Swelling of Macromolecules Grafted on Inert Surfaces and Partitioning of a Solute between Solvent and Grafted Phase

Abstract

A method is proposed for determining the thermodynamic characteristics of macromolecules grafted on an inert plane. Based on Flory's theory for macromolecular solutions and gels, the swelling of such a grafted phase by a solvent is calculated. Results are applied to evaluate the partition coefficient of a solute between grafted molecules and a solvent. Variations of this coefficient with the molecular sizes of the solvent, solute, and grafts and with the interactions between these molecules are studied.The behavior of a macromolecule in the vicinity of an interface is useful for understanding the adsorption of polymer~l-~ and for explaining the fractionation observed in gel permeation chromatography (GPC).4-6In the particular case of a macromolecule attached by one of its ends to a surface, numerous applications are suggested: liquid-liquid chromatography, selective absorption of pollutants, compatibilization of prosthesis with blood, stabilization of polymer emulsions, supported catalysis, etc.The thickness of the polymer layer adsorbed on a surface and its variation with molecular weight has been experimentallyThe segmental distribution of grafted macromolecules has been evaluated both theoretically and by ~i m u l a t i o n~~'~ but their thermodynamic characteristics have not been systematically studied. These characteristics should allow one to better understand the behavior of grafted materials. Hence, we investigated the problem and using Flory's theory on macromolecular solutions,13J4 we calculated the swelling by a solvent of a macromolecular phase grafted on a plane and we deduced the partition coefficient of a solute between the two phases of such a system.15 ModelAs depicted in Figure 1, we take as our model N3 nonentangling polymer chains grafted onto an inert plane. That is, chains are independent and there is no adsorption effect on the wall.According to the lattice liquid theory13J4 solvent and polymer molecules are assumed to be constituted of segments of identical volume. Thus, each molecule of solvent is composed of rl segments and each molecule of polymer is composed of r3 segments.This rough model, representative of graft phases used in practice, requires the specification of only a few parameters and the resulting expressions can be easily applied to experimental data. For example, it elucidates the behavior of chemically bonded stationary phases which have gained increasing importance in liquid chromatography. Free Energy of Mixtures solvent with the grafted phase is AF I F = A F M + A F E L The free-energy change involved in the mixing of a ( l a ) in which A F M is the free energy of mixing AFM = A H M -TASM (Ib) and A F E L is the elastic free energy due to the molecular expansion of the grafted chains in the solvent. 1. Computing E n t r o p y of A S M Mix. Consider a solution consisting of N , molecules of solvent and N3 molecules of polymer. The number of permissible patterns of the two kinds of molecules in such a system is Q.When the polymer molecules have one end attached to a surfa...

Terminally Anchored Chain Interphases: Their Chromatographic Properties

“…Lecourtier et al considered the partitioning of molecules in terminally anchored polymer phases within the Flory-Huggins theory. 26 This approach leads to predictions of global or average properties within the usual Flory-Huggins formulations. Unfortunately, their approach did not consider the effect of surface coverage explicitly and therefore does not completely account for the severe constraints imposed by the interfacial nature of the problem.…”

Phase Equilibria of a Brush-Bearing Coating Swollen with a Lubricant and Regulation of Its Composition to Facilitate Ice Shedding

“…Numerous publications have described the statistical treatment of a brush layer on an impermeable flat plane using either the mean-field or scaling approach. 8−13 In this work, the expression derived by Lecourtier et al 8 is adopted for the Helmholtz free energy change ΔF b occurring during formation of a lubricant-swollen brush layer ( ) ( )…”

“…Numerous publications have described the statistical treatment of a brush layer on an impermeable flat plane using either the mean-field or scaling approach. − In this work, the expression derived by Lecourtier et al is adopted for the Helmholtz free energy change Δ F b occurring during formation of a lubricant-swollen brush layer where n b and n s , b denote the moles of grafted polymer chains and lubricant molecules in the brush layer, respectively. While the first four terms on the right-hand side of eq account for the mixing entropy, the fifth term arises from the mixing enthalpy, and the last term originates from the elasticity of the grafted polymer chains.…”

“…The excess free energy associated with the swelling of the grafted polymer was obtained by taking the derivative of Δ F b / RT with respect to n s , b . Such an operation yielded By setting eq is simplified to …”

“…Statistical thermodynamic treatment of the swelling equilibrium of a cross-linked polymer by a solvent has been discussed in numerous polymer textbooks and journal articles. − There have also been reports on the one-dimensional vertical swelling of cross-linked thin films tethered to rigid substrates. , Furthermore, studies exist on solvent swelling of a polymer end-grafted to an impermeable plane. − However, we are unaware of statistical thermodynamic investigations regarding the partition of a solvent (or lubricant) into a cross-linked coating that resides on a rigid substrate and bears a dense end-tethered polymer monolayer on its upper surface. We report in this paper such a study.…”