We develop a detailed molecular theory that describes the response of weak polyelectrolyte gels to changes in both the pH and salt concentration, c, of the solution. This approach includes specific molecular details and conformational degrees of freedom of the polymeric gel, acid-base equilibrium, and solution entropy as well as electrostatic, van der Waals, and excluded-volume interactions. Here, we study polyacid gels in good solvent. The physical properties of the gel are found to depend on the coupling between charge regulation and the molecular interactions. In particular, the gel's degree of dissociation is not only determined by the bath pH and ionic strength but also by the polymer's ability in regulating charge to modify the local environment and in swelling or shrinking that depends on the externally controlled variables. The gel pH can be several units smaller than the bath pH depending on the salt ion concentration. The gel pH does not respond linearly to changes in neither bath pH nor c, and its behavior results from the complex interplay between the conformational degrees of freedom and all of the interactions mentioned above. The gel system swells if pH > pK a and collapses if pH < pK a . The continuous transition between collapsed and swollen regimes occurs in a very narrow range of bath pH around pK a whose width depends on the salt concentration. In this intermediate region the volume fraction of the polyacid can be controlled by both c and pH.
The binding of small proteins to ligands that are attached to the free ends of polymers tethered to a planar surface is studied using a molecular theory. The effects of changing the intrinsic binding equilibrium constant of the ligand-receptor pair, the polymer surface coverage, the polymer molecular weight, and the protein size are studied. The results are also compared with the case where ligands are directly attached to the surface without a polymer acting as a spacer. We found that within the biological range of binding constants the protein adsorption is enhanced by the presence of the polymer spacers. There is always an optimal surface coverage for which ligand-receptor binding is a maximum. This maximum increases as the binding energy and/or the polymer molecular weight increase. The presence of the maximum is due to the ability of the polymer-bound proteins to form a thick layer by dispersing the ligands in space to optimize binding and minimize lateral repulsions. The fraction of bound receptors is unity for a very small surface coverage of ligands. The very sharp decrease in the fraction of bound ligand-receptor pairs with surface coverage depends on the polymer spacer chain length. We found that the binding of proteins is reduced as the size of the protein increases. The orientation of the bound proteins can be manipulated by proper choice of the grafted layer conditions. At high polymer surface coverage the bound proteins are predominantly perpendicular to the surface, while at low surface coverage there is a more random distribution of orientations. To avoid nonspecific adsorption on the surface, we studied the case where the surface is covered by a mixture of a relatively high molecular weight polymer with a ligand attached to its free end and a low molecular weight polymer without ligand. These systems present a maximum in the binding of proteins, which is of the same magnitude as when only the long polymer-ligand is present. Moreover, when the total surface coverage in the mixed layers of polymers is high enough, nonspecific adsorption of the proteins on the surface is suppressed. The use of the presented theoretical results for the design of surface modifiers with tailored abilities for specific binding of proteins and optimal nonfouling capabilities is discussed.
Nanomaterial-based FET sensors represent an attractive platform for ultrasensitive, real-time, and label-free detection of chemical and biological species. Nevertheless, because their response is screened by mobile ions, it remains a challenge to use them to sense in physiological ionic strength solutions. In this work, it is demonstrated, both experimentally and theoretically, that polyelectrolyte multilayers are capable of increasing the sensing range of graphene-based FETs. Potential shifts at graphene surfaces and film thickness are recorded upon the construction of PDADMAC/PSS polyelectrolyte multilayer (PEM) films. By correlation of the potential shift with the film thickness, the electrostatic screening length and the concentration of mobile ion inside the films have been deduced. Across the polymer interface the Debye length is increased more than 1 order of magnitude. The fundamentals of this strategy are described by a conceptually simple thermodynamic model, which accounts for the entropy loss of ion confinement and incorporates the effect of ions finite volume. Interestingly, the electrostatic screening inside the film strongly depends on the polymer density and the ionic strength of the solution. Of particular interest in physiological condition sensing, the PEM interfaces can extend the Debye length from 0.8 to 10 nm.
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