Polymers interacting with spherical and rodlike particles

Abstract

The interaction of a long flexible polymer chain with mesoscopic particles of spherical or elongated cylindrical shape is investigated by field-theoretic methods using the polymer-magnet analogy. In the case that these particles are immersed in a dilute polymer solution and exhibit purely repulsive surfaces we study density profiles for monomers and chain ends near such a particle, the change of configurational entropy by immersing a particle into the solution, and the depletion interaction between a particle and a distant planar wall. Both ideal chains and chains with an excluded-volume interaction are considered. We also analyze particle surfaces with a short-ranged attraction and the adsorption-desorption transition for an ideal polymer chain. Properties such as the number of surface contacts are evaluated both in the adsorbed limit, in which the thickness of the adsorbed layer is much smaller than the unperturbed polymer size so that ground-state dominance applies, and at the adsorption threshold. ͓S1063-651X͑96͒02308-2͔ PACS number͑s͒: 05.70.Jk, 68.35.Rh, 61.25.Hq, 82.70.Dd ͩ ‫ץ‬ ‫ץ‬L Ϫ⌬ D ͪ Z L ͑ r,rЈ͒ϭ0 ͑1.2a͒ with the ''initial condition''

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

“…This will decrease the blob-blob interaction, measured by B B , while leaving the blob-sphere second virial coefficient B SB still at around σ 3 . The second virial coefficient for the interaction between an ideal chain, R E = σ, and a hard sphere, of diameter σ, is known exactly [11] and is close to 3σ 3 . Thus, when ζ B is no longer much larger than one, the ratio between the sphere-blob and blob-blob excluded volumes, b, will increase as ζ B decreases.…”

“…The interactions between colloidal spheres and polymer molecules have been studied theoretically via a number of techniques: scaling approaches [8][9][10], field theory [11][12][13][14], computer simulation [15,16], integral equations [17,18], and other approaches [19][20][21][22]. The phase behaviour has been studied via computer simulation [15], scaling theory [23], and perturbation theory [24,25], where Refs.…”

Polymer depletion interaction between two parallel repulsive walls

“…We employ the polymer magnet analogy [18,[21][22][23][24][25] in order to calculate the partition functionsẐ HS (z),Ẑ I (z), andẐ b as needed in Eqs. (2.5), (2.6), and (2.8) for a single chain with EV interaction.…”

“…By focusing on long flexible chains in a system of mesoscopic size we obtain mostly universal results which are independent of microscopic details [18,[21][22][23][24][25][26]. Due to the universality of the corresponding properties it is sufficient to choose a simple model for calculating these results.…”

Small mesoscopic particles in dilute and semidilute solutions of nonadsorbing polymers

“…3 Asymptotically exact results can be given for particle radius R much smaller than the other relevant mesoscopic lengths, since the particle can be viewed as a weakly repulsive point-perturbation for chain monomers. With the center of the colloidal particle at r C this leads 12,13 to a reduction factor…”