Linear Polyelectrolyte Chains Research Articles

Analytical study of Linker Formation in Complexation of Two Dendrimers and one Polyelectrolyte

The concept of gene therapy is to fix a genetic problem at its source by repairing defective genetic material. Dendrimers proved to be an effective carrier vectors for gene therapy that efficiently compact and protect DNA from degradation by serum nucleases in the blood when injected intravenously. The complexation between Poly(amido amine) (PAMAM) dendrimer and Deoxyribonucleic acid (DNA) has been studied using the penetrable sphere model describing the interaction between linear polyelectrolyte (LPE) chain and ion penetrable sphere (Porous sphere) representing the dendrimer. It was found that the wrapping degree of LPE around the dendrimer is increased by increasing the LPE length, and the Bjerrum length which represents the strength of the electrostatic interaction and is decreased by increasing the pH of the solution. As a result, the linker, represents the unwrapped part of the LPE chain, is decreased by increasing the Bjerrum length and increased by increasing the pH

Explicit characterization of counterion dynamics around a flexible polyelectrolyte.

The article presents a comprehensive study of counterion dynamics around a generic linear polyelectrolyte chain with the help of coarse-grained computer simulations. The ion-chain coupling is discussed in the form of binding time, mean-square displacement (MSD) relative to the chain, local ion transport coefficient, and spatiotemporal correlations in the effective charge. We have shown that a counterion exhibits subdiffusive behavior 〈δR^{2}〉∼t^{δ}, δ≈0.9 w.r.t. chain's center of mass. The MSD of ions perpendicularly outward from the chain segment exhibits a smaller subdiffusive exponent compared to the one along the chain backbone. The effective diffusivity of ion is the lowest in chain's close proximity, extending up to the length-scale of radius of gyration R_{g}. Beyond R_{g} at larger distances, they attain diffusivity of free ion with a smooth cross-over from the adsorbed regime to the free ion regime. We have shown that the effective diffusivity drastically decreases for the multivalent ions, while the crossover length scale remains the same. Conversely, with increasing salt concentration the coupling-length scale reduces, while the diffusivity remains unaltered. The effective diffusivity of adsorbed-ion reveals an exponential reduction with electrostatic interaction strength. We further corroborate this from the binding time of ions on the chain, which also grows exponentially with the coupling strength of the ion-polymer duo. Moreover, the binding time of ions exhibits a weak dependence with salt concentration for the monovalent salt, while for multivalent salts the binding time decreases dramatically with concentration. Our work also elucidates fluctuations in the effective charge per site, where it exhibits strong negative correlations at short length-scales.

Dendritic polyelectrolyte brushes

The current state of the theory of brushes formed by dendritically branched ionized macromolecules attached by the root segment to a planar substrate and immersed in a polar solvent (water) is discussed. The theory makes it possible to unravel the most distinctive features of such brushes associated with the branched architecture of brush-forming chains and to systematically compare them with the properties of brushes formed by linear polyelectrolyte chains. Owing to their peculiar properties, dendritic polyelectrolyte brushes show promise for designing smart functional polymeric materials.

DNA compaction by poly (amido amine) dendrimers of ammonia cored and ethylene diamine cored

The complexes build–up of DNA and soft particles poly amidoamine (PAMAM) dendrimers of ammonia cored of generations (G1-G6) and ethylenediamine cored of generations (G1-G10) have been studied, using a new theoretical model developed by Qamhieh and coworkers. The model describes the interaction between linear polyelectrolyte (LPE) chain and ion-penetrable spheres. Many factors affecting LPE/dendrimer complex have been investigated such as dendrimer generation, the Bjerrum length, salt concentration, and rigidity of the LPE chain represented by the persistence length. It is found that the wrapping chain length around dendrimer increases by increasing dendrimer`s generation, Bjerrum length, and salt concentration, while decreases by increasing the persistence length of the LPE chain. Also we can conclude that the wrapping length of LPE chain around ethylenediamine cored dendrimers is larger than its length around ammonia cored dendrimers.

Computer simulations of dendrimer-polyelectrolyte complexes.

We carry out a systematic analysis of static properties of the clusters formed by complexation between charged dendrimers and linear polyelectrolyte (LPE) chains in a dilute solution under good solvent conditions. We use single chain in mean-field simulations and analyze the structure of the clusters through radial distribution functions of the dendrimer, cluster size, and charge distributions. The effects of LPE length, charge ratio between LPE and dendrimer, the influence of salt concentration, and the dendrimer generation number are examined. Systems with short LPEs showed a reduced propensity for aggregation with dendrimers, leading to formation of smaller clusters. In contrast, larger dendrimers and longer LPEs lead to larger clusters with significant bridging. Increasing salt concentration was seen to reduce aggregation between dendrimers as a result of screening of electrostatic interactions. Generally, maximum complexation was observed in systems with an equal amount of net dendrimer and LPE charges, whereas either excess LPE or dendrimer concentrations resulted in reduced clustering between dendrimers.

Electrostatic complexation of linear polyelectrolytes with soft spherical nanoparticles

We use Langevin molecular dynamics simulations to study the complexation of a linear polyelectrolyte (LPE) chain with an oppositely charged soft nanoparticle, modeled by a spherical polyelectrolyte brush (SPB). By changing core radius of the SPB and length of polyelectrolyte (GPE) chains grafted at it, a structural transition from a charged, LPE-covered sphere via a softer nanobrush toward a star-like polyelectrolyte is identified. As a result, the LPE chain develops various wrapping conformations around the SPB. Our systematic analysis reveals all relevant conformational binding modes for the polyelectrolyte–nanoparticle complex.

Analytical model study of complexation of dendrimer as an ion penetrable sphere with DNA

Poly (amidoamine) (PAMAM) dendrimers, being protonated under physiological conditions, have great potential as nonviral vectors for gene transfection. Many experimental and simulation studies have been performed to study the effect of dendrimer size, charge, and salt concentration on the structure and transfection efficiency of condensed DNA aggregates. In this study a theoretical model describing a linear polyelectrolyte (LPE) and ion-penetrable spheres has been developed and applied to investigate the interaction between linearized DNA and positively charged dendrimer of different generations. Throughout the study, we emphasized on the effect of the medium’s environments on the complexation of LPE chain with one dendrimer. It is found that the wrapping degree of the chain around the dendrimer increases by increasing dendrimer’s charge (decreasing pH), Bjerum length, salt concentration, and decreases by increasing the rigidity of the chain. Also, the effect of 1:1 salt concentration on complexation of DNA plasmids with one dendrimer of different generations has been investigated, and found that the optimal wrapping length of the LPE chain around the dendrimer depends on dendrimer generation.

Complexation between weakly basic dendrimers and linear polyelectrolytes: effects of grafts, chain stiffness, and pOH

We develop and implement a new hybrid methodology combining self-consistent field theory (SCFT) and Monte Carlo simulations to study the complexation between negatively charged semiflexible linear polyelectrolyte (LPE) molecules and a positively charged dendrimer containing grafts of neutral polymers. We examine the influence of LPE stiffness, length of the dendrimer grafts, and solution pOH upon the characteristics of the resulting complexes. Our results indicate that increasing LPE stiffness reduces the dendrimer–LPE binding affinity and results in an overall higher net charge carried within the dendrimer molecule. When we varied the size of the grafts, the dendrimer–LPE binding strength was seen to decrease with increasing grafting chain length for the flexible LPE chains. In contrast, for stiff LPE chains, the binding strength was not seen to vary significantly with the grafting lengths. Overall, longer grafting lengths were seen to reduce the fraction of exposed LPE molecules, suggesting that grafted dendrimers may better shield nucleic acid material from serum nucleases. Lastly, we found that increasing the solution pOH was seen to enhance both the binding between the dendrimer and LPE molecules and the total positive charge carried by the complex.

Divalent metal‐ion distribution around linear polyelectrolyte chains by continuous diafiltration: comparison of counterion condensation cell models

AbstractConcepts proposed in the two‐state model (Manning), two‐zone model (Deshkovski–Obukhov–Rubinstein) and extensions of these models based on Donnan equilibria around polyelectrolyte phases (Marinsky) were compared and discussed in terms of retention data obtained by continuous diafiltration of various linear polyelectrolyte solutions that were in contact with copper and cadmium salt solutions at pH = 6.0. Concentration and retention profiles were investigated and the metal‐ion retention values of the polymers (Rp) were compared with the respective values calculated using the theoretical assumptions of the models. An adequate connection was not observed between the two‐state model and diafiltration experiments when a null interaction between states 1 and 2 was assumed. If a Donnan equilibrium between states 1 and 2 was assumed, the metal‐ion fraction in state 1 was smaller than the Rp values obtained from the retention profiles for all systems. In contrast, a good correspondence between Rp values and the two‐zone model combined with Donnan's equilibrium was obtained by adding the weakly bound fraction of counterions around the polyelectrolyte chains. Copyright © 2010 Society of Chemical Industry

Charge inversion of dendrimers in complexes with linear polyelectrolytes in the solutions with low pH

Complexes of fully ionized third-generation dendrimers with oppositely charged linear polyelectrolyte chains are studied by the Brownian dynamics method. A freely jointed model of a dendrimer and a linear chain is used. Electrostatic interactions are considered within the Debye-Huckel approximation with the Debye radius exceeding the dimensions of a dendrimer. In these systems, the phenomenon of charge inversion is observed, and the degree of “overcharging” is higher as compared with that taking place in analogous complexes formed by dendrimers in which only terminal groups are charged. The dependence of the amount of chain units adsorbed on a dendrimer on the polyelectrolyte chain length is nonmonotnic and agrees qualitatively with the predictions of the theory proposed by Nguyen and Shklovskii for a complex composed of a spherical macroion with an oppositely charged linear chain. This nonmonotonic character also manifests itself for certain other structural characteristics of the complexes. Upon the formation of a complex, a chain is shown to penetrate deeply into a dendrimer.

Collapse of Linear Polyelectrolyte Chains in a Poor Solvent: When Does a Collapsing Polyelectrolyte Collect its Counterions?

To better understand the collapse of polyions in poor solvent conditions the effective charge and the solvent quality of the hypothetically uncharged polymer backbone need to be known. In the present work this is achieved by utilizing poly-2-vinylpyridine quaternized to 4.3% with ethylbromide. Conductivity and light scattering measurements were utilized to study the polyion collapse in isorefractive solvent/nonsolvent mixtures consisting of 1-propanol and 2-pentanone, respectively, at nearly constant dielectric constant. The solvent quality of the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of the electrostatic interaction prior and during polyion collapse, by comparing to a newly developed theory. Although the Manning parameter for the investigated system is as low as lB/l = 0.6 (lB is the Bjerrum length and l is the mean contour distance between two charges), that is, no counterion binding should occur, a qualitative interpretatio...

Spherical polyelectrolyte brushes in the presence of multivalent counterions: The effect of fluctuations and correlations as determined by molecular dynamics simulations

We consider the interaction of multivalent counterions with spherical polyelectrolyte brushes (SPBs). SPBs result if linear polyelectrolyte chains (contour length 60 nm) are densely grafted to colloidal spheres of 116 nm in diameter. When dispersed in water the surface layer, consisting of chains of the strong polyelectrolyte poly(styrene sulfonic acid), will swell. Recent work [Mei, Phys. Rev. Lett. 97, 158301 (2006)] has demonstrated that spherical polyelectrolyte brushes undergo a collapse in the presence of a mixture of monovalent and multivalent counterions. The collapse crossover could be well described by a mean-field approach. Here we demonstrate that the application of a mean-field approach is well founded by simulation results done with molecular dynamics (MD). MD simulations show that over a wide range of multivalent counterion concentration the effects of ion correlation and fluctuations can be neglected. Higher-valent counterions are shown to interact strongly with the polyelectrolyte chains of the SPBs and thus exhibit a much reduced osmotic activity in the system. This reduction is the driving force for the collapse.

Softening of the stiffness of bottle-brush polymers by mutual interaction

We study bottle-brush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side chains with approximately 60 monomer units. The SLS and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a wormlike chain with a contour length of 380 nm and a persistence length of 17.5 nm. An analysis of the DLS data confirms these model parameters. The scattering intensities taken at finite concentration can be modeled using the polymer reference interaction site model. It reveals a softening of the bottle-brush polymers caused by their mutual interaction. We demonstrate that the persistence decreases from 17.5 nm down to 5 nm upon increasing the concentration from dilute solution to the highest concentration (40.59 gl) under consideration. The observed softening of the chains is comparable to the theoretically predicted decrease of the electrostatic persistence length of linear polyelectrolyte chains at finite concentrations.

Collapse of Spherical Polyelectrolyte Brushes in the Presence of Multivalent Counterions

We consider the interaction of multivalent counterions with spherical polyelectrolyte brushes (SPB). The SPB result if linear polyelectrolyte (PE) chains (contour length: 60 nm) are densely grafted to colloidal spheres of 116 nm in diameter. Dispersed in water, the surface layer consisting of chains of the strong PE poly(styrene sulfonic acid) (PSS) will swell. We demonstrate that successive addition of trivalent ions (La3+) leads to a collapse in which the surface layer is shrinking drastically. All findings are discussed on the base of a theoretical mean-field approach using the Donnan equilibrium. The ion exchange and a strong binding of trivalent ions by PE chains is followed up by a drop in the osmotic pressure inside the brush. This reduction is the driving force for the collapse. The strong ion-chain correlation is discussed with results obtained from molecular dynamics simulations.

Scattering and Viscosimetric Behaviors of Four- and Six-Arm Star Polyelectrolyte Solutions

This paper discusses the scattering and viscosity results of four- and six-arm sodium, cesium, and rubidium polyacrylate (PANa, PACs, PARb) star polyelectrolyte solutions in comparison with their equivalent linear polyelectrolyte chains. The polyelectrolyte effect is highlighted in these systems, and an estimate of the persistence length is deduced from static light scattering and X-ray scattering. Static and dynamic light scattering studies permitted to determine their mass average molar mass 〈Mw〉, their radius of gyration 〈Rg〉, their second virial coefficient A2, their hydrodynamic radius RH, and their persistence length LP. The polyelectrolyte “abnormal” behavior was observed in the variation of the reduced viscosity ηred as a function of the polyelectrolyte concentration CP on linear and star systems (existence of a maximum in ηred vs CP). Additionally to the specific behavior brought by the star architecture, the results also show an important effect due to the type of counterions and the charge para...

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.

Synthesis and vesicular polymerization of novel counter‐ion polymerizable/crosslinkable surfactants

AbstractTwo novel two‐tail surfactants, dicetyldimethylammonium 4‐vinyl benzoate (DDVB) and dicetyldimethylammonium 3,5‐divinyl benzoate (DDDB), were synthesized by neutralizing the corresponding quaternary ammonium hydroxide with the appropriate benzoic acid. As expected, these surfactants formed both homo and mixed‐vesicles, which were readily polymerized with a suitable radical photo‐initiator. The polymerization process was followed by UV–vis spectroscopy and also reconfirmed by NMR and IR spectroscopy. Polymerization of vesicles prepared from DDVB, unlike the more commonly polymerized vesicles, in which the polymerizable group forms an integral part of the surfactant, leads to the formation of a linear polyelectrolyte chain that is only electrostatically bound to the lipid bilayer. On the other hand, polymerization of DDDB vesicles leads to the formation of a crosslinked shell (or net) that encases the vesicle bilayer. Such counterion crosslinked vesicles were shown to be resistant to destabilization both by lysis as well as in the presence of a fairly high volume fraction of an organic solvent, such as ethanol. However, although the simple polymerized (linearly) vesicles, formed from DDVB, exhibit enhanced stability toward lysis when compared to their unpolymerized counterparts, they are readily destabilized in the presence of ethanol, leading to precipitation. This sharp contrast in the behavior of linearly polymerized and crosslinked systems suggests that crosslinking is essential to arrest conformational reorganization of the polyelectrolyte chains induced by a change in the solvent medium, which in turn leads to precipitation. Such counterion crosslinked vesicular systems also have an added advantage; they may retain the fluidityof the lipid bilayer while at the same time possess enhanced stability. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5271–5283, 2004

Adsorption of proteins on spherical polyelectrolyte brushes in aqueous solution

We consider the adsorption of bovine serum albumin (BSA) on spherical polyelectrolyte brushes (SPB). The SPB consist of a solid polystyrene core of 100 nm diameter onto which linear polyelectrolyte chains [poly(acrylic acid), (PAA)] are grafted. The adsorption of BSA is studied at a pH of 6.1 at different concentrations of added salt and buffer. We observe strong adsorption of BSA onto the SPB despite the effect that the particles as well as the dissolved BSA are charged negatively. The adsorption of BSA is strongest at low salt concentration and decreases drastically with increasing amounts of added salt. Virtually no adsorption takes place at salt concentration of 0.1 M. Moreover, the adsorbed protein can be washed out again by raising the ionic strength from low to high values. A major driving force for the adsorption is located at a lower pH within the brush at low ionic strength. Thus, the isoelectric point of the protein may be approached or even reached. In this case strong interaction between the SPB and the protein results. Moreover, the negative charge of the polyelectrolyte interacts with the patches of positive charges on the protein. In this way the protein becomes a multivalent counterion within the brush and monovalent counterions will be released. All results demonstrate that the SPB present a new class of colloidal carrier particles whose interaction with proteins can be tuned in a well-defined fashion.

Interaction of dissolved proteins with spherical polyelectrolyte brushes

AbstractWe consider the adsorption of bovine serum albumin (BSA) on spherical polyelectrolyte brushes (SPB). The SPB consist of a solid polystyrene core of 100nm diameter onto which linear polyelectrolyte chains (poly(acrylic acid), (PAA)) are grafted. The adsorption of BSA is studied at a pH of 6.1 at different concentrations of added salt and buffer (MES). We observe strong adsorption of BSA onto the SPB despite the effect that the particles as well as the dissolved BSA are charged negatively. The adsorption of BSA is strongest at low salt concentration and decreases drastically with increasing amounts of added salt. The adsorbed protein can be washed out again by raising the ionic strength. The various driving forces for the adsorption are discussed. It is demonstrated that the main driving force is located in the electrostatic interaction of the protein with the brush layer of the particles. All data show that the SPB present a new class of carrier particles whose interaction with proteins can be tuned in a well‐defined manner.

Nanoscopic Polymer Particles with a Well‐Defined Surface: Synthesis, Characterization, and Properties

AbstractWe review our recent work on polymeric latex particles having a well‐defined surface of grafted polymers. Two types of particles are discussed: i) particles with a thermosensitive shell, and ii) particles bearing a dense layer of linear polyelectrolyte chains on their surface (“spherical polyelectrolyte brush”). Both types of particles consist of a polystyrene core onto which either linear or crosslinked chains are grafted. The synthesis of these core–shell particles proceeds in a two‐step process which is reviewed in detail. In particular, we discuss the photo‐emulsion polymerization used for the synthesis of the spherical polyelectrolyte brushes. Most of the studies of these particles have been done in aqueous suspension. Here the equilibrium structure of the surface layer of the particles has been investigated by dynamic light scattering and by small‐angle X‐ray scattering. Results deduced from the flow behavior of the particles in dilute solution can directly be derived from static data. Very recent data refer to the interaction of the spherical polyelectrolyte brushes with solid interfaces. It is demonstrated that particles bearing positively charged polyelectrolyte chains interact strongly with negatively charged surfaces. The strong interaction that is directly evident from AFM studies can be used to generate 2D networks of the particles on the surface. Schematic representation of the synthesis of defined spherical polyelectrolyte brushes.magnified imageSchematic representation of the synthesis of defined spherical polyelectrolyte brushes.