Necklace model of randomly charged polymers

Abstract

Spatial conformations of randomly charged polymers (polyampholytes (PAs)) strongly depend on their total (excess) charge Q. For Q larger (smaller) that some critical value the PA is expanded (collapsed). The transition between the collapsed and the expanded states is reminiscent of the Rayley shape instability of a charged drop. The expanded states can be approximately described using the necklace model, as a chain of interconnected compact globules. Randomness of the charge sequence along the chain modiÿes the simple model creating wide distribution of sizes of the "beads" of the necklace. A simple mathematical model was proposed to describe the shape of the necklace. ? 1998 Elsevier Science B.V. All rights reserved. The importance of understanding proteins [1] has attracted much attention to the statistical mechanics of heterogeneous polymers. A particular type of heteropolymers built with a mixture of positively and negatively charged groups along their backbone are called polyampholytes (PAs). Proteins are biomolecules formed from amino-acids. Out of 20 natural amino-acids, three are positively charged (Lys, Arg, His) and two are negatively charged (Asp, Glu) [2]. A statistical study of the charge distribution along the sequences of biomolecules [3] indicates that from the point of view of electrostatic interactions the charge sequences in proteins are only weakly (anti-)correlated. Thus, the proteins can be approximately treated as randomly charged PAs. Experiments on PAs and polyamphilic gels [ 4 -8] reveal an extreme sensitivity of their geometric properties on their overall charge. We will show that the presence of long-range electrostatic interactions indeed causes a rather unique behavior in such polymers: the spatial conformations of a single PA with unscreened electrostatic interactions at a low temperature T strongly depend on its total (excess) charge Q. We will demonstrate that the geometry of the system can be qualitatively described using simple models. PACS

pH‐responsive ampholytic terpolymers of acrylamide, sodium 3‐acrylamido‐3‐methylbutanoate, and (3‐acrylamidopropyl)trimethylammonium chloride. II. Solution properties

“…The decrease is due to electrostatic attractions that occur upon ionization of the AMB units, causing local collapses along the otherwise extended polyelectrolyte chain. This behavior is consistent with the necklace model of Kantor and Kardar13, 15, 16 as well as the predictions of Dobrynin and Rubinstein's polyampholyte theory 9…”

“…Such transitions are accompanied by increases in the hydrodynamic volume and solution viscosity; this phenomenon is often called the antipolyelectrolyte effect . Polyampholyte solubility and solution properties are governed by a complex interplay of polymer–solvent and polymer–polymer interactions 4, 8–18. Of primary importance are the electrostatic interactions that occur among the charged repeat units of the polyampholyte chain.…”

Stimuli-Responsive Polymers With Enhanced Efficiency in Reservoir Recovery Processes

“…The decrease is due to electrostatic attractions that occur upon ionization of the AMB units, causing local collapses along the otherwise extended polyelectrolyte chain. This behavior is consistent with the "necklace" model of Kantor and Kardar, [49][50][51] as well as the predictions of Dobrynin and Rubinstein's polyampholyte theory. 43 AMBATAC-7-3 exhibits a more complex reduced viscosity profile as a function of pH.…”

Stimuli‐responsive ampholytic terpolymers of N‐acryloyl‐valine, acrylamide, and (3‐acrylamidopropyl)trimethylammonium chloride: Synthesis, characterization, and solution properties

“…As the degree of charge imbalance on a polyampholyte chain increases, the polymer tends to behave in a manner that is more charactertistic of a conventional polyelectrolyte. Figure 5 depicts transitions that are experienced by a randomly incorporated polyampholyte chain with increasing charge asymmetry in dilute, salt‐free, aqueous conditions as theorized by current models and Monte Carlo simulations 10, 38, 39. Typically, polymers that have random incorporation of charged species exhibit more profound antipolyelectrolyte behavior than polyampholytes with alternating incorporations of the anionic and cationic moieties.…”