrections.

Ideal polymer chains of various architectures at a surface

The macroscopic behavior of ideal polymer chains is studied by considering that at least one of the units of the chains is in contact with the surface. The present model is an amendment to the model used previously with the one end of a linear chain fixed at the surface. We estimate the mean number of contacts between a chain and the surface for the cases of linear ring, regular star, and regular comb polymers as the basic quantity for the description of both the thermodynamics of chains at a surface and the degree of adsorption of polymers of various architectures

Implications of using the entropy spring model for an ideal polymer chain.

When allowance for the finite orientational fluctuations in the end-to-end separation vector of an ideal Gaussian chain is made, while using a constant-length ensemble, the equation of state is no longer the simple Hooke's-law expression but contains, in addition, a repulsive force which opposes the tendency of the chain to collapse. The implications of this new equation of state are examined.

Adsorption of polymer chains on small particles and complexation

On the basis of the theory of adsorption of ideal polymer chains on rigid adsorbents the authors investigate the conformational structure of a complex formed by one polymer molecule and one or more small particles bound to it. It is shown that even in absence of direct interaction between particles their binding to the polymer matrix is cooperative.

The behaviour of an ideal polymer chain interacting with two parallel surfaces

The behaviour of a long isolated ideal chain polymer interacting with two parallel surfaces is investigated within the context of a simple cubic lattice model in three dimensions. In order to be able to obtain information about the contacts of the polymer with the plates the full chain is subdivided into trains, loops and bridges. A maximum term method is used to calculate the configuration sum of the polymer. In order to find the distribution of the subchains that maximises the partition function in the limit of infinite molecular weight a Lagrange multiplier method has been applied. This gives a closed set of equations from which one can uniquely calculate all relevant thermodynamic quantities as a function of the interaction energy, the temperature and the distance between the plates. In addition to the free energy and the entropy of the chain also the fraction of monomers on the surface and the number of trains is calculated. Next we give results about the ratio between the number of bridges and loops and the fraction of monomers in these loops and bridges. Finally the effective force between the plates due to the polymer material is calculated. The results for large plate separation are compared with those of the single plate.

Resonant Energy Transfer between Localized Excitations in a Linear Polymer Chain

AbstractA linear molecular polymer chain formed by replacing two host molecules by two identical impurities is investigated. Applying a particular theoretical approach the energies of localized excitations appearing in the system are determined and the dependence of these energies on the distance between the impurities is discussed. The theoretical approach is formulated in a way that reduces the problem to the analysis of an ideal polymer chain with some extra off‐diagonal terms in the Hamiltonian. These extra terms are considered as an interaction caused by the nonideality of the polymer chain.