Interchain Monomer Contact Probability in Two-Dimensional Polymer Solutions

Computer simulations of melts of randomly branching polymers

Randomly branching polymers with annealed connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present computer simulations of melts of annealed randomly branching polymers of 3 ≤ N ≤ 1800 segments in d = 2 and d = 3 dimensions. In all cases, we perform a detailed analysis of the observed tree connectivities and spatial conformations. Our results are in excellent agreement with an asymptotic scaling of the average tree size of R ∼ N^1/d, suggesting that the trees behave as compact, territorial fractals. The observed swelling relative to the size of ideal trees, R ∼ N^1/4, demonstrates that excluded volume interactions are only partially screened in melts of annealed trees. Overall, our results are in good qualitative agreement with the predictions of Flory theory. In particular, we find that the trees swell by the combination of modified branching and path stretching. However, the former effect is subdominant and difficult to detect in d = 3 dimensions.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations. V. incompressible homopolymer melts

Using fast lattice Monte Carlo (FLMC) simulations (Wang, Q. Soft Matter 2009, 5, 4564) and the corresponding polymer lattice field theories, including the lattice self-consistent field and Gaussian-fluctuation (LGF) theories, we studied a model system of incompressible homopolymer melts on a hexagonal lattice, where each lattice site is occupied by a total of ρ(0) ≥ 1 polymer segments. We generalized the cooperative motion algorithm (Pakula, T. Macromolecules 1987, 20, 679), as well as the related vacancy diffusion algorithm (Reiter, J.; Edling, T.; Pakula, T. J. Chem. Phys. 1990, 93, 837), originally proposed for the self- and mutual-avoiding walk (where ρ(0) = 1) to the case of ρ(0) > 1, where our generalized algorithm is highly efficient (i.e., nearly rejection-free). On the other hand, we extended the method of Wang (Wang, Z.-G. Macromolecules 1995, 28, 570) to calculate various single-chain properties in LGF theory. Direct comparisons between FLMC and LGF results, both of which are based on the same Hamiltonian (thus without any parameter-fitting between them), unambiguously and quantitatively reveal the effects of non-Gaussian fluctuations neglected by the latter. We found that FLMC results approach LGF predictions with increasing ρ(0), and that the leading order of non-Gaussian fluctuation effects on the single-chain properties is inversely proportional to ρ(0)(2). Our work suggests that theories capturing the first-order non-Gaussian fluctuation effects may give quantitative agreement with FLMC simulations of incompressible homopolymer melts at ρ(0) ≥ 2 in two and three dimensions.

Swelling equilibrium of dentin adhesive polymers formed on the water-adhesive phase boundary: experiments and micromechanical model

During their application to the wet, oral environment, dentin adhesives can experience phase separation and composition change, which can compromise the quality of the hybrid layer formed at the dentin-adhesive interface. The chemical composition of polymer phases formed in the hybrid layer can be represented using a ternary water-adhesive phase diagram. In this paper, these polymer phases are characterized using a suite of mechanical tests and swelling experiments. The experimental results were evaluated using a granular micromechanics-based model incorporating poro-mechanical effects and polymer-solvent thermodynamics. The variation in the model parameters and model-predicted polymer properties was studied as a function of composition along the phase boundary. The resulting structure-property correlations provide insight into interactions occurring at the molecular level in the saturated polymer system. These correlations can be used for modeling the mechanical behavior of the hybrid layer, and are expected to aid in the design and improvement of water-compatible dentin adhesive polymers.

Strictly two-dimensional self-avoiding walks: thermodynamic properties revisited

The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density ρ the expected power law scaling for the interaction energy between different chains e(int) ~ ρ(21/8), the total pressure P ~ ρ(3) and the dimensionless compressibility g(T) = lim(q→0)S(q) ~ 1/ρ(2). Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size ξ(ρ) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wave vector q. We comment briefly on finite persistence length effects.