Adsorption of poly(vinyl pyrrolidone) on silica. II. The fraction of bound segments, measured by a variety of techniques

The adsorption of the flexible, linear, and nonionic homopolymer poly(vinyl pyrrolidone) from water and from 1,4-dioxane onto pyrogenic silica was studied. Results are reported for the adsorbed amount as a function of adsorption time, molecular mass, and molecular mass distribution (polydispersity). It is found that the adsorption of fractionated samples can be qualitatively explained by the recent theory of Scheutjens and Fleer. However, the influence of the solvent type is larger than predicted by this theory, and an extension of the model to account for this influence is suggested. The polydispersity effects encountered in adsorption isotherms are satisfactorily accounted for by a theory published by Cohen Stuart, Scheutjens, and Fleer.     

Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.     

Polydispersity effects and the interpretation of polymer adsorption isotherms

In many cases, polymer adsorption is studied by measuring adsorption isotherms. Quite often it is found that the results are at variance with theoretical predictions. However, usually these adsorption isotherms are interpreted in terms of a single polymeric solute. Most polymers used in experimental studies are polydisperse and should be treated as mixtures. It is well established that the larger molecules in such mixtures adsorb preferentially over the smaller ones. In this paper we show that many discrepancies between polymer adsorption theory and experiment (e.g., the rounded shape of isotherms, the dependence of the adsorbance on adsorbent concentration, and the lack of desorption upon dilution) can be attributed to polydispersity. A quantitative analysis enables us to calculate isotherms for a polymer of arbitrary molecular weight distribution, provided the dependency of the plateau adsorbance on molecular weight is known. Experiments supporting the theory are reported. The fact that polymers do not desorb upon dilution with solvent is often regarded as a proof that polymer adsorption is irreversible. We show that, if a polydisperse sample is in equilibrium with an adsorbing surface, no detectable desorption may take place upon dilution. Therefore, the adsorption of polymers might well be reversible, even if desorption experiments would indicate apparent irreversibility.     

Critical endpoint and analytical phase diagram of attractive hard-core Yukawa spheres

We analytically calculate the gas-liquid critical endpoint (cep) for hard spheres with a Yukawa attraction. This cep is a boundary condition for the existence of a liquid. We use an analytical Helmholtz energy expression for the attractive Yukawa (hard) spheres based on the first-order mean spherical approximation to the attractive Yukawa potential by Tang and Lu (J. Chem. Phys. 1993, 99, 9828). This theory and our analytical simplification of it predict the gas-liquid and fluid-solid phase behavior, as found from computer simulations, very accurately as long as the range 1/kappa of attraction is not too short. We find that the cep is situated at kappasigma approximately 6 and at a contact potential around 2 kT. It follows that a liquid state is only possible when the attraction range is longer than (1/6) of the particle diameter sigma, and the attraction strength is smaller than 2 kT. The liquid region does not span more than 0.6 kT in strength, and there is also a relatively narrow window for the attraction range.     

Power-law exponent in the central region of a polymer layer adsorbed from dilute solution: Comparison between scaling and SCF results

De Gennes predicted the self-similar structure φ(z) ∞ z^−α for adsorbed polymer layers in the semi-dilute (central) region of the adsorption profile of homopolymers. This power-law behaviour is recovered in mean-field SCF calculations. In this case the exponent is α = 2 in good solvents provided D «z «d, where D is the proximal length and d the distal length. We use a ground-state approximation (GSA) to derive expressions for the two lengths D and d, and show that in the central region the profile is in good approximation given by φ = 1/3(z + D)⁻²exp(-(z + D)²/3d²). Unless the chains are extremely long the condition D«z«d is difficult to obtain and corrections on the exponent are necessary. For most chain lengths in the experimental range, the central region is quite narrow. It is shown that for high adsorption energies (small D) α = 2 + 2d⁻¹ in leading order, where d = R/, with R the radius of gyration and φ^b the bulk solution concentration. For weak adsorption the proximal length D is larger, which leads to a smaller exponent α. The d⁻¹ correction is in excellent agreement with numerical self-consistent-field calculations. In poor solvents we have φ = 1/2(z + D)⁻¹exp(-2(z + D)²/3d²) and α = 1 + 4d⁻¹ in the strong adsorption limit, which implies a larger correction in this case. Our analysis suggests that in a polymer adsorption profile with excluded-volume correlations (where α = 4/3) non-universal aspects would also be present if the chain length is finite.     

Flash vacuum thermolysis of acenaphtho[1,2-a]acenaphthylene. Thermal behaviour of a polycyclic aromatic hydrocarbon containing two abutting pentagons

FVT of acenaphtho[1,2-a]acenaphthylene (1) gave acenaphtho[1,2-e]acenaphthylene (2), cyclopenta[cd]perylene (3) and cyclopenta[rst]benzo[hi]chrysene (4). The formation of 3 and 4 indicates that, besides ring contraction/ring expansion of 1 giving 2, homolytic scission of a five-membered ring carbon---carbon single bond of 1 is an important competitive process.     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Forces and mechanisms in the adsorption of uncharged and ionizable macromolecules and of proteins

The main energetic and entropic factors determining the adsorption behaviour of neutral polymers, polyelectrolytes, and proteins are discussed. The driving force is the segment adsorption energy, opposing forces are the loss of chain conformation entropy and the entropy of (de)mixing. Mutual interactions between the segments play an important role, especially if the macromolecules carry charged groups. Several examples are given of the dependency of the adsorption of flexible macromolecules on the adsorption energy, the solvent quality, the salt concentration, and the surface charge. In the case of proteins, the internal coherency of the molecule largely determines the adsorption behaviour. For relatively flexible proteins like HPA, entropic contributions are important and sometimes dominant; the nature of the surface is less critical. For rigid proteins like RNAse, the adsorption is mainly energetically determined, depending largely on the electrostatic interaction between protein and surface.     

Ground-state description of the adsorption of homodisperse and polydisperse polymers

A ground-state approximation (GSA) is employed to model the structure of an adsorbed layer of homodisperse and polydisperse polymer. The model uses the basic assumption that the volume fraction at a distance z from the surface of a component with chain length N can be written as the product of the square of an eigenfunction g(z) and the N-th power of an eigenvalue eϵ. This approximation implies the neglect of end effects (tails): only loops are considered. For a homodisperse polymer, the eigenvalue is defined through ϵN = In(1/ϕ^b), where ϕ^b is the bulk solution concentration. The eigenfuction can be written in terms of two parameters: a “proximal” length D which through the boundary condition may be related to the adsorption energy, and a “distal” length which is inversely proportional to √ε. For a polydisperse polymer, D is the same as for a homodisperse polymer, but ε has to be computed from an implicit equation which involves a summation over all chain lengths present. The contribution of each chain length N in a mixed adsorbed layer is obtained by weighting with e^εN. This approximate analytical model gives results which are in good agreement with numerical self-consistent-field calculations. Examples are given to illustrate the applicability of the model to polydisperse systems. These include adsorption preference of long chains in polymer mixtures and the difference between adsorption and desorption isotherms in polydisperse systems. Simple expressions are obtained for the chain length characterising the transition between (long) adsorbed and (short) non-adsorbed chains and for the width of the transition zone.