P.G. de Gennes

Reptation of a Polymer Chain in the Presence of Fixed Obstacles

We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

Protein-surface interactions in the presence of polyethylene oxide

Abstract The protein resistance character of polyethylene oxide (PEO) chains terminally attached to a hydrophobic solid substrate is theoretically studied. Steric repulsion, van der Waals attraction, and hydrophobic interaction free energies are considered. The results are dependent on the chain length and surface density of PEO. The protein approaches the PEO surface by diffusion and is affected by the van der Waals attraction between the PEO surface and protein through water. Further approach of the protein initiates the compression of PEO chains, which induces a steric repulsion effect; an additional van der Waals attraction becomes important between the substrate and protein through the water solvated PEO layer. The van der Waals component with the substrate decreases with increasing surface density and chain length of terminally attached PEO chains. Other synthetic polymers were also studied, indicating that the protein resistance character is related to the refractive index, with PEO having the lowest refractive index of the common water-soluble synthetic polymers. The osmotic and elastic constants of steric repulsion for terminally attached PEO were estimated as ∼0.007 and 0.02, respectively, from literature data for PEO adsorbed to mica. The steric repulsion free energy and the combined steric repulsion and hydrophobic interaction free energies were calculated as a function of surface density and chain length of PEO. The free energy calculations as a function of surface density and chain length of PEO reveal that a high surface density and long chain length of terminally attached PEO should exhibit optimal protein resistance, with the attainment of high surface density of PEO being more important than long chain length. These theoretical results should be helpful in the design and development of materials resistant to protein adsorption.

Polymers at an interface; A simplified view

Abstract An elementary description of polymers adsorbed, or terminally attached, at an interface is given. Discussion is restricted to linear, flexible, neutral chains in good solvents. Terminally attached systems, in the “brush” regime, have weak fluctuations and are thus amenable to a simple mean field description. On the other hand, the adsorbed, diffuse layers have large fluctuations and cannot be described in mean field terms. Adsorbed layers have a certain self-similar structure which allows for a compact interpretation of most fundamental data (ellipsometry, hydrodynamic thickness). Self-similarity has been proven most explicitly by recent neutron experiments of Auvray and Cotton which were made on long chains with variable contrast techniques. Recent advances on the kinetics of exchange between adsorbed and free polymer are also briefly described.

Dynamics of fluctuations and spinodal decomposition in polymer blends

We discuss here some qualitative features of the concentration fluctuations in binary polymer melts A+B, A and B being long, flexible chains, with a Flory interaction parameter χ which can be positive (favoring segregation), or negative. In the one phase domain, the fluctuations of long wavelength (2π/q) are expected to relax by a reptation process. At shorter wavelengths (qR0≳1, where R0 is the size of one chain) equilibration takes place by local adjustment of each chain inside a fixed ’’tube’’: the predicted relaxation rates τq−1 are proportional to q6 for χ?0. (For a negative χ, opposing segregation, one expects τq−1∼q4). In the two phase domain, where the trend towards segregation is strong (χN≫1, N being the number of monomers per chain), one should observe a very anomalous type of spinodal decomposition: in the early stages, the growing fluctuations have a wavelength comparable to the thickness of the interfacial region, and small compared with R0: the growth is realized through local adjustment. D...

A model for contact angle hysteresis

We discuss the behavior of a liquid partially wetting a solid surface, when the contact angle at equilibrium θ0 is small, but finite. The solid is assumed to be either flat, but chemically heterogeneous (this in turn modulating the interfacial tensions), or rough. For weak heterogeneities, we expect no hysteresis, but the contact line becomes wiggly. For stronger heterogeneities, we first discuss the behavior of the contact line in the presence of a single, localized defect, and show that there may exist two stable positions for the line, obtained by a simple graphic construction. Hysteresis shows up when the strength of the defect is above a certain threshold. Extending this to a dilute system of defects, we obtain formulas for the ‘‘advancing’’ and ‘‘receding’’ contact angles θa, θr, in terms of the distribution of defect strength and defect sharpness. These formulas might be tested by controlled contamination of a solid surface.

An analogy between superconductors and smectics A

Abstract The conformation of a smectic A can be described by a phase function φ(R), the n-th layer corresponding to φ(R) = 2πn. The role of the phase in smectics A and in superfluids is similar. This analogy leads to the following predictions for a second order smectic A ↔ nematic transition: (1) the transition temperature is lowered if twist, or bend distortions are imposed: these distortions correspond to a magnetic field in superconductors. (2) the Frank coefficients K2 and K3 of the nematic phase must show pretransitional anomalies.

Exponents for the excluded volume problem as derived by the Wilson method

Abstract By an expansion to second order in ϵ = 4-d, we derive the mean square extension R2 for a random, self excluding walk of N jumps on a d-dimensional lattice. The result is: R2 = const. N1.195(for d = 3).

Collective motions of hydrogen bonds

Abstract The low frequency collective modes of protons are calculated for ferrroelectric crystals of the KH 2 PO 4 type taking into account the tunneling frequency and a simplified interaction between proton sites. They give rise to a band of frequencies which could be observed by inelastic scattering of neutrons. (In the deuterated salts, on the other hand the band is very narrow and the excitations are only weakly coupled to the neutrons). When the temperature is raised, there is a decrease in frequency and a broadening for each mode. Finally, in the paraelectric state, one expects a broad neutron spectrum from the hydrogen compound, but only quasielastic scattering from the deuterium compound.

Liquid dynamics and inelastic scattering of neutrons

Abstract The energy transfers in one collision between a neutron and a liquid are computed by a method of moments. It is shown that for large momentum transfers a perfect gas model is correct. For small momentum transfers a macroscopic description of the density fluctuations in the liquid is applicable. It is in the intermediate region (where diffraction peaks are observed) that the method of moments is most useful. These different experimental situations are discussed for liquids where recoil and quantum effects are negligible, and numerical results are given for argon. An approximation for the so called autocorrelation function, valid for both long and short time scales and all distances, is also presented.

Collapse of a polymer chain in poor solvents

The behavior of a single, flexible polymer chain near the Flory temperature Θ is analysed in analogy with a magnetic phase transition. The transition to a collapsed state is related to a tricritical point for the magnetic problem.